Compressive chord force

Tensile chord force

Internal lever arm

Values of ωp in the range of 0.25 to 0.3 are usual

Effect of the amount of confining reinforcement on the stress-strain behaviour of concrete

(at support) and 50% at mid-span!

Moment at ‘C’ = -9.43 kNm

Pattern loading

Analysis and design of R.C. framed buildings

Influence lines and gravity load patterns for a continuous beam

Width of a beam shall be less than or equal to the dimension of the column into which

they frame

Beam widths of 200 mm, 250 mm and 300 mm are commonly used. Beam widths of

230 mm are also commonly used in India so that the infill masonry wall resting on a

beam is flush with it

The ratio of overall depth, D, to the width, b, in rectangular beam sections lied in the

range 1.5 – 2. For beams carrying very heavy loads it may be even 3 or more!

For simply supported beams, span/overall depth ≈ 10

For continuous beams, span/overall depth ≈ 12 to 15

In framed structures, the maximum amount of tension reinforcement in a beam is usually

restricted to 1.4% to 1.5%. This generally corresponds to a Mu/bd2 of about 4 to 4.5. Such

values of Mu/bd2 will result in a doubly reinforced section. In general, it is desirable to

design beams with a tension steel content of 0.5 to 0.8 times pt,lim

For simply supported slabs, effective depth ≈ span/25

For continuous slabs, effective depth ≈ span/32

Amount of tension reinforcement in a slab ≈ 0.3% - 0.4%

Column dimensions should not be smaller than the size of the largest beam framing into

the column. Estimate the size very roughly by equally dividing the total gravity load

amongst all columns and dividing this load with the allowable axial stress for the concrete

grade in the column

For rigourous analysis of a highly indeterminte structure like a monolithic frame, the axial, flexural and

torsional stiffness needs to be known. Since axial stiffness of most of the members in a typical RCC moment

resistant frame is very high, the axial deformations are negligible. In the case of compatibility torsion, the

torsional stiffness of a RCC member is drastically reduced following torsional cracking and hence it can be

ignored altogether . Bending or flexural deformations in a typical frame can be significant and hence flexural

stiffness needs to be estimated. Flexural stiffness = 4 E I / l , where EI is the flexural rigidity.

Load paths in a building and tributary areas for beams and columns

Loads

Approximate analysis for vertical loads – substitute frame method

Column moments from frame analysis

Variation of wind speed with height and terrain category

Basic wind speed, Vb, is measured at the reference height of 10 m above ground level

Typical building

Understanding Earthquakes

• Continental drift (Wegener,1915)200 million years ago earth had only one large continent called

Pangea, which eventually broke into pieces that slowly drifted apart to

the present configuration of the continents.

Wegener’s theory of continental drift: (a) 270 million years ago (b) 150 million

years ago (c) 1 million years ago

• Plate tectonics

The more modern theory of plate tectonics believes that the earth’s

surface consists of a number of large intact blocks called plates and

that these plates move with respect to each other. In all, there are six

continental-sized plates:

(i) African (ii) American (iii) Antarctic (iv) Australia-Indian

(v) Eurasian (vi) Pacific

Major Tectonic Plates on the Earth’s surface

Major tectonic plates (earth’s crust is divided into

Six continental sized plates

Internal structure of the earth

Temp: Approx. 2500 ºC

Pressure: 4 million atm.

Density: 13.5 g/cc

Temp: Approx. 25 ºC

Pressure: 1 atm.

Density: 1.5 g/cc

Local Convective Currents in the Earth’s Mantle

Worldwide seismic activity. The dots represent the epicentres of significant erathquakes.

The location of a majority of the earthquakes correspond to boundaries between plates.

Earthquake originates here

Magnitude and Intensity of an Earthquake

Methods of estimating earthquake forces on a building:

(1) Seismic coefficient method or static method

(2) Response spectrum method or dynamic method

The first step in earthquake analysis and design is to find the base shear in a building

VB = Ah W

Where,

Where,

Z Zone factor

I Importance factor

R Response reduction factor

Sa/g Average response acceleration coefficient (Structural response factor)

The above factors are to be taken from IS 1893 (Part 1) : 2002

The total lateral force acting at the base of a building is calculated as

The seismic weight of the structure is calculated by summation of the dead loads and the appropriate fraction of

of the live load acting on each floor of the building.

h

Alternate empirical formula for the fundamental period of a building

T = 0.1 N

Where N is the number of storeys above the ground level

0.75 x 1.5 = 1.125 ≈1.2

Global strong-column, weak-beam

Formula is based on the sum of moment strengths for the columns and beams framing into a level.

Summation Mn of columns Summation Mn of beams to the left and the right. This ratio should be at least 1.20.

The nominal moment capacity of the columns shall be calculated on the basis of concrete grade,column section, the column reinforcement and the axial load on the column. The nominalmoment capacity of the beams shall be calculated on the basis of concrete grade, beam sectionand the amount of tension and compression longitudinal reinforcement.

Moments in members typically framing into a joint