GLOSSARY OF SEISMIC TERMINOLOGY

Acceleration – The time rate of velocity change, commonly measured in “g” (an acceleration of 32 ft/sec/sec or 980 cm/sec/sec = gravity constant on earth). Accelerogram – The record from an accelerograph showing acceleration as a function of time. Accelerograph – A strong motion earthquake instrument recording ground (or base) acceleration. Aftershock – One of a series of smaller quakes following the main shock of the earthquake. Amplification - The period (or frequency) of the ground motion coinciding with the period of the building causing significant increase of acceleration and damage. Amplitude – Maximum deviation from mean of centerline of a wave. Attenuation – Reduction of amplitude or change in wave due to energy dissipation over distance within time. Axial Load – Force coincident with primary axis of a member. Base Isolation – A method using flexible bearings, whereby a building superstructure is detached from its foundation in order to reduce earthquake forces. Base Shear or Equivalent Lateral Force (ELF)– Total shear force acting at the base of a structure. Brittle Failure – Failure in material due to limited plastic range; material subject to sudden failure without warning signs. Center of Mass – Point in the building plan at which the building would be exactly balanced.

Center of Resistance – Resultant of resistance provided by walls and frames.

Configuration Terms:

Building Configuration – Size, shape and proportions of the building; size, shape and location of structural elements; and the type, size and location of nonstructural elements.

Regular Configuration – Building

configurations resisting lateral forces with shear walls, moment resistant frames or braced frames - all in simple and near symmetrical layout.

Irregular Configuration – Deviation from

simple symmetrical building configurations with repetitive plan and volume. (See WBDG Seismic Design Principles resource page for examples).

Structural Configuration – The size,

shape and arrangement of the vertical load carrying the lateral force resistance components of a building.

Core – The central part of the earth below a depth of 2,900 kilometers. It is thought to be composed of iron and nickel and to be molten on the outside with a central solid inner core. Creep (along a fault) - Very slow periodic or episodic movement along a fault trace without earthquakes. Crust - The lithosphere, the outer 80 kilometers of the earth’s surface made up of crustal rocks, sediment and basalt. The general composition is silicon-aluminum-iron.

Damping – The rate at which natural vibration decays as a result of the absorption of energy. In buildings it is an inherent nature to resonate inefficiently to vibration depending on structural connections, kinds of materials and nonstructural elements used. “Damping” design measures can reduce the magnitude of seismic forces. Critical Damping – The minimum damping that will allow a displaced system to return to its initial position without oscillation. Deflection – The horizontal or vertical displacement of a member due to the application of external force. Deformation – Permanent distortion due to seismic forces.

Depth of Focus – the depth of the focus or hypocenter beneath the earth’s surface commonly classes Earthquakes: Shallow (0-70 kilometers), intermediate (70-300 kilometers), and deep (300-700 kilometers). Design Earthquake – Generally defined as 2/3 of the maximum considered earthquake. Diaphragm – Generally a horizontal member, such as a floor or roof slab, which distributes lateral forces to vertical resisting elements. Displacement - Lateral movement of the structure caused by lateral force. Drift - Horizontal displacement of basic building elements due to lateral earthquake forces. Ductility – Ability to withstand inelastic strain without fracturing. Ductility is a material property to fail only after considerable inelastic (permanent) deformation which process dissipates the energy from the earthquake by design. Duration – The period of time within which ground acceleration occurs.

Dynamic - The opposite of “static”, when a body (building) is in motion. Eccentric Braced Frame – A steel frame in which diagonal bracing is arranged eccentric to column/beam joints. Effective Peak Acceleration – A coefficient shown on NEHRP maps used to determine seismic forces. Elasticity – The ability of a material to return to its original form or condition after a displacing force is removed. Materials have an elastic range. Elastoplastic – The total range of stress (deformation), including expansion beyond elastic limit into the plastic range. In the plastic range deformation is permanent. Energy Dissipation – Reduction in intensity of earthquake shock waves with time and distance, or by transmission through discontinuous materials with different absorption capabilities. Epicenter – The point of the earth’s surface directly above the focus or hypocenter of an earthquake. Equivalent Lateral Force (ELF) – The representation of earthquake forces on a building by a single static force applied at the base of a building; also referred as Base Shear (V). Failure Mode – The manner in which a structure fails (column buckling, overturning of structure, etc). Fault Terms: Fault – A fracture plane in the earth’s crust

across which relative displacement has occurred. (Location of slippage between the earth’s plates).

Normal Fault – A fault under tension where the overlying block moves down the dip or slope of the fault plane.

Strike-Slip Fault (or lateral slip) – A fault

whose relative displacement is purely horizontal.

Thrust (Reverse) Fault – A fault under

compression where the overlying block moves up the dip or slope of the fault plane.

Oblique-Slip Fault – A combination of

normal and slip or thrust and slip faults whose movement is diagonal along the dip of the fault plane.

Faulting – The movement which produces relative displacement of adjacent rock masses along a fracture.

Fault Zones – The zone surrounding a major fault, consisting of numerous interlacing small faults. FEMA – Federal Emergency Management Agency. Free publications available at: http://www.fema.gov/ Flexible System – A structural system that will sustain relatively large displacements without failure. Focal Depth – Depth of the earthquake (or hypocenter) below the ground surface. Focus (of an earthquake) or Hypocenter – The point at which the rupture occurs; (It marks the origin of the kinetic waves of an earthquake).

Frame Terms: Braced Frame – One having diagonal

braces for stability and capacity to resist lateral forces.

Concentric Braced Frame – The

centerlines of brace, supporting beam and column coincide.

Eccentric Bracing – The centerlines of brace, beam and of column and do not coincide allowing deformation, thereby utilizing ductility.

Moment Frame – Frames in which

structural members and joints resist lateral forces by bending. There are “ordinary”, “intermediate” and “special” moment frames. The latter provide the most resistance.

Frequency - The number of wave peaks or cycles per second. The inverse of Period. Fundamental or Natural Period – The elapsed time, in seconds, of a single cycle of oscillation. The inverse of Frequency. "g" - see Acceleration. Graben (rift valley) - Long, narrow trough bounded by one or more parallel normal faults. These down-dropped fault blocks are caused by tensional crustal forces. Ground Acceleration - Acceleration of the ground due to earthquake forces. Ground Displacement - The distance that ground moves from its original position during an earthquake. Ground Failure - A situation in which the ground does not hold together such as land sliding, mud flows and liquefaction. Ground Movement - A general term; includes all aspects of motion: acceleration, particle velocity and displacement. (The plates of the earth's crust move slowly relative to one-another accumulating pressure or strain resulting in slippage and complex vibration inducing forces in a building.) Ground Velocity - Velocity of the ground during an earthquake. Hypocenter or Focus - The point below the epicenter at which an earthquake actually begins; the focus.

Input Motion - A term representing seismic forces applied to a structure. Inelastic - Behavior of an element beyond its elastic limit, having permanent deformation. Inertial forces - Earthquake generated vibration of the building's mass causing internally generated inertial forces and building damage. Inertial forces are the product of mass times acceleration (F = m a). Intensity - A subjective measure of the force of an earthquake at a particular place as determined by its effects on persons, structures and earth materials. Intensity is a measure of energy. The principal scale used in the United States today is the Modified Mercalli, 1956 version. MM (or Modified Mercalli) scale is based on observation of the effects of the earthquake MM-I thru MM-XII (MM-I = not felt, MM-XII = damage nearly total). Isoseismals - Map contours drawn to define limits of estimated intensity of shaking for a given earthquake. Jacketing – Encasement of existing columns with steel or Kevlar to increase resistance. Landslide - Earthquake triggering land disturbance on a hillside where one land mass slides over the other. Lateral Force Coefficients - Factors applied to the weight of a structure or its parts to determine lateral force for seismic structural design. Liquefaction - Transformation of a granular material (soil) from a solid state into a liquefied state as a consequence of increased pore-water pressure induced by vibration. Normally solid soil suddenly changes to liquid state (usually sand or granular soil in proximity to water) due to vibration. Macrozones - Large zones of earthquake activity such as zones designated by the International Building Code map.

Machine Isolators – Calibrated mountings with springs used to attenuate vibration generated by machines. For seismic locations they are modified in order to absorb lateral movement and to keep the machine or equipment upright. These devices are available commercially. Magnification Factor - An increase in lateral forces at a specific site for a specific factor. Magnitude - A measure of earthquake size which describes the amount of energy released. See Richter Scale. Mantle - The main bulk of the earth between the crust and the core. Mass – A constant quantity or aggregate of matter. MCE: Maximum Credible Earthquake, about 50% higher than the Design Base Earthquake (DBE). Mercalli Scale – See “Intensity”. Microzonation - Seismic zoning, generally by use of maps, for land areas smaller than regions shown in typical seismic code maps, but larger than individual building sites. Modal Analysis - Determination of seismic design forces based upon the theoretical response of a structure in its several modes of vibration to excitation. Mode - The shape of the vibration curve. Modified Mercalli - See “Intensity”. Moment Magnitude is the measure of total energy released by an earthquake. It is based on the area of the fault that ruptured in the quake. It is calculated in part by multiplying the area of the fault’s rupture surface by the distance the earth moves along the fault. Mud Flow - Mass movement of material finer than sand, lubricated with large amounts of water.

Natural or Fundamental Frequency - The constant frequency of a vibrating system in the state of natural oscillation. NEHERP – National Earthquake Hazard Reduction Program (FEMA). Nonstructural Components - Those building components, which are not intended primarily for the structural support and bracing of the building. Oscillation- Mechanism capable to vibrate. Out of Phases - The state where a structure in motion is not at the same frequency as the ground motion; or where equipment in a building is at a different frequency from the structure. Period - The elapsed time in seconds of a single cycle of oscillation. The inverse of frequency. Performance Based Design – New concept of designing a project for optimum performance within a given life cycle (usually 50 years for institutional use). By definition the building program is to include the careful analysis of all physical, economical, environmental, aesthetic, and sociological factors that will result in the desirable functioning of the project. This, of course, includes hazard mitigation (natural or man-made) and the agreed upon level thereof. Plate Tectonics - The theory and study of plate formation, movement, interaction and destruction; the theory which explains seismicity, volcanism, mountain building and paleomagnetic evidence in terms of plate motions. P-Wave – See “Waves”. Relative Rigidity - The comparative stiffness of interconnected structural members in view of relative distribution of the horizontal force. (Only identical stiffness of interconnected members can share the total load equally.)

Resonance - Induced oscillations of maximum amplitude produced in a physical spectrum when applied oscillatory motion and the natural oscillatory frequency of the system are the same. When the site and building periods coincide, the buildings resonate with the ground. Then the amplitude of building vibration gradually approaches infinity by time, resulting in structural failure. The ground may vibrate at a period of 0.5 to 1.0 sec. Structures may vibrate at a period of 0.1 to 6 sec. depending on the type of structure. Examples: 1 story structure = 0.1 sec. Up to 4 story structure = 0.5 sec. 10-20 story structure = 1 - 2 sec. Water tank structure = 2.5 - 6 sec. Large suspension bridge = 6 sec. Response Spectrum - maximum response (generally acceleration) of a site plotted against increasing periods. Return Period of Earthquakes - The time period (years) in which probability is 63 percent that an earthquake of a certain magnitude will recur. Richter Magnitude Scale - A measure of earthquake size which describes the amount of energy released. The measure is determined by taking the common logarithm (base 10) of the largest ground motion observed during the arrival of a P-wave or seismic surface wave and applying a standard correction for distance to the epicenter. (Each unit of the Richter Scale represents a 10 times increase in wave amplitude. This corresponds to approx. 31 times increase of energy discharge for each unit on the Richter Scale.) – See Moment Magnitude Scale an alternative. Rift - A fault trough formed in a divergence zone or in other areas in tension. (See Graben)

Rigidity - Relative stiffness of a structure or element. In numerical terms, equal to the reciprocal of displacement caused by a unit force. Scarp - A cliff, escarpment, or steep slope of some extent formed by a fault or a cliff or steep slope along the margin of a plateau, mesa or terrace. Seiche - A standing wave on the surface of water in an enclosed or semi-enclosed basin (lake, bay or harbor). Seismic - Pertaining to earthquake activities. Seismic Zone – Areas defined on a map within which seismic design requirements are constant. Seismicity - The worldwide or local distribution of earthquakes in space and time; a general term for the number of earthquakes in a unit of time, or for relative earthquake activity. Seismograph - A device, which writes or tapes a permanent, continuous record of earth motion, a seismogram. Shear Distribution - Distribution of lateral forces along the height or width of a building. Shear Strain - The ratio obtained by dividing shear displacement by the thickness of the rubber layer in shear. Shear Strength - The stress at which a material fails in shear. Shear Wall - A wall designed to resist lateral forces parallel to the wall. A shear wall is normally vertical, although not necessarily so. Simple Harmonic Motion - Oscillatory motion of a wave, single frequency. Essentially a vibratory displacement such as that described by a weight, which is attached to one end of a spring and allowed to vibrate freely.

Soil Structure Interaction - The effects of the properties of both soil and structure upon response of the structure. Spectra - A plot indicating maximum earthquake response with respect to natural period or frequency of the structure or element. Response can show acceleration, velocity, displacement, shear or other properties of response. Stability - Resistance to displacement or overturning. Stiffness - Rigidity, or resistance to deflection or drift. A measure of deflection or of staying in alignment within a certain stress. Strain – Deformation per unit of material of the original dimension. Strain Release - Movement along a fault plane; can be gradual or abrupt. Strength - A measure of load bearing without exceeding a certain stress. Stress – Internal resistance within a material opposing a force to deform it. Subduction - The sinking of a plate under an overriding plate in a convergence zone. S-Wave – See “Waves”. Time Dependent Response Analysis - Study of the behavior of a structure as it responds to a specific ground motion. Torque – The action of a force that tends to produce torsion. The product of a force and a lever arm. Torsion - Twisting around an axis. (The center of the mass does not coincide with the center of resultant force of the resisting building elements causing rotation or twisting action in plans and stress concentrations. Symmetry in general reduces torsion.)

Trench - A long and narrow deep trough in the sea floor; interpreted as marking the line along which a plate bends down into a subduction zone. Tsunami - A sea wave produced by large area displacements of the ocean bottom, the result of earthquakes or volcanic activity. (Tidal wave caused by ground motion.) Tuning - To modify the period of the building beyond the range of the site period to avoid resonance. Examples of "tuning" include lowering the height of a building; lowering the position of weight in a building; changing materials; changing fixity of base, etc. The longer the period, the less inertial forces can be expected. Short periods close to the fault and long periods far from the fault are usual. Velocity – Rate of change of distance traveled with time in a given direction in centimeters/second. Vibration - A periodic motion that repeats itself after a definite interval of time. Wave Terms: Body Wave – Seismic waves within the

earth. Longitudinal Wave - Pure compressional

wave with volume changes. Love Wave – Surface waves that produce

a sideways motion. Rayleigh Wave - Forward and elliptical

vertical seismic surface waves. P-Wave - The primary or fastest waves

traveling away from a seismic event

through the earth's crust, and consisting of a train of compressions and dilatations of the material (push and pull).

S-Wave - Shear wave, produced

essentially by the shearing or tearing motions of earthquakes at right angles to the direction of wave propagation.

Seismic Surface Wave - A seismic wave

that follows the earth's surface only, with a speed less than that of S-waves.

Wave Length - The distance between successive similar points on two wave cycles.

The Islamic University of Gaza Earthquake Engineering ENGC 6336

Instructor: Dr. Samir Shihada Second Semester, 2010-2011

First Assignment (submittal date is 23-03-2011)

For the 4-storey building frame system with shear walls, shown in the figure, do the following:

(1) Find the base shear V using UBC-94 provisions. (2) Design the five shear walls for shear and flexure (as ordinary shear walls).

Provided Data:

- The building is used for residential purposes, and located in Gaza City. - Soil profile is classified as S2. - Use 2

c cm/Kg4200'f = and 2y cm/Kg4200f = .

- Floor sustained dead load = 1000 kg/m2. - Floor live load = 200 kg/m2. - Columns are 40 cm x 40 cm in cross section. - Base your reinforced concrete design, including load combinations, on ACI

318-08.

Plan Elevation

١

H.W1 Solution (Prepared by Dr. Shihada): a- First Direction (shear walls A, B and C)

2.1S ,1I ,075.0Z === Weight of floor = ( )( ) tons22515150.1 = Total seismic weight = ( ) tons9004225 = Building natural frequency

( )c

n

AhT

43

0743.0=

+=∑

2

n

eic h

D2.0AA 9.0/ ≤ne hD

( )( ) ( ) 23

1i

2

c m4725.01232.032.03A =

+= ∑

= , 9.025.0

123

<= O.K

CCaallccuullaattiioonn ooff TT,, ( ) ( ) sec697.0

4725.0120743.0

Ah0743.0T

4/3

c

4/3n ===

( )( )

75.2908.1697.0

2.125.1

T

S25.1C3

22

2 <=== O.K.

( ) K.O8075.0908.1C >= 8=wR

( ) ( ) tons1.168

908.10.1075.0R

WCIZVw

===

Vertical Distribution of Force:

( )∑ =

−= 7

1i i

xxtx

FhwFVF

Since tons0.0F,ondsec7.0T t =<

level iw tons

xh m

xxhw ton. m

xF tons

٢٧٠٠ ١٢ ٢٢٥ ٤ 6.44 ٢٠٢٥ ٩ ٢٢٥ ٣ 4.83 ١٣٥٠ ٦ ٢٢٥ ٢ 3.22 ٦٧٥ ٣ ٢٢٥ ١ 1.61 ٠ ٠ ٠ 0

Σ ٦٧٥٠ 16.1

٢

NNeegglleeccttiinngg mmoommeennttss ooff iinneerrttiiaa aabboouutt tthhee wweeaakk aaxxeess,, ( ) 4

3CyByAy m45.0

1232.0III ====

( ) 43

1iiy m35.1345.0I ==∑

=

( ) 43

Dx m45.012

32.0I ==

( ) 43

Ex m067.112

42.0I ==

42

1iix m517.1067.145.0I =+=∑

=

( ) ( ) m33.835.1

01045.01545.0

I

yIy 3

1iiy

3

1iiiy

=++

==∑=

∑=

( ) m55.10517.1

015067.1

I

xIx 2

1iix

2

1iiix

=+

==∑=

∑=

m83.05.733.8ey =−=

Torsion caused by eccentricity ( )75.083.0FT x ±=

ixixix FFF ′′+′=

xx

CxBxAx F33.035.1

F45.0'F'F'F ====

( )

( )( ) ( )

( ) ( ) ( ) ( ) ( )T0243.0

67.145.067.645.033.845.045.4067.155.1045.0

45.067.6T

IyIx

IyT''F

222225

1iiyi

2ixi

2

iyiAx =

++++=

+=

∑=

( )

( )( ) ( )

( ) ( ) ( ) ( ) ( )T0061.0

67.145.067.645.033.845.045.4067.155.1045.0

45.067.1T

IyIx

IyT''F

222225

1iiyi

2ixi

2

iyiBx =

++++=

+=

∑=

٣

( )

( )( ) ( )

( ) ( ) ( ) ( ) ( )T0303.0

67.145.067.645.033.845.045.4067.155.1045.0

45.083.8T

IyIx

IyT''F

222225

1iiyi

2ixi

2

iyiCx =

++++=

+=

∑=

Total force on wall A: ( ) xxxA F328.0F75.083.00243.0F33.0F =−−= Total force on wall B: ( ) xxxB F33.0F75.083.00061.0F33.0F =−−= Total force on wall C: ( ) xxxC F378.0F75.083.00303.0F33.0F =++=

Total Forces (x-direction)

b- Second Direction (shear walls D and E)

2.1S ,1I ,075.0Z === Weight of floor = ( )( ) tons22515150.1 = Total seismic weight = ( ) tons9004225 = Building natural frequency

( )c

n

AhT

43

0743.0=

+=∑

2

n

eic h

D2.0AA 9.0/ ≤ne hD

( )( ) ( )( ) 222

c m4064.01242.02.04

1232.02.03A =

++

+= , 9.025.0

123

<=

O.K

9.033.0124

<= O.K

CCaallccuullaattiioonn ooff TT,, ( ) ( ) sec751.0

4064.0120743.0

Ah0743.0T

4/3

c

4/3n ===

٤

( )( )

75.2816.1751.0

2.125.1

T

S25.1C3

22

2<=== O.K.

( ) K.O8075.0816.1C >= 8=wR

( ) ( ) ( ) tons32.158

900816.10.1075.0R

WCIZVw

===

Vertical Distribution of Force:

( )∑ =

−= 7

1i i

xxtx

FhwFVF

Since ( ) ( ) tons805.032.15751.007.0VT07.0F,ondsec7.0T t ===>

m05.35.755.10ex =−= Torsion caused by eccentricity ( )75.005.3FT y ±=

iyiyiy ''F'FF +=

level iw tons

xh m

xxhw ton. m

tx FF + tons

٢٧٠٠ ١٢ ٢٢٥ ٤ 6.62 ٢٠٢٥ ٩ ٢٢٥ ٣ 4.35 ١٣٥٠ ٦ ٢٢٥ ٢ 2.90 ٦٧٥ ٣ ٢٢٥ ١ 1.45 ٠ ٠ ٠ 0

Σ ٦٧٥٠ 15.32

٥

yy

Dy F297.0517.1

F45.0'F ==

yy

Ey F703.0517.1

F067.1'F ==

( )

( )( ) ( )

( ) ( ) ( ) ( ) ( )T038.0

67.145.067.645.033.845.045.4067.155.1045.0

45.055.10T

IyIx

IxT''F

222225

1iiyi

2ixi

2

ixiDy =

++++=

+=

∑=

( )

( )( ) ( )

( ) ( ) ( ) ( ) ( )T038.0

67.145.067.645.033.845.045.4067.155.1045.0

067.145.4T

IyIx

IxT''F

222225

1iiyi

2ixi

2

ixiEy =

++++=

+=

∑=

Total force on wall D: ( ) yyyD F44.0F75.005.3038.0F297.0F =++=

Total force on wall E: ( ) yxyE F62.0F75.005.3038.0F703.0F =−−=

Total Forces (y-direction)

Design of shear wall as an example Forces on shear wall D (service):

F4 = 0.44(6.62) = 2.913 tons

F3= 0.44(4.35) = 1.914 tons

F2= 0.44(2.90) = 1.276 tons

F1= 0.44(1.45) = 0.638 tons

Shear forces on shear wall D (service):

V4 = 0.44(6.62) = 2.913 tons

V3= 0.44(4.35) = 4.827 tons

V2= 0.44(2.90) = 6.103 tons

V1= 0.44(1.45) = 6.741 tons

V0= 6.741 tons

Moments on shear wall D (service):

M4= 0 t.m

٦

M3= 8.739 t.m

M2= 23.22 t.m

M1= 41.529 t.m

M0= 61.752 t.m

Bending moment diagram (service)

1- Design for shear:

Check for maximum nominal shear force

dh'f65.2V cmax,n =

( ) ( )( ) tons32.2201000/3008.02030065.2 == ( ) ( ) K.Otons44.94.1741.6tons24.16532.22075.0V max,u =⟩==

dh'f53.0V cc =

( )( )( ) tons06.441000/3008.02030053.0Vc ==

( ) tons045.3306.4475.0Vc ==Φ

( ) tons523.162/045.332/Vc ==Φ In zones 1, 2, 3 and 4 2/VV cu φ< 1-1 Horizontal shear reinforcement:

0025.0t =ρ

ofsmaller the2 =S cm

cmhcmlw

45603

605/=

=

٧

or cmS 45max,2 =

( ) cm/cm05.0SA

and 200025.0h0025.0SA 2

2

t

2

t ===

For two curtains of reinforcement and trying φ 10 mm bars ( )

max,222

Scm4.31S , 05.0S785.02

<== O.K

Use φ 10 mm bars @ 30cm. 1-2 Vertical shear reinforcement:

[ ]0025.00025.03215.25.00025.0l −

−+=ρ

tl 0025.0 ρρ ≤=

ofsmaller the1 =S cm

cmhcmlw

45603

1003/=

=

or cmS 45max,1 =

For two curtains of reinforcement, and trying φ 10 mm bars

( ) ( )11

lS

0.7852 200025.0h0025.0SA

===

And max,11 40.31 ScmS <= Use φ 10mm bars @ 30cm.

2- Design for flexure and axial loads:

−

+φ=

wys

uwysu l

c1fA

P1lfA5.0M

Where:

1w 85.02lc

β+ωα+ω

= , 'fhl

fA

cw

ys=ω and 'fhl

p

cw

u=α

For the vertical shear reinforcement of φ 10 mm @ 30cm, 2s cm28.17A = ,

( ) 836.0280300

7005.085.0 =−−=β , ( )

( )( ) 04032.030020300

420028.17'fhl

fA

cw

ys ===ω

, ( )

( )( ) uu

cw

u P00055.030020300

1000P'fhl

P===α ,

( ) ( ) 79124.0P00055.004032.0

836.085.004032.02P00055.004032.0

lc uu

w

+=

++

=

For zone 4 (at the base):

٨

( )( )( )( ) tons20.165.21232.09.0Pu == ( ) 0622.0

79124.02.1600055.004032.0

lc

w=

+=

( ) m.t4.1752.61m.t455.112Mu >= , i.e. no boundary elements are required at wall

ends along the entire height of the wall.

The Islamic University of Gaza Earthquake Engineering ENGC 6336

Instructor: Prof. Samir Shihada First Semester, 2012-2013

Second Assignment

For the 8-storey building frame system with shear walls, shown in the figure, do the following:

(1) Evaluate the base shear V using UBC-97 provisions (both orthogonal directions).

(2) Design walls (A) for shear and flexure (as special shear wall). Provided Data:

- The building is used for residential purposes, and located in Gaza City. - Story height is 3.0 m. - Soil profile is classified as SD. - Use 2/350' cmKgf c = and 2/4200 cmKgfy = . - Floor sustained dead load = 1200 kg/m2. - Floor live load = 200 kg/m2. - Columns are 40 cm x 40 cm in cross section. - Reinforced concrete design is to be based on ACI 318-08.

Plan

1

INTRODUCTION TO SEISMOLOGY

2

Earthquake Engineering

• Earthquake engineering can be defined as the branch of engineering devoted to

mitigating earthquake hazards.

• Earthquake engineering involves planning, designing, constructing and

managing earthquake-resistant structures and facilities.

3

1.1 Earth's Interior

• The earth's radius is 6371 km.

• Direct drilling went only to 13 km.

• Materials brought up by volcanoes are only from the outer 200 km.

• Physical conditions are brought about by computer modeling, laboratory

experiments and data generated from seismic waves generated by earthquakes

and nuclear explosions.

Major layers of the Interior

The principal layers of the earth include crust, the mantle and the core (including a

fluid outer core and a solid inner core), shown in Figure (1.1).

Figure (1.1): The earth's interior

The Crust:

• The crust is a thin outer shell, about 30 km in thickness on average.

• Its thickness exceeds 70 km in some mountain belts, such as the Himalayas.

• Its thickness ranges from 3 km to 15 km in oceanic crust.

The Mantle:

• It is a solid rocky layer.

• It extends to a depth of about 2900 km.

The core:

4

Inner core:

• Its radius is 1220 km.

• The inner core is solid due to generated pressure.

• It is made of iron.

Outer Core:

• Its radius is about 3400 km.

• It is made of iron mixed with other elements.

5

1.2Tectonic Plates

Stress that causes an earthquake is created by a movement of almost rigid plates,

called tectonic plates, which fit together and make up the outer shell of the earth

(crust). These plates float on a dense, liquid layer beneath them. These plates move at

such a slow rate (approximately the same rate as a fingernail grows), which is not

perceptible.

Over time, however, this small movement can build up enough stress to produce

earthquakes.

Most frequently earthquakes occur on or near the edges of the plates where stress is

most concentrated, such earthquakes are called interplate earthquakes.

A significant number of earthquakes, including some large and damaging ones, do

occur within the plates; these earthquakes are known as intraplate earthquakes.

Figure (1.2) shows various tectonic plates that constitute the surface of the earth.

Figure (1.2): Various tectonic plates that constitute the surface of the earth

6

1.3 Major Earthquakes of the World

• Earthquakes can strike any location at any time. But history shows they occur in

the same general patterns year after year, principally in three large zones of the

earth.

• The world's greatest earthquake belt, the circum-Pacific seismic belt, is found

along the rim of the Pacific Ocean, where about 81 percent of the world's largest

earthquakes occur. The belt extends from Chile, northward along the South

American coast through Central America, Mexico, the West Coast of the United

States, and the southern part of Alaska, through the Aleutian Islands to Japan,

the Philippine Islands, New Guinea, the island groups of the Southwest Pacific,

and to New Zealand.

• The second important belt, the Alpide, extends from Java to Sumatra through

the Himalayas, the Mediterranean, and out into the Atlantic. This belt accounts

for about 17 percent of the world's largest earthquakes.

• The third prominent belt follows the submerged mid-Atlantic Ridge.

• The remaining shocks are scattered in various areas of the world. Earthquakes

in these prominent seismic zones are taken for granted, but damaging shocks

occur occasionally outside these areas.

Figure (1.3) shows major earthquakes of the world.

7

Figure (1.3): Major earthquakes of the world

8

1.4 Fault Types A fault, shown in Figure (1.4), is a large fracture in rocks, across which the rocks have

moved. Faults can be microscopic or hundreds-to-thousands of kilometers long and

tens of kilometers deep. The width of the fault is usually much smaller, on the order of

a few millimeters to meters.

Normal Fault (extensional):

• The hanging wall block moves down relative to the footwall block.

• The fault plane makes 45 degree or larger angles with the surface.

• These faults are associated with crustal tension.

Figure (1.4): Fault types

Reverse Fault (Compressional)

• The hanging wall block moves up relative to the footwall block.

• The fault plane usually makes 45 degree or smaller angles with the surface.

• The faults are associated with crustal compression.

Strike-Slip Fault (Transformal)

• The two blocks move either to the left or to the right relative to one another.

• These faults are associated with crustal shear.

9

1.5 Earthquakes An earthquake is a sudden movement of the ground that releases built-up energy in

rocks and generates seismic waves. The elastic waves radiate outward from the source

and vibrate the ground. The point where a rupture starts is termed the focus or

hypocenter and may be many kilometers deep within the earth. The point on the

surface directly above the focus is called the earthquake epicenter, shown in Figure

(1.5).

Figure (1.5): Earthquake fracture

Earthquakes can occur anywhere between the Earth's surface and about 700 kilometers

below the surface. For scientific purposes, this earthquake depth range of 0-700 km is

divided into three zones: shallow, intermediate, and deep .

Shallow earthquakes are between 0 and 70 km deep; intermediate earthquakes, 70 -

300 km deep; and deep earthquakes, 300 - 700 km deep. In general, the term "deep-

focus earthquakes" is applied to earthquakes deeper than 70 km.

The Elastic Rebound Theory:

It states that as tectonic plates move relative to each other, elastic strain energy builds

up along their edges in the rocks along fault planes. Since fault planes are not usually

very smooth, great amounts of energy can be stored as movement is restricted due to

interlock along the fault. When the shearing stresses induced in the rocks on the fault

planes exceed the shear strength of the rock, rupture occurs.

10

1.6 Seismic Waves Seismic waves are the vibrations from earthquakes that travel through the earth. The

amplitude of a seismic wave is the amount the ground moves as the wave passes by.

1- Body waves:

They are waves moving through the body of the earth from the point of fracture,

shown in Figure (1.6).

A- Primary waves (P-waves):

They are longitudinal waves that oscillate the ground back and forth along

the direction of wave travel. They are considered the fastest to reach a

recording station. The primary waves can travel through solids, liquids and

gases.

B- Secondary waves (S-waves):

They oscillate the ground perpendicular to the direction of wave travel. They

are slower than the P-waves. These waves are second in reaching a recording

station. They can travel through solids only.

Figure (1.6): Body waves

2- Surface Waves:

They are slower than the primary or the secondary waves and propagate along

the earth's surface rather than through the deep interior, thus causing more

property damage, see Figure (1.7). Two principal types of surface waves; Love

and Raleigh waves, shown in Figure (1.8), are generated during the earthquake.

11

Raleigh waves cause both vertical and horizontal ground motion, and Love

waves cause horizontal motion only. They both produce ground shaking at the

earth's surface but very little motion deep in the earth. Because the amplitude of

surface waves diminishes less rapidly with distance than the amplitude of

primary or secondary waves, surface waves are often the most important

component of ground shaking far from the earthquake source.

Figure (1.7): Seismic wave arrival time

Figure (1.8): Surface waves

12

1.7 Measurement of Ground Motion

Seismographs

Seismographs generally consist of two parts, a sensor of ground motion which we call

a seismometer, and a seismic recording system. Modern seismometers are sensitive

electromechanical devices but the basic idea behind measuring ground movement can

be illustrated using a simpler physical system that is actually quite similar to some of

the earliest seismograph systems, shown in Figure (1.9).

Figure (1.9): The basic ideas behind of seismic recording systems.

Seismometers are spread throughout the world, but are usually concentrated in regions

of intense earthquake activity or research. These days, the recording system is

invariably a computer, custom designed for seismic data collection and harsh weather.

Often they are also connected to a satellite communication system. Such systems

enable us to receive seismic signals from all over the world, soon after an earthquake,

see Figure (1.10).

Figure (1.10): A real-time seismic recording system with

digital storage and satellite communications

13

Classic Seismograms

For most of the last century, seismograms were recorded on sheet of paper, either with

ink or photographically. We call such records "analog" records to distinguish them

from digital recordings. These records are read just like a book - from top-to-bottom

and left-to-right, shown in Figure (1.11).

Figure (1.11): Classic seismogram

One problem with these mechanical systems was the limited range of ground motion

that could be recorded - vibrations smaller than a line thickness and those beyond the

physical range of the ink pen were lost. To elude these limitations we often operated

high and low-gain instruments side-by-side, but that was neither as efficient nor

effective as the modern digital electronic instruments. However, modern "digital" or

computerized instruments are relatively new, only about 15-20 years old, and most of

our data regarding large earthquakes are actually recorded on paper (or film).

Additionally, we still use paper recording systems for display purposes so we can see

what is going on without a computer.

Digital Seismograms

Today, most seismic data are recorded digitally (see Figure 1.12), which facilitates

quick interpretations of the signals using computers. Digital seismograms are

"sampled" at an even time interval that depends on the type of seismic instrument and

the interest of the people who deploy the seismometer.

14

Figure (1.12): Digital seismogram

Also, since we live in a three-dimensional space, to record the complete ground

motion, we must record the motion in three directions. Usually, we usually choose:

• Up-down • North-south • East-west

Accelerometers

Another important class of seismometers was developed for recording large amplitude

vibrations that are common within a few tens of kilometers of large earthquakes -

these are called strong-motion seismometers. Strong-motion instruments were

designed to record the high accelerations that are particularly important for designing

buildings and other structures. An example set of accelerations from a large

earthquake that occurred in near the coast of Mexico in September of 1985 are shown

in Figure (1.13).

Figure (1.13): Set of accelerations from a 1985 Mexico earthquake

15

1.8 Locating Earthquakes

• Difference between arrival times of the P and S waves is determined.

• Using the Travel-Time Curve shown in Figure (1.14), the distance of the

seismograph from the epicenter is evaluated.

• Three seismographs are triangulated to find actual location of the epicenter, as

shown in Figure (1.15). In practice, a computer carries out the whole process of

locating an earthquake. The computer estimates the arrival time of the P and S

waves for each seismic station, a seismologist checks out the estimates and then

the location is calculated.

Figure (1.14): Distance versus time curves

Figure (1.15): Locating the epicenter, the old way

16

1.9 Measuring the Size of an Earthquake

The severity of an earthquake can be expressed in terms of the following:

Amplitude

It is based on the amplitude and distance measured from seismograms. The most

common scale is the Richter scale which measures the magnitude on a logarithmic

scale.

The Richter magnitude scale was developed in 1935 by Charles F. Richter of the

California Institute of Technology as a mathematical device to compare the size of

earthquakes. The magnitude of an earthquake is determined from the logarithm of the

amplitude of waves recorded by seismographs. Adjustments are included for the

variation in the distance between the various seismographs and the epicenter of the

earthquakes. On the Richter Scale, magnitude is expressed in whole numbers and

decimal fractions. For example, a magnitude 5.3 might be computed for a moderate

earthquake, and a strong earthquake might be rated as magnitude 6.3. Because of the

logarithmic basis of the scale, each whole number increase in magnitude represents a

tenfold increase in measured amplitude; as an estimate of energy, each whole number

step in the magnitude scale corresponds to the release of about 31 times more energy

than the amount associated with the preceding whole number value.

At first, the Richter Scale could be applied only to the records from instruments of

identical manufacture. Now, instruments are carefully calibrated with respect to each

other. Thus, magnitude can be computed from the record of any calibrated

seismograph.

17

Richter Earthquake Magnitudes Effects Less than 3.5 Generally not felt, but recorded. 3.5-5.4 Often felt, but rarely causes damage. Under 6.0 At most slight damage to well-designed buildings. Can cause major damage to poorly constructed buildings over small regions. 6.1-6.9 Can be destructive in areas up to about 100 kilometers across where people live. 7.0-7.9 Major earthquake. Can cause serious damage over larger areas. 8 or greater Great earthquake. Can cause serious damage in areas several hundred kilometers across. The Richter Scale has no upper limit and doesn't tell you anything about the physics of

the earthquake. Recently, another scale called the moment magnitude scale has been

devised for more precise study of great earthquakes.

Intensity

It is based on the observed effects of ground shaking on people and buildings. It varies

from place to place within the disturbed region depending on the location of the

observer with respect to the earthquake epicenter. The most common scale is the

Modified Mercalli Scale, which uses a twelve-point scale to describe damage. The

scale is named after the Italian Seismologist Giuseppe Mercalli (1850-1914) who

amended the Rossi-Forrel scale to a 12-point scale in 1902. The Americans Harry

Wood and Frank Neumann who amended the Mercalli Scale in 1931.

18

Modified Mercalli Intensity Scale

Mercalli

Intensity

Equivalent Richter

Magnitude

Witness Observations

I 1.0 to 2.0 Felt by very few people; barely noticeable.

II 2.0 to 3.0 Felt by a few people, especially on upper floors.

III 3.0 to 4.0 Noticeable indoors, especially on upper floors, but may not be recognized as

an earthquake.

IV 4.0 Felt by many indoors, few outdoors. May feel like heavy truck passing by.

V 4.0 to 5.0 Felt by almost everyone, some people awakened. Small objects moved.trees

and poles may shake.

VI 5.0 to 6.0 Felt by everyone. Difficult to stand. Some heavy furniture moved, some

plaster falls. Chimneys may be slightly damaged.

VII 6.0 Slight to moderate damage in well built, ordinary structures. Considerable

damage to poorly built structures. Some walls may fall.

VIII 6.0 to 7.0 Little damage in specially built structures. Considerable damage to ordinary

buildings, severe damage to poorly built structures. Some walls collapse.

IX 7.0 Considerable damage to specially built structures, buildings shifted off

foundations. Ground cracked noticeably. Wholesale destruction. Landslides.

X 7.0 to 8.0 Most masonry and frame structures and their foundations destroyed. Ground

badly cracked. Landslides. Wholesale destruction.

XI 8.0 Total damage. Few, if any, structures standing. Bridges destroyed. Wide

cracks in ground. Waves seen on ground.

XII 8.0 or greater Total damage. Waves seen on ground. Objects thrown up into air.

19

Seismic Moment:

A new scale has been developed to overcome the shortcomings of the Richter scale. It

is based on seismic waves and field measurements that describe the fault area. It is

considered very accurate because it takes into account fault geometry.

Seismic moment is a quantity that combines the area of the rupture and the amount of

fault offset with a measure of the strength of the rocks - the shear modulus µ.

Seismic Moment = µ x (Rupture Area) x (Fault Offset)

For scientific studies, the moment is the measure we use since it has fewer limitations

than the magnitudes, which often reach a maximum value (we call that magnitude

saturation).

To compare seismic moment with magnitude, Mw , we use a formula constructed by

Hiroo Kanamori of the California Institute of Seismology:

Mw = 2 / 3 * log(Seismic Moment) - 10.73

20

Part (2)

Effects of Earthquakes on Structures and Planning Considerations

• The Nature of Earthquake Hazard

• Architectural and Structural Considerations

• The Effects of Earthquakes on Buildings

• General Goals in Seismic-Resistant Design

21

The Nature of Earthquake Hazard

• Ground Shaking: The shaking resulting from an earthquake is not life threatening in itself; it is the

consequential collapse of structures that is the main cause of death, injury, and

economic loss.

• Ground Failure: Ground failure can primarily cause any of the following:

• Tsunamis: Tsunami or sea waves, which may threaten coastal regions.

They are caused by the sudden change in seabed level that may occur in

an offshore earthquake.

• Liquefaction: Loss of strength in saturated granular soil due to the

build-up of pore water pressure under cyclical loading.

• Landslides: Which are often triggered by liquefaction of a soil stratum.

• Fault Movement: It can be troublesome to structures directly crossing a

fault. However, the number of structures directly over a fault break is

small compared with the total number of structures affected by the

earthquake. Faults are mainly a problem for extended facilities such as

pipelines, canals, and dams.

• Fires: They break out following earthquakes. They can be caused by

flammable materials being thrown into a cooking or heating fire or

broken gas lines. Fires can easily get out of control since the earthquake

may have broken water mains or blocked roads firefighters need to use.

22

• Damage Due to Ground Shaking (Figure 2.1)

Figure (2.1) Damage due ground shaking

23

2- Damage Due to Ground Failure

A- Due to Surface Faulting (Figure 2.2)

Fault, 1980 El Asnam Earthquake

Overturned Train, 1980 El Asnam Earthquake

Collapsed Bridge, 1976 Guatemala Earthquake

Damage to A building, 1971 San Fernando Earthquake

Figure (2.2) Damage due to surface faulting

24

B- Due to Liquefaction (Figure 2.3)

Tilting of Buildings, 1964 Niigata Earthquake

Collapsed Bridge, 1964 Niigata Earthquake

Linear Fissure, 1977 Caucete Earthquake

Sand Blows

Figure (2.3) Damage due to liquefaction

25

Liquefaction Liquefaction Process Liquefaction is a process by which sediments below the water table temporarily lose

strength and behave as a viscous liquid rather than a solid. The types of sediments

most susceptible are clay-free deposits of sand and silts; occasionally, gravel liquefies.

The actions in the soil which produce liquefaction are as follows: seismic waves,

primarily shear waves, passing through saturated granular layers, distort the granular

structure, and cause loosely packed groups of particles to collapse (Fig. 2.4). These

collapses increase the pore-water pressure between the grains if drainage cannot occur.

If the pore-water pressure rises to a level approaching the weight of the overlying soil,

the granular layer temporarily behaves as a viscous liquid rather than a solid.

Liquefaction has occurred.

Figure (2.4) Sketch of a packet of water-saturated sand grains illustrating the process

of liquefaction. Shear deformations (indicated by large arrows) induced by earthquake

shaking distort the granular structure causing loosely packed groups to collapse as

indicated by the curved arrow.

In the liquefied condition, soil may deform with little shear resistance; deformations

large enough to cause damage to buildings and other structures are called ground

failures. The ease with which a soil can be liquefied depends primarily on the

looseness of the soil, the amount of cementing or clay between particles, and the

26

amount of drainage restriction. The amount of soil deformation following liquefaction

depends on the looseness of the material, the depth, thickness, and areal extent of the

liquefied layer, the ground slope, and the distribution of loads applied by buildings and

other structures.

Liquefaction does not occur at random, but is restricted to certain geologic and

hydrologic environments, primarily recently deposited sands and silts in areas with

high ground water levels. Generally, the younger and looser the sediment, and the

higher the water table, the more susceptible the soil is to liquefaction. Liquefaction has

been most abundant in areas where ground water lies within 10 m of the ground

surface; few instances of liquefaction have occurred in areas with ground water deeper

than 20 m. Dense soils, including well-compacted fills, have low susceptibility to

liquefaction. Effect of Liquefaction on the Built Environment

The liquefaction phenomenon by itself may not be particularly damaging or

hazardous. Only when liquefaction is accompanied by some form of ground

displacement or ground failure is it destructive to the built environment. For

engineering purposes, it is not the occurrence of liquefaction that is of prime

importance, but its severity or its capability to cause damage. Adverse effects of

liquefaction can take many forms. These include: flow failures; lateral spreads; ground

oscillation; and increased lateral pressure on retaining walls.

Flow Failures Flow failures are the most catastrophic ground failures caused by liquefaction. These

failures commonly displace large masses of soil laterally tens of meters and in a few

instances; large masses of soil have traveled tens of kilometers down long slopes at

velocities ranging up to tens of kilometers per hour. Flows may be comprised of

completely liquefied soil or blocks of intact material riding on a layer of liquefied soil.

Flows develop in loose saturated sands or silts on relatively steep slopes, usually

greater than 3 degrees.

27

Lateral Spreads Lateral spreads involve lateral displacement of large, surficial blocks of soil as a result

of liquefaction of a subsurface layer. Displacement occurs in response to the

combination of gravitational forces and inertial forces generated by an earthquake.

Lateral spreads generally develop on gentle slopes (most commonly less than 3

degrees) and move toward a free face such as an incised river channel. Horizontal

displacements commonly range up to several meters. The displaced ground usually

breaks up internally, causing fissures and scarps to form on the failure surface. Lateral

spreads commonly disrupt foundations of buildings built on or across the failure, sever

pipelines and other utilities in the failure mass, and compress or buckle engineering

structures, such as bridges, founded on the toe of the failure.

Damage caused by lateral spreads is severely disruptive and often pervasive. For

example, during the 1964 Alaska earthquake, more than 200 bridges were damaged or

destroyed by spreading of floodplain deposits toward river channels. The spreading

compressed the superstructures, buckled decks, thrust stringers over abutments, and

shifted and tilted abutments and piers. Lateral spreads are particularly destructive to

pipelines. For example, every major pipeline break in the city of San Francisco during

the 1906 earthquake occurred in areas of ground failure. These pipeline breaks

severely hampered efforts to fight the fire that ignited during the earthquake; that fire

caused about 85% of the total damage to San Francisco. Thus, rather inconspicuous

ground-failure displacements of less than 2 m were in large part responsible for the

devastation that occurred in San Francisco.

Ground Oscillation Where the ground is flat or the slope is too gentle to allow lateral displacement,

liquefaction at depth may decouple overlying soil layers from the underlying ground,

allowing the upper soil to oscillate back and forth and up and down in the form of

28

ground waves. These oscillations are usually accompanied by opening and closing of

fissures and fracture of rigid structures such as pavements and pipelines. The

manifestations of ground oscillation were apparent in San Francisco’s Marina District

due to the 1989 Loma Prieta earthquake; sidewalks and driveways buckled and

extensive pipeline breakage also occurred.

Loss of Bearing Strength When the soil supporting a building or other structure liquefies and loses strength,

large deformations can occur within the soil which may allow the structure to settle

and tip. Conversely, buried tanks and piles may rise buoyantly through the liquefied

soil. For example, many buildings settled and tipped during the 1964 Niigata, Japan,

earthquake. The most spectacular bearing failures during that event were in the

Kawangishicho apartment complex where several four-story buildings tipped as much

as 60 degrees. Apparently, liquefaction first developed in a sand layer several meters

below ground surface and then propagated upward through overlying sand layers. The

rising wave of liquefaction weakened the soil supporting the buildings and allowed the

structures to slowly settle and tip.

Settlement In many cases, the weight of a structure will not be great enough to cause the large

settlements associated with soil bearing capacity failures described above. However,

smaller settlements may occur as soil pore-water pressures dissipate and the soil

consolidates after the earthquake. These settlements may be damaging, although they

would tend to be much less so than the large movements accompanying flow failures,

lateral spreading, and bearing capacity failures. The eruption of sand boils (fountains

of water and sediment emanating from the pressurized, liquefied sand) is a common

manifestation of liquefaction that can also lead to localized differential settlements.

29

Increased Lateral Pressure on Retaining Walls If the soil behind a retaining wall liquefies, the lateral pressures on the wall may

greatly increase. As a result, retaining walls may be laterally displaced, tilt, or

structurally fail, as has been observed for waterfront walls retaining loose saturated

sand in a number of earthquakes.

Can Liquefaction Be Predicted?

Although it is possible to identify areas that have the potential for liquefaction, its

occurrence cannot be predicted any more accurately than a particular earthquake can

be (with a time, place, and degree of reliability assigned to it). Once these areas have

been defined in general terms, it is possible to conduct site investigations that provide

very detailed information regarding a site’s potential for liquefaction. Mapping of the

liquefaction potential on a regional scale has greatly furthered our knowledge

regarding this hazard. These maps now exist for many regions of the United States,

Japan and several other areas of the world.

30

Tsunamis

Tsunami is a Japanese term that means “harbor wave”. Tsunamis are the result of a

sudden vertical offset in the ocean floor caused by earthquakes, submarine landslides,

and volcanic deformation.

Tsunami Initiation:

A sudden offset changes the elevation of the ocean and initiates a water wave that

travels outward from the region of sea-floor disruption. Tsunami can travel all the way

across the ocean and large earthquakes have generated waves that caused damage and

deaths, shown in Figure (2.5).

Figure (2.5) Tsunami initiation

The speed of this wave depends on the ocean depth and is typically about as fast as a

commercial passenger jet (about 700 km/hr). This is relatively slow compared to

seismic waves, so we are often alerted to the dangers of the Tsunami by the shaking

before the wave arrives. The trouble is that the time to react is not very long in regions

close to the earthquake that caused the Tsunami.

Figure (2.6) Tsunami in deep water

31

Tsunamis pose no threat in the deep ocean because they are only a meter or so high in

deep water. But as the wave approaches the shore and the water shallows, all the

energy that was distributed throughout the ocean depth becomes concentrated in the

shallow water and the wave height increases (Figures 2.6 and 2.7).

Figure (2.7) Tsunami in shallow water

Typical heights for large Tsunamis are on the order of 10’s of meters and a few have

approached 90 meters. These waves are typically more devastating to the coastal

region than the shaking of the earthquake that caused the Tsunami. Even the more

common Tsunamis of about 10-20 meters can “wipe clean” coastal communities.

32

Architectural and Structural Considerations

Building Configuration:

In recent years, there has been increased emphasis on the importance of a building’s

configuration in resisting seismic forces. Early decisions concerning size, shape,

arrangement, and location of major elements can have a significant influence on the

performance of a structure. Since the design professional plays a large role in these

early decisions, it is imperative that the architect thoroughly understand the concepts

involved.

Building configuration refers to the overall building size and shape and the size and

arrangement of the primary structural frame, as well as the size and location of the

nonstructural components of the building that may aspect its structural performance.

Significant nonstructural components include such things as heavy nonbearing

partitions, exterior cladding, and large weights like equipment or swimming pools.

In the current UBC, elements that constitute both horizontal and vertical irregularities

are specifically defined, so it is clear which structures must be designed with the

dynamic method and which structures may be designed using the static analysis

method. The code states that all buildings must be classified as either regular or

irregular. Whether a building is regular or not helps determine if the static method may

be used. Irregular structures generally require design by the dynamic method, and

additional detailed design requirements are imposed depending on what type of

irregularity exists.

The following sections describe some of the important aspects of building

configuration.

• Torsion

Lateral forces on a portion of a building are assumed to be uniformly distributed and

can be resolved into a single line of action acting on a building. In a similar way, the

shear reac

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33

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.

es the stru

e inside co

not coinc

e structure

by the

ct or engin

imize the

t, they can

(Figures 2

m plan sha

will beco

centrations

of the m

ucture to m

orners. In

cide, there

e as discus

site, the

neer. In th

problem.

n be tied

2.10 and 2.

apes

ome appar

s of stres

most com

move in su

addition,

e is an ec

ssed in th

program,

he cases w

The porti

together

.11).

35

rent in the

s, both of

mmon and

uch a way

since the

ccentricity

e previous

or other

where such

ons of the

across the

5

e

f

d

y

e

y

s

r

h

e

e

A second

stiffness a

d common

and streng

n problem

gth of the p

Figure

Figure (2

m that ari

perimeter.

(2.11): So

2.12): Var

ises with

olution to r

riation in p

building

re-entrant

perimeter

plans is

corners

stiffness

a variati

36

ion in the

6

e

37

Even though a building may be symmetric, the distribution of mass and lateral

resisting elements may place the centers of mass and rigidity in such a way that torsion

is developed.

During an earthquake, the open end of the building acts as a cantilevered beam

causing lateral displacement and torsion. There are four possible ways to alleviate the

problem. In the first instance, a rigid frame can be constructed with symmetric rigidity

and then the cladding can be made nonstructural. Secondly, a strong, moment-resisting

or braced frame can be added that has stiffness similar to the other walls. Third, shear

walls can be added to the front if this does not compromise the function of the

building. Finally, for small buildings, the structure can simply be designed to resist the

expected torsion forces.

The ratio of plan dimensions should not be inordinately large to prevent different types

of forces acting on different plan sections. If this cannot be achieved, then seismic

joint should be provided in such a building.

Elevation Design

The ideal elevation from a seismic design standpoint is one that is regular,

symmetrical, continuous, and that matches the other elevations in configuration and

seismic resistance. Setbacks and offsets should be avoided for the same reason as re-

entrant corners in plan should be avoided; that is, to avoid areas of stress

concentration. Of course, perfect symmetry is not always possible due to the

functional and aesthetic requirements of the building, but there are two basic

configurations that should (and can) be avoided by the architect early in the design

process.

The first problem configuration is a discontinuous shear wall. This is a major mistake

and should never happen. Discontinuities can occur when large openings are placed in

shear walls, when they are stopped short of the foundation, or when they are altered in

some other way. Since the entire purpose of a shear wall is to carry lateral loads to the

foundatio

this is cou

be placed

Two com

wall is sto

to open u

great that

2.13).

The secon

floors abo

shear wal

load path

transfer o

In all case

continuou

n and act

unterprodu

in shear w

mmon exam

opped at th

up the first

t even ext

nd exampl

ove are ca

l continue

for the la

f forces fr

es of disco

usly to the

as a beam

uctive. Of

walls if pr

mples of d

he second

t floor, bu

tra reinfor

Figure

le is also

antilevered

es, the offs

ateral load

rom one sh

ontinuous

foundatio

m cantilev

f course, sm

oper reinf

discontinuo

d floor lev

ut it create

rcing cann

e (2.13): D

a common

d slightly

fset also cr

ds is inter

hear wall t

shear wal

on.

vered out

mall open

forcement

ous shear

vel and sup

es a situat

not alway

Discontinu

n design f

from the

reates an u

rrupted, an

to the nex

lls, the sol

of the fou

nings like d

is provide

walls are

pported by

tion where

ys resist th

uous shear

feature wh

first floor

undesirabl

nd the flo

xt.

lution is si

undation,

doors and

ed.

shown. In

y columns

e stress co

he build-u

r walls

here the s

r shear wa

le situation

oor structu

imple: she

any inter

d small win

n the first

s. This is o

oncentrati

up of stre

econd flo

all. Even t

n because

ure has to

ear walls s

38

rruption of

ndows can

, the shear

often done

ons are so

ss (Figure

or and the

though the

e the direc

o carry the

should run

8

f

n

r

e

o

e

e

e

t

e

n

Another s

when the

at any flo

the greate

case of th

or when t

2.14).

A soft sto

story and

these situ

floors abo

When ear

weak floo

members.

There are

eliminate

serious pr

ground flo

or, it is m

est. The di

he soft stor

the first st

ory can als

the groun

ations to o

ove for the

rthquake

or instead

.

e several w

it and try

roblem w

oor is wea

most seriou

scontinuo

ry. Others

tory is hig

F

so be crea

nd level is

occur. For

e guest roo

loads occ

of being

ways to so

y to work

ith buildin

aker than t

us at grade

ous shear w

s can occu

gh compar

Figure (2.

ated when

open. Of

r example

oms.

cur, the fo

uniformly

olve the pr

k the arch

ng config

the floors

e level bec

wall discu

ur when al

red with th

14) Soft f

n there is h

f course, th

e, a hotel m

orces and

y distribut

roblem of

hitectural

guration is

above. Al

cause this

ssed in the

ll columns

he other f

first storie

heavy ext

here are u

may need

deformat

ted among

f a soft sto

solution a

s the soft

lthough a

is where

e previous

s do not e

floors of th

s

erior cladd

sually val

a high fir

tions are

g all the f

ory. The f

around th

t story. Th

soft story

the lateral

s section i

extend to t

he structu

dding abov

lid reasons

rst story, b

concentra

floors and

first, of co

he extra co

39

his occurs

can occur

l loads are

s a specia

the ground

ure (Figure

ve the firs

s for all of

but shorter

ated at the

d structura

ourse, is to

olumns or

9

s

r

e

l

d

e

t

f

r

e

l

o

r

40

lower height. If height is critical, extra columns can be added at the first floor. Another

solution is to add extra horizontal and diagonal bracing. Finally, the framing of the

upper stories can be made the same as the first story. The entire structure then has a

uniform stiffness. Lighter, intermediate floors can be added above the first between

the larger bays so they do not aspect the behavior of the primary structural system.

Lightweight Construction:

The greater the structural mass, the greater the seismic forces. In contrast to wind

design, seismic design calls for lighter construction with a high strength-to-weight

ratio to minimize the internal forces.

Ductility:

The ductility of the structure can be considered as a measure of its ability to sustain

large deformations without endangering its load-carrying capacity. Therefore, in

addition to seismic strength, the ductility of the structure should be given serious

consideration.

• The required ductility can be achieved by proper choice of framing and

connection details.

• Ductility is improved by limiting the ratio of reinforcement on the tension

side of beams.

• Using compression reinforcement in beams enhances ductility.

• Using adequate shear reinforcement enhances ductility.

• Provision of spiral reinforcement or closely spaced ties improved ductility.

Adequate Foundations:

Differential settlement of buildings is to be minimized through proper design of

footings. Earthquake oscillations can cause liquefaction of loose soils, resulting in an

uneven settlement. Stabilization of the soil prior to building construction and the use

of deep footings are some remedial measures needed to overcome such a problem.

Short Co

Frequentl

in design,

due to the

Even if ve

collapses

concept; e

following

Separatio

The mutu

caused sig

sufficient

Joints an

Joints are

strong ho

concrete f

olumn Eff

y a colum

, such as

e short len

ery strong

have been

eliminatin

g relation V

on of Stru

ual hamme

gnificant

clearance

nd Connec

e often th

orizontal c

frames are

fects:

mn is short

the partia

ngth of the

g stirrups a

n frequent

ng such pa

V = 2 M (p

Figure (2.

uctures:

ering rece

damage. T

e so that th

ctions:

he weakes

confining

e often res

ened by el

al-height i

e column

are used it

t. The onl

rtial heigh

plastic) / L

.15): Failu

eived by b

The simpl

he free mo

t link in

reinforcem

ponsible f

lements, w

infill walls

when subj

t is difficu

ly possibl

hts of infil

L (Figure

ure due to

buildings

lest metho

otion of th

a structur

ment with

for collaps

which hav

s. This cr

bjected to v

ult to save

e solution

ll walls. T

2.15).

short colu

in close p

od of prev

e two stru

ral system

hin the joi

ses in eart

ve not been

eates very

very large

such colu

n is to use

he shear f

umn effect

proximity

venting da

uctures can

m. It is ne

int zone. J

hquakes.

n taken int

y large sh

e bending

umns, ther

e different

force is giv

t

of one an

amage is t

n occur.

ecessary t

Joints in

41

to accoun

hear forces

moments

efore such

t structura

ven by the

nother has

to provide

to provide

reinforced

1

t

s

.

h

l

e

s

e

e

d

42

Inadequate Shear Strength:

To enhance shear capacity one should first use suitable amount of stirrups and ties to

prevent the brittle type of failure associated with shear. Diagonal reinforcement is

recommended for deep members to resist diagonal tension.

Materials and Workmanship:

It is obvious that no design can save the structure if bad materials are used or if

workmanship is not good. The best available quality design codes are deemed useless

unless quality control is kept starting from the design process and ending up with the

site execution.

Bond, Anchorage, and Splices:

Bond, when effectively developed, enables the concrete and reinforcement to form a

composite structure. If the area of concrete surrounding the bar is small, splitting is the

common mode of failure. One should avoid splices and anchorage at the location

where the surrounding concrete is extensively cracked (i.e., plastic hinges).

Detailing of Structural Elements:

Closely spaced stirrups and ties are used in columns and walls, to hold the

reinforcement in place and to prevent buckling of longitudinal bars. Closely spaced

stirrups and ties are used in potential hinge regions of beams, to ensure strength

retention during cyclic loading. Detailing of special transverse steel through beam-

column joints in ductile frames to maintain the integrity of the joints during adjacent

beam hinge plastic deformation is required.

Detailing of Non-Structural Elements:

The tendency of non-structural elements to be damaged, as the building sways need to

be addressed. To overcome such problems, either separation is kept between structural

and non-structural members, or the forces resulting from the attachment of structural

elements need to be taken into consideration.

The Effec

When an

the inertia

the groun

the buildi

opposite d

vibrate ba

Theoretic

states that

by the giv

acting on

the structu

If a buildi

from side

one full s

of the bui

ct of Eart

earthquak

a of the st

nd causes t

ing and a

direction.

ack and fo

Fi

ally, the f

t force eq

ven earth

it. Howev

ure- its na

ing is defl

to side. T

ide-to-sid

lding.

thquakes

ke occurs,

tructure m

the buildin

shear forc

As the dir

rth.

igure (2.16

force on t

quals mass

quake, the

ver, the ac

atural perio

lected by a

The period

e oscillati

on Buildi

the first re

mass. Almo

ng to mov

ce at the b

rection of

6): Buildin

the buildin

s times ac

e greater

cceleration

od (Figure

a lateral fo

d is the tim

on. The p

ings

esponse o

ost instant

ve sideway

base, as th

f the accel

ng motion

ng can be

cceleration

the mass

n of the bu

e 2.16).

orce such

me in seco

period is d

of a buildin

taneously,

ys at the b

hough forc

eration ch

n during an

found by

n. Since th

of the bu

uilding de

as the win

onds it tak

dependent

ng is not to

however,

base causi

ces were b

hanges, the

n earthqua

y using Ne

he acceler

uilding, th

epends on

nd or an e

kes for a b

on the ma

to move at

, the accel

ing a later

being app

e building

ake

ewton’s la

ration is e

he greater

another p

earthquake

building to

ass and th

43

t all due to

leration of

ral load on

lied in the

g begins to

aw, which

established

r the force

property of

e, it moves

o complete

he stiffness

3

o

f

n

e

o

h

d

e

f

s

e

s

In a theor

is zero. Th

When the

accelerati

force on t

induced, a

Natural p

cabinet to

retical, com

he acceler

e building

on decrea

the buildin

and stiff, s

periods va

o about 0.1

mpletely s

ration of s

g is mor

ases. As m

ng. Theref

short-perio

ary from a

1 sec. for a

Fig

stiff buildi

such an in

e flexible

mentioned

fore, flexib

od buildin

about 0.05

a one-story

gure (2.18

ing, there

nfinitely ri

e, its per

above, as

ble, long-

ngs have m

5 sec. for

y building

8): Fundam

is no mov

gid buildi

riod incre

the accele

period bu

more latera

r a piece

g.

ments perio

vement, an

ng is the s

ases and

eration de

ildings ha

al force ind

of furnitu

ods

nd the natu

same as th

the corr

ecreases, s

ave less la

nduced.

ure such a

44

ural period

he ground

responding

o does the

teral force

as a filing

4

d

d.

g

e

e

g

45

A rule of thumb is that the building period equals the number of stories divided by 10.

As the building moves, the forces applied to it are either transmitted through the

structure to the foundation, absorbed by the building components, or released in other

ways such as collapse of structural elements.

The goal of seismic design is to build a structure that can safely transfer the loads to

the foundation and back to the ground and absorb some of the energy present rather

than suffering damage.

The ability of a structure to absorb some of the energy is known as ductility, which

occurs when the building deflects in the inelastic range without failing or collapsing.

The elastic limit is the limit beyond which the structure sustains permanent

deformation. The greater the ductility of a building, the greater is its capacity to absorb

energy.

Ductility varies with the material. Steel is a very ductile material because of its ability

to deform under a load above the elastic limit without collapsing. Concrete and

masonry, on the other hand, are brittle materials. When they are stressed beyond the

elastic limit, they break suddenly and without warning. Concrete can be made more

ductile with reinforcement, but at a higher cost.

Resonance

The ground vibrates at its natural period. The natural period of ground varies from

about 0.4 sec. to 2 sec. depending generally on the hardness of the ground.

The terrible destruction in Mexico City in the earthquake of 1985 was primarily the

result of response amplification caused by the coincidence of building and ground

motion periods. Mexico City was some 400 km from the earthquake focus, and the

earthquake caused the soft ground under downtown buildings to vibrate for over 90

seconds at its long natural period of around 2 seconds. This caused tall buildings

around 20 stories tall to resonate at a similar period, greatly increasing the

accelerations within them. This amplification in building vibration is undesirable. The

possibility of it happening can be reduced by trying to ensure that the building period

46

will not coincide with that of the ground. Other buildings, of different heights and with

different vibrational characteristics, were often found undamaged even though they

were located right next to the damaged 20 story buildings. Thus, on soft (long period)

ground, it would be best to design a short stiff (short period) building.

General Goals in Seismic-Resistant Design and Construction

• If basic, well-understood principles are ignored and short cuts taken, disaster can

occur.

• Many tall buildings that survived major earthquakes show that adherence to these

principles can produce structures out of which people can be sure of walking alive,

even if some structural damage has occurred.

The philosophy of earthquake design for structures other than essential facilities has

been well established and proposed as follows.

• To prevent non-structural damage in frequent minor ground shaking.

• To prevent structural damage and minimize non-structural damage in occasional

moderate ground shaking.

• To avoid collapse or serious damage in rare major ground shaking.

Structura

The Unifo

structural

1- Be

2- Bu

3- Mo

4- Du

1- Bearin

wall lines

used to re

not contai

support fl

2- Buildin

vertical lo

building f

3- Momen

frame thro

frame elem

al System

form Build

systems:

aring Wa

uilding Fr

oment Re

ual System

g wall sys

s and at in

esist latera

in comple

loor and ro

ng frame

oads, but

frame syst

nt-resistin

oughout th

ments to r

Earms Defined

ding Code

all System

ame Syste

esisting Fr

ms

stems con

nterior loc

al forces a

te vertical

oof vertica

systems u

use either

tem with s

Figu

ng frame s

he buildin

resist later

rthquaked:

e (UBC)

ms

ems

rame Syst

nsist of ve

ations as n

and are th

l load carr

al loads.

use a com

r shear w

shear walls

ure (2.19)

ystems, sh

ng to carry

ral forces.

e-Resista

earthquak

tems

ertical load

necessary

hen called

rying spac

mplete thre

walls or br

s is shown

Building

hown in F

y vertical l

ant Syst

ke provisio

d carrying

y. Many of

d shear wa

ce frames b

ee dimens

raced fram

n in Figure

Frame Sy

Figure (2.2

loads, and

ems

ons recog

g walls loc

f these be

alls. Bearin

but may u

ional spac

mes to resi

e (2.19).

stem

20), provid

they use

gnize these

cated alon

earing wal

ing wall s

use some c

ce frame t

ist lateral

de a comp

some of th

47

e building

ng exterior

ls are also

ystems do

columns to

to suppor

forces. A

plete space

hose same

7

g

r

o

o

o

rt

A

e

e

4. A dua

provides

specially

moment-r

shear, an

proportion

This syste

buildings

Lateral-F

Lateral-fo

wind and

walls, bra

Shear Wa

A shear w

wall throu

foundatio

(2.21) sho

another in

al system

support f

detailed

resisting f

nd the tw

n to their r

em, which

where per

Force-Res

orce-resist

d seismic

aced frame

alls:

wall is a ve

ugh shear

n, and, ju

ows two e

n a multist

Figure (2

is a stru

for gravity

moment-r

frame mus

wo system

relative rig

h provide

rimeter fra

sisting Ele

ting eleme

forces. T

es, and mo

ertical stru

r and bend

st as with

examples

tory buildi

2.20): Mo

uctural sy

y loads, a

resisting f

st be capa

ms must b

gidities.

es good re

ames are u

ements

ents must b

he three

oment- res

uctural ele

ding. Such

a beam, p

of a shea

ing.

oment resis

ystem in w

and resista

frame and

able of re

be designe

edundancy

used in co

be provide

principal

sisting fram

ement that

h a wall a

part of its

ar wall, on

sting fram

which an

ance to la

d shear w

sisting at

ed to res

y, is suita

onjunction

ed in ever

types of

mes.

resists lat

acts as a b

strength d

ne in a si

me system

essential

ateral load

walls or b

least 25 p

sist the to

able for m

with cent

ry structur

resisting

teral force

beam cant

derives fro

imple one

lly compl

ds is prov

braced fra

percent o

otal latera

medium-to

tral shear w

re to brace

elements

es in the pl

ntilevered

om its dep

e-story bui

48

lete frame

vided by a

ames. The

f the base

al load in

o-high rise

wall core.

e it agains

are shear

lane of the

out of the

pth. Figure

ilding and

8

e

a

e

e

n

e

t

r

e

e

e

d

49

Figure (2.21): Shear walls

In Figure (2.21.a), the shear walls are oriented in one direction, so only lateral forces

in this direction can be resisted. The roof serves as the horizontal diaphragm and must

also be designed to resist the lateral loads and transfer them to the shear walls. Figure

(2.21.a) also shows an important aspect of shear walls in particular and vertical

elements in general. This is the aspect of symmetry that has a bearing on whether

torsional effects will be produced. The shear walls in Fig. (2.21.a) are symmetrical in

the plane of loading.

Figure (2.21.b) illustrates a common use of shear walls at the interior of a multistory

building. Because walls enclosing stairways, elevator shafts, and mechanical shafts are

mostly solid and run the entire height of the building, they are often used for shear

walls. Although not as efficient from a strictly structural point of view, interior shear

walls do leave the exterior of the building open for windows. Notice that in Figure

(2.21.b) there are shear walls in both directions, which is a more realistic situation

because both wind and earthquake forces need to be resisted in both directions. In this

diagram, the two shear walls are symmetrical in one direction, but the single shear

wall produces a nonsymmetrical condition in the other since it is off center. Shear

walls do n

torsional e

Shear wal

high.

Shear wa

their abili

What is a

Reinforce

Walls (Fi

start at fo

thickness

walls are

like verti

foundatio

Advantag

Properly

performan

not need t

effects.

lls, when

lls may h

ity to resis

a Shear W

ed concret

igure 2.22

foundation

can be as

usually p

cally-orien

n.

ges and D

designed

nce in pas

to be symm

used alon

have openi

st lateral lo

Wall Build

te buildin

2) in addit

n level an

s low as 1

provided a

nted wide

Figure (

Disadvanta

and deta

t earthqua

metrical in

ne, are suit

ings in th

oads is red

ding?

ngs often

tion to sla

nd are con

50mm, or

along both

e beams t

2.22): Rei

ages of Sh

ailed build

akes.

n a buildi

table for m

hem, but t

duced dep

have vert

abs, beam

ntinuous t

r as high a

h length an

that carry

inforced c

hear Wall

dings with

ng, but sy

medium r

the calcula

ending on

tical plate

ms and col

throughou

as 400mm

nd width

y earthqua

concrete sh

ls in Rein

h shear w

ymmetry i

ise buildin

ations are

n the perce

e-like RC

umns. Th

ut the bui

m in high r

of buildin

ake loads

hear wall

nforced Co

walls have

is preferre

ngs up to

e more dif

entage of o

walls cal

hese walls

ilding heig

rise buildin

ngs. Shear

downwar

oncrete B

e shown v

50

d to avoid

20 stories

fficult and

open area.

lled Shear

generally

ght. Their

ngs. Shear

r walls are

rds to the

Buildings:

very good

0

d

s

d

.

r

y

r

r

e

e

:

d

51

Shear walls in high seismic regions require special detailing. However, in past

earthquakes, even buildings with sufficient amount of walls that were not specially

detailed for seismic performance (but had enough well-distributed reinforcement)

were saved from collapse. Shear wall buildings are a popular choice in many

earthquake prone countries, like Chile, New Zealand and USA. Shear walls are easy to

construct, because reinforcement detailing of walls is relatively straightforward and

therefore easily implemented at site. Shear walls are efficient, both in terms of

construction cost and effectiveness in minimizing earthquake damage in structural and

nonstructural elements (like glass windows and building contents).

On the other hand, shear walls present barriers, which may interfere with architectural

and services requirement. Added to this, lateral load resistance in shear wall buildings

is usually concentrated on a few walls rather than on large number of columns.

Architectural Aspects of Shear Walls:

Most RC buildings with shear walls also have columns; these columns primarily carry

gravity loads (i.e., those due to self-weight and contents of building). Shear walls

provide large strength and stiffness to buildings in the direction of their orientation,

which significantly reduces lateral sway of the building and thereby reduces damage

to the structure and its contents.

Since shear walls carry large horizontal earthquake forces, the overturning effects on

them are large. Thus, design of their foundations requires special attention. Shear

walls should be provided along preferably both length and width. However, if they are

provided along only one direction, a proper grid of beams and columns in the vertical

plane (called a moment-resistant frame) must be provided along the other direction to

resist strong earthquake effects.

Door or window openings can be provided in shear walls, but their size must be small

to ensure least interruption to force flow through walls. Moreover, openings should be

symmetrically located. Special design checks are required to ensure that the net cross-

sectional

force.

Shear wal

twist in bu

directions

perimeter

Ductile D

Just like r

perform m

wall, type

the buildin

Overall G

Shear wal

much larg

shaped se

shafts aro

taken adv

area of a

lls in build

uildings (F

s in plan

r of the bu

Design of S

reinforced

much bett

es and am

ng help in

Geometry

lls are rec

ger than t

ections are

ound the e

vantage of

wall at an

dings mus

Figure 2.2

. Shear w

ilding–suc

F

Shear Wa

d concrete

ter if desig

mount of re

n improvin

y of Walls

tangular i

the other.

e also use

elevator c

to resist e

n opening

st be symm

23). They c

walls are

ch a layou

Figure (2.2

alls:

beams an

gned to b

einforcem

ng the duc

:

n cross-se

While re

ed (Figure

core of bu

earthquake

g is suffici

metrically

could be p

more ef

ut increase

23): Shear

nd column

be ductile.

ment, and c

ctility of w

ection, i.e.

ectangular

e 2.24). Th

uildings a

e forces.

ient to car

y located i

placed sym

ffective w

es resistanc

wall layo

ns, reinfor

Overall

connection

walls.

., one dim

r cross-sec

hin-walled

also act as

rry the ho

n plan to

mmetricall

when loca

ce of the b

ut

ced concr

geometric

n with rem

mension of

ction is co

d hollow

s shear w

orizontal e

reduce ill

ly along o

ated along

building to

rete shear

c proportio

maining el

f the cross

ommon, L

reinforced

walls, and

52

earthquake

effects of

one or both

g exterior

o twisting

walls also

ons of the

lements in

-section is

L- and U-

d concrete

should be

2

e

f

h

r

.

o

e

n

s

-

e

e

Braced F

A braced

lateral for

the brace

forces fro

one-story

other end

uses com

compressi

Figure 2.2

compressi

from eith

same resu

direction.

Braced fr

placed in

problems

resisting s

Frames:

frame is

rces are re

d frame d

om each b

braced fr

d only one

mpression b

ion, depen

25.b) show

ion memb

her directio

ult, but the

raming ca

one struc

for windo

system.

Fig

a truss s

esisted thr

depends o

building el

frame. At

e bay is b

braces be

nding on w

ws two me

ber in one

on. Altern

ey must be

n be plac

ctural bay

ows and d

gure (2.24)

system of

rough axia

on diagon

lement to

one end o

braced. Th

cause the

which way

ethods of

e bay can

nately, ten

e run both

ed on the

or several

doorways,

): Shear w

f the conc

al stresses

nal membe

the found

of the bui

his buildin

e diagonal

y the force

bracing a

n be used

nsion diag

ways to a

e exterior

l. Obviou

, but it is

wall geome

centric or

s in the m

ers to pro

dation. Fig

ilding two

ng is only

l member

e is applied

multistor

to brace

gonals can

account fo

or interio

sly, a brac

a very ef

etry

eccentric

members. J

ovide a lo

gure (2.25

o bays are

braced in

may be e

d.

y building

against la

n be used

r the load

or of a bu

ced frame

fficient and

c type in

Just as wi

oad path

5.a) shows

e braced a

n one dire

either in

g. A single

ateral load

d to accom

coming fr

uilding, an

e can pres

d rigid lat

53

which the

ith a truss

for latera

s a simple

and at the

ection and

tension or

e diagona

ds coming

mplish the

from either

nd may be

ent design

teral force

3

e

,

l

e

e

d

r

l

g

e

r

e

n

e

j

Moment-

Moment-r

joints. Joi

and theref

and beam

The UBC

is the spe

ductile be

The secon

with less

intermedi

The third

frame doe

concrete f

Moment-r

frames; th

become m

other, and

which inc

Two type

-Resisting

resisting f

ints are de

fore any l

ms. They ar

C differenti

ecial mom

ehavior an

nd type is

restrictiv

ate frames

type is th

es not mee

frames can

resisting

he horizon

more prob

d special

creases the

s of mome

g Frames:

frames car

esigned an

lateral def

re used in

iates betw

ment-resist

d comply

the interm

ve require

s cannot b

e ordinary

et the spe

nnot be us

frames ar

ntal deflec

blematic.

attention

e column b

ent-resisti

Figure (2

:

rry lateral

nd constru

flection of

low-to-m

ween three

ting frame

with the p

mediate mo

ements tha

be used in

y moment-

cial detail

sed in zone

re more

ction, or d

Adjacent

must be

bending st

ng frames

2.25) Brac

l loads pri

ucted so t

f the fram

medium rise

types of m

e that mu

provisions

oment-res

an specia

seismic zo

-resisting

ling requir

es 3 or 4.

flexible t

drift, is gre

buildings

paid to th

tresses.

s are show

ed frames

imarily by

they are th

me occurs f

e building

moment re

ust be spe

s of the UB

sisting fram

l moment

ones 3 or

frame. Th

rements fo

than shea

eater, and

s cannot b

he eccentr

wn in Figur

y flexure i

heoreticall

from the b

gs.

esisting fra

ecifically

BC.

me, which

t-resisting

4.

his concret

for ductile

ar wall st

thus non-

be located

ricity dev

re (2.26)

in the mem

ly comple

bending o

rames. The

detailed t

h is a conc

g frames.

te momen

behavior

tructures

-structura

d too clos

veloped in

54

mbers and

etely rigid

of columns

e first type

to provide

rete frame

However

nt-resisting

. Ordinary

or braced

l elements

se to each

n columns

4

d

d,

s

e

e

e

r,

g

y

d

s

h

,

Advantag

- Pro

whi

ext

- The

from

Disadvan

- Poo

cata

fail

- Bea

con

- Req

Horizont

In all late

the vertic

most com

A diaphra

There are

ges:

ovide a po

ich can a

ernal clad

eir flexibi

m the forc

ntages:

orly desi

astrophica

lures aroun

am colum

nsiderable

quires goo

tal Elemen

eral force-

cal resistin

mmon way

agm acts a

two types

Figur

otentially

allow free

dding.

ility and a

cing motio

gned mo

ally in ea

nd beam-c

mn joints re

skill to de

od fixing s

nts (Diaph

resisting s

ng elemen

used is th

as a horizo

s of diaphr

re (2.26) M

high-duct

edom in

associated

ons on stif

oment res

arthquakes

column jo

epresent a

esign succ

skills and c

hragms):

systems, t

nts. This i

he diaphra

ontal beam

ragms: fle

Moment r

tile system

architectu

d long per

ff soil or ro

sisting fr

s, mainly

oints.

an area of

cessfully.

concreting

there must

s done wi

agm.

m resisting

exible and

esisting fr

m with a

ural plann

riod may

ock sites.

rames ha

y by form

high stres

g.

t be a way

ith severa

forces wi

d rigid.

rames

good deg

ning of in

serve to d

ave been

mation of

ss concent

y to transm

al types of

ith shear a

gree of re

nternal sp

detune the

observed

f weak st

tration, wh

mit latera

f structure

and bendin

55

dundancy

paces and

e structure

d to fai

tories and

hich needs

l forces to

es, but the

ng action.

5

y,

d

e

l

d

s

o

e

Although

between t

distributed

A flexible

times the

comparing

adjoining

distributed

With a r

vertical el

(assuming

diagram a

to each e

between t

The illust

However,

unequal.

Concrete

deck cons

of their co

no horiz

the two ty

d.

e diaphrag

average

g the midp

vertical re

d accordin

rigid diaph

lements w

g there is

are twice a

end wall a

these two.

tration sho

, if the ve

floors are

struction.

onstruction

ontal elem

ypes beca

gm is one

story drif

point in-p

esisting el

ng to tribu

hragm, th

will be in p

s no torsio

as stiff as

and one-th

ows symm

ertical res

e consider

Steel deck

n. Wood d

Figure

ment is co

ause the ty

e that has

ft of that

lane defle

lements un

utary areas

he shear f

proportion

on), as sh

the interio

hird to th

metrically

sisting ele

red rigid d

ks may be

decks are c

e (2.27) Di

ompletely

ype affect

a maximu

story. Th

ection of th

nder equiv

s as shown

forces tra

n to the re

hown in F

or walls, t

he two int

placed sh

ements are

diaphragm

e either fle

considere

iaphragm

y flexible

ts the way

um lateral

his deform

he diaphra

valent trib

n in Figure

ansmitted

lative stiff

Fig, (2.27

then one-t

terior wal

hear walls

e asymme

ms, as are

exible or ri

d flexible

load distr

or rigid,

y in whic

l deforma

mation can

agm with t

utary load

e (2.27.a).

from the

ffness of th

7.b). If th

third of th

lls, which

, so the d

etric, the

steel and

igid, depe

diaphragm

ibution

distinction

ch lateral

ation more

n be deter

the story d

d. The late

.

e diaphrag

he vertica

he end wa

he load is d

h is equall

distribution

shearing

concrete

ending on

ms.

56

n is made

forces are

e than two

rmined by

drift of the

eral load is

gm to the

l elements

alls in the

distributed

ly divided

n is equal

forces are

composite

the details

6

e

e

o

y

e

s

e

s

e

d

d

.

e

e

s

57

Load Path:

The structure shall contain one complete load path for Life Safety for seismic force

effects from any horizontal direction that serves to transfer the inertial forces from the

mass to the foundation.

There must be a complete lateral-force-resisting system that forms a continuous load

path between the foundation, all diaphragm levels, and all portions of the building for

proper seismic performance.

The general load path is as follows: seismic forces originating throughout the building

are delivered through structural connections to horizontal diaphragms; the diaphragms

distribute these forces to vertical lateral-force-resisting elements such as shear walls

and frames; the vertical elements transfer the forces into the foundation; and the

foundation transfers the forces into the supporting soil.

If there is a discontinuity in the load path, the building is unable to resist seismic

forces regardless of the strength of the existing elements. Mitigation with elements or

connections needed to complete the load path is necessary to achieve the selected

performance level. The design professional should be watchful for gaps in the load

path. Examples would include a shear wall that does not extend to the foundation, a

missing shear transfer connection between a diaphragm and vertical element, a

discontinuous chord at a diaphragm notch, or a missing collector.

In cases where there is a structural discontinuity, a load path may exist but it may be a

very undesirable one. At a discontinuous shear walls, for example, the diaphragm may

transfer the forces to frames not intended to be part of the lateral-force-resisting

system. While not ideal, it may be possible to show that the load path is acceptable.

Primary Load-Path Elements:

Within every building, there are multiple elements that are used to transmit and resist

lateral forces. These transmitting and resisting elements define the building’s lateral-

load path.

and conne

An appre

everyone

resist eart

There are

such as sh

horizontal

The roof a

force-tran

stories at

immediate

method of

depends o

Shear wa

perform f

an upper-

therefore

a shear w

elements t

. This path

ection, to t

eciation of

involved

thquakes.

two orien

hear walls

l, such as

and floor

nsmitting o

and abo

ely below

f distribut

on that cla

alls and fr

force-trans

-story inte

must tran

wall, forces

that partic

Fi

h extends

the founda

f the criti

in the de

ntations of

s, braced f

the roof, f

elements

or force-d

ve their l

w. Diaphra

ting earthq

assification

rames are

smitting fu

erior shear

nsmit its fo

s are trans

cipate in th

igure (2.2

from the u

ation.

ical impor

esign, cons

f primary

frames, an

floors, and

are known

distributing

level and

agms are

quake forc

n. Concre

primarily

unctions. F

r wall ma

orces to a

smitted in

he earthqu

8): Primar

uppermos

rtance of

struction,

elements

nd momen

d foundati

n as diaph

g element

deliver t

classified

ces from t

ete diaphra

y lateral f

For examp

ay not con

floor diap

nto a found

uake load p

ry structur

t roof or p

a comple

and inspe

in the load

nt frames,

ion.

hragms. D

ts that tak

them to w

d as eithe

the diaphr

agms are c

force- res

ple and wh

ntinue to

phragm. A

dation ele

path are sh

ral load pa

parapet, th

ete load p

ection of

d path: tho

and those

Diaphragm

ke horizon

walls or f

er flexible

agm to th

considered

isting elem

hile not ne

the base o

Also, at the

ement. The

hown in F

ath elemen

hrough eac

path is ess

buildings

ose that ar

e that are e

ms serve pr

ntal forces

frames in

e or rigid

he resisting

d rigid.

ments but

ecessarily

of the bui

e base of a

e primary

Figure (2.2

nts

58

ch elemen

sential for

that mus

re vertical

essentially

rimarily as

s from the

the story

d, and the

g elements

t can also

desirable

ilding and

a frame or

y structura

28).

8

t

r

t

,

y

s

e

y

e

s

o

,

d

r

l

Foundatio

transmitti

of friction

of soil in w

Foundatio

forces fro

Secondar

Within th

needed to

forces ar

between h

Two impo

member a

forces. A

walls or fr

In the cas

because th

perimeter

ons form

ng it to th

nal resista

which the

ons must

om shear w

ry Load-P

he primar

o resist sp

e transmi

horizontal

ortant sec

along the

collector

frames. Fig

Figu

se of floor

hey form

r is typic

the final

he ground

ance along

ey are emb

also supp

walls and f

Path Elem

ry load-pa

pecific for

itted. Par

seismic e

ondary el

e boundary

is a struc

gure (2.29

ure (2.29):

rs and roof

the interfa

ally the

link in th

d. Foundat

g their low

bedded.

port addit

frame colu

ments:

ath eleme

rces or to

ticular at

elements (d

ements ar

y of a di

ctural mem

9) depicts t

: Function

fs, the per

face betwe

location f

he load p

tions resis

wer surfac

tional vert

umns.

ents, ther

provide

ttention m

diaphragm

re chords

iaphragm

mber that

the overal

n of diagra

rimeter ed

een the dia

for vertic

path by co

st lateral f

e and late

tical load

re are ind

specific p

must be g

ms) and ve

and colle

that resis

transmits

ll function

am chords

dges or bou

aphragms

cal seismi

ollecting

forces thro

eral bearin

s caused

dividual s

pathways a

given to

ertical seis

ctors. A c

sts tension

diaphragm

n of chords

and collec

undaries a

and the p

ic elemen

the base

ough a co

ng against

by the ov

secondary

along wh

transmitti

smic elem

chord is a

n and co

gm forces

s and colle

ctors

are critical

perimeter w

nts, althou

59

shear and

ombination

t the depth

verturning

elements

ich latera

ing forces

ents.

structura

mpression

into shear

ectors.

l locations

walls. The

ugh many

9

d

n

h

g

s

l

s

l

n

r

s

e

y

buildings

resistance

Boundary

depending

As shown

tend to be

and comp

greatest b

vertical re

which the

side is in

forces re

compressi

In concret

plane ben

frame in

diaphragm

walls are

frames ar

boundary

also hav

e also crea

y element

g on the ax

n in Figur

end the di

pression. S

bending str

esisting s

e forces ar

tension. T

everse. Th

ion.

te walls, r

nding in t

the story

m boundar

often inte

re normal

.

Figure

e shear w

ates a diaph

ts in diap

xis along w

re (2.30), t

iaphragm

Similar to

ress and l

eismic ele

re being a

These tens

herefore,

reinforcing

the wall. C

y immedia

ry (See Fig

errupted b

lly located

e (2.30): U

walls or fr

hragm bou

phragms u

which late

the forces

and the c

o a uniform

argest def

ements. T

applied is

sion and c

each cho

g steel is p

Collectors

ately belo

gure 3.12)

y opening

d in only

Use of coll

frames at

undary.

usually s

eral loads

s acting pe

chord mem

mly loade

flection at

The chord

in compr

compressi

ord must

placed at t

s are need

ow the di

). This is a

gs for win

y a few o

lector elem

interior lo

serve as b

are consid

erpendicu

mber must

ed beam,

t or near th

d on the s

ression, an

on forces

be desig

the diaphra

ded when

aphragm

a very com

ndows and

of the fram

ment at int

ocations.

both chor

dered to b

ular to the

t resist the

a diaphrag

he center

side of th

nd the cho

reverse w

gned for

agm level

an indiv

is not co

mmon situ

d doors, an

me bays

terior shea

An interi

rds and

e applied.

boundary

e associate

gm exper

of its span

he diaphra

ord on the

when the e

both ten

l to resist t

vidual shea

ontinuous

uation bec

nd becaus

along a d

ar wall

60

ior line of

collectors

y elements

ed tension

riences the

n between

agm along

e opposite

earthquake

nsion and

the out-of-

ar wall or

along the

ause shear

e resisting

diaphragm

0

f

,

s

n

e

n

g

e

e

d

f-

r

e

r

g

m

61

The following statements contained in the 1997 UBC clearly require that a complete

load path be provided throughout a building to resist lateral forces. “All parts of a

structure shall be interconnected and connections shall be capable of transmitting the

seismic force induced by the parts being connected.”

“Any system or method of construction shall be based on a rational analysis... Such

analysis shall result in a system that provides a complete load path capable of

transferring all loads and forces from their point of origin to the load-resisting

elements.”

To fulfill these requirements, connections must be provided between every element in

the load path. When a building is shaken by an earthquake, every connection in the

lateral-force load path is tested. If one or more connections fail because they were not

properly designed or constructed, those remaining in parallel paths receive additional

force, which may cause them to become overstressed and to fail. If this progression of

individual connection failures continues, it can result in the failure of a complete

resisting seismic element and, potentially, the entire lateral-force-resisting system.

Consequently, connections are essential for providing adequate resistance to

earthquakes and must be given special attention by both designers and inspectors.

Connections are details of construction that perform the work of force transfer

between the individual primary and secondary structural elements discussed above.

They include a vast array of materials, products, and methods of construction.

In concrete construction, diaphragm-reinforcing steel resists forces in the diaphragm

and chord tension stresses, and reinforcing dowels are generally used to transfer forces

from the diaphragm boundaries to concrete walls or frames.

62

EVOLUTION OF UBC AND IBC STATIC LATERAL FORCE PROCEDURE

Introduction:

A model building code is a document containing standardized building requirements applicable throughout the United States. Model building codes set up minimum requirements for building design and construction with a primary goal of assuring public safety, and a secondary goal of minimizing property damage and maintaining function during and following an earthquake. Since the risk of severe seismic ground motion varies from place to place, seismic code provisions vary depending on location.

The three model building codes in the United States were: the Uniform Building Code (predominant in the west), the Standard Building Code (predominant in the southeast), and the BOCA National Building Code (predominant in the northeast), were initiated between 1927 and 1950.

The US Uniform Building Code was the most widely used seismic code in the world, with its last edition published in 1997. Up to the year 2000, seismic design in the United States has been based on one these three model building codes. Representatives from the three model codes formed the International Code Council (ICC) in 1994, and in April 2000, the ICC published the first edition of the International Building Code, IBC-2000. In 2003, 2006, 2009 and 2012 the second, third, fourth and fifth editions of the IBC followed suit. The IBC was intended to, and has been replacing the three independent codes throughout the United States. Initiation of the Static Lateral Force Procedure:

The work done after the 1908 Reggio-Messina Earthquake in Sicily by a committee of nine practicing engineers and five engineering professors appointed by the Italian government may be the origin of the equivalent static lateral force method, in which a seismic coefficient is applied to the mass of the structure, or various coefficients at different levels, to produce the lateral force that is approximately equivalent in effect to the dynamic loading of the expected earthquake. The Japanese engineer Toshikata Sano independently developed in 1915 the idea of a lateral design force V proportional to the building’s weight W. This relationship can be written as

WCF ′= , where C is a lateral force coefficient, expressed as some percentage of gravity. The first official implementation of Sano’s criterion was the specification C′ = 10 percent of gravity, issued as a part of the 1924 Japanese Urban Building Law Enforcement Regulations in response to the destruction caused by the great 1923

63

Kanto earthquake. In California, the Santa Barbara earthquake of 1925 motivated several communities to adopt codes with C ′ as high as 20 percent of gravity.

Evolution of the Equivalent Static Lateral Force Method:

The equivalent lateral seismic force on a structures V was firstly taken as a percentage of the building weight, as stated above. Secondly it was based on the seismic zone factor, building period, building weight and system type. Thirdly, it was based on site specific ground motion maps, building period, importance factors, soil site factors and building response modification factors, as shown in Table (1). The first edition of the U.S. Uniform Building Code (UBC) was published in 1927 by the Pacific Coast building Officials (PCBO), contained an optional seismic appendix, also adopted Sano’s criterion, allowing for variations in C ′ depending on the region and foundation material. For building foundations on soft soil in earthquake-prone regions, the UBC’s optional provisions corresponded to a lateral force coefficient equal to the Japanese value. For buildings on hard ground, the lateral force coefficient is 7.5 percent. While not the most advanced analytical technique, the equivalent static lateral force analysis method has been and will remain for some considerable time the most often used lateral force analysis method.

The 1937 UBC stipulated a lateral force coefficient, which is dependent on soil conditions, applied not only to dead loads but also to 50 % of the live load.

The 1943 UBC introduced a lateral force coefficient in terms of number of stories and limited this number to 13. In subsequent code editions the equation was modified for number of stories in excess of 13.

UBC 1949 edition contained the first USA seismic hazard map, which was published in 1948 by US Coast and Geodetic Survey and was adopted in 1949 by UBC, as well as subsequent editions until 1970. The seismic design provisions remained in an appendix to the UBC until the publication of the 1961 UBC.

The 1961 UBC Code introduced the use of four factors to categorize building system types. The 1970 UBC used a zoning map which divided the United States into four zones numbered 0 through 3. The 1973 UBC contained many modern enhancements including the V = ZKCW equation for seismic design, which was revised in the aftermath of San Fernando earthquake. Also, UBC 1973 introduced the impact of irregular parameters in estimating the seismic force levels.

The concept of soil factor was first acknowledged by recognizing the importance of local site effects in the 1976 edition of UBC. In addition to this, UBC 1976 Added zone 4 to California, and included new seismic provisions especially those related to

64

the importance of local site effects. The lateral force structural factor, wR was increased to take advantage of ductility of lateral force resisting systems.

The 1985 UBC used a Z factor that was roughly indicative of the peak acceleration on rock corresponding to a 475-year return period earthquake.

The 1988 UBC introduced the use of twenty- nine response modification factors plus three additional for inverted pendulum systems. Also, the base shear equation was changed from the 1985 UBC edition, and six seismic risk zones 0, 1, 2a, 2b, 3 and 4 are used.

Until 1997 edition of UBC, seismic provisions have been based on allowable stress design. In UBC 1997 revised base shear and based it on ultimate strength design. Added to this, a new set of seismic-zone dependent soil profile categories AS

through FS , has been adopted and replaced the four site coefficients 1S to 4S of

the UBC 1994, which are independent of the level of ground shaking. Also, old wR factor has been replaced by a new R factor, which is based on strength design, and two new structural system classifications were introduced: cantilevered column systems and shear wall-frame interaction systems. Moreover, the 1997 edition of UBC included a reliability factor for redundant lateral force systems, and the earthquake load (E) is a function of both the horizontal and vertical components of the ground motion.

In response to an appeal for more unified design procedures across regional boundaries, the International Building Code was developed and the first edition introduced in 2000. Subsequent IBC code editions were introduced in 2003, 2006 and 2009. The 2000 IBC has established the concept of Seismic Design Category (SDC), which is based on the location, the building use and the soil type, as the determinant for seismic detailing requirement. One of the most significant improvements in the 2000 IBC over the 1997 UBC is the ground parameters used for seismic design. In 2000 IBC, the 1997 UBC seismic zones were replaced by contour maps giving MCE spectral response accelerations at short period and 1-second for class B soil. The IBC Code versions 2000, 2003, 2006, 2009 reference to ASCE 7-05, contain up-to-date seismic provisions, including eighty-three building system response modification factors. The 2006 IBC and 2009 IBC reference ASCE 7-05 for virtually all of its seismic design requirements.

65

Table (1): Development of seismic base shear formulas based on UBC and IBC codes UBC/IBC Code Editions Lateral Force Specific Notes UBC 1927- UBC 1946 WCF ′=

- Seismic design provisions included in an appendix, for optional use.

- C′ , which is dependent on soil bearing capacity, is in % of weight.

UBC 1949- UBC 1958 WCF ′= - C′ is dependent on number of

stories. - First USA seismic hazard map

included. UBC 1961- UBC 1973 WCKZV = - Seismic design provisions moved

to the main body of the code. - Seismic zones introduced. - Lateral force system structural

factors included. - Fundamental period of vibration

included. UBC 1976- UBC 1979 WSCKIZV = - Seismic zone 4 introduced.

- Soil profiles introduced. - Building importance factors

included. UBC 1982- UBC 1985 WSCKIZV = - Soil profiles expanded. UBC 1988- UBC 1994 wRWCIZV /= - Soil profiles expanded.

- Seismic zones modified. UBC 1997 TRWICV v /= - Soil profiles expanded, and

dependent on soil dynamics. - System redundancy factor

introduced. - Additional structural systems

introduced. - Vertical component of ground

shaking included. - Seismic provisions are based on

strength-level design. IBC- 2000- IBC-2012 WCV s= - Spectral accelerations introduced.

- Safety concept redefined. - Seismic design categories, SDC

introduced. - System response modification

factors expanded.

66

Seismic Code Provisions Are Based on Earthquake Historical Data:

The equations used to determine Seismic Design Forces throughout the United States as well as the rest of the world are based on historical data that has been collected during past earthquakes. The 1925 Santa Barbara earthquake led to the first introduction of simple Newtonian concepts in the 1927 Uniform Building Code. As the level of knowledge and data collected increases, these equations are modified to better represent these forces.

In response to the 1985 Mexico City earthquake, a fourth soil profile type, 4S , for

very deep soft soils was added to the 1988 UBC, with the factor 4S equal to 2.0. The heavily instrumented San Francisco (1989-Loma Prieta) and Las Angeles (1994-Northridge) earthquakes increased this knowledge dramatically.

The 1994 Northridge Earthquake resulted in addition of near-fault factor to base shear equation, and prohibition on highly irregular structures in near fault regions. Also, redundancy factor added to design forces.

The 1997 UBC incorporated a number of important lessons learned from the 1994 Northridge and the 1995 Kobe earthquake, where four site coefficients use in the earlier 1994 UBC has been extended to six soil profiles, which are determined by shear wave velocity, standard penetration test, and undrained shear strength.

Safety Concepts:

Structures designed in accordance with the UBC provisions should generally be able to: 1. Resist minor earthquakes without damage. 2. Resist moderate earthquakes without structural damage, but possibly some nonstructural damage. 3. Resist major earthquakes without collapse, but possibly some structural and nonstructural damage.

The code is intended to safeguard against major failures and loss of life; the protection of property is not its purpose. While it is believed that the code provides reasonably for protection of life, even that cannot be completely assured. The UBC intended that structures be designed for “life-safety” in the event of an earthquake with a 10-percent probability of being exceeded in 50 years (475-year return period). The IBC intends design for “collapse prevention” in a much larger earthquake, with a 2-percent probability of being exceeded in 50 years (2,475-year return period).

67

Detailing Requirements of ACI 318-08:

Based on R1.1.1.9.1 of ACI 318-08, for UBC 1991 through 1997, Seismic Zones 0 and 1 are classified as classified as zones of low seismic risk. Thus, provisions of chapters 1 through 19 and chapter 22 are considered sufficient for structures located in these zones. Seismic Zone 2 is classified as a zone of moderate seismic risk, and zones 3 and 4 are classified as zones of high seismic risk. Structures located in these zones are to be detailed as per chapter 21 of ACI 318-08 Code.

For Seismic Design Categories A and B of IBC 2000 through 2006, detailing is done according to provisions of chapters 1 through 19 and chapter 22 of ACI 318-08. Seismic Design Categories C, D, E and F are detailed as per the provisions of chapter 21.

68

Earthquake Resistant Design According To 1994 UBC

The Static Lateral Force Procedure

Applicability: The static lateral force procedure may be used for the following structures:

A. All structures, regular or irregular (see Tables 1.a and 1.b) in seismic zone no. 1 and in standard occupancy- structures in seismic zone no. 2 (see Table 2 for zone classification and Table 4 for occupancy factors).

B. Regular structures less than 73 m in height with lateral force resistance provided by systems given in Tables 5.a and 5.b except for structures located in soil profile type S4 which have a period greater than 0.70 sec. (see Table 3 for soil profiles).

C. Irregular structures not more than five stories or 20 m in height.

D. Structures having a flexible upper portion supported on a rigid lower portion where both portions of the structure considered separately can be classified as being regular, the average story stiffness of the lower portion is at least ten times the average stiffness of the upper portion and the period of the entire structure is not greater than 1.10 times the period of the upper portion considered as a separate structure fixed at the base.

Regular Structures:

Regular structures are structures having no significant physical discontinuities in plan or vertical configuration or in their lateral force resisting.

Irregular Structures:

Irregular structures are structures having significant physical discontinuities in configuration or in their lateral force resisting systems (See Table 1.a and 1.b for detailed description of such structures).

Load Combinations:

The total design forces are calculated from the following cases of loading.

)(4.1 ELDU ±+= (1)

EDU 4.19.0 ±= (2)

Where

69

U = Ultimate design force D = Service dead load L = Service live load E = Service earthquake load

Concept of Method:

• The 1994 UBC equivalent static method considers only horizontal movement and neglects effects of vertical ground movement.

• Statically models the inertial effects using Newton’s 2nd Law of Motion given by Eqn. (3).

aMF = (3)

Where F = resulting force on structure M = building mass a = acceleration of ground but

gWM = and Eqn. (3) can be written as

⎟⎟⎠

⎞⎜⎜⎝

⎛=

gaWF (4)

Minimum Design Lateral Forces:

The design seismic forces may be assumed to act non-concurrently in the direction of each principal axis of the structure.

The total design base shear in a given direction is to be determined from the following Eqn.

wRWCIZV = (5)

Where

V = total seismic lateral force at the base of the structure W = total seismic load

- In storage and warehouse occupancies, a minimum of 25 % of floor live load is to be considered.

70

- Total weight of permanent equipment is to be included. - Where a partition load is used in floor design, a load of not less than 50 kg/m2 to be

included.

wRCIZ = seismic base shear coefficient, somewhat equivalent to ga / but accounts

for additional factors that affect building response like: underlying soil, the structural configuration, the type of structure and occupancy of the building.

Z = seismic zone factor given in Table (2) and is related to the seismicity of the zone. It is the effective peak ground acceleration with 10 % probability of being exceeded in 50 years.

I = Building importance factor given in Table (4), which accounts for building use and importance

wR = structural factor, accounting for building ductility and damping, given in Tables (5.a) and (5.b). A larger wR value means a better seismic performance.

C = dynamic response value, and accounts for how the building and soil can amplify the

basic ground acceleration

( ) wRCT

SC 075.075.225.13/2 ≥≥= (6)

S = site Coefficient depending on the soil characteristics given in Table (4.3). T = structural fundamental period in seconds in the direction under consideration

evaluated from the following equations.

For moment-resisting frames, ( ) 4/3073.0 nhT = (7)

For shear walls, ( )

c

n

AhT

4/3

0743.0= (8)

For other buildings,

( ) 4/3048.0 nhT = (9)

Where

nh = total height of building in meters

71

cA = effective cross-sectional area of shear walls

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛+=∑

2

2.0n

eic h

DAA 9.0/ ≤ne hD (10)

iA = cross-sectional area of individual shear walls in the direction of loads in m2

eD = length of each shear wall in the direction of loads

Ductility is defined as the ability to deform in the inelastic range prior to fracture, while damping is resistance to motion provided by material friction

Vertical Distribution of Force:

The base shear evaluated from Eqn. (5) is distributed to the various stories of the building according to the following Eqn.

( )∑=

−= n

iii

xxtx

hw

hwFVF

1

(11)

Figure (1): Vertical distribution of force

Where

0=tF for 7.0≤T sec.

VVTFt 25.007.0 ≤= for 7.0>T sec.

The shear force at each story is given by Eqn. (12)

∑=

+=n

xiitx FFV (12)

Where

72

n = number of stories above the base of the building tF = the portion of the base shear, concentrated at the top of the structure to account for

whiplash effects xni FFF ,, = lateral forces applied at levels xorni ,, , respectively

xni hhh ,, = height above the base to levels xorni ,, , respectively xV = design shear in story x Horizontal Distribution of Force:

The design story shear in any direction, xV , is distributed to the various elements of the lateral force-resisting system in proportion to their rigidities.

Horizontal Torsional Moment:

To account for the uncertainties in locations of loads, the mass at each level is assumed to be displaced from the calculated center of mass in each direction a distance equal to 5 % of the building dimension at that level perpendicular to the direction of the force under consideration. The torsional design moment at a given story is given by moment resulting from eccentricities between applied design lateral forces applied through each story’s center of mass at levels above the story and the center of stiffness of the vertical elements of the story, in addition to the accidental torsion.

Overturning Moments:

The overturning moments are to be determined at each level of the structure.

The overturning moment xM at level x is given by Eqn. (13).

( ) ( )∑+=

−+−=n

xixiixntx hhFhhFM

1 (13)

Overturning moments are distributed to the various elements of the vertical lateral force-resisting system in proportion to their rigidities.

∆−P Effects:

The resulting member forces, moments and story drifts induced by ∆−P effects are to be considered in the evaluation of overall structural frame stability. ∆−P effects are neglected when the ratio given by Eqn. (14) is .1.0≤

xx

xx

primary

ondary

hVP

MM ∆

=sec (14)

73

xP = total seismic weight at level x and above ∆ = drift of story x

xV = shear force of story x xh = height of story x

In seismic zones no. 3 and 4, ∆−P effects are neglected when the story drift wR/02.0≤ times the story height.

Design of Cantilevers:

Horizontal cantilever components are to be designed for a net upward force of pw2.0 , where pw is the weight of the cantilevered element.

Story Drift Limitations:

Story drift is the displacement of one level relative to the level above or below due to the design lateral forces. Calculated drift is to include translational and torsional deformations. Calculated story drift shall not exceed wR/04.0 or 005.0 times the story height for buildings with periods 7.0< second. For structures with periods 7.0≥ sec., the calculated story drift is not to exceed wR/03.0 or 004.0 the story height.

Design of Diaphragms:

Floor and roof diaphragms are to be designed to resist the forces determined from the following formula

pxn

xii

n

xiit

px ww

FFF

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡+

=

∑

∑

=

= (15)

The force pxF need not exceed 0.75 pxwIZ , but shall not be less than 0.35 pxwIZ

Where

pxw = weight of the diaphragm at level x

pxF = diaphragm lateral design force at level x

74

Table (1.a) Vertical Structural Irregularities (illustrated in Fig. 2) Irregularity Type and Definition How to Deal with A- Stiffness Irregularity- - -Soft Story A soft story is one in which the lateral stiffness is less than 70 percent of that in the story above or less than 80 percent of the average stiffness of the three stories above.

Use the dynamic lateral force procedure.

B- Mass Irregularity Mass irregularity is considered to exist where the effective mass of any story is more than 150 percent of the effective mass of an adjacent story.

Use the dynamic lateral force procedure.

C- Vertical Geometric Irregularity Vertical geometric irregularity shall be considered to exist where the horizontal dimension of the lateral force-resisting system in any story is more than 130 percent of that in an adjacent story.

Use the dynamic lateral force procedure.

D- In-Plane Discontinuity in Vertical Lateral Force-resisting Element An in-plane offset of the lateral load-resisting elements greater than the length of these elements.

The Structure is to be designed to resist the overturning effects caused by seismic forces, down to the foundations level.

E- Discontinuity in Capacity-Weak Story A weak story is one in which the story strength is less than 80 percent of that in the story above. The story strength is the total strength of all seismic-resisting elements sharing the story shear for the direction under consideration.

Structures are not to be over two stories or 9 m in height where the weak story has calculated strength of less than 65 % of the story above.

75

Figure (2): Vertical irregularities

76

Table (1.b) Plan Structural Irregularities (illustrated in Fig. 3) Irregularity Type and Definition How to Deal with A- Torsional Irregularity Torsional irregularity is to be considered to exist when the maximum story drift, computed including accidental torsion, at one end of the structure transverse to an axis is more than 1.2 times the average of the story drifts of the two ends of the structure.

The one-third increase usually permitted in allowable stresses for elements resisting earthquake forces is to be discarded.

B- Re-entrant Corners Plan configurations of a structure and its lateral force-resisting system contain re-entrant corners, where both projections of the structure beyond a re-entrant corner are greater than 15 % of the plan dimension of the structure in the given direction.

The one-third increase usually permitted in allowable stresses for elements resisting earthquake forces is to be discarded.

C- Diaphragm Discontinuity Diaphragms with abrupt discontinuities or variations in stiffness, including those having cutout or open areas greater than 50 % of the gross enclosed area of the diaphragm, or changes in effective diaphragm stiffness of more than 50 % from one story to the next.

The one-third increase usually permitted in allowable stresses for elements resisting earthquake forces is to be discarded.

D- Out-of-plane Offsets Discontinuities in a lateral force path, such as out-of-plane offsets of the vertical elements.

Structures are to be designed to resist the overturning effects caused by earthquake forces and are these effects are to be carried down to the foundation.

E- Nonparallel Systems The vertical lateral load-resisting elements are not parallel to or symmetric about the major orthogonal axes of the lateral force-resisting system.

The requirement that orthogonal effects be considered may be satisfied by designing such elements for 100 % of the prescribed seismic forces in one direction plus 30 % of the prescribed forces in the perpendicular direction. Alternately, the effects of the two orthogonal directions may be combined on a square root of the sum of the squares basis.

77

Figure (3): Plan irregularities

78

Table (2) Seismic Zone Factor Zone 1 2A 2B 3 4

Z 0.075 0.15 0.20 0.30 0.40

Table (3) Site Coefficients Type Description S Factor

S1 - Rock-like material characterized by a shear wave velocity greater than 750 m/s or by other means of classification. - Stiff or dense soil condition where the soil depth is less than 60 m.

1.0

S2 A soil profile with dense or stiff soil conditions, where the soil depth exceeds 60 m.

1.20

S3 A soil profile 20 m or more in depth and containing more than 6 m of soft to medium stiff clay but not more than 12 m of soft clay.

1.50

S4 A soil profile containing more than 12 m of soft clay characterized by a shear wave velocity less than 150 m/s.

2.0

Table (4) Occupancy Importance Factors

Occupancy Category

Functions of Structure Importance Factor I

Essential Facilities Hospitals, fire stations, police stations, water tanks, garages, shelters, disaster control centers, and communications centers.

1.25

Hazardous Facilities Structures containing toxic, atomic, and explosive substances.

1.25

Special Occupancy Public assembly, schools, jails, power-generating stations.

1.0

Standard Occupancy Structures not listed above. 1.0

79

Table (5.a) Structural Factors (building structures) Basic Structural

System Lateral Load-Resisting System Rw

Height (m) Zones 3 &

4 Building Frame

Shear Walls (without vertical loads)

Shear Walls (with vertical loads) 8 6

73 73

Moment-Resisting Frame

SMRF IMRF OMRF

12 8 5

No Limit Not Used Not Used

Dual Systems Shear Walls + SMRF Shear Walls + IMRF

12 9

No Limit 48

Table (5.b) Structural Factor (non-building structures)

No. Structure Type Rw1- Tanks, vessels or pressurized spheres on braced or

unbraced legs. 3

2- Cast-in-place concrete soils and chimneys having walls continuous to the foundation.

5

3- Inverted pendulum-type structures. 3 4- Cooling towers. 5

80

Figure (4): Seismic map of Palestine

81

7x3

= 21

m

Example 1: A seven-story building frame system (residential) with shear walls has the dimensions shown in the Figure 5. The total sustained dead load is 800 kg/m2. This building is located in Gaza Strip and lies on top of a deep clayey deposit. Eight shear walls, each 3 m long and 0.2 m thick are used as a lateral force resisting system. Determine the seismic loads at the floor levels of the building in a direction perpendicular to axis 1-1, 2-2, 3-3, and 4-4 using the 1994 UBC.

Figure (5): Building layout

A B

C D

E F G H

6m 6m 6m

4.5m

4.

5m

4.5m

4.

5m

1

1

2

2

3

3

4

4

82

Solution:

8,0.2 ,1 ,075.0 ==== wRSIZ

Weight of floor = ( )( ) tons2.25918188.0 =

Total seismic weight = ( ) tons4.181472.259 = Building natural period, T

( )c

n

AhT

43

0743.0=

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛+=∑

2

2.0n

eic h

DAA 9.0/ ≤ne hD

( )( ) 24

1

2

529.02132.02.03 mA

ic =

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛+=∑

= , 9.0142.0

213

<= O.K

( ) ( ) sec002.1529.0

210743.00743.04/34/3

===c

n

AhT

( )( )

75.2sec5.2002.1

225.125.13/23/2 <===

TSC and ( )8075.0>

The base shear V is given by

( )( )( ) tonsV

RZICWV

w

52.428

4.18145.20.1075.0==

=

( )( )( ) KOtF

TVFforT

t

t

.52.4225.097.2 52.42107.007.0 sec,7.0

<===>

Vertical Distribution of Force: ( )∑ =

−= 7

1i i

xxtx

FhwFVF

Story shears:

∑=+=

7

1i itx FFV

83

Overturning moment:

( ) ( )xin

xi ixntx hhFhhFM −+−= ∑ += 1 Lateral displacement:

( )i

i

i

i

i

ii w

FwF

wFTg 248.01

481.9

42

2

2

2 =⎟⎠⎞

⎜⎝⎛=∗=ππ

δ

Story drift:

w

nniii R

hh 03.0004.01 ≤≤−=∆ −δδ

∆−P effects:

When 1.0<∆

xx

ix

hVP

, ∆−P effects are to be neglected.

Lateral force distribution:

level iw xh xxhw xF xV xM ( )mmiδ i∆ ∑ xP xx

ix

hVP ∆

7 259.2 21 5443.2 9.89 12.86 - 12.33 4.21 259.2 0.028 6 259.2 18 4665.6 8.48 21.33 38.57 8.12 1.35 518.4 0.011 5 259.2 15 3888 7.06 28.40 102.57 6.77 1.35 777.6 0.0124 259.2 12 3110.4 5.65 34.05 187.76 5.42 1.36 1036.8 0.014 3 259.2 9 2332.8 4.24 38.28 289.89 4.06 1.36 1296 0.015 2 259.2 6 1555.2 2.83 41.11 404.74 2.70 1.35 1555.2 0.017 1 259.2 3 777.6 1.41 42.52 528.06 1.36 1.35 1814.4 0.019 0 0 42.52 655.62 0

∑ 21772.8

84

Example 2: A seven-story reinforced concrete special moment-resisting frame (SMRF) has the dimensions shown in Figure 6. The total sustained dead load is 800 kg/m2 and the live load is 250 kg/m2. The building which is characterized as a residential building is located in Gaza City and lies on top of a deep clayey deposit. Evaluate the seismic loads at the floor levels of the building in a direction perpendicular to axis 1-1, 2-2, 3-3, and 4-4 using the 1994 UBC.

Figure (6): Building layout

85

Solution:

12,0.2 ,1 ,075.0 ==== wRSIZ Since the building is residential, no live load is to be used in seismic weight calculation

Weight of floor = ( )( ) tons3245.22188.0 =

Total seismic weight = ( ) tons22687324 = Building natural period, T

( ) 4/3073.0 nhT =

( ) sec716.021073.0 4/3 ==T

( )( )

75.2sec12.3716.0

225.125.13/23/2 >===

TSC N.O.K

075.0229.01275.2

>==wR

C O.K

The base shear V is given by

( )( )( ) tonsR

WCIZVw

98.3812

226875.20.1075.0===

( )( ) tonsTVFT t 95.198.38716.007.007.0 sec,7.0 ===>V5.0< O.K

Vertical Distribution of Force: ( )∑ =

−= 7

1i i

xxtx

FhwFVF

86

Lateral force distribution:

level iw xh xxhw xF xV xM 7 324 21 6804 9.26 11.21 - 6 324 18 5832 7.93 19.14 33.63 5 324 15 4860 6.61 25.75 91.05 4 324 12 3888 5.29 31.04 168.3 3 324 9 2916 3.97 35.01 261.42 2 324 6 1944 2.64 37.65 366.45 1 324 3 972 1.32 38.97 479.40 0 0 38.97 596.31

∑ 27216

87

Horizontal Distribution of Forces to Individual Shear Walls

Interaction of Shear Walls with Each Other

In the shown figure the slabs act as horizontal diaphragms extending between cantilever walls and they are expected to ensure that the positions of the walls, relative to each other, don't change during lateral displacement of the floors. The flexural resistance of rectangular walls with respect to their weak axes may be neglected in lateral load analysis.

The distribution of the total seismic load, xF or yF among all cantilever walls may be approximated by the following expressions.

ixixix FFF ′′+′= iyiyiy FFF ′′+′=

wwhheerree::

ixF′ == load induced in wall by inter-story translation only, in x-direction iyF ′ = load induced in wall by inter-story translation only, in y-direction

ix"F = load induced in wall by inter-story torsion only, in x-direction iy"F = load induced in wall by inter-story torsion only, in y-direction

ixF = total external load to be resisted by a wall, in x-direction iyF = total external load to be resisted by a wall, in y-direction

To obtain ixF ′ and iyF ' , the forces xF and yF are distributed to the individual shear walls in proportion to their rigidities.

88

The force resisted by wall i due to inter-story translation, in x-direction, is given by

∑=′

iy

iyxix I

IFF

The force resisted by wall i due to inter-story translation, in y-direction, is given by

∑=′

ix

ixyiy I

IFF

where: xF = total external load to be resisted by all walls, in x-direction yF = total external load to be resisted by all walls, in y-direction

ixI = second moment of area of a wall section about x axis iyI = second moment of areas of a wall section about y axis ∑ ixI = total second moment of areas of all walls in x-direction

∑ iyI = total second moment of area of all walls in y-direction

The force resisted by wall i due to inter-story torsion, in x-direction, is given by

( )( )∑ +

=′′iyiixi

iyiyxix IyIx

IyeFF 22

The force resisted by wall i due to inter-story torsion, in y-direction, is given by

( )( )∑ +

=′′iyiixi

ixixyiy IyIx

IxeFF 22

where:

ix = x-coordinate of a wall with respect to the center of rigidity C.R of the lateral load resisting system

iy = y-coordinate of a wall with respect to the center of rigidity C.R of the lateral load resisting system

xe = eccentricity resulting from non-coincidence of center of gravity C.G and center of rigidity C.R, in x-direction

ye = eccentricity resulting from non-coincidence of center of gravity C.G and center of rigidity C.R, in y-direction

89

Example (3): In Example (1), determine the forces acting on shear wall G.

Neglecting moments of inertia about weak axes, second moments of area of each of the shear walls about y-axis are given by

( ) 43

45.012

32.0 mIIII HyGyByAy =====

Total second moments of area about y-axis are given by

( ) 44

1

8.1445.0 mIi

iy ==∑=

Second moments of area of each of the shear walls about x-axis are given by

( ) 43

45.012

32.0 mIIII FxExDxCx =====

Total second moments of area about x-axis are given by

( ) 44

18.1445.0 mI

iix ==∑

=

To locate the center of rigidity C.R, the distance from the origin to the C.R y in the y-direction is given by

( )( ) ( )( ) mI

yIy

iiy

iiiy

25.118.1

5.445.0218245.04

1

4

1 =+

==

∑

∑

=

=

The distance from the origin to the C.R in the x-direction x is given by

90

( )( )( ) mI

xIx

iix

iiix

0.98.1

1845.024

1

4

1 ===

∑

∑

=

=

Thus, the eccentricity in y-direction mey 25.20.925.11 =−=

And the eccentricity in x-direction mex 0.00.90.9 =−=

Torsion caused by eccentricity ye , 1T xF25.2= Torsion caused by accidental eccentricity , 2T ( )( ) xx FF 9.01805.0 == Total torsion, 21 TT ± ( )xx FF 9.025.2 ±=

∑=′

iy

iyxix I

IFF

xx

HxGxBxAx FFFFFF 25.08.1

45.0==′=′=′=′

( )( )∑ +

=′′iyiixi

iyiyxix IyIx

IyeFF 22

( )( )( )

( )( ) ( )( ) ( )( ) ( )( )( )xx

xxHxGxBxAx

FF

FFFFFF

9.025.20133.0945.02945.0275.645.0275.645.02

45.075.69.025.22222

±=+++

±=′′=′′=′′=′′

xF042.0=

The forces acting on shear wall G are given by the following expression

x

xx

FFF

292.0042.025.0

=+=

Using the story forces evaluated in Example (1), the forces acting on shear wall G at each of floor level are shown in the next figure.

Distribution of forces at each floor level (Shear wall G)

91

Classification of Structural Walls According To Seismic Risk

According to Chapters 2 and 21 of ACI 318-08, structural walls are defined as being walls proportioned to resist combinations of shears, moments, and axial forces induced by earthquake motions. A shear wall is a structural wall.

Reinforced concrete structural walls are categorized as follows:

1- Ordinary reinforced concrete structural walls: They are walls complying with the requirements of Chapters 1 through 18.

2- Special reinforced concrete structural walls: They are cast-in-place walls complying with the requirements of 21.2 and 21.7 in addition to the requirements for ordinary reinforced concrete structural walls.

Special Provisions for Earthquake Resistance

• According to Clause 1.1.9.1 of ACI 318-08, the seismic risk level of a region is regulated by the legally adopted general building code of which ACI 318-08 forms a part, or determined by local authority.

Correlation between Seismic-Related Terminologies In Model Codes

Code/ Standard Level of seismic risk as defined in the code section Low

(21.1.2) Moderate/Intermediate

(21.1.2 and 21.1.8) High

(21.1.2 through 21.1.8) and (21.11

through 21.13) International Building Code 2000, 2003, 2006

SDC A, B SDC C SDC D, E, F

Uniform Building Code 1991, 1994, 1997

Seismic Zone 0, 1

Seismic Zone 2 Seismic Zone 3, 4

SDC = Seismic Design Category

• According to Clauses 1.1.9.2 and 21.1.1.7 of ACI 318-08, in regions of low and intermediate seismic risk, provisions of Chapter 21 are not to be applied. (Chapter 1 through 18 are applicable)

• According to ACI 318-08, in regions of high seismic risk, special structural walls complying with 21.9 are to be used for resisting forces induced by earthquake motions.

92

Classification of Shear Walls According To Their Height-to-Length Ratios

Shear walls are classified as short or long according to their aspect ratios (the ratio of its height wh to length in the plane of loading wl ), as follows:

1- For 2/ <ww lh , they are called short or squat shear walls. Their design is dominated by shear, rather than flexure. Aspect ratios below 2 mark the transition from slender to short behavior, and walls with such dimensions require considerable care in design if a ductile failure mode is required. Without this attention, shear walls are likely to fail in brittle failure modes such as diagonal tension or sliding shear rather than undergoing the more ductile flexural failure possible in slender walls. Short shear walls may need increased strength or special detailing, including diagonal steel to overcome these problems. 2- For 2/ ≥ww lh , they are called long or slender shear walls. Their design is

dominated by flexure. Aspect ratios are normally restricted to 7; higher ratios may result in inadequate stiffness, problems in anchoring the tension side of the shear wall and possibly significant amplifications due to ∆−P effects.

The above stated classification is not explicitly stated in ACI 318-08 Code.

93

Design of Ordinary Shear Walls

The shear wall is designed as a cantilever beam fixed at the base, to transfer load to the foundation. Shear forces, bending moments and axial loads are maximums at the base of the wall.

Types of Reinforcement:

To control cracking, shear reinforcement is required in the horizontal and vertical directions, to resist in plane shear forces.

The vertical reinforcement in the wall serves as flexural reinforcement. If large moment capacity is required, additional reinforcement can be placed at the ends of the wall within the section itself, or within enlargements at the ends. The heavily reinforced or enlarged sections are called boundary elements.

Shear Strength:

According to ACI 11.1.1, design of cross sections subject to shear are based on

un VV ≥Φ (1)

where uV is the factored force at the section considered and nV is the nominal shear strength computed by

scn VVV += (2)

where cV is nominal shear strength provided by concrete and sV is nominal shear strength provided by shear reinforcement.

94

Based on ACI 11.9.3, max,nV at any horizontal section for shear in plane of the wall is not to be taken greater than

dhfV cn ′= 65.2max, (3)

where h is thickness of wall, and d is the effective depth in the direction of bending, may be taken as wl8.0 , where wl is length of wall considered in direction of shear force, as stated in ACI 11.9.4. A larger value of d , equal to the distance from extreme compression fiber to center of force of all reinforcement in tension, be permitted to be used when determined by a strain compatibility analysis.

Based on ACI 11.9.5, the shear strength provided by concrete cV is given by any of the following equations, as applicable.

For axial compression, Eqn. (4) is applicable

dhfV cc ′= 53.0 (4)

For axial tension, Eqn. (5) is applicable

dhfA

NV cg

uc ′⎟

⎟⎠

⎞⎜⎜⎝

⎛−=

35153.0

(5)

where gA is the gross area of wall section and uN is the factored axial tension force in Eqn. (5). ACI 11.9.6 specifies that a more detailed analysis is permitted to evaluate cV as follows, where cV is the lesser of the two values shown in Eqns. (6) and (7).

w

ucc l

dNdhfV4

'88.0 += (6)

hdlVM

hlNfl

fVw

u

u

w

ucw

cc

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

−

⎟⎟⎠

⎞⎜⎜⎝

⎛+

+=

2

2.0'33.0'16.0

(7)

Where uN is positive for compression and negative for tension. If ( )2// wuu lVM − is negative, Eqn. (7) is not applicable.

95

Shear Reinforcement:

A- When the factored shear force uV is less than 2/cVΦ , minimum wall reinforcement according to ACI 11.9.9 or in accordance with Chapter 14 of ACI code.

A-1 Minimum Horizontal Reinforcement Ratio:

Ratio of horizontal shear reinforcement area to gross concrete area of vertical section, tρ , shall not be less than 0.0025. Spacing of this reinforcement

2S is not to exceed the smallest of cmhlw 45,3,5/ .

A-2 Minimum Vertical Reinforcement Ratio: Ratio of vertical reinforcement area to gross concrete area of horizontal section, lρ is not to be taken less than the larger of

( )0025.05.250.00025.0 −⎟⎟⎠

⎞⎜⎜⎝

⎛−+= t

w

wl l

h ρρ

(8)

and 0.0025, but need not be greater than tρ required by Eqn. (9). Spacing of this reinforcement 1S is not to exceed the smallest of cmhlw 45,3,3/ .

Chapter 14 Provisions: Minimum ratio of vertical reinforcement area to gross concrete area, lρ , shall be

• 0.0012 for deformed bars up to 16 mm in diameter, with yf not less than 4200 kg/cm2.

• 0.0015 for other deformed bars.

Minimum ratio of horizontal reinforcement area to gross concrete area, tρ , shall be • 0.0020 for deformed bars up to 16 mm in diameter, with yf not less than

4200 kg/cm2. • 0.0025 for other deformed bars.

B- When the factored shear force exceeds 2/cVΦ , minimum wall reinforcement for resisting shear, according to ACI 11.9.9, must be provided.

C- According to ACI 11.9.9.1 when the factored shear force uV exceeds cVΦ , horizontal shear reinforcement must be provided according to the following equation.

2S

dfAV yv

s =

(9)

where vA is area of horizontal shear reinforcement within a distance 2S . Vertical shear reinforcement is provided using Eqn. (8), shown above.

96

The critical section for shear is taken at a distance equal to half the wall length 2/wl , or half the wall height 2/wh , whichever is less. Sections between the base of the wall and the critical section are to be designed for the shear at the critical section, as specified in ACI 11.9.7.

Shear wall Reinforcement

Design for Flexure:

The wall must be designed to resist the bending moment at the base and the axial force produced by the wall weight or the vertical loads it carries. Thus, it is considered as a beam-column.

For rectangular shear walls containing uniformly distributed vertical reinforcement and subjected to an axial load smaller than that producing balanced failure, the following equation, developed by Cardenas and Magura in ACI SP-36 in 1973, can be used to determine the approximate moment capacity of the wall.

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟

⎟⎠

⎞⎜⎜⎝

⎛+Φ=

wys

uwysu l

CfA

PlfAM 115.0

Where:

97

185.02 βωαω

++

=wlC

cw

ys

fhlfA′

=ω and cw

u

fhlP

′=α

=C distance from the extreme compression fiber to the neutral axis sA = total area of vertical reinforcement

wl = horizontal length of wall uP = factored axial compressive load yf = yield strength of reinforcement

Φ = strength reduction factor for bending

Lateral Ties for Vertical Reinforcement:

Based on ACI 14.3.6, vertical reinforcement need not be enclosed by lateral ties if vertical reinforcement is not greater than 0.01 times the gross concrete area, or where vertical reinforcement is not required as compression reinforcement.

Additional Reinforcement around Openings:

In addition to the required horizontal and vertical reinforcement explained earlier, ACI 14.3.7 states that not less than mm162φ bars are provided around all window and door openings. Such bars are to be extended to develop yf in tension at the corners of the openings.

Additional reinforcement around wall openings

98

Example (4):

For shear wall 'G' in example (3), design the reinforcement required for shear and flexure using UBC-94 load combinations and ACI 318-02 for reinforced concrete design. Use 22 /4200 and /300 cmkgfcmkgf yc ==′ . Solution: UBC-94 Load combinations are given

( )EDU

ELDU4.19.0

4.1±=

±±=

Critical section for shear is located at a distance not more than the smaller

of 2/h2/l

w

w , i.e., at 1.5 m from the base of the wall.

1- Design for shear:

Check for maximum nominal shear force

dh'f65.2V cmax,n =

( ) ( )( ) tons32.2201000/3008.02030065.2 == ( ) K.Otons374.17tons24.16532.22075.0V max,u ⟩==

dh'f53.0V cc = ( )( )( ) tons06.441000/3008.02030053.0Vc ==

( ) tons045.3306.4475.0Vc ==Φ

( ) tons523.162/045.332/Vc ==Φ

In zones 1, 2, 3 and 4 2/VV cu φ< and in zones 5, 6 and 7 cu VV φ⟨

99

1-1 Horizontal shear reinforcement:

0025.0t =ρ

ofsmaller the2 =S cm

cmhcmlw

45603

605/==

or cmS 45max,2 =

( ) cm/cm05.0SA

and 200025.0h0025.0SA 2

2

t

2

t ===

For two curtains of reinforcement and trying φ 10 mm bars ( )

max,222

Scm4.31S , 05.0S785.02

<== O.K

Use φ 10 mm bars @ 30cm. 1-2 Vertical shear reinforcement:

[ ]0025.00025.03215.25.00025.0l −⎥⎦⎤

⎢⎣⎡ −+=ρ

tl 0025.0 ρρ ≤=

ofsmaller the1 =S cm

cmhcmlw

45603

1003/==

or cmS 45max,1 =

For two curtains of reinforcement, and trying φ 10 mm bars

( ) ( )11

lS

0.7852 200025.0h0025.0SA

===

And max,11 40.31 ScmS <= Use φ 10mm bars @ 30cm.

2- Design for flexure and axial loads:

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟

⎟⎠

⎞⎜⎜⎝

⎛+φ=

wys

uwysu l

c1fA

P1lfA5.0M

Where:

1w 85.02lc

β+ωα+ω

= , 'fhl

fA

cw

ys=ω and 'fhl

p

cw

u=α

For the vertical shear reinforcement of φ 10 mm @ 30cm, 2s cm28.17A = ,

( ) 836.0280300

7005.085.0 =−−=β , ( )

( )( ) 04032.030020300

420028.17'fhl

fA

cw

ys ===ω

100

, ( )( )( ) u

u

cw

u P00055.030020300

1000P'fhl

P===α ,

( ) ( ) 79124.0P00055.004032.0

836.085.004032.02P00055.004032.0

lc uu

w

+=

++

=

For zone 7:

( )( )( )( ) tons35.285.22132.09.0Pu == ( ) 07066.0

79124.035.2800055.004032.0

lcw

=+

=

m.t002.268m.t70.126Mu ⟨= , i.e. boundary elements are required at wall ends m.t302.14170.126002.268'M u =−=

( )( )( ) ( ) 2

additional,s cm62.15785.0226642009.0

100000302.141A =+=

Use 8φ 16 mm bars in each of the two boundary elements.

For zone 6: ( )( )( )( ) tons30.245.21832.09.0Pu ==

( ) 06785.079124.0

30.2400055.004032.0lc

w=

+=

m.t88.215m.t98.121Mu ⟨= , i.e. boundary elements are required at wall ends

m.t90.9398.12188.215'M u =−= ( )

( )( ) ( ) 2additional,s cm91.10785.02

26642009.010000090.93A =+=

Use 8φ 14 mm bars in each of the two boundary elements.

101

For zone 5: ( )( )( )( ) tons25.205.21532.09.0Pu ==

( ) 06503.079124.0

25.2000055.004032.0lcw

=+

=

m.t48.165m.t23.117Mu ⟨= i.e., boundary elements are required at wall ends m.t25.4823.11748.165'M u =−=

( )( )( ) ( ) 2

additional,s cm37.6785.0226642009.0

10000025.48A =+=

Use 6φ 12 mm bars in each of the two boundary elements.

For zone 4: ( )( )( )( ) tons20.165.21232.09.0Pu ==

( ) 0622.079124.0

20.1600055.004032.0lc

w=

+=

m.t524.18m.t46.112Mu ⟨= , i.e. boundary elements are required at wall ends

m.t064.646.112524.118'M u =−= ( )

( )( ) ( ) 2additional,s cm17.2785.02

26642009.0100000064.6A =+=

Use 2φ 12 mm bars in each of the two boundary elements.

For Zone 3

( )( )( )( ) tons15.125.2932.09.0Pu == ( ) 05940.0

79124.015.1200055.004032.0

lcw

=+

=

102

m.t776.76m.t65.107Mu ⟩= , i.e. no boundary elements are required at wall ends For Zone 2

( )( )( )( ) tons10.85.2632.09.0Pu == ( ) 05659.0

79124.01.800055.004032.0

lc

w=

+=

m.t958.41m.t81.102Mu ⟩= , i.e. no boundary elements are required at wall

ends For Zone 1

( )( )( )( ) tons05.45.2332.09.0Pu == ( ) 05377.0

79124.005.400055.004032.0

lc

w=

+=

m.t792.15m.t94.97Mu ⟩= , i.e. no boundary elements are required at wall

ends

103

Special Reinforced Concrete Structural Walls

The requirements of this section apply to special reinforced concrete structural walls serving as part of the earthquake force-resisting system. Shear Strength: Based on ACI 21.9.4.1, nominal shear strength nV of structural walls is not to exceed

( )ytcccvn f'fAV ρα +=

Where cα is a coefficient defining the relative contribution of concrete strength to wall strength, given as follows. • cα = 0.80 for 5.1/ ≤ww lh ;

• cα = 0.53 for 0.2/ ≥ww lh ;

• cα = 0.53 to 0.80 (linear variation) for ww lh / between 1.5 and 2.0.

cvA = gross area of concrete section bounded by web thickness and length of section in the direction of shear force considered, cm2. Shear Reinforcement: At least two curtains of reinforcement shall be used in a wall if the in-plane factored shear force assigned to the wall exceeds ccv fA ′53.0 , as specified by ACI 21.9.2.2. Based on ACI 21.9.2.1, the distributed web reinforcement ratios, lρ and

tρ for structural walls shall not be less than 0.0025, except if uV does

not exceed ccv fA ′265.0 , lρ and tρ shall be permitted to be reduced to the values required in 14.3. Reinforcement spacing each way in structural walls shall not exceed 45 cm. reinforcement contributing to uV shall be continuous and shall be distributed a cross the shear plane. According to ACI 21.9.4.3, walls are to be reinforced with shear reinforcement in two orthogonal directions in the plane of the wall.

104

If 0.2/ ≤ww lh , reinforcement ratio lρ shall not be less than

reinforcement ratio tρ . Design for Flexure and Axial Loads: Based on ACI 21.9.5.1, structural walls and portions of such walls subject to combined flexural and axial loads shall be designed in accordance with 10.2 and 10.3 except that 10.3.6 and the nonlinear strain requirements of 10.2.2 shall not apply. In ACI 10.3.2, balanced strain conditions exist at a cross section when the tension reinforcement reaches the strain corresponding to its specified yield strength yf just as concrete in compression reaches its assumed ultimate strain of 0.003. In ACI 10.3.3, sections are compression-controlled when the strain in the extreme tension steel, tε , is equal to or less than yε when the concrete in compression reaches its crushing strain of 0.003. In ACI 10.3.4, sections are tension-controlled when the net tensile strain in the extreme tension steel is equal to or greater than 0.005, just as the concrete in compression reaches its assumed strain limit of 0.003. Sections with net tensile strain in the extreme tension steel between the compression controlled strain limit and 0.005 constitute a transition region between compression-controlled and tension-controlled sections. In ACI 10.3.5, for flexural members with axial loads less than gc Af ′1.0 ,

the net tensile strain tε at nominal strength shall not be less than 0.004. Boundary Elements: Two design approaches for evaluating the need of boundary elements at the edges of structural walls are provided in ACI 21.9.6 and explained below. A- For walls or wall piers that are effectively continuous from the base of the structure to top of wall and designed to have a single critical section for flexure and axial loads, ACI 21.9.6.2 requires that compression zones be reinforced with special boundary elements where:

( )wu

wh

lc/600 δ

≥

105

And c corresponds to the largest neutral axis depth calculated for the factored axial force and nominal moment strength consistent with the design displacement uδ . The quantity wu h/δ in the previous equation shall not be taken less than 0.007. Special boundary element reinforcement shall extend vertically from the critical section a distance not less than the larger of wl or uu VM 4/ . The above stated design approach uses a displacement-based model. In this method, the wall is displaced an amount equal to the expected design displacement, and boundary elements are required to confine the concrete when the strain at the extreme compression fiber of the wall exceeds a critical value. Confinement is required over a horizontal length equal to at least the length where the compressive strain exceeds the critical value. B- Structural walls not designed to the provisions of ACI 21.9.6.2, shall have special boundary elements at boundaries and edges around openings of structural walls where the maximum extreme fiber compressive stress, corresponding to factored forces including earthquake effect, exceeds

cf ′2.0 . The special boundary element shall be permitted to be

discontinued where the calculated compressive stress is less than cf ′15.0 . Stresses are calculated for the factored forces using a linearly elastic model and gross section properties, as given here

( )g

wu

g

uIlM

APf 2/

±=

Boundary Element Dimensions: As required by ACI 21.9.6.4, boundary elements are to extend horizontally from the extreme compression fiber a distance not less than the larger of

wlc 1.0− and .2/c

106

Boundary Element Requirements (ACI 21.9.6.2)

Boundary Element Requirements (ACI 21.9.6.3)

Boundary Element Transverse Reinforcement: Special boundary element transverse reinforcement shall satisfy the requirements of ACI 21.6.4.2 through 21.6.4.34, except ACI Eqn. (21-4) need not be satisfied and the transverse reinforcement spacing limit of 21.6.4.3 (a) shall be one-third of the least dimension of the boundary element. In ACI 21.4.4.1, transverse reinforcement as required below shall be provided. The total cross-sectional area of rectangular hoop reinforcement shall not be less than that required by the following Equation.

yt

ccsh f

'fbs09.0A = ACI (21-5)

where: s = spacing of transverse reinforcement measured along the longitudinal

axis of the structural member.

cb = dimension of core perpendicular to the tie legs that constitute shA .

107

ytf = specified yield strength of transverse reinforcement. Based on ACI 21.6.4.2, transverse reinforcement shall be provided by either single or overlapping hoops. Crossties of the same bar size and spacing as the hoops shall be permitted. Each end of the crossties shall engage a peripheral long reinforcing bar. Consecutive crossties shall be alternated end for end and along the longitudinal reinforcement. Spacing of crossties or legs of rectangular hoops, xh within a cross section of the member shall not exceed 35 cm on center. Based on ACI 21.6.4.3, transverse reinforcement shall be spaced at a distance not exceeding (a) one-quarter of the minimum member dimension,

(b) six times the diameter of the longitudinal reinforcement, and (c) os as

defined by ⎟⎠⎞

⎜⎝⎛ −

+=3

h3510s xo , where xh is maximum horizontal spacing

of ties or cross ties. In ACI 21.9.6.5, where special boundary elements are not required by 21.9.6.2 or 21.9.6.3, (a) and (b) shall be satisfied.

(a) If the longitudinal reinforcement ratio at the wall boundary is greater than yf/28 , boundary transverse reinforcement shall satisfy 21.6.4.2 and 21.9.6.4 (a). The maximum longitudinal spacing of transverse reinforcement in the boundary shall not exceed 20 cm;

(b) Except when uV in the plane of the wall is less than

ccv fA ′265.0 , horizontal reinforcement terminating at the edges of structural walls without boundary elements shall have a standard hook engaging the edge reinforcement or the edge reinforcement shall be enclosed in U-stirrups having the same size and spacing as and spliced to the horizontal displacement.

108

Reinforcement Details for Boundary Elements (US system)

Anchorage and Splicing of Reinforcement: In ACI 21.7.5.1, the development length dhl for a bar with a standard 90

degree hook shall not be less than the largest of bd8 , 15 cm, and the length required by the following equation, which is applicable to bar diameters ranging from 10 mm to 36 mm.

c

ybdh 'f2.17

fdl =

The 90-degree hook shall be located within the confined core of a boundary element.

In ACI 21.7.5.2, for bar diameters 10 mm through 36 mm, the development length , in tension, for a straight bar shall not be less than (a) and (b):

109

(a) 2.5 times the length required by the above-mentioned equation if the depth of the concrete cast in one lift beneath the bar does not exceed 30 cm, and

(b) 3.5 times the length provided by the same equation if the depth of the concrete cast in one lift beneath the bar exceeds 30 cm.

In ACI 21.7.5.3, straight bars terminated at a joint shall pass through the confined core of a boundary element. Any portion of dl not within the confined core shall be increased by a factor of 1.6.

• Based on ACI 21.6.4.4, specified boundary element transverse reinforcement at the wall base shall extend into the support at least

dl of the largest longitudinal reinforcement in the specified boundary element unless the special boundary element terminates on a footing or mat, where special boundary element transverse reinforcement shall extend at least 30 cm into the footing or mat.

110

Example (5):

Redesign shear wall 'G' in example (4) as a special shear wall using UBC-94 load combinations and ACI 318-08 for reinforced concrete design. Use 22 /4200 and /300 cmkgfcmkgf yc ==′ . Solution:

Design for shear: -1

At least two curtains of reinforcement shall be used in a wall if the in-plane factored shear force exceeds ccv 'fA53.0

( )( ) tons374.17tons08.551000/3003002053.0'fA53.0V ccvn >=== Thus, one curtain of reinforcement is required. Nevertheless, two curtains of reinforcement are to be used here.

1-3 Horizontal shear reinforcement:

0025.0t =ρ cm45S max,2 =

( ) cm/cm05.0SA

and 200025.0h0025.0SA 2

2

t

2

t ===

For two curtains of reinforcement and trying φ 10 mm bars ( )

max,222

Scm4.31S ,05.0S785.02

<== . Use φ 10 mm bars @ 30cm.

( ) ( ) tons374.17tons06.281000/3003002027.0'fA27.0 ccv >== Thus tρ and lρ may be reduced based on ACI 14.3.

1-2 Vertical shear reinforcement:

cm45S max,1 = For two curtains of reinforcement, and trying φ 10 mm bars

111

( ) ( )11

lS

0.7852 200025.0h0025.0SA

===

And max,11 Scm40.31S <= . Use φ 10mm bars @ 30cm.

Check for shear reinforcement capacity

( )ytcccvn f'fAV ρα += 27l/h ww ⟩= ,i.e. 53.0c =α

( )( ) ( )( ) ( ) K.Otons75.0/374.17tons08.11842000025.030053.01000

20300Vn ⟩=+= 2- Design for flexure and axial loads:

Boundary elements are required where the maximum fiber compression stress > c'f2.0 , calculated from the following equation:

( )g

wu

g

uI

2/lMAP

f ±=

The boundary elements may be disconnected where the compressive stress < c'f15.0 The load combinations to be considered are shown below

)ELD(4.1U ±+= E4.1D9.0U ±=

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟

⎟⎠

⎞⎜⎜⎝

⎛+=

wys

uwysu l

c1fA

P1lfA5.0M φ

Where:

1w 85.02lc

βωαω

++

= , 'fhl

fA

cw

ys=ω and 'fhl

p

cw

u=α

For the vertical shear reinforcement of φ 10 mm

@30cm, 2s cm28.17A = ( ) 836.0280300

7005.085.0 =−−=β ,

( )( )( ) 04032.0

30020300420028.17

'fhlfA

cw

ys ===ω

, ( )( )( ) u

u

cw

u P00055.030020300

1000P'fhl

p===α ,

( ) ( ) 79124.0P00055.004032.0

836.085.004032.02P00055.004032.0

lc uu

w

+=

++

=

For zone 7: ( )( )( )( ) tons1.445.22132.04.1Pu ==

112

( )( )

( )( )( )

( ) 223

cm/Kg3002.0cm/Kg684.9612/30020

2/300100000002.2683002010001.44f >=±=

i.e., special boundary elements are required at wall ends.

Flexural capacity at section of maximum moment:

( )( )( )( ) tons1.445.22132.04.1Pu == ( ) 081065.0

79124.01.4400055.004032.0

lc

w=

+=

( ) cm32.24300081065.0c == , and length of boundary element is not less than

the larger of wl1.0c − and cm16.12,2/c ≈ m.t002.268m.t744.144Mu <=

and m.t258.123744.144002.268'M u =−=

For a boundary element 35 cm in length, additional reinforcement in each of the two boundaries is given as follows

( )( )( ) ( ) 2

additional,s cm44.15785.0426542009.0

100000258.123A =+= (tension-controlled)

Use 8φ 16 mm bars in each of the two boundary elements. Boundary element transverse reinforcement:

yt

ccsh f

'fbs09.0A =

( )cm15cm67.16

3153510s

cm6.96.16cm54/20

ofsmallesttheSmax

≤=⎟⎠⎞

⎜⎝⎛ −

+=

==

⇒≤

o

For the longer direction of boundary, ( ) ( )hoopsmm8cm2.118.04220bc φ=−−= ( )( )( ) 2

sh cm36.04200

3002.11509.0A ==

Use 2-legged mm8φ ties @ 5 cm

For the shorter direction of boundary, ( )hoopsmm8cm2.308.0435bc φ=−−=

( )( )( ) 2sh cm97.0

42003002.30509.0A ==

Use 2-legged mm8φ ties @ 5 cm Anchorage of horizontal shear reinforcement: For 10 mm bars hooked at 180 degree,

( )( ) )K.O(cm15astakencm10.143002.17

14200'f2.17

dfl

c

bydh ===

113

For straight bars ( ) )K.O.N(cm50astakencm21.4906.145.3ld ==

For zone 6:

( )( )( )( ) tons8.375.21832.04.1Pu == ( )( )

( )( )( )

( ) 223

cm/Kg3002.0cm/Kg26.7812/30020

2/30010000088.2153002010008.37f >=±=

i.e., special boundary elements are required at wall ends.

Flexural Capacity at section of maximum moment:

( )( )( )( ) tons8.375.21532.04.1Pu == ( ) 076688.0

79124.08.3700055.004032.0

lc

w=

+=

length of boundary element is not less than the larger of wl1.0c − and

cm150.11,2/c ≈ m.t88.215m.t58.137M u <=

and m.t30.7858.13788.215'M u =−=

For a boundary element 35 cm in length, additional reinforcement in each of the two boundaries is given as follows

( )( )( ) ( ) 2

additional,s cm96.10785.0426542009.0

1000003.78A =+=

Use 8φ 14 mm bars in each of the two boundary elements. Boundary element transverse reinforcement:

yt

ccsh f

'fbs09.0A =

( )cm15cm67.16

3153510s

cm4.84.16cm54/20

ofsmallesttheSmax

≤=⎟⎠⎞

⎜⎝⎛ −

+=

==

⇒≤

o

For the longer direction of boundary, ( ) ( )hoopsmm8cm2.118.04220bc φ=−−= ( )( )( ) 2

sh cm36.04200

3002.11509.0A ==

114

Use 2-legged mm8φ ties @ 5 cm

For the shorter direction of boundary, ( )hoopsmm8cm2.308.0435bc φ=−−=

( )( )( ) 2sh cm97.0

42003002.30509.0A ==

Use 2-legged mm8φ ties @ 5 cm

For zone 5:

( )( )( )( ) tons5.315.21532.04.1Pu == ( )( )

( )( )( )

( ) 223

cm/Kg3002.0cm/Kg41.6012/30020

2/30010000048.1653002010005.31f >=±=

i.e., special boundary elements are required at wall ends.

Flexural Capacity at section of maximum moment:

( )( )( )( ) tons5.315.21532.04.1Pu == ( ) 072311.0

79124.08.3700055.004032.0

lc

w=

+=

length of boundary element is not less than the larger of wl1.0c − and

cm85.10,2/c ≈ m.t48.165m.t34.130M u >=

and m.t14.3534.13048.165'M u =−=

For a boundary element 35 cm in length, additional reinforcement in each of the two boundaries is given as follows

( )( )( ) ( ) 2

additional,s cm65.6785.0426542009.0

10000014.35A =+=

Use 6φ 12 mm bars in each of the two boundary elements. Boundary element transverse reinforcement:

yt

ccsh f

'fbs09.0A =

( )cm15cm67.16

3153510S

cm2.72.16cm54/20

ofsmallesttheSmax

<=⎟⎠⎞

⎜⎝⎛ −

+=

==

⇒≤

o

115

For the longer direction of boundary, ( ) ( )hoopsmm8cm2.118.04220bc φ=−−= ( )( )( ) 2

sh cm36.04200

3002.11509.0A ==

Use 2-legged mm8φ ties @ 5 cm

For the shorter direction of boundary, ( )hoopsmm8cm2.308.0435bc φ=−−=

( )( )( ) 2sh cm97.0

42003002.30509.0A ==

Use 2-legged mm8φ ties @ 5 cm

For zone 4:

( )( )( )( ) tons2.255.21232.04.1Pu == ( )( )

( )( )( )

( ) 223 cm/Kg3002.0cm/Kg71.43

12/300202/300100000524.118

3002010002.25f <=±=

i.e., no special boundary elements are required at wall ends.

Flexural Capacity at section of maximum moment:

( )( )( )( ) tons2.255.21232.04.1Pu == ( ) 067934.0

79124.08.3700055.004032.0

lc

w=

+=

m.t524.118m.t03.123Mu >=

Thus, no additional reinforcement required at wall ends.

For zone 3: ( )( )( )( ) tons9.185.2932.04.1Pu == ( ) 2cm/Kg3002.0f <

i.e., no special boundary elements are required at wall ends. Flexural Capacity at section of maximum moment:

( )( )( )( ) tons9.185.2932.04.1Pu == ( ) 0635567.0

79124.08.3700055.004032.0

lc

w=

+=

m.t776.76m.t64.115M u >= Thus, no additional reinforcement required at wall ends.

116

For zone 2: ( )( )( )( ) tons6.125.2632.04.1Pu == ( ) 2cm/Kg3002.0f <

i.e., no special boundary elements are required at wall ends.

Flexural Capacity at section of maximum moment:

( )( )( )( ) tons6.125.2632.04.1Pu == ( ) 0591796.0

79124.08.3700055.004032.0

lc

w=

+=

m.t958.41m.t18.108M u >=

Thus, no additional reinforcement required at wall ends.

For zone 1: ( )( )( )( ) tons3.65.2332.04.1Pu == ( ) 2cm/Kg3002.0f <

i.e., no special boundary elements are required at wall ends.

Flexural Capacity at section of maximum moment:

( )( )( )( ) tons3.65.2332.04.1Pu == ( ) 0548024.0

79124.08.3700055.004032.0

lc

w=

+=

m.t792.15m.t65.100M u >=

Thus, no additional reinforcement required at wall ends.

117

Earthquake Resistant Design According To 1997 UBC

Major Changes from UBC 1994

(1) Soil Profile Types: The four site coefficients S1 to S4 of the UBC 1994, which are independent of the level of ground shaking, were expanded to six soil profile types, which are dependent on the seismic zone factors, in the 1997 UBC (SA to SF) based on previous earthquake records.

The new soil profile types were based on soil characteristics for the top 30 m of the soil. The shear wave velocity, standard penetration test and undrained shear strength are used to identify the soil profile types.

(2) Structural Framing Systems: In addition to the four basic framing systems (bearing wall, building frame, moment-resisting frame, and dual), two new structural system classifications were introduced: cantilevered column systems and shear wall-frame interaction systems.

(3) Load Combinations: The 1997 UBC seismic design provisions are based on strength-level design rather than service-level design.

(4) Earthquake Loads: In the 1997 UBC, the earthquake load (E) is a function of both the horizontal and vertical components of the ground motion.

(5) Design Base Shear: The design base shear in the 1997 UBC varies in inverse proportion to the period T, rather than T2/3 prescribed previously. Also, the minimum design base shear limitation for Seismic Zone 4 was introduced as a result of the ground motion that was observed at sites near the fault rupture in 1994 Northridge earthquake.

(6) Simplified Design Base Shear: In the 1997 UBC, a simplified method for determining the design base shear (V) was introduced for buildings not more than three stories in height (excluding basements).

(7) Displacement and Drift: In the 1997 UBC, displacements are determined for the strength-level earthquake forces.

(8) Lateral Forces on Elements of Structures: New equations for determining the seismic forces (Fp) for elements of structures, nonstructural components and equipment are given.

118

The Static Lateral Force Procedure Applicability:

The static lateral force procedure may be used for the following structures:

A. All structures, regular or irregular (Table A-1), in Seismic Zone no. 1 (Table A-2) and in Occupancy Categories 4 and 5 (Table A-3) in Seismic Zone 2.

B. Regular structures under 73 m in height with lateral force resistance provided by systems given in Table (A-4) except for structures located in soil profile type SF, that have a period greater than 0.70 sec. (see Table A-5 for soil profiles).

C. Irregular structures not more than five stories or 20 m in height.

D. Structures having a flexible upper portion supported on a rigid lower portion where both portions of the structure considered separately can be classified as being regular, the average story stiffness of the lower portion is at least ten times the average stiffness of the upper portion and the period of the entire structure is not greater than 1.10 times the period of the upper portion considered as a separate structure fixed at the base.

Regular Structures:

Regular structures are structures having no significant physical discontinuities in plan or vertical configuration or in their lateral force resisting systems. Irregular Structures: Irregular structures are structures having significant physical discontinuities in configuration or in their lateral force resisting systems (See Table A-1.a and A-1.b for detailed description of such structures).

Design Base Shear:

The total design base shear in a given direction is to be determined from the following formula.

TRWICV v= (A-1)

The total design base shear need not exceed the following:

RWICV a5.2

= (A-2)

119

The total design base shear shall not be less than the following:

WICV a11.0= (A-3)

In addition, for Seismic Zone 4, the total base shear shall not be less than the following:

RWINZV v8.0

= (A-4)

The minimum design base shear limitation for Seismic Zone 4 was introduced as a result of the ground motion effects observed at sites near fault rupture in 1994 Northridge earthquake.

Where

V = total design lateral force or shear at the base.

W = total seismic dead load - In storage and warehouse occupancies, a minimum of 25 % of floor live load is to

be considered. - Total weight of permanent equipment is to be included. - Where a partition load is used in floor design, a load of not less than 50 kg/m2 is to

be included.

I = Building importance factor given in Table (A-3). Z = Seismic Zone factor, shown in Table (A-2).

R = response modification factor for lateral force resisting system, shown in Table

(A-4).

aC = acceleration-dependent seismic coefficient, shown in Table (A-6).

vC = velocity-dependent seismic coefficient, shown in Table (A-7).

aN = near source factor used in determination of aC in Seismic Zone 4, shown in Table (A-8).

vN = near source factor used in determination of vC in Seismic Zone 4, shown in

Table (A-9).

120

T = elastic fundamental period of vibration, in seconds, of the structure in the direction under consideration evaluated from the following equations:

For reinforced concrete moment-resisting frames,

( ) 4/3073.0 nhT = (A-5) For other buildings,

( ) 4/30488.0 nhT = (A-6)

Alternatively, for shear walls, ( )

c

n

AhT

4/3

0743.0= (A-7)

Where

nh = total height of building in meters

cA = combined effective area, in m2, of the shear walls in the first story of the structure, given by

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛+=∑

2

2.0n

eic h

DAA 9.0/ ≤ne hD (A-8)

Where eD is the length, in meters, of each shear wall in the first story in the direction parallel to the applied forces.

iA = cross-sectional area of individual shear walls in the direction of loads in m2

Load Combinations:

Based on section 1612 of UBC, structures are to resist the most critical effects from the following combinations of factored loads:

LD 7.14.1 + (A-9) )7.17.14.1(75.0 WLD ++ (A-10)

WD 3.19.0 + (A-11) ELfD 1.11.132.1 1 ++ (A-12)

ED 1.199.0 + (A-13) Where

121

1f = 1.0 for floors in public assembly, live loads in excess of 500 kg/m2 and for garage live loads

1f = 0.5 for other live loads

Earthquake Loads:

Based on UBC 1630.1.1, horizontal earthquake loads to be used in the above-stated load combinations are determined as follows:

vh EEE += ρ (A-14)

hm EE oΩ= (A-15)

Where: E = earthquake load resulting from the combination of the horizontal component hE , and the vertical component, vE

Eh = the earthquake load due to the base shear, V

Em = the estimated maximum earthquake force that can be developed in the structure

Ev = the load effects resulting from the vertical component of the earthquake ground motion and is equal to the addition of DICa50.0 to the dead load effects D

=Ωo seismic force amplification factor as given in Table (A-4), and accounts for structural over-strength =ρ redundancy factor, to increase the effects of earthquake loads on structures with few lateral force resisting elements, given by

gArmax

10.62 −=ρ (A-16)

=gA the minimum cross-sectional area in any horizontal plane in the first story of a shear wall in m2

=maxr the maximum element-story shear ratio For a given direction of loading, the element story shear ratio is the ratio of design story shear in the most heavily loaded single element divided by the total design story shear.

maxr is defined as the largest of the element story shear ratio, ir , which occurs in any of the story levels at or below two-thirds height level of the building.

122

• For moment-resisting frames, ir is taken as the maximum of the sum of the shears in any two adjacent columns in a moment-resisting frame bay divided by the story shear

• For shear walls, ir is taken as the maximum of the product of the wall shear multiplied by wl/05.3 and divided by the total story shear, where wl is the length of the wall in meters.

• For dual ≤ρ 80 % of the values calculated above. • When calculating drift, or when the structure is located in Seismic Zones 0, 1, or

2, ρ shall be taken as 1.0. • ρ can't be smaller than 1.0 and can't be grater than 1.5.

Vertical Distribution of Force:

The base shear evaluated from Eqn. (A-17) is distributed over the height of the building according to the following Eqn.

( )∑=

−= n

iii

xxtx

hw

hwFVF

1

(A-17)

Fig. (A-1) Vertical Distribution of Force

Where

0=tF for 7.0≤T sec.

123

VVTFt 25.007.0 ≤= for 7.0>T sec. The shear force at each story is given by Eqn. (A-18)

∑=

+=n

xiitx FFV (A-18)

Where

n = number of stories above the base of the building

tF = the portion of the base shear, concentrated at the top of the structure to account for higher mode effects

xni FFF ,, = lateral forces applied at levels xorni ,, , respectively

xni hhh ,, = height above the base to levels xorni ,, , respectively

xV = design shear in story x

Horizontal Distribution of Force:

The design story shear in any direction xV , is distributed to the various elements of the lateral force-resisting system in proportion to their rigidities, considering the rigidity of the diaphragm. Horizontal Torsional Moment:

To account for the uncertainties in locations of loads, the mass at each level is assumed to be displaced from the calculated center of mass in each direction a distance equal to 5 % of the building dimension at that level perpendicular to the direction of the force under consideration. The torsional design moment at a given story is given by moment resulting from eccentricities between applied design lateral forces applied through each story’s center of mass at levels above the story and the center of stiffness of the vertical elements of the story, in addition to the accidental torsion.

Overturning Moments:

Buildings must be designed to resist the overturning effects caused by the earthquake forces.

The overturning moment xM at level x is given by Eqn. (A-19).

( ) ( )∑+=

−+−=n

xixiixntx hhFhhFM

1 (A-19)

124

Overturning moments are distributed to the various elements of the vertical lateral force-resisting system in proportion to their rigidities.

Displacement and Drift:

The calculated story drifts are computed using the maximum inelastic response displacement drift ( m∆ ), which is an estimate of the displacement that occurs when the structure is subjected to the design basis ground motion. According to UBC 1630.9.2,

sm R ∆=∆ 7.0 (A-20) Where:

=∆ s design level response displacement, which is the total drift or total story drift that occurs when the structure is subjected to the design seismic forces.

• Calculated story drift m∆ shall not exceed 0.025 times the story height for structures having a fundamental period of less than 0.70 seconds.

• Calculated story drift m∆ shall not exceed 0.020 times the story height for structures having a fundamental period equal to or greater than 0.70 seconds.

∆−P Effects:

∆−P effects are neglected when the ratio given by Eqn. (A-21) is .1.0≤

xsx

x

primary

ondary

hVP

MM ∆

=sec (A-21)

xP = total unfactored gravity load at and above level x ∆ = seismic story drift by design seismic forces ( s∆ )

xV = seismic shear between levels x and 1−x

xsh = story height below level x

• In seismic zones no. 3 and 4, ∆−P need not be considered when the story drift ( s∆ ) Rh xs /02.0≤ times the story height.

125

Simplified Design Base Shear Applicability:

• Buildings of any occupancy and buildings not more than three stories in height, excluding basements, in standard occupancy structures.

• Other buildings not more than two stories in height, excluding basements.

Base Shear: The total design base shear in a given direction is determined from the following formula:

R

WCV a0.3= (A-22)

• When the soil properties are not known in sufficient detail to determine the soil profile type, type DS is used in Seismic Zones 3 and 4.

• When the soil properties are not known in sufficient detail to determine the soil profile type, type ES is used in Seismic Zones 1, 2A and 2B.

Vertical Distribution of Force: The forces at each level are calculated from the following formula:

RwCF ia

x0.3

= (A-23)

126

Table (A-1.a) Vertical Structural Irregularities Irregularity Type and Definition 1- Stiffness Irregularity- - -Soft Story A soft story is one in which the lateral stiffness in less than 70 percent of than in the story above or less than 80 percent of the average stiffness of the three stories above. 2- Mass Irregularity Mass irregularity is considered to exist where the effective mass of any story is more than 150 percent of the effective mass of an adjacent story. A roof that is lighter than the floor below need not be considered. 3- Vertical Geometric Irregularity Vertical geometric irregularity shall be considered to exist where the horizontal dimension of the lateral force-resisting system in any story is more than 130 percent of that in an adjacent story. One-story penthouses need not be considered. 4- In-Plane Discontinuity in Vertical Lateral Force-resisting Element An in-plane offset of the lateral load-resisting elements greater than the length of these elements. 5- Discontinuity in Capacity-Weak Story A weak story is one in which the story strength is less than 80 percent of that in the story above. The story strength is the total strength of all seismic-resisting elements sharing the story shear for the direction under consideration.

127

Table (A-1.b) Plan Structural Irregularities Irregularity Type and Definition 1- Torsional Irregularity Torsional irregularity is to be considered to exist when the maximum story drift, computed including accidental torsion, at one end of the structure transverse to an axis is more than 1.2 times the average of the story drifts of the two ends of the structure. 2- Re-entrant Corners Plan configurations of a structure and its lateral force-resisting system contain re-entrant corners, where both projections of the structure beyond a re-entrant corner are greater than 15 % of the plan dimension of the structure in the given direction. 3- Diaphragm Discontinuity Diaphragms with abrupt discontinuities or variations in stiffness, including those having cutout or open areas greater than 50 % of the gross enclosed area of the diaphragm, or changes in effective diaphragm stiffness of more than 50 % from one story to the next. 4- Out-of-plane Offsets Discontinuities in a lateral force path, such as out-of-plane offsets of the vertical elements. 5- Nonparallel Systems The vertical lateral load-resisting elements are not parallel to or symmetric about the major orthogonal axes of the lateral force-resisting system. Table (A-2) Seismic Zone Factor Z

Zone 1 2A 2B 3 4 Z 0.075 0.15 0.20 0.30 0.40

Note: The zone shall be determined from the seismic zone map.

128

Table (A-3) Occupancy Importance Factors

Occupancy Category Seismic Importance Factor, I 1-Essential facilities

1.25 2-Hazardous facilities

1.25 3-Special occupancy structures

1.00

4-Standard occupancy structures

1.00

5-Miscellaneous structures 1.00

Table (A-4) Structural Systems Basic Structural System

Lateral- force resisting system description

R oΩ Height limit Zones 3 &4. (meters)

Bearing Wall Concrete shear walls 4.5 2.8 48 Building Frame Concrete shear walls 5.5 2.8 73 Moment-Resisting Frame

SMRF IMRF OMRF

8.5 5.5 3.5

2.8 2.8 2.8

N.L ---- ----

Dual Shear wall + SMRF Shear wall + IMRF

8.5 6.5

2.8 2.8

N.L 48

Cantilevered Column Building

Cantilevered column elements 2.2 2.0 10

Shear-wall Frame Interaction

5.5 2.8 48

129

Table (A-5) Spoil Profile Types

Soil Profile Type

Soil Profile Name/Generic Description

Average Soil Properties For Top 30 m Of Soil Profile Shear Wave Velocity, sv m/s

Standard Penetration Test, N (blows/foot)

Undrained Shear Strength, uS kPa

AS Hard Rock > 1,500 --- ---

BS Rock 760 to 1,500

CS Very Dense Soil and Soft Rock

360 to 760 > 50 > 100

DS Stiff Soil Profile 180 to 360 15 to 50 50 to 100

ES Soft Soil Profile < 180 < 15 < 50

FS Soil Requiring Site-specific Evaluation Table (A-6) Seismic Coefficient aC Soil Profile Type

Seismic Zone Factor, Z Z =0.075 Z = 0.15 Z = 0.2 Z = 0.3 Z = 0.4

AS 0.06 0.12 0.16 0.24 0.32 aN

BS 0.08 0.15 0.20 0.30 0.40 aN

CS 0.09 0.18 0.24 0.33 0.40 aN

DS 0.12 0.22 0.28 0.36 0.44 aN

ES 0.19 0.30 0.34 0.36 0.36 aN

FS See Footnote Footnote: Site-specific geotechnical investigation and dynamic response analysis

shall be performed to determine seismic coefficients for soil Profile Type FS .

130

Table (A-7) Seismic Coefficient vC Soil Profile Type

Seismic Zone Factor, Z Z =0.075 Z = 0.15 Z = 0.2 Z = 0.3 Z = 0.4

AS 0.06 0.12 0.16 0.24 0.32 aN

BS 0.08 0.15 0.20 0.30 0.40 aN

CS 0.13 0.25 0.33 0.45 0.56 aN

DS 0.18 0.32 0.40 0.54 0.64 aN

ES 0.26 0.50 0.64 0.84 0.96 aN

FS See Footnote Footnote: Site-specific geotechnical investigation and dynamic response analysis shall be performed to determine seismic coefficients for soil Profile Type FS .

Table (A-8) Near-Source Factor aN

Seismic Source Type

Closest Distance to Known Seismic Source ≤ 2 km 5 km ≥ 10 km

A 1.5 1.2 1.0 B 1.3 1.0 1.0 C 1.0 1.0 1.0

Table (A-9) Near-Source Factor vN

Seismic Source Type

Closest Distance to Known Seismic Source ≤ 2 km 5 km 10 km ≥ 15 km

A 2.0 1.6 1.2 1.0 B 1.6 1.2 1.0 1.0 C 1.0 1.0 1.0 1.0

131

Example (6):

Using UBC 97, evaluate the seismic base shear acting on a regular twelve-story building frame system with reinforced concrete shear walls in the principal directions, as the main lateral force-resisting system. The building which is located in Gaza City is 31.2 m by 19 m in plan and 32.8 m in height (Standard Occupancy). It is constructed on a sandy soil profile with SPT values ranging from 20 to 50 blows/foot.

Solution:

From Table A-2 and for Zone 1, Z = 0.075

From Table A-3 and for Standard Occupancy, I = 1.0

From Table A-5, Soil Profile Type is DS

From Table A-4, R = 5.5

From Table A-6, aC = 0.12

From Table A-7, vC = 0.18

From Eqn. (A-6),

( ).sec75.0

28.380488.0 4/3

==T

From Eq. (A-1), the total base shear is

( ) WWTRWICV v 0436.0

75.05.518.0

===

From Eq. (A-2), the total base is not to exceed

( ) WW

RWICV a 0545.0

5.512.05.25.2

=== O.K

From Eq. (A-3), the total design base is not to be less than

WWWICV a 0132.0)12.0(11.011.0 === O.K

132

Earthquake Loads According to IBC 2003

The process of determining earthquake loads according to IBC 2003 Spectral Design Method can be broken down into the following basic steps:

• Determination of the maximum considered earthquake and design spectral response accelerations.

• Determination of the seismic base shear associated with the building or the

structure’s fundamental period of vibration. • Distribution of the seismic base shear within the building or the structure.

IBC Safety Concept • The IBC intends to design structures for “collapse prevention” in the event of an

earthquake with a 2 % probability of being exceeded in 50 years

133

Introduction Seismic Response Spectra: - A response spectrum provides the maximum response of a SDOF system, for a given damping ratio and a range of periods, for a specific earthquake. - A design response spectrum is a smoothed spectrum used to calculate the expected seismic response of a structure Figure (1) shows six inverted, damped pendulums, each of which has a different fundamental period of vibration. To derive a point on a response spectrum, one of these pendulum structures is analytically subjected to the vibrations recorded during a particular earthquake. The largest acceleration of this pendulum structure during the entire record of a particular earthquake can be plotted as shown in Figure 1(b). Repeating this for each of the other pendulum structures shown in Figure 1(a) and plotting and connecting the peak values for each of the pendulum structures produces an acceleration response spectrum. Generally, the vertical axis of the spectrum is normalized by expressing the computed accelerations in terms of the acceleration due to gravity g . In Figure (2), displacement, velocity, and acceleration spectra for a given earthquake are shown. In this figure, structures with short periods of 0.2 to 0.5 seconds are almost rigid and are most affected by ground accelerations. Structures with medium periods ranging from 0.5 to 2.5 seconds are affected most by velocities. Structures with long periods greater than 2.5 seconds, such as tall buildings or long span bridges, are most affected by displacements.

134

Viscous damping

(a) Damped pendulums of varying natural frequencies

0 1.0 2.0 3.0 4.0

0.5% Damping

2% Damping

5% Damping

4

3

2

1

Acc

eler

atio

n Sa

Natural period of vibration, T (sec)

Acceleration response spectrum

Figure (1): Earthquake Response Spectrum

Reference: MacGregor, J and Wight, J., "Reinforced Concrete Mechanics and Design" 4th Edition, Prentice Hall, NJ, 2005.

135

136

Analysis Procedure

1- Determination of maximum considered earthquake and design spectral response accelerations:

• Determine the mapped maximum considered earthquake MCE spectral response accelerations, sS for short period (0.2 sec.) and 1S for long period (1.0 sec.) using the spectral acceleration maps in IBC Figures 1615(1) through 1615(10). Straight-line interpolation is allowed for sites in between contours or the value of the higher contour shall be used. Acceleration values obtained from the maps are given in % of g , where g is the gravitational acceleration.

• Determine the site class, which is based on the types of soils and their engineering

properties, in accordance with IBC Section 1615.1.1. Site classes A, B, C, D, E, and F, obtained from Table 1615.1.1, are based on the average shear velocity, sv , average standard penetration resistance, N , or the average undrained shear strength, us . These parameters represent average values for the top 30 m of soil. When the soil properties are not known in sufficient detail to determine the site class, site class D shall be used. Unless the building official determines that the site class E or F is likely to be present at the site.

• Determine the maximum considered earthquake spectral response accelerations

adjusted for site class effects, MSS at short period and 1MS at long period in accordance with IBC 1615.1.2.

137

138

saMS SFS = 11 SFS vM =

where:

aF = short-period site coefficient, given in Table 1615.1.2(1) vF = long-period site coefficient, given in Table 1615.1.2(2)

• Determine the 5% damped design spectral response accelerations DSS at short

period and 1DS at long period in accordance with IBC 1615.3.

MSDs SS )3/2(= 11 )3/2( MD SS =

139

2- Determination of seismic use group and occupancy important factor:

• Each structure shall be assigned a seismic use group and a corresponding occupancy importance factor EI , in accordance with Table 1604.5. Seismic use group I are structures not assigned to either seismic use group II or III. Seismic use group II are structures the failure of which would result in a substantial public hazard due to occupancy or use as indicated in Table 1604.5. Seismic use group III are structures required for post earthquake recovery and those containing substantial quantities of hazardous substances as indicated in Table 1604.5.

140

3- Determination of seismic design category: All structures shall be assigned to a seismic design category based on the seismic use group and the design spectral response acceleration coefficients, DSS and 1DS . Each building and structure shall be assigned to the worst severe seismic design category in accordance with Table 1616.3(1) or 1616.3(2), irrespective of the fundamental period of vibration of the structure.

141

4- Determination of the Seismic Base Shear: 4-1 Simplified Analysis:

• A simplified analysis, in accordance with Section 1617.5, shall be determined to be used for any structure in Seismic Use Group I, subject to the following limitations, or a more rigorous analysis shall be made:

1- Building of light-framed construction not exceeding three stories in height,

excluding basement.

142

2- Building of any construction other than the light-framed construction, not exceeding two stories in height, excluding basement, with flexible diaphragm at every level.

• Since the above limitations rule out the use of this method for concrete buildings, it will not be covered here.

4-2 Index Force Analysis: Structures assigned to Seismic Design Category A need only comply with the requirements of Section 1616.4.1 through 1616.4.5, summarized below:

• Structures shall be provided with a complete lateral force resisting system designed to resist the minimum lateral force, xF , applied simultaneously at each floor level according to the following equation:

xx wF 01.0=

Where: xF = The design lateral force applied at level x

=xw The portion of the total gravity load of the structure, W , located or assigned to level x

=W The total dead load and other loads listed below: 1- In areas used for storage, a minimum of 25 % of the reduced floor live load. 2- Where an allowance for partition load is reduced in the floor load design, the

actual partition weight or 2/50 mkg of the floor area, whichever is greater.

3- The total weight of permanent equipment. 4- 20 % of flat roof snow load where flat roof snow load exceeds

2/145 mkg . • The direction of application of seismic forces used in design shall be such that

which will produce the most critical load effect in each component. • The design seismic forces are permitted to be applied separately in each of the

two orthogonal directions. • Load combinations as per Section 9.2 of ACI Code.

4-3 Equivalent Lateral Force Analysis: Section 9.5.5 of ASCE 7-02** shall be used. **ASCE, ASCE Standard Minimum Design Loads for Buildings and Other Structures, ASCE 7-02, American Society of Civil Engineers, Reston, VA, 2002.

143

• The seismic base shear V in a given direction is determined in accordance with the following equation:

WCV s=

where:

sC = Seismic response coefficient

( ) ( )TIRS

IRS

E

D

E

DS

//1≤=

DSS044.0≥ R = Response modification coefficient, given in Table 1617.6.2

EI = Seismic occupancy importance factor T = Fundamental period of vibration An approximate value of aT may be obtained from:

75.0nTa hCT =

where: TC = Building period coefficient

= 0.073 for moment frames resisting 100% of the required seismic force = 0.049 for all other buildings

nh = Height of the building above the base in meters The calculated fundamental period, ,T cannot exceed the product of the coefficient, uC , in the following table times the approximate fundamental period, aT . The base shear V is to be based on a fundamental period, T , in seconds, of 1.2 times the coefficient for the upper limit on the calculated values, uC , taken from the following table, times the approximate fundamental period, aT

144

Vertical Structural Irregularities Irregularity Type and Description 1a- Stiffness Irregularity- Soft Story A soft story is one in which the lateral stiffness is less than 70 percent of that in the story above or less than 80 percent of the average stiffness of the three stories above. 1b- Stiffness Irregularity- Extreme Soft Story An extreme soft story is one in which the lateral stiffness is less than 60 percent of that in the story above or less than 70 percent of the average stiffness of the three stories above. 2- Weight (Mass) Irregularity Mass irregularity shall be considered to exist where the effective mass of any story is more than 150 percent of the effective mass of an adjacent story. A roof that is lighter than the floor below need not be considered. 3- Vertical Geometric Irregularity Vertical geometric irregularity shall be considered to exist where the horizontal dimension of the lateral force-resisting system in any story is more than 130 percent of that in an adjacent story. 4- In-Plane Discontinuity in Vertical Lateral Force-Resisting Elements An in plane offset of the lateral load-resisting elements greater than the length of these elements or a reduction in stiffness of the resisting element in the story below. 5- Discontinuity in Capacity-Weak Story A weak story is one in which the story strength is less than 80 percent of that in the story above. The story strength is the total strength the story above or less than 80 percent of that in the story above. The story strength is the total strength of all seismic-resisting elements sharing the story shear for the direction under consideration.

145

Plan Structural Irregularities Irregularity Type and Description 1a- Torsional Irregularity – to be considered when diaphragms are not flexible Torsional irregularity shall be considered to exist when the maximum story drift, computed including accidental torsion, at one end of the structure transverse to an axis is more than 1.2 times the average of the story drifts at the two ends of the structure. 1b- Extreme Torsional Irregularity – to be considered when diaphragms are not flexible Extreme torsional irregularity shall be considered to exist when the maximum story drift, computed including accidental torsion, at one end of the structure transverse to an axis is more than 1.4 times the average of the story drifts at the two ends of the structure. 2- Re-entrant Corners Plan configurations of a structure and its lateral force-resisting system contain re-entrant corners, where both projections of the structure beyond a reentrant corner are greater than 15 % of the plan dimension of the structure in the given direction. 3- Diaphragm Discontinuity Diaphragms with abrupt discontinuities or variations in stiffness, including those having cutout or open areas greater than 50 % of the gross enclosed area of the diaphragm, or changes in effective diaphragm stiffness of more than 50 % from one story to the next. 4- Out-of-plane Offsets Discontinuities in a lateral force path, such as out-of-plane offsets of the vertical elements. 5- Nonparallel Systems The vertical lateral load-resisting elements are not parallel to or symmetric about the major orthogonal axes of the lateral force-resisting system.

146

147

148

149

150

Coefficient for Upper Limit on Calculated Period Design Spectral Response, 1DS Coefficient uC

4.0≥ 0.3 0.2

0.15 1.0≤

1.2 1.3 1.4 1.5 1.7

In cases where moment resisting frames do not exceed twelve stories in height and having a minimum story height of 3 m, an approximate period aT in seconds in the following form can be used: NTa 1.0= where N = number of stories

151

5- Vertical Distribution of Forces: The vertical distribution of seismic forces is determined from:

VCF vxx = and

∑=

= n

ii

ki

kxx

vx

hw

hwC

1

where: xF = Lateral force at level x vxC = Vertical distribution factor

V = total design lateral force or shear at the base of the building xw and iw = the portions of W assigned to levels xand i

xh and ih = heights to levels xand i k = a distribution exponent related to the building period as follows: k = 1 for buildings with T less than or equal to 0.5 seconds k = 2 for buildings with T more than or equal to 2.5 seconds Interpolate between k = 1 and k = 2 for buildings with T between 0.5 and 2.5

6- Horizontal Distribution of Forces and Torsion: Horizontally distribute the shear xV

∑=

=x

iix FV

1

where: iF = Portion of the seismic base shear, V , introduced at level i

Accidental Torsion, taM

taM = ( )BVx 05.0 Total Torsion, TM tatT MMM +=

F

F

F wn

wx

w1

h

hh

152

7- Overturning Moments: The overturning moment xM is given by the following equation:

( )xi

n

xiix hhFM −= ∑

=

τ

where:

iF = Portion of the seismic base shear, V , introduced at level i =τ Overturning moment reduction factor

= 1.0 for the top 10 stories = 0.8 from the 20th story from the top and below = Values between 1.0 and 0.8 determined by a straight linear interpolation for

stories between the 20th and 10th stories below the top

8- Story Drift: The story drift, ∆ , is defined as the difference between the deflection of the center of mass at the top and bottom of the story being considered.

E

xedx I

C δδ =

Where:

dC = Deflection amplification factor, given in Table 1617.6.2 xeδ = Deflection determined by elastic analysis

The allowable story drifts, ∆ , are shown in Table 1617.3.1. 9- P-delta Effect: The P-delta effects can be ignored if the stability coefficient, θ , from the following expression is equal to or less than 0.10.

25.05.0≤≤

∆=

βθ

ddsxx

x

CChVP

Where:

xP = Total unfactored vertical design load at and above level x

153

xV = Seismic shear force acting between level x and 1−x sxh = Story height below level x

∆ = Design story drift occurring simultaneously with xV β = Ratio of shear demand to shear capacity for the story between level x and

1−x . Where the ratio β is not calculated, a value of β = 1.0 shall be used.

When the stability coefficient, θ , is greater than 0.10 but less than or equal to maxθ , P-delta effects are to be considered. To obtain the story drift for including the P-delta effects, the design story drift shall be multiplied by )1/(0.1 θ− . When θ is greater than maxθ , the structure is potentially unstable and has to be redesigned. 10- Combination of Load Effects: The value of seismic load E for use in ACI 318-08 load combinations is defined by the following equations for load combinations in which the effects of gravity loads and seismic loads are additive:

DSQE DSE 2.0+= ρ DSQE DSE 2.0+Ω= o (Need not apply to SDC A)

where: E = the effect of horizontal and vertical earthquake-induced forces

DSS = the design spectral response acceleration at short period D = the effect of dead load ρ = the reliability factor related to the extent of structural redundancy of the lateral

force resisting system EQ = the effect of horizontal seismic forces oΩ = the system over strength factor given in Table 1617.6.2.

The value of seismic load E for use in ACI 318-08 load combinations is defined by the following equations for load combinations in which the effects of gravity loads and seismic loads are counteractive:

DSQE DSE 2.0−= ρ

DSQE DSE 2.0−Ω= o (Need not apply to SDC A)

154

Redundancy: Seismic Design Categories A, B, and C: For structures in seismic design categories A, B and C, the value of ρ may be taken as 1.0. Seismic Design Category D: For structures in seismic design category D, ρ shall be taken as the largest of the values of xρ calculated at each story of the structure “x” in accordance with this equation

xx Ar

xmax

10.62 −=ρ

where: xA = the floor area in square meters of the diaphragm level immediately above the story.

xrmax = the ratio of the design story shear resisted by the single element carrying the

most shear force in the story to the total story shear for a given direction of loading. For moment frames,

xrmax shall be taken as the maximum of the sum of the shears in any

two adjacent columns in the plane of a moment frame divided by the story shear. For columns common to two bays with moment resisting connections on opposite sides at the level under consideration, 70 percent of the shear in that column may be used in the column shear summation. For shear walls,

xrmax shall be taken equal to the maximum ratio, ixr , calculated as the

shear in each wall or wall pier multiplied by 3.3/ wl , where wl is the wall or wall pier length in meters divided by the story shear and where the ratio 3.3/ wl need not be taken greater than 1.0 for buildings of light frame construction. For dual systems,

xrmax shall be taken as the maximum value as defined above

considering all lateral-load-resisting elements in the story. The lateral loads shall be distributed to elements based on their relative rigidities considering the interaction of the dual system. For dual systems, the value of ρ need not exceed 80 percent of the value calculated above. The value of ρ need not exceed 1.5, which is permitted to be used for any structure. The value of ρ shall not be taken as less than 1.0. 11- Diaphragm Forces: Diaphragms are designed to resist design seismic forces determined in accordance with the following equation:

155

pxn

xii

n

xii

px ww

FF

∑

∑

=

== ranges from pxEDS wIS)4.02.0( →

Where: iF = The design force applied to level i pxF = The diaphragm design force

iw = The weight tributary to level i pxw = The weight tributary to the diaphragm at level x

12- Seismic Detailing Requirements

• Level of detailing required depends on the level of seismic risk:

- Low Seismic Risk: SDC* A, B - Medium Seismic Risk: SDC C - High Seismic Risk: SDC D, E, F

*SDC= Seismic Design Category

156

157

Example (7): For the building shown in Example (1) and using IBC-03 evaluate the forces at the floor levels perpendicular to axes 1-1, 2-2, 3-3 and 4-4. Note that site class is D, g25.0Ss = and g10.0S1 = . Solution:

• Using Tables 1615.1.2(1) and 1615.1.2(2), short-period site coefficient 60.1Fa = and long-period site coefficient 40.2Fv = .

• Maximum considered earthquake spectral response accelerations adjusted for site class effects are evaluated.

( ) g4.0g25.060.1SFS saMS === and

( ) g24.0g10.040.2SFS 1v1M === • The 5% damped design spectral response accelerations DSS at short period and

1DS at long period in accordance are evaluated.

( ) g267.0g40.032S

32S MSDS ===

( ) g16.0g24.0

32S

32S 1M1D ===

• Occupancy importance factor, 0.1IE = as evaluated from Table 1604.5. • From Table 16136.3(1) and for g267.0SDS = , Seismic Design Category (SDC) is

B. For g16.0S 1D = and using Table 1616.3(2), SDC is C. Therefore, seismic design category (SDC) is “C”.

• For ordinary shear walls and using Table 1617.6.2, response modification coefficient 0.5R = .

• The seismic base shear V in a given direction is determined in accordance with the following equation:

WCV s=

( ) ( ) TI/RS

I/RSC

E

1D

E

DSs ≤=

DSS044.0≥

Approximate period ( ) .sec48.021049.0T 75.0a ==

( ) .sec676.048.0408.1TC au == ( ) K.O.sec676.0.sec576.048.02.1T <==

158

<== 0534.0

0.5267.0Cs ( ) ( )267.0044.00555.0

576.0)0.5(16.0

>= O.K

i.e., 0534.0Cs = The seismic base shear

( ) tons89.964.18140534.0V ==

• Vertical distribution of forces:

VCF vxx = and ∑

=

=

n

1ii

ki

kxx

vxhw

hwC

K = 1.038 (from linear interpolation).

Shear forces ∑==

x

1iix FV

Overturning moment ( )xin

xiix hhFM −∑τ=

=,

where 0.1=τ

Vertical Distribution of Forces:

Level iw xh ( ) 038.1xx hw vxC

xF 7 259.2 21 495.09 0.35 34.26 6 259.2 18 361.61 0.26 25.02 5 259.2 15 249.39 0.18 17.26 4 259.2 12 158.26 0.11 10.95 3 259.2 9 88.05 0.06 6.09 2 259.2 6 38.54 0.03 2.67 1 259.2 3 9.38 0.01 0.65 0 ∑ 1814.4 0 1400.32 1.00 96.89

160

Seismic Loads Based on IBC 2012/ASCE 7-10

Based on Section 1613.1 of IBC 2012, “Every structure, and portion thereof, including

nonstructural components that are permanently attached to structures and their supports

and attachments, shall be designed and constructed to resist the effects of earthquake

motions in accordance with ASCE 7, excluding Chapter 14 and Appendix 11A. The

seismic design category for a structure is permitted to be determined in accordance with

Section 1613 or ASCE 7”.

Exceptions:

1. Detached one- and two-family dwellings, assigned to Seismic Design Category A, B

or C, or located where the mapped short-period spectral response acceleration, SS, is less

than 0.4 g.

2. The seismic force-resisting system of wood-frame buildings that conform to the

provisions of Section 2308 are not required to be analyzed as specified in this section.

3. Agricultural storage structures intended only for incidental human occupancy.

4. Structures that require special consideration of their response characteristics and

environment that are not addressed by this code or ASCE 7 and for which other

regulations provide seismic criteria, such as vehicular bridges, electrical transmission

towers, hydraulic structures, buried utility lines and their

161

Analysis Procedure 1- Determination of maximum considered earthquake and design spectral response accelerations:

• Determine the mapped maximum considered earthquake MCE spectral response accelerations, sS for short period (0.2 sec.) and 1S for long period (1.0 sec.) using the spectral acceleration maps in IBC Figures 1613.3.1(1) through 1613.3.1(6). Where 1S is less than or equal to 0.04 and sS is less than or equal to 0.15, the structure is permitted to be assigned to Seismic Design Category A.

• Determine the site class based on the soil properties. The site shall be classified as Site Class A, B, C, D, E or F in accordance with Chapter 20 of ASCE 7. Where the soil properties are not known in sufficient detail to determine the site class, Site Class D shall be used unless the building official or geotechnical data determines Site Class E or F soils are present at the site.

• Determine the maximum considered earthquake spectral response accelerations adjusted for site class effects, MSS at short period and 1MS at long period in accordance with IBC 1613.3.3.

saMS SFS = 11 SFS vM =

where: aF = Site coefficient defined in IBC Table 1613.3.3(1). vF = Site coefficient defined in IBC Table 1613.3.3(2).

162

• Determine the 5% damped design spectral response accelerations DSS at short

period and 1DS at long period in accordance with IBC 1613.3.4.

MSDS SS )3/2(= 11 )3/2( MD SS =

where: MSS = The maximum considered earthquake spectral response accelerations for

short period as determined in section 1613.3.3. 1MS = The maximum considered earthquake spectral response accelerations for

long period as determined in section 1613.3.3.

2- Determination of seismic design category and Importance factor:

Risk categories of buildings and other structures are shown in IBC Table 1604.5. Importance factors, Ie , are shown in ASCE 7-10 Table 1.5-2. Structures classified as Risk Category I, II or III that are located where the mapped spectral response acceleration parameter at 1-second period, 1S , is greater than or equal to 0.75 shall be assigned to Seismic Design Category E. Structures classified as Risk Category IV that are located where the mapped spectral response acceleration parameter at 1-second period, 1S , is greater than or equal to 0.75 shall be assigned to Seismic Design Category F. All other structures shall be assigned to a seismic design category based on their risk category and the design spectral response acceleration parameters,

163

DSS and 1DS , determined in accordance with Section 1613.3.4 or the site-specific procedures of ASCE 7. Each building and structure shall be assigned to the more severe seismic design category in accordance with Table 1613.3.5(1) or 1613.5.5(2), irrespective of the fundamental period of vibration of the structure.

164

3- Determination of the Seismic Base Shear:

The structural analysis shall consist of one of the types permitted in ASCE 7-10 Table 12.6-1, based on the structure’s seismic design category, structural system, dynamic properties, and regularity, or with the approval of the authority having jurisdiction, an alternative generally accepted procedure is permitted to be used. The analysis procedure selected shall be completed in accordance with the requirements of the corresponding section referenced in Table 12.6-1.

165

166

3.1 Equivalent Lateral Force Analysis: Section 12.8 of ASCE 7-10 shall be used.

• The seismic base shear V in a given direction is determined in accordance with the following equation:

WCV s=

where: W = effective seismic weight

The effective seismic weight, W, of a structure shall include the dead load above the base and other loads above the base as listed below:

1. In areas used for storage, a minimum of 25 percent of the floor live load shall be

included.

Exceptions a. Where the inclusion of storage loads adds no more than 5% to the effective seismic

weight at that level, it need not be included in the effective seismic weight.

b. Floor live load in public garages and open parking structures need not be included.

2. Where provision for partitions is required in the floor load design, the actual

partition weight or a minimum weight of 0.48 kN/m2 of floor area, whichever is

greater.

3. Total operating weight of permanent equipment.

sC = Seismic response coefficient

( )e

DS

IRS/

=

R = response modification factor, given in ASCE 7-10 Table 12.2-1 eI = importance factor

The value of sC shall not exceed the following:

( )e

Ds IRT

SC/1= for LTT ≤

167

( )e

LDs IRT

TSC/2

1= for LTT >

The value of sC shall not be less than:

01.0044.0 ≥= eDSs ISC

For structures located where 1S is equal to or greater than 0.6g, sC shall not be less than

( )es IR

SC/

5.0 1=

where: T = fundamental period of the structure

LT = long-period transition period, (given in ASCE 7-10 Figure 22), which is the transition period between the velocity and displacement-controlled portions of the design spectrum (about 5 seconds for Gaza Strip).

An approximate value of aT may be obtained from:

xnta hCT =

where: nh = height of the building above the base in meters tC = building period coefficient given in Table 12.8-2

x = constant given in Table 12.8-2

The calculated fundamental period, ,T cannot exceed the product of the coefficient, uC , in Table 12.8-1 times the approximate fundamental period, aT .

168

Table 12.8-1: Coefficient for upper limit on calculated period Design Spectral Response, 1DS Coefficient uC

4.0≥ 0.3 0.2

0.15 1.0≤

1.4 1.4 1.5 1.6 1.7

In cases where moment resisting frames do not exceed twelve stories in height and having a minimum story height of 3 m, an approximate period aT in seconds in the following form can be used: NTa 1.0= where N = number of stories above the base

169

3.2 Vertical Distribution of Seismic Forces:

VCF vxx = and

∑=

= n

ii

ki

kxx

vx

hw

hwC

1

where: xF = Lateral force at level x vxC = Vertical distribution factor

V = total design lateral force or shear at the base of the building xw and iw = the portions of W assigned to levels x and i

xh and ih = heights to levels x and i k = a distribution exponent related to the building period as follows: k = 1 for buildings with T less than or equal to 0.5 seconds k = 2 for buildings with T more than or equal to 2.5 seconds Interpolate between k = 1 and k = 2 for buildings with T between 0.5 and 2.5

3.3 Horizontal Distribution of Forces and Torsion: Horizontally distribute the shear xV

∑=

=x

iix FV

1

where: iF = portion of the seismic base shear, V , introduced at level i

Accidental Torsion, taM

taM = ( )BVx 05.0 Total Torsion, TM tatT MMM +=

F

F

F wn

wx

w1

h

hh

170

3.4 Story Drift:

The story drift, ∆ , is defined as the difference between the deflection of the center of mass at the top and bottom of the story being considered.

e

xedx I

C δδ =

Where:

dC = deflection amplification factor, given in Table 12.2-1 xeδ = deflection determined by elastic analysis

171

172

173

174

175

176

4- Seismic Load Effects and Combinations:

4.1 Seismic Load Effect Use DSQE DSE 2.0+= ρ for these combinations

Use DSQE DSE 2.0−= ρ for these combinations

The vertical seismic load effect, DSS , is permitted to be taken as zero when SDs is equal to or less than 0.125. 4.2 Load Effect with Over-strength Factor

177

4.3 Redundancy:

• The value of ρ is permitted to equal 1.0 for the following: 1. Structures assigned to Seismic Design Category B or C. 2. Drift calculation and P-delta effects. 3. Design of collector elements. 4. Design of members or connections where the seismic load effects including over-strength factor are required for design. 5. Diaphragm loads.

• For structures assigned to Seismic Design Category D, E, or F, ρ shall equal 1.3 unless one of the following two conditions is met, whereby ρ is permitted to be taken as 1.0:

a. Each story resisting more than 35 percent of the base shear in the direction of interest shall comply with Table 12.3-3. b. Structures that are regular in plan at all levels provided that the seismic force-resisting systems consist of at least two bays of seismic force-resisting perimeter framing on each side of the structure in each orthogonal direction at each story resisting more than 35 percent of the base shear. The number of bays for a shear wall shall be calculated as the length of shear wall divided by the story height or two times the length of shear wall divided by the story height, hsx , for light-frame construction.

178

Example (8): For the building shown in Example (1), using IBC 2012/ASCE 7-10, evaluate the forces at the floor levels perpendicular to axes 1-1, 2-2, 3-3 and 4-4. Note that site class is D, gSs 25.0= and gS 10.01= . Solution:

• Using Tables 1613.3.3(1) and 1613.3.3(2), short-period site coefficient 60.1=aF and long-period site coefficient 40.2=vF .

• Maximum considered earthquake spectral response accelerations adjusted for site class effects are evaluated.

( ) ggSFS saMS 4.025.060.1 === and

( ) ggSFS vM 24.010.040.211 === • The 5% damped design spectral response accelerations DSS at short period and

1DS at long period in accordance are evaluated.

( ) ggSS MSDS 267.040.032

32

===

( ) ggSS MD 16.024.032

32

11 ===

• Occupancy importance factor, 0.1=eI as evaluated from IBC 2012 Table 1604.5 and ASCE 7-10 Table 1604.5.

• From Table 1613.3.5(1) and for gSDS 267.0= , Seismic Design Category (SDC) is B. For gSD 16.01 = and using Table 1613.3.5(2), SDC is C. Therefore, seismic design category (SDC) is “C”.

• For ordinary shear walls and using ASCE 7-10 Table 12.2-1, response modification coefficient 0.5=R .

• The seismic base shear V in a given direction is determined in accordance with the following equation:

WCV s=

( ) ( )e

D

e

DSs IRT

SIR

SC//1≤=

01.0044.0 ≥≥ eDS IS

Approximate period ( ) .sec48.021049.0 75.0 ==aT ( ) .sec758.048.058.1 ==au TC > 0.48 sec.

179

<== 0534.00.5

267.0sC ( ) ( )267.0044.00667.0

48.0)0.5(16.0

>= O.K

i.e., 0534.0=sC The seismic base shear ( ) tonsV 89.964.18140534.0 ==

• Vertical distribution of forces:

VCF vxx = and ∑=

= n

ii

ki

kxx

vx

hw

hwC

1

K = 1.038 (from linear interpolation).

Shear forces ∑=

=x

iix FV

1

Vertical Distribution of Forces:

Level iw xh ( ) 038.1xx hw vxC

xF 7 259.2 21 495.09 0.35 34.26 6 259.2 18 361.61 0.26 25.02 5 259.2 15 249.39 0.18 17.26 4 259.2 12 158.26 0.11 10.95 3 259.2 9 88.05 0.06 6.09 2 259.2 6 38.54 0.03 2.67 1 259.2 3 9.38 0.01 0.65

0 ∑ 1814.4 0 1400.32 1.00 96.89

180

Calculation of Wind Loads on Structures according to ASCE 7-10 Permitted Procedures

The design wind loads for buildings and other structures, including the MWFRS and component and cladding elements thereof, shall be determined using one of the procedures as specified in the following section. An outline of the overall process for the determination of the wind loads, including section references, is provided in Figure (1).

Main Wind-Force Resisting System (MWFRS)

Wind loads for MWFRS shall be determined using one of the following procedures:

(1) Directional Procedure for buildings of all heights as specified in Chapter 27 for buildings meeting the requirements specified therein;

(2) Envelope Procedure for low-rise buildings as specified in Chapter 28 for buildings meeting the requirements specified therein;

(3) Directional Procedure for Building Appurtenances (rooftop structures and rooftop equipment) and Other Structures (such as solid freestanding walls and solid freestanding signs, chimneys, tanks, open signs, lattice frameworks, and trussed towers) as specified in Chapter 29;

(4) Wind Tunnel Procedure for all buildings and all other structures as specified in Chapter 31.

181

Figure (1): Dtermination of Wind Loads

182

Directional Procedure

Step 1: Determine risk category of building or other structure, see Table 1.5-1.

Step 2: Determine the basic wind speed, V, for the applicable risk category, see Figure 26.5-1A, B or C (United States). Basic wind speed is a three-second gust speed at 10 m above the ground in Exposure C.

Step 3: Determine wind load parameters:

• Wind directionality factor, , see Table 26.6.1

Table 26.6.1: Wind directionality factor,

183

The directionality factor used in the ASCE 7 wind load provisions for components and cladding is a load reduction factor intended to take into account the less than 100% probability that the design event wind direction aligns with the worst case building aerodynamics.

• Exposure category, for each wind direction considered, the upwind exposure shall be based on ground surface roughness that is determined from natural topography, vegetation, and constructed facilities.

Surface Roughness B: Urban and suburban areas, wooded areas, or other terrain with numerous closely spaced obstructions having the size of single-family dwellings or larger.

Surface Roughness C: Open terrain with scattered obstructions having heights generally less than 9.1 m. This category includes flat open country and grasslands.

Surface Roughness D: Flat, unobstructed areas and water surfaces. This category includes smooth mud flats, salt flats, and unbroken ice.

• Topographic factor, , see Figure 26.8-1. = (1 + ) , where , and are given in Fig. 26.8-1. For flat terrains, = . .

184

• Gust factor, G:

The gust effect factor for a rigid building is permitted to be taken as 0.85.

• Enclosure classification:

Open Building: A building having each wall at least 80 percent open. This condition is expressed for each wall by the equation Ao ≥ 0.8 Ag where

Ao = total area of openings in a wall that receives positive external pressure Ag = the gross area of that wall in which Ao is identified

185

Partially Enclosed Building: A building that complies with both of the following conditions: 1. The total area of openings in a wall that receives positive external pressure exceeds the sum of the areas of openings in the balance of the building envelope (walls and roof) by more than 10 percent. 2. The total area of openings in a wall that receives positive external pressure exceeds (0.37 m2) or 1 percent of the area of that wall, whichever is smaller, and the percentage of openings in the balance of the building envelope does not exceed 20 percent.

Enclosed Building: It is a building that is not classified as open or partially enclosed.

• Internal pressure coefficient, , see Table 26.11-1. Table 26.11-1; Internal Pressure Coefficient

Step 4: Determine velocity pressure exposure coefficient, , see Table 27.3-1. Note that is constant and calculated for mean height of the building, while varies with heights measured from the base of the building.

186

Step 5: Determine velocity pressure, , see equation below. = 0.613

where: = velocity pressure calculated at height z, (N/m2) = velocity pressure calculated at mean roof height h, (N/m2) = wind directionality factor = velocity pressure exposure coefficient = topographic factor = basic wind speed, in m/s

187

Step 6: Determine external pressure coefficients, (Figure 27.4-1)

188

Step 7: Determine wind pressure, p, on each building surface (enclosed and partially enclosed). = − ( ) Design wind load cases are shown in Figure 27.4-8.

189

190

Example: It is required to calculate the lateral wind loads acting on the 8-story building, considering that the wind acts in the North-South direction. The building which is used as headquarter for police operation, is 30 m x 15 m in plan as shown in the figure (enclosed), and located right on the Gaza Beach (flat terrain). Note: Use a basic wind speed of 100 Km/hr and ASCE 7-10 Directional Procedure.

Plan

Elevation

191

Step 1: Building risk category: • Based on Table 1.5-1, building risk category is IV.

Step 2: Basic wind speed:

• It is given as 100 km/hr.

Step 3: Building wind load parameters: • 85.0=dK (wind directionality factored evaluated from Table 26.6.1) • Exposure category is D • 0.1=ztK (Topographic factor for flat terrain) • Gust factor, G , is 0.85 for rigid buildings • Building is enclosed • Internal pressure coefficient for enclosed buildings, , is 18.0±

Step 4: Velocity pressure coefficients, hK and zK :

• 384.1=hK (Interpolating from Table 27.3-1) and zK varies with height

Step 5: Determine velocity pressure, hq and zq :

• 2613.0 VKKKq dzthh =

( ) ( ) ( ) 22

/43.5566060

000,10085.00.1384.1613.0 mN=

∗

=

• 2613.0 VKKKq dztzz =

( ) ( ) ( ) 22

/05.4026060

000,10085.00.1613.0 mNKK zz =

∗

=

Step 6: External pressure coefficients, pC :

For 5.03015B/L == and using Figure 27.4.1, the external pressure coefficients are

shown in the figure.

192

Step 7: Wind pressure, p : For the windward walls,

( )piipz CGqCGqp −= ( )( ) ( )( )18.085.043.5568.085.0 ±−= zq

( ) (max)/13.8568.0 2mNqz ±=

For the leeward walls, ( )piiph CGqCGqp −=

( )( ) ( )( )18.085.043.5565.085.043.556 ±−−= (max)/62.321 2mN−=

For the side walls, ( )piiph CGqCGqp −=

( )( ) ( )( )18.085.043.5567.085.043.556 ±−−= (max)/21.416 2mN−=

Height, meters

zK zq p 0 to 4.6 m 1.03 414.17 366.76 4.6 to 6.1m 1.08 434.17 380.36 6.1 to 7.6 m 1.12 450.28 391.32 7.6 to 9.1 m 1.16 466.39 402.27 9.1 to 12.2 m 1.22 490.56 418.71 12.2 to 15.2 m 1.27 510.56 432.31 15.2 to 18 m 1.31 526.67 443.26 18 to 21.3 m 1.34 538.89 451.57 21.3 to 24.4 m 1.38 554.72 462.34 24.4 to 25 m 1.40 562.78 467.82

193

Moment Frames

Based on ACI 2.2, Moment Frames are defined as frames in which members and

joints resist forces through flexure, shear, and axial force. Moment frames are

categorized as follows:

• Ordinary Moment Frames — Concrete frames complying with the

requirements of Chapters 1 through 18 of the ACI Code. They are used in

regions of low-seismic risk.

• Intermediate Moment Frames — Concrete frames complying with the

requirements of 21.3 in addition to the requirements for ordinary moment

frames. They are used in regions of moderate-seismic risk.

• Special Moment Frames — Concrete frames complying with the

requirements of 21.5 through 21.8, in addition to the requirements for

ordinary moment frames. They are used in regions of moderate and high-

seismic risks.

194

Beam-Column Joints

A- Corner Joints:

A-1 Opening: If a corner joint of a rigid frame tends to be opened by the applied moments it is called “opening joint”.

Measured Efficiency of Opening Joints

195

A-2 Closing: If a corner joints tends to be closed by the applied moments it is called “closing joints”.

B- T- Joints:

196

Exterior Beam Column Joint

C- Cross- Joints:

(a) Forces due to gravity loads (b) Forces due to lateral loads

197

Design Of Non-seismic Beam-Column Joints According To ACI 352

The ACI committee 352R-02 report on the design of reinforced concrete beam-column joints (Recommendations for Design of Design of Beam-column Joints in Monolithic Reinforced Concrete Structures) divides joints into two groups depending on the deformation of the joints.

(a) Non-seismic joints, which are joints not subjected to large inelastic deformations and need not be designed according to ACI Chapter 21.

(b) Seismic joints, which are joints designed to sustain large inelastic deformations, according to ACI Chapter 21.

In the following section, design of non-seismic joints is to be dealt with. Shear Forces at the Joint: Consider the equilibrium of the upper half of the joint as shown in the figure. The horizontal shear at mid-height of an exterior beam-column joint intjo,uV is given by

.int, colnjou VTV −= Where:

nT = normal force in the top steel in the joint = ys fAα and 0.1=α

.colV = column shear, which can be evaluated from frame analysis or from the free body diagram assuming the points of inflection at mid-height of each story. For an interior beam-column joint, the horizontal shear at mid-height of the joint

intjo,uV is given by

.21int, colnnjou VCTV −+=

Where: 1nT = normal force in the top steel in the joint = ys fAα and 0.1=α

2nC = compressive force in concrete to the other side of the joint

198

Shear Strength of the Joint: The nominal shear strength on a horizontal plane at mid-height of the joint is given by

.'265.0 coljcn hbfT γ= The factored shear force on a horizontal plane at mid-height of the joint is to satisfy the following equation.

nu VV φ= Where: beam-column joint intjo,uV is given by γ = constant related to the confinement of the joint

.colh = column dimension parallel to the shear force direction jb = effective width of the joint

= .colb.colb hb

2bb

+≤+

bb = width of the beam parallel to the applied force cb = dimension of the column perpendicular to the applied force

φ = strength reduction factor for shear = 0.75

If the previous equation is not satisfied, either the size of the column needs to be increased or the shear force transferred to the joint needs to be decreased.

199

Width of Joint, jb

Values of Type-I joints, γ

200

201

Values of γ (ACI 352R-02)

Anchorage requirements at the Joint: Beam reinforcement terminating in a non-seismic joint should have 90-deg hooks with

c

bdh f

dl′

= 318 where dhl is not to be less than db8 nor less than 15 cm.

The critical section for developing tension in the beam reinforcement is taken at the face of the joint. If the development length for hooked bars dhl is not satisfied, either the size of the column will need to be increased or the amount of shear being transferred to the joint will need to be decreased. Transverse Reinforcement at the Joint:

ACI committee 352 recommends that non-seismic joints be provided with at least two layers of transverse reinforcement (ties) between the top and bottom levels of longitudinal reinforcement in the deepest beam framing into the joint. For gravity load only maximum spacing is kept to 30 cm and to 15 cm for non-seismic lateral loads.

202

Example (8):

Check the adequacy of Joint "B" in terms of shear resistance.

Note that story height is 3.0 m, 2c cm/Kg300'f = and 2

y cm/Kg4200f = .

Solution:

Shear force at centreline of joint

.colnintjo,u VTV −=

Where ysn fAT α= and 0.1=α for non-seismic joints

( )( ) tons922.1311000

420041.310.1Tn ==

From equilibrium of forces, nn TC = and

( )( )( ) ( )1000922.13140a30085.0 = and a = 12.93 cm

203

cm75.7125.121480d =−−−−=

( ) ( )( ) [ ] m.t125.862/93.1275.7110

420041.312/adfAM5ysn =−=−=

( ) npc.col MlV = and tons708.283/125.863/MV n.col ===

tons214.103708.28922.131V intjo,u =−=

K.Ocm)6040(cm402

4040b j +≤=+

=

( ) ( )( ) tons32.2201000

604030020265.0hb'f265.0V .coljcn ==γ=

( ) tons214.103tons24.16532.22075.0Vn >==Φ

i.e., joint is adequate in terms of resisting shear

Two ties, as a minimum, are to be provided at the joint, where

y

wv f

SbA 5.3min, =

For mm10φ bars (3-legged)

( )( )( ) cmS 65.70405.3

4200785.03==

Provide two sets of mm10φ ties (3-legged) spaced at 30 cm (Smax = 30 cm)

204

Anchorage of top reinforcement in girder: ( ) cm

fdlc

bdh 72.36

3002318

'318

===

Available development length = 60 - 4 - 1 - 2 - 2.5 = 50.50 cm > 36.72 cm O.K

205

A- Flexural Members (Beams) of Special Moment Frames Requirements of ACI 21.5 are applicable for special moment frame members proportioned primarily to resist flexure with factored axial forces gc Af ′≤ 1.0 . If such members are subjected to axial forces gc Af ′> 1.0 , they are treated as beam-columns.

1- General Requirements:

• Clear span for the member, nl , shall not be less than four times the effective span.

• Width of member, wb , is not to be less than the smaller of 0.3 h and 25

cm, where wb is web width and h is overall thickness of member. • Width of member is not to be more than the width of supporting member

plus distances on each side of the supporting member equal to the smaller of (a) and (b):

(a) Width of supporting member in the direction of the span, C2, and

(b) 0.75 times width of the supporting member in direction perpendicular to C2.

2- Longitudinal Reinforcement: • Minimum amounts of top as well as bottom reinforcement, min,sA , is not

to be less than the larger of

y

wc

fdbf '80.0

and y

w

fdb14

This requirement needs not be satisfied if the tension reinforcement provided at every section is 1/3 larger than required by analysis. • Maximum reinforcement ratio is not to exceed 0.025. • At least two bars are to be provided continuously both top and bottom. • Positive moment strength at joint face is not to be less than ½ of the

negative moment strength provided at the face of the joint. • The negative or positive moment at any section along the member is not

to be less than ¼ the maximum moment strength provided at face of either joint.

206

• Lap splices of flexural reinforcement are permitted only if hoop or spiral reinforcement is provided over the lap length. Maximum spacing of the transverse reinforcement in the lap region is not to exceed the smaller of d/4 or 10 cm.

• Lap splices are not to be used within the joints, within a distance of twice the member depth from the face of the joint, and at locations where analysis indicates flexural yielding caused by inelastic lateral displacements of the frame.

Reinforcement Requirements for Flexural Members of Special Moment Frames

3- Transverse Reinforcement:

• Hoops are to be provided in the following regions of frame members: (a) Over a length equal to twice the member depth measured from the face of

the supporting member toward mid span, at both end of the flexural member;

(b) Over lengths equal to twice the member depth on both sides of a section where flexural yielding is likely to occur in connection with inelastic lateral displacements of the frame.

• The first hoop is to be located at a distance not more than 5 cm from the face of the supporting member. Spacing of such reinforcement is not to exceed the smallest of: d/4,

bd8 where bd is the diameter of the smallest longitudinal

bars, 24 times the diameter of hoop bars and 30 cm.

207

• Where hoops are required, they are arranged in away similar to that of column ties.

• Where hoops are not required, stirrups with seismic hooks at both ends are to spaced at a distance not more than d/2 throughout the length of the member.

• Hoops in flexural members are permitted to be made up of two pieces of reinforcement: a stirrup having seismic hooks at both ends and closed by a crosstie. Consecutive crossties engaging the same longitudinal bar shall have their 90 deg hooks at opposite sides of a flexural member. If the longitudinal reinforcing bars secured by the crossties are confined by a slab on only one side of the flexural frame member, the 90-degree hooks of the crossties shall be placed on that side.

Transverse Reinforcement for Flexural Members of Special Moment Frames

208

Splices and Hoop Reinforcement for Flexural Members of Special Moment Frames

3- Shear Strength Reinforcement:

• The design shear force, eV , is to be determined from consideration of the

static forces on the portion of the member between faces of the joint. It is assumed that moments of opposite sign corresponding to probable flexural moment strength, prM , act at the joint faces and that the member is loaded with the factored tributary gravity load along its span. For calculation of prM it is assumed that tensile strength in the longitudinal bars is 1.25 yf and a strength reduction factor φ of 1.0.

( )( )2/25.1 adfAM yspr −=

209

where ( )

bffA

ac

ys

'85.025.1

=

• Transverse reinforcement over the lengths identified in 3(a) and 3(b) shall be

proportioned to resist shear assuming 0=cV when both of the following conditions occur: (a) The design shear force, eV , represents ½ or more of the maximum

required shear strength within these lengths; (b) The factored axial compressive force, uP , including earthquake

effects is less than cg fA '05.0 .

Design Shear Forces For Flexural Members of Special Moment Frames

210

Example (8):

Design the transverse reinforcement for the potential hinge regions of the earthquake resisting beam in a monolithic reinforced concrete frame shown in the figure. The beam which is part of a special moment resisting frame is subjected to a service dead load of 3.0 t/m and a service live load of 2.0 t/m. Note that 2

c cm/Kg300'f = and 2y cm/Kg4200f = .

Solution: In this example requirements of section 21.5 of ACI 318-08 are to be satisfied.

A- ACI 21.5.1 "Scope": • Based on ACI 21.5.1.1, factored axial compressive force acting on the

member gc A'f1.0< . (O.K)

211

• Based on ACI 21.5.1.2, clear span of beam is not to be less than four times its effective depth.

cm75.5325.11460d =−−−=

0.43.1775.53

930 >= (O.K)

• Based on ACI 21.5.1.3, the width-to-depth ratio is not to be less than 0.30. • Based on ACI 21.5.1.3, width of beam is not to be less than 25 cm. (O.K)

30.075.06045 >= (O.K).

- Width of beam is not to be more than column width plus three-fourths depth of beam on each side of the column. Width of beam = width of column. (O.K)

B- ACI 21.5.2 "Longitudinal Reinforcement": • Based on ACI 21.5.2.1, minimum ratio of top as well as bottom

reinforcement is not to be less than the larger of:

0033.04200

06.14= and 00327.0

4200300792.0

=

( ) ( ) 0033.000406.075.5345

817.9providedmin >==ρ (O.K)

- Maximum reinforcement ratio is not to exceed 0.025. ( ) ( ) 025.001217.0

75.5345452.29providedmax <==ρ (O.K)

- At least two bars are to be provided continuously top and bottom. mm252 φ bars are provided throughout the length of the beam on the top side,

while mm254 φ bars are provided continuously on the bottom side. (O.K)

• Based on ACI 21.5.2.2, positive moment strength at joint face is not to be less than 1/2 of the negative moment strength provided at the face of the joint.

Positive moment strength at face of joint is evaluated as follows:

( ) ( ) ( )2/adfAveM yve,sn −=+ +

From equilibrium of forces, ( ) ( )veTveC nn +=+ and

( )( )( ) ( )420063.1945a30085.0 = and cm18.7a =

212

( ) ( )( ) [ ] m.t35.412/18.775.5310

420063.19veM

5n =−=+

Negative moment strength at face of joint is evaluated as follows:

( ) ( ) ( )2/adfAveM yve,sn −=− −

From equilibrium of forces, ( ) ( )veTveC nn −=− and

( )( )( ) ( )420045.2945a30085.0 = and cm78.10a =

( ) ( )( ) [ ] m.t82.592/78.1075.5310

420045.29veM5n =−=+

Thus, ( ) ( )2

veMveM nn

−>+ at face of joint. (O.K)

- The negative or positive moment at any section along the member is not to be less than 1/4 the maximum moment strength provided at face of either joint.

At section of least reinforcement moment strength is evaluated as follows:

From equilibrium of forces, nn TC = and

( )( )( ) ( )4200817.945a30085.0 = and cm59.3a =

( )( ) [ ] m.t482.59m.t42.212/59.375.53

104200817.9M 5n >=−= (O.K)

• Based on ACI 21.5.2.3, lap splices of flexural reinforcement are permitted only if hoop or spiral reinforcement is provided over the lap length. Maximum spacing of the transverse reinforcement in the lap region is not to exceed the smaller of d/4 or 10 cm. Thus, maximum spacing is not to exceed 10 cm within the lap length.

- Lap splices are not to be used (a) within the joints; (b) within a distance of twice the member depth from the face of the joint and (c) at locations where analysis indicates flexural yielding caused by inelastic lateral displacements of the frame.

213

Development length of top bars (in tension):

b

cb

trb

setyd d

fd

Kcf

l

+=

'5.3 λ

ψψψ

3.1=tψ , 1=eψ , 1=sψ , and 1=λ bc = 4.0 + 1.0 + 1.25 = 6.25 cm

or bc = [(45 – 4 (2) – 2 (1) – 2.5]/ (2) = 16.25 cm

i.e., bc is taken as 6.25 cm

( ) cmnsAK tr

tr 14.32)10(

)785.0)(2(4040===

5.2756.35.2

14.325.6>=

+=

+

b

trb

dKc , taken as 2.5.

( )

( )( ) 07.905.2

3005.25.33.14200

=

=dl

Required development length cm90ld = Development length of bottom bars (in tension):

b

cb

trb

setyd d

fd

Kcf

l

+=

'5.3 λ

ψψψ

1=tψ , 1=eψ , 1=sψ , and 1=λ bc = 4.0 + 1.0 + 1.25 = 6.25 cm

or bc = [(45 – 4 (2) – 2 (1) – 2.5]/ (6) = 5.42cm

i.e., bc is taken as 5.42 cm

( ) cmnsAK tr

tr 57.14)10(

)785.0)(2(4040===

214

5.279.25.2

57.142.5>=

+=

+

b

trb

dKc , taken as 2.5.

( )( ) 28.695.2

3005.25.34200

=

=dl

Required development length cm70ld =

C- ACI 21.5.3 "Transverse Reinforcement":

• Based on ACI 21.5.3.1, hoops are to be provided in the following regions of frame members:

(c) Over a length equal to twice the member depth measured from the face of the supporting member toward mid span, at both end of the member;

(d) Over lengths equal to twice the member depth on both sides of a section where flexural yielding is likely to occur in connection with inelastic lateral displacements of the frame.

• Based on ACI 21.5.3.2, the first hoop is to be located at a distance not more than 5 cm from the face of the supporting member. Maximum spacing of such reinforcement is not to exceed the smallest of: d/4, bd8 where bd is the diameter of the smallest longitudinal bars; 24 times the diameter of hoop bars, and 30 cm.

Hoops are to be provided over a distance of 2 h = 120 cm from faces of joints.

Maximum hoop spacing ( )( )

cm30cm24124d24cm205.28d8

cm44.134/75.534/d

h

b

=======

≤ , taken as 12.5 cm.

• Based on ACI 21.5.3.3, where hoops are required they are arranged in away similar to that of column ties.

215

• Based on ACI 21.5.3.4, where hoops are not required, stirrups with seismic hooks at both ends are to spaced at a distance not more than d/2 throughout the length of the member. Maximum spacing = d/2 = 53.75/2 = 26.875 cm, taken as 25 cm.

D- ACI 21.5.4 "Shear Strength Requirements":

• Based on ACI 21.5.4.1, the design shear force eV is to be determined from consideration of the static forces on the portion of the member between faces of the joint. It is assumed that moments of opposite sign corresponding to probable flexural moment strength prM act at the joint faces and that the member is loaded with the factored tributary gravity load along its span. For calculation of prM it is assumed that tensile strength in the longitudinal bars is 1.25 yf and a strength reduction factor φ of 1.0.

216

( ) ( ) m/t6.425.032.1wu =+=

( ) t39.212/3.96.42

wclu

==

( ) ( ) ( )2/adfveA25.1veM yspr −+=+ ( )( )( ) ( )( )420063.1925.145a30085.0 = and cm98.8a =

( ) ( )( ) [ ] m.t77.502/98.875.5310

420063.1925.1veM5pr =−=+

( ) ( ) ( )2/adfveA25.1veM yspr −−=− ( )( )( ) ( )( )420045.2925.145a30085.0 = and cm47.13a =

( ) ( )( ) [ ] m.t69.722/47.1375.5310

420045.2925.1veM5pr =−=−

( ) ( )

t27.133.9

69.7277.50l

M

c

veMvepr pr =+

=

−++

t66.3439.2127.13V max,e =+= For sway to the right max,eV occurs at the right side, while it occurs at the left side for sway to the left.

• Based on ACI 21.5.4.2, transverse reinforcement over the lengths identified

in 3(a) and 3(b) shall be proportioned to resist shear assuming 0Vc = when both of the following conditions occur: (b) The design shear force represents ½ or more of the maximum required

shear strength within these lengths; (c) The factored axial compressive force including earthquake effects is

less than cg 'fA05.0 . Seismic induced shear tons2/66.34tons27.13 <= and the above-mentioned requirement is not applicable.

( )( ) tons20.221000/75.534530053.0db'f53.0V cc ===

cns VVV −= and cu

s VVV −Φ

=

tons01.2420.2275.066.34Vs =−=

For two-legged 10 mm transverse reinforcement,

217

( )( )( ) )1000(01.24S

75.534200785.02S

dfAV yv

s === and cms76.14S=

Use two-legged 10 mm stirrups @ 12.5 cm, cms12.14S= Stirrups at other locations:

At the end of the hoop region, 3.91.8

12.866.3412.8Vu =

++ and tons14.29Vu =

cns VVV −= and cu

s VVV −Φ

=

tons65.1620.2275.014.29Vs =−=

For two-legged 10 mm transverse reinforcement, ( )( )( ) )1000(65.16

S75.534200785.02

SdfA

V yvs === and cms28.21S= < 53.75/2

cm Use 10 mm stirrups @ 20 cm.

218

219

B- Special Moment Frame Members Subjected to Bending and Axial Load Requirements of ACI 21.6 are applicable for special moment frame members proportioned to resist axial forces gc Af ′> 1.0 .

1- General Requirements:

• The shortest cross-sectional dimension, measured on a straight line passing through the geometric centroid, shall not be less than 30 cm.

• The ratio of shortest cross-sectional dimension to the perpendicular dimension shall not be less than 0.40.

2- Minimum Flexural Strength of Columns:

• The flexural strengths of the columns shall satisfy the following equation:

∑∑ ≥ nbnc M2.1M Where ∑ ncM = sum of nominal flexural strengths of columns framing into the joint, evaluated at the faces of the joint. Column flexural strength shall be calculated for the factored axial force, consistent with the direction of the lateral forces considered, resulting in the lowest flexural strength. ∑ nbM = sum of nominal flexural strengths of the beams framing into the joint, evaluated at the faces of the joint. Flexural strengths shall be summed such that the column moments oppose the beam moments. The intent of the above equation is to reduce the likelihood of inelastic action. If columns are not stronger than beams framing into a joint, flexural yielding can occur at both ends of all columns in a given story, resulting in a column failure mechanism that can lead to collapse.

• Columns not satisfying the previous equation shall be ignored in determining the calculated strength and stiffness of the structure, and shall conform to ACI 21.13 (frame members not proportioned to resist forces induced by earthquake motions).

220

Strong column-weak beam requirements for special moment frames

3- Longitudinal Reinforcement: • The reinforcement ratio gρ shall not be less than 0.01 and shall not

exceed 0.06. • Lap splices are permitted only within the center half of the member

length, and shall be designed as tension lap splices and enclosed within transverse reinforcement conforming to ACI 21.6.4.2 and 21.6.4.3.

Typical lap splice details of columns in special moment frames

221

4- Transverse Reinforcement:

• Transverse reinforcement shall be provided over a length ol from each joint face and on both sides of any section where flexural yielding is likely to occur as a result of inelastic lateral displacements of the frame. The length ol shall not be less than the largest of:

(a) The depth of the member at the joint face or that section where flexural yielding is likely to occur;

(b) 1/6 of the clear span of the member; and (c) 45 cm.

• Transverse reinforcement shall be provided by either single or overlapping hoops, spirals, circular hoops or rectilinear hoops, with or without crossties. Crossties of the same or smaller bar size as the hoops shall be permitted. Each end of the crossties shall engage a peripheral long reinforcing bar. Consecutive crossties shall be alternated end for end and along the longitudinal reinforcement. Spacing of cross ties or legs of rectilinear hoops,

xh , within a cross section of the member shall not exceed 35 cm on center.

Example of transverse reinforcement in columns

• Spacing of transverse reinforcement along the length ol of the member shall not exceed the smallest of (a), (b) and (c): (a) one-quarter of the minimum member dimension;

222

(b) six times the diameter of the smallest longitudinal bar, and

(c)

−

+=3

3510 xhso , where os shall not exceed 15 cm and need not be

taken less than 10 cm. In the same expression xh is maximum horizontal spacing of hoop or crosstie legs on all faces of the column.

• The volumetric ratio of spiral or circular hoop reinforcement

sρ shall not be less than the larger value evaluated from the following equations:

yt

cs f

f '12.0=ρ

yt

c

ch

gs f

fAA '145.0

−=ρ

where

ytf = yield stress of the transverse reinforcement

gA = gross cross-sectional area of concrete section

chA = cross-sectional area of a structural member measured to the outside edges of transverse reinforcement.

• The total cross-sectional area of rectangular hoop reinforcement shall not be less than that required by the following equations:

−

= 1'30.0

ch

g

yt

ccsh A

Af

fbsA

yt

ccsh f

fbsA '09.0=

Where =s center-to-center spacing of transverse reinforcement measured along the

longitudinal axis of the structural member =cb cross-sectional dimension of column core measured to the outside

edges of the transverse reinforcement composing shA =chA cross-sectional area of a structural member measured to the outside

edges of transverse reinforcement

223

• Beyond the length ol , the column shall contain spiral or hoop reinforcement with center-to-enter spacing, s , not exceeding the smaller of six times the diameter of the smallest longitudinal column bars and 15 cm.

• Columns supporting reactions from discontinued stiff members, such as

walls, shall satisfy (a) and (b): (a) Transverse reinforcement as required in 4 shall be provided over their full height at all levels beneath the discontinuity if the factored axial compressive force in these members, related to earthquake effect, exceeds gc Af '1.0 . Where design forces have been magnified to account for the over strength of the vertical elements of the seismic-force-resisting system, the limit of

gc Af '1.0 shall be increased to gc Af '25.0 . • (b) The transverse reinforcement shall extend into the discontinued member

at least dl of the largest longitudinal column bar, where dl is determined in accordance with ACI 21.7.5. Where the lower end of the column terminates on a wall, the required transverse reinforcement shall extend into the wall at

least dl of the largest longitudinal column bar at the point of termination. Where the column terminates on a footing or mat, the required transverse reinforcement shall extend at least 30 cm into the footing or mat.

Confinement requirements at column ends

(a) Spiral hoop reinforcement

224

Confinement requirements at column ends (b) Rectangular hoop reinforcement

Columns supporting discontinued stiff members

225

5- Shear Strength Requirements: • The design shear force, eV , is to be determined from consideration of

maximum forces that can be generated at the faces of the joint at each end of the member. These joint forces shall be determined using the maximum probable moment strengths, prM , of the member associated with the range of

factored axial loads, uP , acting on the member. The member shears need not exceed those determined from joint strengths based on the probable moment strength prM of the transverse members framing into the joint. In no case shall eV be less than the factored shear determined by analysis of the structure.

• Transverse reinforcement over the length ol shall be proportioned to resist

shear assuming 0=cV when both (a) and (b) occur: i. The earthquake-induced shear force represents ½ or more of the maximum

required shear strength within ol ; ii. The factored axial compressive force, uP , including earthquake effects is

less than cg fA '05.0 .

Loading cases for design of shear reinforcement in columns of special

moment frames

226

Example (9):

For the column shown in the figure, check the requirements of ACI 21.6 in relation to columns which are part of special moment frames. Note that design column loads are: tons337Pu = and tons4.84Mu = . Use 2

c cm/Kg300'f = and 2y cm/Kg4200f = .

227

Solution: A- ACI 21.6.1 "Scope": • Based on ACI 21.6.1, ( )( )( ) tons337tons5.941000/70453001.0A'f1.0 gc <== .

Thus, requirements of section ACI 21.6 apply. • Based on ACI 21.6.2, the shortest cross-sectional dimension, measured on a

straight line passing through the geometric centroid shall not be less than 30 cm. This requirement is satisfied since shortest cross-sectional dimension = 45 cm.

• The ratio of the shortest cross-sectional dimension to the perpendicular dimension shall not be less than 0.40. Ratio = 40.064.0

7045 >= (O.K)

B- ACI 21.6.2 "Minimum Flexural Strengths of Columns":

• Based on ACI 21.6.2.2, the flexural strengths of the columns shall satisfy the following equation:

∑≥∑ gc M2.1M

Considering the columns on both sides of the joint are of equal flexural strengths, the flexural strength of each of the columns is determined using strength interaction diagrams.

228

01558.0g =ρ , ksi4'f c ≅ , ( ) ( ) 821.070

5.2124270=

−−−=γ , tons337Pu =

( )( )( )( ) 55.0

457030065.01000337

/ ===gc

nn Af

PK

Using nominal load-moment strength interaction diagram, L4-

60.80, 165.0' =hAf

M

gc

n and mtMn .15.109=

From example (8), ( ) ( ) m.t35.41veMveM nlnr =+=+ and ( ) ( ) m.t82.59veMveM nlnr =−=−

mtMc .30.21815.10915.109 =+=∑ , m.t17.10182.5935.41Mg =+=∑

2.116.217.1013.218

>==∑∑

g

c

MM (O.K)

C- ACI 21.6.3 "Longitudinal Reinforcement": • Based on ACI 21.6.3.1, the reinforcement ratio gρ shall not be less than 0.01

and shall not exceed 0.06.

( )( ) 01558.07045

087.49g ==ρ (O.K)

• Based on ACI 21.6.3.2, lap splices are only permitted within the center half of the member length and shall be designed as tension lap splices enclosed within transverse reinforcement conforming to ACI 21.6.4.2 and 21.6.4.3. Length of lap splice of longitudinal bars (in tension): For Class "B" lap splice, dsp l3.1l =

b

cb

trb

setyd d

fd

Kcf

l

+=

'5.3 λ

ψψψ

1=tψ , 1=eψ , 1=sψ , and 1=λ bc = 4.0 + 1.0 + 1.25 = 6.25 cm

or bc = [(45 – 4 (2) – 2 (1) – 2.5]/ (8) = 4.0625 cm

i.e., bc is taken as 4.0625 cm

229

Ignoring the effect of transverse reinforcement, 0K tr =

5.2625.15.2

00625.4<=

+=

+

b

trb

dKc

( )( )

( ) 59.1065.2300625.15.3

0.14200=

=dl

Required splice length ( ) cmlsp 57.13859.1063.1 == , taken as 140 cm.

• Based on ACI 21.6.4.2, transverse reinforcement shall be spaced at a distance not exceeding (a) one-quarter of the minimum member dimension, (b) six times the diameter of the longitudinal reinforcement, and (c)

−

+=3

3510 xhso , where oS is maximum longitudinal spacing of transverse

reinforcement, shall not exceed 15 cm and need not be taken less than 10 cm. In the same expression xh is maximum horizontal spacing of hoop or crosstie legs on all faces of the column.

Maximum vertical spacing of transverse reinforcement is not to exceed the smallest of : i. 45/4 = 11.25 cm

ii. 6 (2.5) = 15 cm

iii.

−

+=3

3510 xhso = 10 cm

( ) cm5.302

14270h x =−−

= . Thus maximum spacing is limited to 10 cm

(based on the minimum of a, b and c). • Based on ACI 21.6.4.3, crossties or legs of overlapping hoops shall not be

spaced more than 35 cm on center-to-center in the direction perpendicular to the longitudinal axis of a structural member. Two cross ties are added to the present mm10φ hoops to satisfy this requirement (maximum spacing of 35 cm).

D- ACI 21.6.4 "Transverse Reinforcement":

• Based on ACI 21.6.4.1 (b), the total cross-sectional area of rectangular hoop reinforcement shall not be less than that required by ACI equations (21-4) and (21-5).

For shear in the direction of longer side of the column:

230

( )( )( ) ( )( )

21 96.21

62377045

420030037103.0 cmAsh =

−=

( )( )( ) 2'1 38.2

4200300371009.0 cmAsh ==

i.e., 21 96.2 cmAsh =

Use mm12φ tie plus one mm10φ cross tie ( 204.3 cmAsh = )

For shear in the direction of shorter side of the column: ( )( )( ) ( )

( )2

2 96.4162377045

420030062103.0 cmAsh =

−=

( )( )( ) 2'2 98.3

4200300621009.0 cmAsh ==

i.e., 22 96.4 cmAsh =

Use mm12φ tie plus three mm12φ cross ties ( ( ) 2

sh cm65.513.15A == )

• Based on ACI 21.6.4.4, transverse reinforcement in amount specified before shall be provided over a length ol from each joint face and on both sides of any section where flexural yielding is likely to occur as a result of inelastic lateral displacements of the frame. The length ol shall not be less than the largest of:

(d) The depth of the member at the joint face = 70 cm (e) 1/6 of the clear span of the member= 400/6 = 66.67 cm (f) 45 cm.

i.e., ol = 70 cm.

• Based on ACI 21.6.4.6, where transverse reinforcement as specified before is not provided throughout the full length of the column, the remainder of the column length shall contain spiral or hoop reinforcement with center-to-

231

center spacing not exceeding the smaller of six times the diameter of the longitudinal column bars or 15 cm. Smax = the larger of 6 (2.5) cm and 15 cm = 15 cm

E- ACI 21.6.5 "Shear Strength Reinforcement": • The design shear force eV is to be determined from consideration of

maximum forces that can be generated at the faces of the joint at each end of the member. These joint forces shall be determined using the maximum probable moment strengths prM of the member associated with the range of factored axial loads on the member. The member shears need not exceed those determined from joint strengths based on the probable moment strength

prM of the transverse members framing into the joint. In no case shall eV be less than the factored shear determined by analysis of the structure.

( ) ( ) tons865.30

477.5069.7277.5069.722/1Ve =

+++= (see Example 8 for prM

values)

cm55.6325.12.1470d =−−−= ( )( ) tons25.261000/55.634530053.0Vc == (neglecting effect of axial force)

cns VVV −= and cu

s VVV −Φ

=

tons90.1425.2675.0865.30Vs =−=

SdfA

V yvs = and ( )

( ) 0558.055.634200

10009.14df

VS

A

y

sv ===

232

( ) 0558.00375.04200

455.3S

A

min

v <==

(O.K)

For cms10S= , 2v cm558.0A =

Available vA (within the length ol ) = 3.04 cm2 > 0.558 (O.K) .

233

234

C- Joints of Special Moment Frames

Requirements of ACI 21.7 are applicable for joints of special moment frames.

1- General Requirements: • Forces in longitudinal beam reinforcement at the joint face shall be

determined by assuming that the stress in the flexural tensile reinforcement is yf25.1 .

• Beam longitudinal reinforcement terminated in a column shall be extended to the far face the confined column core and anchored in tension according to 21.7.5 and in compression according to chapter 12.

• Where longitudinal beam reinforcement extends through abeam-column joint, the column dimension parallel to the beam reinforcement shall not be less than 20 times the diameter of the largest longitudinal bar.

1- Transverse Reinforcement:

• Transverse reinforcement as discussed in B shall be provided within the joint, unless the joint is confined by structural members as shown below.

• Within the depth of the shallowest framing member, transverse reinforcement equal to at least ½ the amount shown in B shall be provided where members frame into all four sides of the joint and where each member width is at least ¾ the column width. At these locations spacing is permitted to be increased to 15 cm.

• Transverse reinforcement as required in B shall be provided through the joint to provide confinement for longitudinal beam reinforcement outside the column core if such confinement is not provided by a beam framing into the joint.

Effective area of joint

235

2- Shear Strength: • The nominal shear strength of the joint shall not be taken greater

than the values specified below: - For joints confined on all four sides jc Af ′3.5 - For joints confined on three faces or on two opposite faces jc Af ′4 - For others jc Af ′2.3

A member that frames into a face is considered to provide confinement to the joint if at least ¾ of the face of the joint is covered by the framing member. A joint is considered to be confined if such members frame into all faces of the joint.

jA is the effective cross-sectional area within a joint computed from joint depth times effective joint width. Joint depth shall be the overall depth of the column, h. Effective joint width shall be the overall width of the column, except where a beam frames into a wider column, effective joint width shall not exceed the smaller of (a) and (b): (a) Beam width plus joint depth (b) Twice the smaller perpendicular distance from longitudinal axis of beam to column side.

3- Development length of bars in tension:

• The development length dhl for a bar with a standard 90 degree hook shall not be less than the largest of

bd8 , 15 cm, and the length required by the following equation which is applicable to bar diameters ranging from 10 mm to 36 mm.

c

bydh f

dfl

′=

2.17

The 90-degree hook shall be located within the confined core of a column.

• For bar diameters 10 mm through 36 mm, the development length

dl for a straight bar shall not be less than (a) and (b): (a) 2.5 times the length required by the previous equation if the depth of the concrete cast in one lift beneath the bar does not exceed 30 cm, and

236

(b) 3.5 times the length provided by the same equation if the depth of the concrete cast in one lift beneath the bar exceeds 30 cm.

Horizontal shear in beam-column connection

237

Example (10): Determine the transverse reinforcement and shear strength requirements for the

interior beam-column connection shown in Example (9).

Solution:

A- ACI 21.7.1 "General Requirements"

Based on ACI 21.7.2.1, forces in longitudinal beam reinforcement at the joint

face shall be determined as assuming that the stress in the flexural tensile

reinforcement is yf25.1 .

• Based on ACI 21.7.2.3, where longitudinal beam reinforcement extends

through a beam-column joint, the column dimension parallel to the beam

reinforcement shall not be less than 20 times the diameter of the larger

longitudinal bar.

( ) cm70cm505.220d20 b <== (O.K)

B- ACI 21.7.4 "Transverse Reinforcement":

Based on ACI 21.7.3.1, transverse reinforcement shall be provided within the joint. 2

sh cm88.2A =

238

C- ACI 21.7.4 "Shear Strength":

tons84.266.4

77.5069.72V .col =+

=

.col21intjo,u VCTV −+=

tons83.23084.2606.10361.154 =−+=

cm)7045(cm45x2bb bj +≤=+=

( )( ) 2coljj cm31504570hbA ===

( ) tonsVn 24.2181000/31503004 ==

( ) tonsVn 68.16324.21875.0 ==Φ

nu VV Φ> and column dimension in the direction of shear force needs to be

increased.

For nu VV Φ= , ( ) ( )( ) tonshcol 83.2301000/45300475.0 = and 72.98=colh

Increase column cross sectional dimension to 45 cm x 100 cm.

Plan

239

Requirements for Intermediate Moment Resisting Frames

A- Beams

1- General Requirements: Requirements of ACI 21.3.2 are applicable for intermediate moment frame members proportioned primarily to resist flexure with factored axial forces

gc Af ′≤ 1.0 . If such members are subjected to axial forces gc Af ′> 1.0 , they are treated as beam-columns.

2- Longitudinal Reinforcement:

• Positive moment strength at joint face is not to be less than 1/3 of the negative moment strength provided at the face of the joint.

• The negative or positive moment at any section along the member is not to be less than 1/5 the maximum moment strength provided at the face of either joint.

3- Transverse Reinforcement:

• At both ends of the member, hoops shall be provided over lengths equal to twice the member depth measured from the face of the supporting member toward midspan.

• The first hoop is to be located at a distance not more than 5 cm from the face of the supporting member. Maximum hoop spacing is not to exceed the smallest of: d/4, bd8 where bd is the diameter of the smallest longitudinal bar, 24 times the diameter of hoop bar, and 30 cm.

• Where hoops are not required, stirrups are spaced at not more than d/2 throughout the length of the member.

4- Shear Strength Reinforcement:

• nVΦ of beams resisting earthquake effect, E, shall not be less than the smaller of (a) or (b):

(a) The sum of the shear associated with development of nominal moment strengths of the member at each restrained end of the clear span and the shear calculated for factored gravity loads;

240

(b) The maximum shear obtained from design load combinations that include earthquake effect E, with E assumed to be twice that prescribed by the legally adopted general building code for earthquake resistant design.

Design Shear, ACI 318-2008

241

B- Beam-Columns

1- General Requirements:

Requirements of ACI 21.3.5 are applicable for intermediate moment frame members proportioned to resist axial forces gc Af ′> 1.0 .

2- Transverse Reinforcement::

• At both ends of the member, hoops shall be provided at spacing os over a length ol measured from the face of the joint.

The length ol shall not be less than the largest of:

(a) 1/6 of the clear span of the member (b) Maximum cross-sectional dimension of the column (c) 45 cm.

• The spacing os shall not exceed the smallest of: (b)

bd8 (c) 24 diameter of the hoop bar (c) One-half of the smallest cross-sectional dimension of the column (d) 30 cm.

• The first hoop shall be located at not more than spacing 2/os from the joint face.

• Outside the length ol spacing of the transverse reinforcement shall conform to ACI 7.10 (ordinary column ties) and ACI 11.4.5.1 (beam shear reinforcement spacing limits).

• Columns supporting reactions from discontinuous stiff members, such as walls, shall be provided with transverse reinforcement at the spacing, os , as defined in 2 over the full height beneath the level at which the discontinuity occurs if the portion of factored axial compressive force in these members related to earthquake effects exceeds gc Af '1.0 . Where design forces have been magnified to account for the overstrength of the vertical elements of the seismicforce- resisting system, the limit of gc Af '1.0 shall be

242

increased to gc Af '25.0 . This transverse reinforcement shall extend above and below the columns as required in 21.6.4.6(b).

3- Shear Strength Requirements:

• Design shear strength of columns resisting earthquake effect shall not be less than the smaller of (a) or (b):

(a) The sum of the shear associated with development of nominal moment strengths of the member at each restrained end of the clear span and;

(b) The maximum shear obtained from design load combinations that include earthquake effect E, with E assumed to be twice that prescribed by the legally adopted general building code for earthquake resistant design.

Design Shear, ACI 318-2008

C- Joints

• Joints of intermediate moment resisting frames are designed in a way similar to ordinary moment resisting frame joints.

243

Requirements for Ordinary Moment Resisting Frames

These provisions were introduced in the 2008 Code and apply only to ordinary moment frames assigned to SDC B.

A- Beams

Based on 21.2.2, beams shall have at least two of the longitudinal bars continuous along both the top and bottom faces. These bars shall be developed at the face of support.

B- Columns

Based on 21.2.3, columns having clear height less than or equal to five times the dimension c1 (in the direction of the span for which moments are being determined) shall be designed for shear in accordance with 21.3.3 (requirements for intermediate moment resisting frames.

Requirements for Structural Integrity

A structure is said to have structural integrity if localized damage does not spread progressively to other parts of the structure. Experience has shown that the overall integrity of a structure can be substantially enhanced by minor changes in detailing of reinforcement. The 1989 ACI Code introduced section 7.13. which provides details to improve the integrity of joist construction, beams without stirrups and perimeter beams. These requirements were updated in the 2002 ACI Code.

• In detailing of reinforcement and connections, members of a structure shall be effectively tied together to improve integrity of the overall structure.

• In joist construction, at least one bottom bar shall be continuous and at non-continuous supports shall be terminated with a standard hook.

• Beams along the perimeter of the structure shall have continuous reinforcement consisting of:

(a) at least 1/6 of the tension reinforcement required for negative moment at the support, but not less than 2 bars;

(b) at least ¼ of the tension reinforcement required for positive moment at mid span , but not less than 2 bars.

244

- The above reinforcement shall be enclosed by the corners of U-stirrups having not less than 135-deg hooks around the continuous top bars, or by one piece closed stirrup with not less than 135-deg hooks around one of the continuous bars. - Where splices are needed to provide the required continuity, top reinforcement shall be spliced at or near mid span and bottom reinforcement shall be spliced at or near the support. Splices shall be Class B tension splices or mechanical or welded splices.

245

Diaphragm Key Components

Diaphragm Slab (Sheathing):

It is the component of the diaphragm which acts primarily to resist shear forced developed in the plane of the diaphragm.

Diaphragm Chords:

They are components along the diaphragm edges with increased longitudinal and transverse reinforcement, acting primarily to resist tension and compression forces generated by bending in the diaphragm.

Diaphragm Collectors:

They are components that serve to transmit the internal forces within the diaphragm to elements of the lateral force resisting system. They shall be monolithic with the slab, occurring either within the slab thickness or being thickened.

Diaphragm Struts:

They are components of a structural diaphragm used to provide continuity around an opening in the diaphragm. They shall be monolithic with the slab, occurring either within the slab thickness or being thickened.

Distribution of Forces:

For rigid diaphragms the distribution of forces to vertical elements will be essentially in proportion to their relative stiffness with respect to each other.

246

17

Diaphragm Chord / Beam Analogy

Tensile Stress

Compressive Stress

Load

SupportSupport

Load

shearwall

shearwallCompression

Tension

247

12

Horizontal Diaphragm Boundaries

Boundaries

Boundaries

Interior shear wall

Boundary

Boundaries

Diaphragm boundaries may not just occur at the perimeter of the diaphragm. Interior shear walls and drag members create diaphragm boundaries.

Boundaries

Boundaries

248

Requirements for Structural Diaphragms

Floor and roof slabs acting as structural diaphragms to transmit forces induced by earthquake ground motions in structures assigned to SDC D, E, or F shall be designed in accordance with this section 21.11 of ACI Code.

1- Scope:

Diaphragms are used in building construction are structural elements such as floors and roofs that provide some or all of the following actions:

• Support for building elements such as walls, partitions, and cladding resisting horizontal forces but not acting as part of the building vertical lateral force resisting system.

• Transfer of lateral forces from the point of application to the building vertical lateral force resisting system.

• Connection of various components of the building lateral force resisting system with appropriate stiffness so the building responds as intended in the design.

2- Minimum Thickness of Slab:

• Concrete slabs serving as structural diaphragms used to transmit earthquake forces shall not be less than 5 cm thick.

3- Reinforcement:

• The minimum reinforcement ratio for structural diaphragms shall not be less than the shrinkage and temperature reinforcement ratio. Reinforcement spacing each way shall not exceed 45 cm

• Diaphragm chord members and collector elements with compressive stresses exceeding cf ′2.0 at any section shall have transverse reinforcement over the length of the element as per transverse reinforcement of boundary elements of special shear walls. The special transverse reinforcement is allowed to be discontinued at a section where the calculated compressive stress is less than cf ′15.0 . Stresses are calculated for the factored forces using a linearly elastic model and gross-section properties of the elements considered.

249

4- Design Forces:

The seismic design forces for structural diaphragms shall be obtained from the lateral load analysis in accordance with the design load combinations.

5- Shear Strength:

Nominal shear strength nV of structural diaphragms shall not exceed

( ) '12.2'53.0 ccvytccvn fAffAV ≤+= ρλ where cvA is gross area of concrete section in the direction of shear force considered and tρ is ratio of transverse reinforcement.

Example (11):

Determine the diaphragm forces for the building shown in Example (1).

Solution:

pxpxnxi i

n

xiit

Px wZI35.0wW

FFF ≥

∑

∑+=

=

=

pxwZI75.0≤ Diaphragm Forces:

level iF

∑=

n

xiiF iw

∑=

n

xiiw

PxF min,PxF max,PxF used,PxF7 12.86 12.86 259.2 259.2 12.86 6.804 14.58 12.86 6 8.47 21.33 259.2 518.4 10.67 6.804 14.58 10.675 7.06 28.39 259.2 777.6 9.46 6.804 14.58 9.46 4 5.65 34.04 259.2 1036.8 8.51 6.804 14.58 8.513 4.24 38.28 259.2 1296 7.66 6.804 14.58 7.662 2.82 41.10 259.2 1555.2 6.85 6.804 14.58 6.85 1 1.41 42.51 259.2 1814.4 6.07 6.804 14.58 6.80

Maximum forces occur at the seventh floor, where tons86.12FPx = Load/m'= 12.86/18 = 0.714 t/m.

Chord forces:

( ) ( ) m.t55.408/18714.087.175.0M 2u ==

250

tons253.218

55.40TC ===

( )2

required,s cm596.02.49.0

253.2A == (use minimum reinforcement)

For a beam 40 cm x 25 cm in cross section, ( )( ) ( )3002.0cm/Kg253.225401000253.2

f 2 <== , i.e., no special transverse reinforcement

required. Collector Forces:

( )( ) tons02.987.175.0286.12Vu ==

( ) ccvynccvn 'fA12.2f'f53.0AV ≤+= ρ For a topping slab 5 cm in thickness,

( )( )tons47.330300

100051800

12.2'fA12.2 ccv == ( )( ) ( )[ ] tons47.330tons66.15042000018.030053.0

100051800

Vn <=+= O.K

For seismic forces in the other orthogonal direction, chords and collectors trade places. For this condition, the same forces are evaluated.

251

Requirements For Foundations

Requirements for foundations supporting buildings assigned to high seismic performance or design categories were added to the 1999 Code. They represent a consensus of a minimum level of good practice in designing and detailing concrete foundations including piles, drilled piers, and caissons. The requirements for foundations are given in ACI 21.12, presented below.

• Longitudinal reinforcement of columns and structural walls resisting seismic forces shall extend into the footing, mat, or pile cap, and shall be developed for tension at the interface.

• Columns designed assuming fixed-end conditions at the foundation, and if hooks are required, longitudinal reinforcement resisting flexure shall have 90 deg hooks near the bottom of the foundation with the free end of the bars oriented toward the center of the column.

• Columns or boundary elements of special structural walls that have an edge within one-half the footing depth from the edge of the footing shall have transverse reinforcement provided below the top of the footing. This reinforcement shall extend into the footing a distance no less than the smaller of the depth of the footing, mat, or pile cap, or the development length in tension of the longitudinal reinforcement.

• Where earthquake effects create uplift forces in boundary elements of special structural walls or columns, flexural reinforcement shall be provided in the top of the footing, mat, or pile cap to resist the design load combination, and shall not be less than minimum reinforcement in beams.

• Grade beams designed to act as horizontal ties between pile caps and footings shall have continuous longitudinal reinforcement developed within or beyond the supported column or anchored within the pile cap or footing at all discontinuities.

• Grade beams designed to act as horizontal ties between pile caps or footings shall be proportioned such that the smallest cross-sectional dimension shall be equal or greater than the clear spacing between connected columns divided by 20, but not greater than 45 cm. closed ties shall be provided at a spacing not to exceed the lesser of one-half the smallest orthogonal cross-sectional dimension or 30 cm.

• Piles, piers, or caissons resisting tension loads shall have continuous longitudinal reinforcement over the length resisting design tension

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forces. The longitudinal reinforcement shall be detailed to transfer tension forces within the pile cap to supported structural members.

• Piles, piers, or caissons shall have transverse reinforcement in accordance with 21.12.2 at locations (a) and (b):

(a) At the top of the member for at least 5 times the member cross-sectional dimension, but not less than 1.80 m below the bottom of the pile cap;

(b) For the portion of piles in soil that is not capable of providing lateral support, or in air and water, along the entire unsupported length plus the length required in (a).