PCA Report SN2961 Walls Restrepo

8/12/2019 PCA Report SN2961 Walls Restrepo

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PCA R&D Serial No. SN2961

Response Verification of a ReinforcedConcrete Bearing Wall Building Located in

An Area of High Seismic Hazard

by Marios Panagiotou, Geonwoo Kim, Andre Barbosa,and Jos I. Restrepo

Portland Cement Association 2009All rights reserved

5420 Old Orchard Road

Skokie, Illinois 60077-1083

847.966.6200 Fax 847.966.8389

www.cement.org


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Response Verification of a Reinforced Concrete BearingWall Building Located in an Area of High Seismic Hazard

Marios Panagiotou, Ph.D. Candidate, UCSD, La Jolla, CA

Geonwoo Kim, Ph.D, Visiting Scholar, UCSD, La Jolla, CA

Andre Barbosa, Ph.D., Candidate, UCSD, La Jolla, CA

Jos I. Restrepo, Professor, UCSD, La Jolla, CA


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LIST OF CONTENTS

1. Introduction......................................................................................................................... 5

2. Building Description........................................................................................................... 5

2.1. Design Lateral Forces ..................................................................................................... 5

2.2. Design of Shear Wall on Line 5...................................................................................... 7

2.2.1. Specified Material Properties...................................................................................... 7

2.2.2. Design Summary......................................................................................................... 7

3. Response Verification....................................................................................................... 10

3.1. Probable Material Properties......................................................................................... 10

3.2. Wall Probable Shear Strength....................................................................................... 10

3.3. Effective Flange Width................................................................................................. 10

3.4. Section Analysis............................................................................................................ 12

3.5. Kinematic Overstrength................................................................................................ 13

3.6. Quantification of the Coupling Actions........................................................................ 15

3.7. Computational Model ................................................................................................... 17

4. Results of the Analysis...................................................................................................... 19

4.1. Monotonic Pushover Analysis ...................................................................................... 19

4.2. Nonlinear Dynamic Time History Analysis (NDTHA)................................................ 22

5. Discussion......................................................................................................................... 29

6. Design Recommendations ................................................................................................ 32

7. Summary and Conclusions ............................................................................................... 34

8. Acknowledgments............................................................................................................. 36

9. References......................................................................................................................... 36


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LIST OF FIGURES

Figure 1. Typical Floor Plan and Elevation along Line B or C. ..................................................... 6

Figure 2. Reinforcement Details for T-wall along Line 5. ............................................................. 9

Figure 3. UCSD 7-Story building: T-wall cross-section showing strain gauged flanged

longitudinal bars and tensile strain profile envelope of Level 1 bars. .......................................... 11

Figure 4. Moment Curvature response of T-wall section, effect of flange width and flange in

tension. .......................................................................................................................................... 12

Figure 5. Design and measured shear forces along the height of UCSD 7-story building slice... 13

Figure 6. Deformed state - coupling actions, reactions and additional lateral forces of external

walls coupled. ............................................................................................................................... 14

Figure 7. Development of slab yield lines due to unintended wall-slab coupling........................ 16Figure 8. Results of finite element analysis, yield line theory and idealized finite element results

of unintended slab coupling. North wall rotation versus total coupling reaction force per floor. 16

Figure 9. Part of the building considered in the 2-D analysis....................................................... 17

Figure 10. Refined variable-angle truss model representing a wall panel. .................................. 18

Figure 11. Plan view of building slice and mass distribution....................................................... 18

Figure 12. PCA building slice monotonic pushover response - ACI flange - Base shear of each

wall versus roof drift ratio. (With and without effect of coupling). ............................................. 20

Figure 13. Monotonic Response - ACI flange width- Base moment at midlength of each wall

versus roof drift ratio. (With and without the effect of coupling). ............................................... 21

Figure 14. Monotonic Response full flange - Base shear of each wall versus roof drift ratio.

(With and without the effect of coupling)..................................................................................... 21

Figure 15. Monotonic Response full flange - Base moment at midlength of each wall versus

roof drift ratio. (With and without effect of coupling).................................................................. 22

Figure 16. Acceleration time histories and Acceleration Response Spectra of input ground

motions 5% damping ratio. ........................................................................................................ 23

Figure 17. Sylmar record - ACI flange width Without coupling - Base Shear of Walls versus

Roof Drift Ratio. (a) 5%, (b) 2%, (c) 0.3% damping ratio. .......................................................... 25

Figure 18. Sylmar record ACI flange - Base Shear of Walls versus Roof Drift Ratio - Effect of

Wall Coupling. (a) 5%, (b) 2%, (c) 0.3% damping ratio.............................................................. 27


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Figure 19. Sylmar record - Base Shear of Walls versus Roof Drift Ratio No wall Coupling -

Effect of Effective Flange Width. (a) 5%, (b) 2%, (c) 0.3% damping ratio. ................................ 28

LIST OF TABLES

Table 1. Design Seismic Forces and Story Shears.......................................................................... 7

Table 2. Summary of Design Axial Forces, Bending Moments, and Shear Forces on Web Wall

in First Story on Line 5. .................................................................................................................. 8

Table 3. Summary of Design Axial Forces, Bending Moments, and Shear Forces on Flange

Wall in First Story on Line 5. ......................................................................................................... 9

Table 4. Modal period of the first two modes............................................................................... 23

Table 5. Modal mass of the first two modes................................................................................. 23

Table 6. Drift ratios at the development of probable shear and web crushing strength ............... 29

Table 7. Model web crushing strength normalized to probable web crushing strength ............... 29

Table 8. Shear force demand normalized by the probable shear strength Vp ............................... 30

Table 9. Shear force demand normalized by the probable web crushing strength ....................... 31


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1. IntroductionThis report discusses the results of an investigation performed to evaluate the seismic

response of the draft example of a 7-story bearing wall reinforced concrete residential building

proposed as a design model by the Portland Cement Association (PCA), thereafter termed the

PCA building. The building is that described by PCA (2006) for a region of high seismicity. The

bearing walls were designed and detailed for the combined effects of gravity and lateral forces.

This report is focused on the seismic shear force demand on the walls. The study considers

the effect of the effective flange width as well as the effect of unintended coupling between walls

through the slab. It is noted that these two effects were found to have an important contribution

on the shear force demand in the 7-story building slice tested at UCSD on the Large High-

Performance Outdoor Shake Table (Panagiotou and Restrepo, 2007).

The building walls were modeled with a dynamic strut and tie model. This model was

successfully implemented and used to analyze the UCSD 7-story building slice (Panagiotou and

Restrepo, 2006). Both, monotonic pushover and nonlinear dynamic time history analysis

(NDTHA) were employed to investigate the response of the PCA building. Because of the

location of the building in a region considered to be in the vicinity of an active fault, the NDTHA

made use of two California historical records that had distinct near fault characteristics. These

records closely matched the spectral acceleration of the design earthquake in the period of

interest.

2. Building DescriptionThis section summarizes the draft design example of the PCA building including the

derivation of the design forces, the design of the wall for shear and flexure and the final

reinforcement detailing. The PCA building was designed for Berkeley, CA (zip code 94705)

which is less than 2 miles from the Hayward fault. This building was designed to meet the

requirements of IBC-2006 (IBC, 2006) and of the ACI 318-05 building code (ACI, 2005). The

walls were considered as special shear walls and were detailed accordingly.

2.1.Design Lateral ForcesA floor plan and interior elevation of the building considered is shown in Figure 1. In this

design example, it was assumed that the local building code legally adopts the 2006 edition of


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the International Building Code (IBC, 2006). In turn, the IBC-2006 code adopts by reference the

2005 edition of ASCE 7-05 (ASCE, 2006) and the ACI 318-05 building code (ACI, 2005).

The seismic weight of the building was W=12,762 kips. The base shear coefficient calculated

for the building using the equivalent static lateral force method was C s = 0.274 and the

corresponding base shear was V= CsW=3497 kips. The base shear force was distributed over the

height of the building following Eqs. 12.8-11 and 12.8-12 of ASCE 7-05. These equations are

reproduced below for reference:

Fx= C

vxV where C

vx=

wxhx

( )k

wihi

( )k

i=1

n

!

(1)

where Fxis the lateral force induced at level x, wx and wiare the portions of W assigned to levels

x or i, and k is the exponent related to the structure period, which is defined in ASCE 7-05 Eq.

12.8.3. For T = 0.48 sec (calculated from Eq. 12.8-7 of ASCE 7-05), k = 1.0. The lateral forces

Fx and the story shears Vxare listed on Table 1.

Figure 1. Typical Floor Plan and Elevation along Line B or C.


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Table 1. Design Seismic Forces and Story Shears.

Level

Story

weight,

(kips)

Height,

(ft)

Lateral force,

(kips)

Story Shear,

(kips)

7 1,380 70 96,600 683 683

6 1,897 60 113,820 804 1,487

5 1,897 50 94,850 670 2,157

4 1,897 40 75,880 536 2,693

3 1,897 30 56,910 402 3,095

2 1,897 20 37,940 268 3,363

1 1,897 10 18,970 134 3,497

! 12,762 494,970 3,497

The example used the load combinations given by ACI 318-05 Eq. 9.7. These combinations

are:

U = 1.2D + 0.5L + (2)

U = 0.9D + (3)

where D are the design forces due to dead load, L are the design forces due to live load, Q E are

the design seismic forces and SDSthe design spectral acceleration at short periods.

2.2.Design of Shear Wall on Line 52.2.1. Specified Material Properties

The specified material properties for the concrete and reinforcement in the design of the PCA

building were = 4 ksi and fy = 60 ksi, respectively.

2.2.2. Design SummaryThe PCA building walls were designed for internal forces obtained from a three-dimensional

elastic analysis for the design seismic forces listed in Table 1. The analysis was performed using

a commercial computer program, which assumed rigid diaphragms at every level. The stiffness

properties of the walls were determined considering cracked section properties. To this end the

moment of inertia of the cracked section Ieffwas Ieff =0.5Ig where is the moment of inertia

of the gross section. P-Delta effects were also considered in the analysis. This model conforms to

the structural modeling requirements of Section12.7.3 of ASCE 7-05.


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In the design the flange and the web in the T-walls were assumed to act independently as two

rectangular 10 in. thick shear walls, each providing lateral force resistance in its plane only. The

web wall was 28 ft. 5 in. long and the flange was 22 ft. long. Table 2 lists the design axial forces,

bending moments, and shear forces at the base the web wall due the design N-S lateral forces.

Similarly, the design forces at the base of the flange wall due to the design E-W lateral forces

are listed on Table 3. The definition of web and flange and of the North direction can be

seen in Figure 1.

The demands on the web wall were small. Hence, this wall was detailed to meet the

minimum reinforcement requirements stated on Cl. 21.7.2.1 of ACI 318-05 of !"=0.0025 and

maximum spacing of 18 in. c-c. The longitudinal reinforcement was detailed with two curtains

of No. 5 bars at 14 in. c-c resulting in a reinforcement ratio !" = 0.0047. The horizontal

reinforcement was detailed with two curtains of No. 5 bars at 18 in. c-c resulting in a

reinforcement ratio !t= 0.0034. Special boundary elements with No. 4 hoops at 2.5 in. c-c were

detailed at the web wall ends on levels 1 to 3, see Figure 2.

The longitudinal and transverse reinforcement for the flange wall consisted of two curtains

of No. 5 bars at 18 in. c-c. That is, the longitudinal and transverse reinforcement ratios were !"=

0.0035, !t = 0.0034, respectively. The longitudinal and horizontal reinforcement both in the

flange and the web were assumed in this study to be equal at each level of the building.

Figure 2 shows a plan view of the reinforcement details of the T-wall section.

Table 2. Summary of Design Axial Forces, Bending Moments, and Shear Forces on Web

Wall in First Story on Line 5.

Load Case

Axial

Force

(kips)

Bending

Moment

(ft-kips)

Shear

Force

(kips)

Dead (D) 1,044 0 0

Live (L) 95 0 0

Seismic (QE) 503 8,276 308

Load Combination

1.4D 1,462 0 01.2D + 1.6L 1,405 0 0

1.47D + 0.5L +QE 2,085 8,276 3080.63D QE 155 -8,276 -308


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Table 3. Summary of Design Axial Forces, Bending Moments, and Shear Forces on

Flange Wall in First Story on Line 5.

Load Case

Axial

Force

(kips)

Bending

Moment

(ft-kips)

Shear

Force

(kips)

Dead (D) 316 0 0

Live (L) 39 0 0

Seismic (QE) 9 6,203 324

Load Combination

1.4D 442 0 0

1.2D + 1.6L 442 0 0

1.47D + 0.5L +QE 493 6,203 3240.63D QE 190 -6,203 -324

Figure 2. Reinforcement Details for T-wall along Line 5.


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3. Response Verification3.1. Probable Material PropertiesFor the verification of the response the longitudinal and transverse reinforcement were

assumed to have a median yield strength of fy = 66 ksi and the concrete to have a mediancompressive strength of = 5 ksi.

3.2.Wall Probable Shear StrengthEq. 21-7 of ACI 318-05 was used in the design example to determine the probable wall shear

strength Vp:

Vp

= Acv

(!c "f

c+ #

tf

y) (4)

where !c = 2 for walls with a ratio of wall height to length 70/28.42 = 2.5 > 2

(ACI 318-05 Cl. 21.7.4.1). For 2 curtains of No. 5 horizontal bars spaced at 18 in.

:

Vp

= 3410![2 5000+ 0.0034!66000( )]/1000 = 1247 kips

for walls with 2 (ACI 318-05 Cl. 9.3.4(a)). Vp = 1247 kips is less than the

upper limit on shear strength associated with web crushing, which is 8Acv

!fc=1928 kips

(ACI 318-05 Cl. 21.7.4.4).

Eq. 4 does not recognize the gradual degradation on the contribution of the concrete in

carrying shear once a plastic hinge develops. Such degradation has been addressed when

calculating the concrete contribution in shear for beams and columns (Priestley et al., 1996).

Note also that at least one code, the New Zealand Concrete Design Standard (SNZ 1995), does

recognize this gradual loss in the design of walls in shear. For this reason, Eq. 4 should be taken

as an upper bound solution for calculating the probable shear strength of a wall.

3.3. Effective Flange WidthCl. 8.10.2 of ACI 318-05 estimates that the width of slab effective as a T-beam flange should

not exceed one quarter of the span length and the effective overhanging flange width on each


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side of the web wall which should not exceed: (i) eight times the slab thickness and (ii) one-half

the clear distance to the next web. Based on this for the specific case the maximum effective

flange width that can be considered is controlled from the distance to the next web and is

wfe = 2x110/2+10 = 120 in. corresponding to 45% of the full flange width of wf = 264 in..

The two independently designed walls act as a single T-wall in reality. This is because there

are two mechanisms that allow shear flow between these two walls (i) the web wall shear

reinforcement is anchored on the flange and (ii) the slab acts as a partial mechanism that hampers

any relative shear displacement between the web and the flange.

Note that recent shake table testing at UCSD only included detailing (i) described previously.

Such detail was sufficient to enable sufficient shear flow to mobilize the entire flange in tension,

see Figure 3. This figure shows the envelope of the longitudinal bar tensile strains measured in

first level of the flange wall. The peak tensile strain in the reinforcing bars of the flange reached

3%, while the reinforcing steel yielded along all the length of the flange wall in EQ2, EQ3 and

EQ4. Note that according to ACI 318-05 the effective flange width for the UCSD building would

have been 71% of the entire width. As a result the important contribution towards flexural

resistance contributed to by the longitudinal reinforcement in the flange end boundary elements

would have been ignored. At first glance this flexural strength underestimation seems

conservative but the reality is that such outcome results in an underestimation of the shear force

that has to be transferred through the walls web once a plastic hinge, engaging the entire flange

in tension, develops.

Figure 3. UCSD 7-Story building: T-wall cross-section showing strain gauged flanged

longitudinal bars and tensile strain profile envelope of Level 1 bars.


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The draft design example ignored all together the contribution of the flange in tension in the

flexural strength of the T-wall and, consequently, it ignored the larger shear force demand on the

wall. ACI 318-05 code recommends an effective flange width for T-walls derived for T-section

beams. The intention of the design recommendations for T-beams is to provide a close and

conservative approximation to this width. As in other provisions that are given for gravity load

design, conservative estimates are reckoned to be adequate. In seismic design this philosophy no

longer holds true. An apparent underestimation of the flange width in a T-wall that will develop

a flexural plastic hinge will result in shear forces that are greater than those used in design.

Given the consequences of shear failures in reinforced concrete gravity load carrying members,

such failures should be avoided as far as practicable and certainly the probability of such failures

occurring under the design earthquake should be very low.

3.4.Section AnalysisThis section presents the moment-curvature sectional response of the T-wall section when

subjected to bending as indicated in Figure 4 and for a compressive axial force Pu = 2578 kips.

The program Columna (Kuebitz, 2002) was used to perform the analyses.

Figure 4 plots the moment curvature of the T-wall for the ACI 318-05 flange width as well as

for the full flange width. The response of the T-wall section with its flange in tension results in

an increase of the moment capacity. The definition of the effective flange width affects primarily

the response of the section when flange is in tension. When the T-wall has its flange in tension,

an increase of the flange width causes an increase in the moment capacity as well as an increase

of the secant stiffness to yield point.

Figure 4. Moment Curvature response of T-wall section, effect of flange width and flange in

tension.


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3.5.Kinematic OverstrengthKinematic overstrength is defined here as the increase in resistance due to the interaction

between the wall and the elements framing into it. This type of interaction can cause significant

reaction forces into the walls and an increase of the shear forces in the walls. The effects of

kinematic overstrength were first cited by Bertero et al. (1985).

To explain this effect we make reference to the response of the UCSD 7-story building slice

(Panagiotou and Restrepo, 2007). Figure 5 compares the design shear forces and those measured

during Phase I of the UCSD 7-story bearing wall building slice. The design shear forces

correspond to the flexural strength of the wall. The measured shear overstrength is of the order of

400% for EQ4 which is the strongest intensity earthquake used in the experimental program.

EQ4 was the design earthquake. Seventy percent of the measured shear overstrength shown in

Figure 4 was due to the effect of kinematic overstrength.

Figure 5. Design and measured shear forces along the height of UCSD 7-story building

slice.

A usual case in buildings incorporating load bearing walls is the unintended coupling of

walls through the floor slabs. Figure 6 shows a schematic representation of the case of two-

dimensional coupling between walls. During nonlinear response, and due to the migration of the

neutral axis depth towards the compressed end, the wall tensile chord elongates significantly.

Because of deformation compatibility the slabs have to follow the walls and they may be forced

to develop yield lines or even to develop punching shear failures. Deformation compatibility

causes unintended wall coupling actions. Figure 6 considers the case where the full plastic

capacity of the slabs has developed and shows the coupling actions and reactions on the walls.


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The positive and negative moment capacity of the coupling elements is Mfand the shear force

Vf. It is assumed that the coupling elements have enough shear capacity.

Knowing the moment capacity Mfand the lengths lwand ls, the lateral force #Vfiat floor i to

mobilize the plastic capacity of the floor coupling system is given in Eq.4.

(4)

where and (5)

Figure 6. Deformed state - coupling actions, reactions and additional lateral forces of

external walls coupled.

In Eq. 5 #VfiS and #VfiN are approximate solutions for the additional forces in the South and

North wall, respectively, due to mobilization of the plastic capacity of the coupling elements at

level i. Note that forces #VfiS and #VfiN are inversely proportional to the height hi. Thus,coupling in the lower floors generates larger lateral forces. The lateral forces and the resultant

lateral force #Vfrequired to mobilize the mechanism are shown also in Figure 5. Eq. 5 indicates

that #VfiN > #VfiS. In the case of the PCA building, the North wall of the schematic wall shown

in Figure 6 corresponds to the wall with the flange in tension. This is important for the evaluation

of shear force demand of the PCA building. For the specific configuration in addition to the


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increase of the developed shear force due to response of the flange in tension the shear force will

increase even more due to coupling between the walls.

All these lateral forces need to be sustained by the walls if a flexural plastic hinge is to

develop and be maintained at the wall bases. Note that in some cases the resultant additional

lateral force #Vf can be of similar order or even exceeds the base shear corresponding to the

flexural strength of the base cantilever wall. In summary, the effect of coupling can be addressed

in design and since it has a large effect in the development of shear forces and floor accelerations

it should not be ignored.

3.6. Quantification of the Coupling ActionsThis section presents results of the three dimensional wall-slab analysis performed to

calibrate the coupling actions between the walls of the PCA building. Figure 7 shows a plan viewof the part of the building assumed for the three dimensional analysis of the slab including an

elevation of the deformed shape of the slab between the walls. Figure 7 assumes a response

towards North resulting in response of the North wall with its flange in tension. Incremental

rotations were applied to the walls about their neutral axis depth until the mobilization of the

flexural capacity of the slab.

Area of steel close to the minimum amount of reinforcement was considered for the slab. The

slab reinforcement was assumed to consist on No. 5 bars at 12 in. c-c in the N-S direction. The

corresponding longitudinal reinforcement ratio is 0.31/(9x12) = 0.28%.

A nonlinear finite element model in the program DIANA (DIANA, 2007) of the

subassemblage was developed to simulate the response of the slab. Eight node plane stress

curved shell elements with embedded reinforcements were used.

Figure 8 shows the response obtained from the finite elements analysis (FEA) in terms of

wall rotation versus the accumulated reaction force Vfalong the yield lines. Figure 8 also shows

the results based on the yield line theory as well as the idealized FEA response considered for

modeling the effect of coupling in the two dimensional analysis of the building slice.

The values obtained from the finite element analysis can be easily justified by fundamental

concepts of plastic analysis. For the specified reinforcing details of the slab section the plastic

moment capacity including section overstrength per unit width of the slab is Mf = 19 kips-ft/ft.

Considering the plastification along the yield line, the yield moment along each yield line is


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19x28 = 532 kips-ft. Based on the total yield moment the total reaction forces on the two ends of

the part of the slab between the walls is Vf = 2x $Mf/ls = 177 kips. This is very close to the value

estimated from the finite element analysis. The difference in results is primarily because the

yield line analysis ignores the axial compression that develops in the slab as a result of restricted

slab growth.

Figure 7. Development of slab yield lines due to unintended wall-slab coupling.

Figure 8. Results of finite element analysis, yield line theory and idealized finite element

results of unintended slab coupling. North wall rotation versus total coupling reaction force

per floor.


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3.7. Computational ModelThis section examines the model developed to analyze the PCA building. The analysis will

be done on a slice of the building. The slice includes the two T-walls on line 5, see Figure 9.

Figure 9. Part of the building considered in the 2-D analysis.

A dynamic strut and tie model was created for the PCA building. This model is similar to that

developed by Panagiotou and Restrepo (2007) for the verification of the experimental response

of the UCSD 7-story building slice. For the dynamic strut and tie model of the T-wall, see Figure

10, vertical overlapping nonlinear truss elements were used for the concrete and the reinforcing

steel. The flange was modeled as two single overlapping non-linear truss elements representing

the reinforcing steel and the concrete of the effective flange width. Figure 11 shows a plan view

of the building slice modeled as well as an elevation of the computational model. The computer

program Ruaumoko (Carr, 1998) was used for the analysis.

Additional truss elements were used for modeling the wall horizontal reinforcement as well

as the diagonal concrete carrying compressive and tensile stress in a bi-axial stress field. Frame

elements used for modeling the slab at every floor. The axial and bending stiffness of these

elements was estimated assuming an effective slab width equal to eight times the thickness of the

slab. Two different levels of trusses were used along the height of the building. A refined truss

employed on the first two levels since there were expected the majority of the inelastic response.

In levels 3 to 7 the wall section was discretized with a coarser truss. The wall segment on these


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levels was expected to respond elastically and the main focus of attention was given to the loss

of tension stiffening.

Along its width, the T-wall section was subdivided in 8 vertical layers, each associated with

the location of the longitudinal reinforcement. The area of each section was calculated based on

the effective area around each reinforcing bar. The area of concrete and steel of the flange area

was condensed to two overlapping single truss element. Two different cases of effective flange

width were considered, one equal to 0.45 of the flange width based on ACI 318-05 and a second

case of effective width equal to the total width of the flange. The longitudinal reinforcement was

considered continuous along the height and the details of splicing were ignored.

Figure 10. Refined variable-angle truss model representing a wall panel.

Figure 11. Plan view of building slice and mass distribution.


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For modeling the diagonal compression field, 30% of the equivalent effective area around

every diagonal was considered. The reduction factor of 30% of the diagonal area is a result of

relevant calibration of this type of models with experimental results. Based on the modified

compression field theory the compressive strength of the concrete in the diagonal was properly

decreased to account for the transverse tensile strain of the biaxial field.

For modeling the unintended slab coupling, shear and rotational springs at the wall faces

were used. The calibration of these springs is discussed on the next section. Regarding the axial

coupling between the walls an effective slab width equal to eight times the slab thickness at

every side of the web wall was considered.

The main advantage of the dynamic strut and tie model is the physical representation of shear

flexure interaction due to yielding of the diagonal concrete in compression and of the horizontal

shear reinforcement as well as the representation of the coupling between the walls due to the

realistic representation of the deformed state at the ends of the wall. The model also captures

naturally the spread of plasticity and requires no empirical formulations to define equivalent

plastic hinge lengths.

4. Results of the Analysis4.1.Monotonic Pushover AnalysisThis section discusses results of the nonlinear monotonic pushover analysis of the building

slice with and without considering the effect of unintended slab coupling. The pushover was

conducted by displacing the building slice northwards, thus inducing tension in the flange of the

North T-wall.

Figures 12 and 13 plot the results for the case where the effective flange width is 45% of the

flange width calculated from ACI 318-05. Figure 12 plots the base shear force in each of the

walls versus the roof drift ratio. Both figures show results with and without the unintended slab

coupling effect. The analysis considered a reduction of 40% of the compressive strength of the

concrete in the diagonal because the effect of the transverse tensile strain. It appears at first

glance that the walls should fail at the probable shear strength Vp, or at least fail once the

probable web crushing shear strength is attained. It will be shown in this report that occasionally

the model predicts greater values of the shear strength to the transverse strain (Vecchio and

Collins, 1986). However, because of the large variability expected when predicting the shear


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strength in a wall subjected to seismic input, shear forces obtained from the model above the

probable shear strength Vpshould be judged cautiously.

In any of the cases investigated we observe that a larger base shear force develops in the

North wall which has its flange in tension. This is due to the larger flexural strength and initial

stiffness of this wall.

For the case without flexural coupling of the walls we observe that the shear force in the

North wall, did not reached the probable web crushing shear strength calculated with

ACI 318-05 of 1928 kips. ACI 318-05 limit is to avoid a diagonal compression failure. The shear

forces on both walls exceed the probable shear strength at a roof drift ratio of less than 0.1%.

Unintended coupling of the walls through the slab results in a significant increase of the

shear force demand on the North wall and in a reduction of the roof drift ratio at which this wall

is deemed to have failed in diagonal compression. The North wall reaches the probable web

crushing shear strength of 1928 kips at 0.19% roof drift ratio. In comparison with the case of no

coupling, to the case of coupling, the North wall responds in a more brittle manner with severe

degradation of the diagonal and development of excessive shear deformations.

Figure 12. PCA building slice monotonic pushover response - ACI flange - Base shear of

each wall versus roof drift ratio. (With and without effect of coupling).

The response of the building slice after crushing of the diagonal compression field is

relatively uncertain, especially if compared with the prediction of the response up to this point.

The main consideration of this work is to show that shear forces, corresponding to a crushing ofthe diagonal compression field and initiation of a brittle shear failure, occurs for small roof drift

ratios with or without the effect of coupling between walls.

Figure 13 plots the base moment of the two walls versus the roof drift ratio. As expected the

North wall developed the greatest moment because its flange is in tension. Slab coupling

increases the base moment of the North wall because the coupling reactions increase the axial


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compressive load in this wall. In contrast, slab coupling decreases the moment in the South wall

because the slab reactions decrease the axial force on this wall.

The contribution of the design axial compressive load is important for the developed moment

and the corresponding shear. For a compressive axial load Pu = -2578 kips taking moments

around the midlength this axial compressive force results in a moment increase of

2578x14 = 36000 kips-ft. This is a significant part of the moment capacity in both walls.

Figure 13. Monotonic Response - ACI flange width- Base moment at midlength of each wall

versus roof drift ratio. (With and without the effect of coupling).

Figures 14 and 15 depict the base shear force and base moment versus roof drift ratio,

respectively. In this case due to increase of the flexural strength of the North wall larger shear

forces develop. Crushing of the diagonal compression field occurs at a smaller roof drift ratio

than in the case with the reduced flange width. Crushing of the diagonal compression field

occurs at a roof drift ratio of 0.3% and 0.18% for the case without and with coupling,

respectively.

Figure 14. Monotonic Response full flange - Base shear of each wall versus roof drift

ratio. (With and without the effect of coupling).


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Figure 15. Monotonic Response full flange - Base moment at midlength of each wall

versus roof drift ratio. (With and without effect of coupling).

4.2.Nonlinear Dynamic Time History Analysis (NDTHA)The NDTHA was aimed at obtaining the response of the building to earthquake excitations

corresponding to the design earthquake. Two historical records of California were employed in

the NDTHA: (i) the 360oOV Sylmar record from the 1994 Northridge earthquake, best known as

simply the Sylmar record, and (ii) the LGP000 record from the 1989 Loma Prieta earthquake,

best known as Los Gatos. Note that the Sylmar record was used as the design earthquake EQ4 in

the testing of the UCSD 7-story building slice. Figure 16 plots the acceleration time histories,

and acceleration response spectra for these records as well as the design spectrum for the PCA

building.

Table 4 shows the first two modal periods for all four different models, including coupling

and different effective flange widths. The periods are for uncracked sections.At the fundamental

period the spectral accelerations of the two earthquake records match closely the design

spectrum. The spectral accelerations of the Sylmar record has spectral accelerations in the period

region between 0.3 and 0.5 seconds that exceed the design spectrum. This is because of the

distinct near fault-pulse characteristics of this record. Similarly, the Los Gatos record exceeds the

design target spectrum beyond 0.5 seconds.

If the ASCE-7 2005 approach for scaling earthquake records to the 5% damped response

spectra of the design earthquake would have been used in this study, the records would have

been scaled up by 1.37. However, because of the dependency of frequency content to magnitude

and distance on near fault earthquakes, these records were left unscaled.


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Table 5 shows the modal mass of the first two modes for all the different four models. The

modal mass of the first mode varies between 77% and 81%. The modal mass of the second mode

varies between 15% and 19%. An increase of the effective flange width and the coupling of the

walls through the slab result in a slight increase the modal mass of the first mode and in a slight

reduction of the modal mass of the second mode.

Table 4. Modal period of the first two modes

ACI 318-05 flange width Full flange width

Uncoupled walls Coupled walls Uncoupled walls Coupled walls

T1(sec) 0.223 0.212 0.202 0.198

T2(sec) 0.072 0.070 0.067 0.066

Table 5. Modal mass of the first two modes



Mode 1 0.77 0.79 0.80 0.81

Mode 2 0.19 0.17 0.16 0.15

Figure 16. Acceleration time histories and Acceleration Response Spectra of input ground

motions 5% damping ratio.

The amount of viscous damping used in the analysis was a main consideration in this study.

The work of Panagiotou and Restrepo (2006) clearly showed that for the verification of the

experimental response of the UCSD 7-story building slice very small values of viscous damping

were required to accurately match the demands observed in the medium and high intensity input


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24

motions when the building responded in the inelastic range. Panagiotou and Restrepo (2006)

demonstrated that after all the sources of hysteretic behavior have been determined very small

values of viscous damping should be used. The use of larger values of viscous damping can

cause significant underestimation of the buildings response to strong shaking. It should be noted

that the damping ratios determined for elastic response of the UCSD 7-story building under low

amplitude excitation for this building were in agreement with commonly accepted values

(Moaveni et. al. 2006).

For the NDTHA of the PCA building, Raleigh damping based on the initial stiffness was

used. Three cases of damping were considered: (i) 5% damping ratio, (ii) 2% damping ratio and

(iii) 0.3% damping ratio. Equal damping ratios were applied to the first two modes.

Figure 17(a) plots the hysteretic response caused by the Sylmar record for 5% damping

ratio. The hysteretic response is presented in terms of the base shear force of each wall versus the

roof drift ratio. This case does not consider the coupling between the walls and makes use of the

ACI 318-05 effective flange width. The maximum roof drift ratio obtained from the Sylmar

record was 0.3%. The base shear forces observed for both walls of the building exceeded the

probable shear strength Vp calculated in Section 3.2. Yielding of the shear reinforcement was

observed during the analysis but no crushing of the diagonal compression field occurred.

Figure 17(b) plots the hysteretic response caused by the Sylmar record for 2% damping ratio.

The hysteretic response is presented in terms of the base shear force of each wall versus the roof

drift ratio. This case does not consider the coupling between the walls and makes use of the

ACI 318-05 effective flange width. The maximum roof drift ratio obtained from the Sylmar

record was 0.45%. The base shear forces observed for both walls of the building exceeded the

probable shear strength Vp calculated in Section 3.2. Yielding of the shear reinforcement was

observed during the analysis but no crushing of the diagonal compression field occurred.

Figure 17(c) plots the results for 0.3% damping ratio. In this case crushing of the diagonal

compression field is observed in the North wall. Web crushing resulted in excessive shear

deformations and strength degradation. The roof drift ratio for this case reached 0.64%. The

shear force in the North wall also exceeded the probable shear strength but did not reach the

probable shear strength given by ACI 318-05 for web crushing.


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(a) 5% damping ratio

(b) 2% damping ratio

(c) 0.3% damping ratio

Figure 17. Sylmar record - ACI flange width Without coupling - Base Shear of Walls

versus Roof Drift Ratio.


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Figure 18 plots the shear force versus roof drift ratio obtained at the base of the North wall

for 5%, 2% and 0.3% damping ratio. These plots compare the effect of slab coupling. Figure

18(a) plots the results for 5% damping ratio. Wall coupling through the slab stiffens the system,

reduces the maximum displacement and increases slightly the shear force demand in the wall.

Figure 18(b) plots the results for 2% damping ratio. For this case, wall coupling through the slab

increases significantly the shear force demand in the wall. Note that in this case the shear force

nearly equals the probable web crushing force predicted by ACI 318-05. For 5% and 2%

damping ratio, yielding of the shear reinforcement was observed but no crushing of the diagonal

compression field occurred. Figure 18(c) shows the results for 0.3% damping ratio. In this case

crushing of the diagonal compression field and strength degradation occurs. Note that in this

particular case the shear force demand in the North wall exceeds the probable web crushing

shear force predicted by ACI 318-05.

Figure 19 compares the results for the North wall when considering the full flange and the

ACI 318-05 effective flange widths. The results are plotted for 5%, 2% and 0.3% damping. No

slab coupling effects are considered at this stage.

Figure 19(a) plots the results for 5% damping ratio. An increase of the effective flange

width stiffens the system, reduces the displacement demand and increases slightly the shear force

demand when the North wall flange is in tension. Figure 19(b) plots the results for 2% damping

ratio. An increase of the effective flange width stiffens the system, reduces the displacement

demand and increases the shear force demand when the North wall flange is in tension. For both

cases of 5% and 2% damping and full flange the shear force exceeded the probable shear

strength.

Figure 19(c) plots the effect of effective flange width for 0.3% damping ratio. In this case the

shear force in the North wall when the full flange is in tension not only exceeds the ACI 318-05

probable shear strength but it practically reaches the web probable crushing strength. The model

detected yielding of the shear reinforcement but crushing of the diagonal compression field was

not observed. The shear force demand in the wall for the ACI 318-05 effective flange width

exceeded the probable shear strength but remained less than the probable web crushing strength.

The buildings dynamic response to the Los Gatos excitation was less severe than for the

Sylmar excitation. Nevertheless, in most cases studied the shear force demand nearly reached or


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exceeded the probable shear strength of the walls. A summary of all cases investigated will be

discussed in the following section.




Figure 18. Sylmar record ACI flange - Base Shear of Walls versus Roof Drift Ratio -

Effect of Wall Coupling.


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Figure 19. Sylmar record - Base Shear of Walls versus Roof Drift Ratio No wall Coupling

- Effect of Effective Flange Width.


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5. DiscussionTables 6 and 7 summarize the results obtained from the monotonic pushover analyses. Table

6 lists the roof drift ratio at the development of the probable shear strength Vp and the web

crushing strength of the North wall. The shear force exceeds the probable shear strength in the

North wall at very small roof drift ratios in all the cases. Wall coupling through the slab

decreases the roof drift ratio at which the North wall attains the probable shear strength.

The probable web crushing strength is exceeded in all the cases at small roof drift ratios,

except the case of ACI flange width without slab coupling. Both the effect of slab coupling and

increase of effective flange width decrease the roof drift ratio corresponding to development of

the ACI 318-05 probable web crushing strength.

Table 7 shows the observed web crushing strength, from the pushover analyses, normalized

to the ACI 318-05 probable web crushing strength. As it can be seen the ACI 318-05 probable

shear strength does not necessarily coincide with those given by the model. This is because the

model updates the strength of the diagonal compression field based on the tensile strain demands

and accounts for the influence of the previous cyclic load history. The model gives a smaller

strength for the case of no slab coupling and greater strength for the case of slab coupling. Shear

strengths provided by the model should be judged with caution, especially because the database

available for calibrating the model is rather limited. For this reason it is advisable to focus the

results on the probable strength calculated from ACI 318-05.

Table 6. Drift ratios at the development of probable shear and web crushing strength



Roof Drift Ratio at

Vp(%)0.115 0.082 0.071 0.067

Roof Drift Ratio at

ACI Web Crushingstrength (%)

not reached 0.187 0.310 0.160

Table 7. Model web crushing strength normalized to probable web crushing strength



0.84 1.13 0.94 1.15


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Tables 8 and 9 summarize the results of the NDTHA. Table 8 presents the shear force

demand obtained from the NDTHA normalized by the probable shear strength Vp. The shear

force demand in all cases investigated are greater than 82% of the probable shear strength Vp

calculated from ACI 318-05 using probable material properties. Moreover, for the Sylmar record

the force demand exceeded the probable shear strength in all cases.

Table 9 presents the shear force demand normalized by the ACI 318-05 probable web

crushing shear strength. For Sylmar record the shear force demand reached at least 77% of the

probable web crushing strength. The force demand reached and exceeded the probable web

crushing strength in two cases when 0.3% damping ratio was used. Crushing of the diagonal

compression field occurred in the NDTHA for all cases under the Sylmar excitation for 0.3%

damping ratio, except for the case of the full flange width with wall coupling. For Los Gatos

excitation web crushing was not observed in the NDTHA.

Table 8. Shear force demand normalized by the probable shear strength Vp

ACI 318-05 flange Full flange

No slab

couplingSlab coupling

No slab


Sylmar 1.19 1.29 1.27 1.21

5%

da

mping

ratio

Los Gatos 0.82 0.83 0.83 0.83

Sylmar 1.24 1.45 1.37 1.24

2%

damping

ratio

Los Gatos 0.95 0.94 0.98 1.03

Sylmar 1.34 1.63 1.53 1.42

0.3

%

damping

ratio

Los Gatos 1.20 1.12 1.05 1.20


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Table 9. Shear force demand normalized by the probable web crushing strength

ACI 318-05 flange Full flange

No slab


No slab


Sylmar 0.77 0.83 0.82 0.78

5%

damping

ratio

Los Gatos 0.53 0.54 0.54 0.54

Sylmar 0.80 0.94 0.89 0.80

2%

damping

ratio

Los Gatos 0.62 0.61 0.63 0.67

Sylmar 0.86* 1.06* 0.99* 0.92

0.3

%

damping

ratio

Los Gatos 0.77 0.73 0.68 0.78

Note: * web crushing observed in the analysis

It should be noted that the dynamic response of all the walls analyzed can vary significantly

from the monotonic pushover response. This is mainly due to two reasons. The first reason is the

loss of tension stiffening through cyclic response. This effect depends mainly on the amplitude

of the maximum displacement response before the excursion of interest. As an example observe

the analysis case of Sylmar record, with ACI 318-05 flange width and no wall coupling. The

maximum shear force, 80% of the probable web crushing strength, is smaller than the value of

the shear force corresponding to crushing, 84% of the probable web crushing strength, of the

monotonic analysis. This is because during the Sylmar, there is a smaller excursion which causes

loss of a part of the tension stiffening prior to the main pulse that causes crushing of the wall

web.

The second reason is the effect the higher modes have on the magnitude of the base shear

force. For this reason the base shear force can vary significantly under dynamic excitation in

comparison with the monotonic response for the same roof drift ratio. The different frequency

content among the excitations used also explains the differences observed in the shear force

demand.

Wall coupling and the use of the full flange width resulted in stiffening of the system and

reduction of the roof drift ratio demand. The shear force demand increased generally. However,


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there were also cases where stiffening of the system resulted in a reduction of the displacement

and shear force demands.

For the cases where the shear force reached the web crushing strength, a small increase in the

displacement demand drastically changed the response and caused a theoretical collapse. The

brittle nature of a shear failure, the post-failure response is very sensitive to the subsequent

demands the excitation will impose.

6. Design RecommendationsThe analysis performed in this study indicates that there appear to be a potential for shear

failures with the current ACI 318-05 seismic design approach for walls. Avoidance or at least

minimization of shear failures in reinforced concrete structures is a very important goal when

designing for the design earthquake. The analysis performed on the design example shows that

such goal is not achieved with the current approach. It is the view of the authors that the seismic

design of special shear walls should be performed under the same framework established by

ACI 318-05 for the design of special moment resisting frames. In the design of moment resisting

frames shear forces are slaved to the overstrength of the critical regions where flexural plastic

hinges will develop, thus effectively capacity designing the elements. Additional requirements

beyond the evaluation of the shear force corresponding to the overstrength of the critical section

are required for walls. This is because shear force demands in walls are sensitive also to the

coupling of the walls through the slabs and to dynamic effects. The authors propose that the

design of walls with sections other than rectangular should not be performed as a series of

independent rectangular walls. Moreover, the authors propose the following steps to capacity

design a special shear wall of a multistory building:

1. Establish the design moments due to the design lateral forces in the N-S, S-N, E-W andW-E directions. Note that the direction indicated is only schematic and it refers to at

least two directions in two orthogonal axes.

2. Determine the (Pu, Mu) design pairs that meet the ACI 318-05 or ASCE-7 2005 loadcombination requirements.

3. Calculate the longitudinal reinforcement for the most critical N-S, S-N, E-W and W-Eload combination. This can easily be done using a program like PCA Column. This


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program could result in overestimation of the flange width in walls with complex plan

geometries. Note that in the seismic design case, an overestimation of flange widths

could result in overestimation of the flexural capacity of the section, but also in

overestimation of the shear force demand when walls with complex plan geometries are

designed. This is because the conventional Hooke-Bernoulli assumption of plane

sections before bending remain plane after bending is incorrect for these sections.

Because of the consequences of failure, in seismic design of reinforced concrete elements

overestimation of the shear force demand is preferable than the opposite.

4. Starting from the reinforcement as detailed in the drawings and using probable materialproperties, calculate the section flexural overstrength in the N-S, S-N, E-W and W-E

directions. Calculate also the corresponding section overstrength factors.

5. Calculate the wall shear forces compatible with the bending moments established in (1)above. Obtain the wall base shear force at section overstrength by multiplying these

shear forces by their corresponding section overstrength factors. Distribute the wall base

shear force along the height of the wall following a first mode shape function (i.e. code-

like lateral force distribution) and determine the shear force and bending moment

diagrams in the four directions.

6. Determine the shear forces in the walls caused by coupling with the slabs. Determine theshear force and bending moment diagrams due to these forces.

7. Combine the shear force and bending moment diagrams obtained from (5) and (6). Thelateral force vector {F1} resulting in these diagrams is termed here First mode lateral

force vector.

8. Determine the lateral force vector {F2} due to the second mode. Determine the shearforce and bending moment diagrams caused by these lateral forces.

9. Combine the first and second mode shear force and bending moment diagrams.Recognize in the combination the (lack of) correlation between these two modes.

Eq. 6 gives the equation of combining the shear forces due to the flexural overstrength of the

system and the forces due to the second mode response. In Eq. 6 Voiare the shear forces obtained

in (7) and V2ithe shear forces obtained in (8).


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Eq. 7 gives the equation of combining the shear forces due to the flexural overstrength of the

system and the forces due to the second mode response. In Eq. 6 Moiare the shear forces due to

flexural overstrength of the system and M2ithe shear forces due to second mode response.

V

i

=Voi

+!12 V2i

(6)

Mi=M

!

i+ "

12M

2

i

(7)

where !12%1 is the correlation factor between modes 1 and 2. An extensive discussion of the

design approach described can be found in Panagiotou and Restrepo (SEAOC, 2007).

7. Summary and Conclusions(i) This study performed a verification response analysis of the PCA draft design

example of a seven-story reinforced concrete bearing wall building located in an area

of high seismic hazard (zip code 94705). Two dimensional pushover and nonlinear

dynamic time history analyses (NDTHA) were performed on a slice of the building to

evaluate its possible seismic response.

(ii) The analysis tested the effect of the effective flange width, the effect of couplingbetween walls through the slab as well as the effect of viscous damping. The response

was investigated for the effective flange width recommended by ACI 318-05 and alsofor the full flange width. The latter width was studied because the shake table testing

of the UCSD 7-story building indicated this to be the case. Moreover, the response of

the walls in an ideal uncoupled scenario and that of walls coupled by the floor slabs

was also investigated. Finally, the effect of the amount of viscous damping in the

model was also studied. Traditionally a value of 5% damping ratio is used in design.

The elastic response of the UCSD 7-story building to low amplitude excitation gave

damping ratios close to but generally less than 5%. However, the inelastic response of

the building to strong intensity excitation suggested damping ratios approaching zero

at these amplitudes. The analyses performed in this study included two strong

intensity excitations that closely matched the design earthquake response spectrum in

the period band of interest. Because of the proximity of the building to an active fault

the two records used contained distinct near-fault earthquake characteristics. The


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response of the building to these motions was investigated for 0.3, 2% and 5%

damping ratios.

(iii) The monotonic pushover analysis indicated demands at low drift rations thatexceeded the shear force capacity calculated with the ACI 318-05 approach using

probable material strengths. The shear force demand obtained from the NDTHA in all

the cases investigated exceeded 82% of the probable shear strength calculated from

ACI 318-05.

(iv) The observed shear force demand increase was due to three main sources: (i) theparticipation of the T-wall flange in tension in the flexural strength, (ii) the coupling

of the walls through the slab, and (iii) the participation of the higher modes in the

dynamic response. If avoidance of shear failures is a design objective for the design

earthquake then all sources resulting in an increased shear force demand should be

considered.

(v) The flange was considered as an independent member in the design and the effect ofincreasing the flexural capacity and shear force demand was ignored. It is

recommended here that walls with section geometries should not be designed as a

number of independent elements. In addition, the section flexural overstrength and

corresponding shear force increase be evaluated for the design for shear.

(vi) Coupling between the walls through the slab also causes additional increase in theshear force demand in walls. For the specific configuration studied the increase was

mainly on the wall responding with its flange in tension. Thus, for the case of the T-

wall responding with its flange in tension both the effects of flange in tension and

coupling are combined increasing significantly the shear force demand.

(vii) Another source increasing the shear force demand in the walls studied was theparticipation of the higher modes in the response. Because of the dynamic nature of

this effect, such increase was observed only in the NDTHA.

(viii) It is the view of the authors that the seismic design of special shear walls should beperformed under the same framework established by ACI 318-05 for the design of

special moment resisting frames. That is, special walls should be capacity designed.

In the design of moment resisting frames shear forces are slaved to the overstrength

of the critical regions where plastic hinges will develop, thus effectively capacity


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designing the elements. Additional requirements beyond the evaluation of the shear

force corresponding to the overstrength of the critical section are required for walls.

This is because shear force demands in walls are sensitive also to the coupling of the

walls through the slabs and to dynamic effects. This report proposes a framework to

capacity design special shear walls.

8. AcknowledgmentsThe authors sincerely thank the Portland Cement Association for the support in preparing this

report.

9. ReferencesACI 318-05, 2005, Building Code Requirements for Structural Concrete and Commentary, ACI

Committee 318, Farmington Hills, 430 pp.

ASCE 7-2005, 2006, Minimum Design Loads for Buildings and Other Structures, ASCE/SEI 7-

05, American Society of Civil Engineers.

Bertero, V. V., Atkan, A. E., Charney, F., and Sause, R., 1985, Earthquake Simulator Tests and

Associated Experiments, Analytical and Correlation Studies of One-Fifth Scale Model, in

Earthquake Effects on Reinforced Concrete Structures, U.S.-Japan Research, ACI Publication

SP-84, American Concrete Institute, Detroit, , pp. 375-424.

Carr, A. J., 1998, Ruaumoko A Program for Inelastic Time-History Analysis, Department of

Civil Engineering, University of Canterbury, New Zealand.

DIANA, 2007, A finite element program, TNO DIANA, Netherlands.

Kuebitz, K. J., 2002, Columna A Moment-Curvature Program for Columns of Arbitrary

Cross-Sections, University of California San Diego, USA.

Moaveni, B., He, X., Conte, J. P., and Restrepo, J. I., 2006, System Identification of a Seven-

Story Reinforced Concrete Shear Wall Building Tested on UCSD-NEES Shake Table., Proc. of

the 4th World Conference on Structural Control and Monitoring, San Diego, USA.

NZS 3101, 1995, New Zealand Standard, Part 1- The Design of Concrete Structures, Standards

New Zealand, New Zealand.


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Panagiotou, M., Restrepo, J. I., 2006, Model Calibration For The UCSD 7-Story Building

Slice. NEES/UCSD Seminar on Analytical Modeling of Reinforced Concrete Walls for

Earthquake Resistance, La Jolla, California.

Panagiotou, M., Restrepo, J. I. and Conte, J.P., 2007, Shake table test of a 7-story full scalereinforced concrete structural wall building slice Phase I: Rectangular wall, Report No SSRP

07/07, University of California San Diego.

Panagiotou, M., Restrepo, J. I. and Conte, J.P., 2007, Shake table test of a 7-story full scale

reinforced concrete structural wall building slice Phase II: T-wall section, Report No SSRP

07/08, University of California San Diego.

Panagiotou, M., Restrepo, J. I., 2007, Lessons Learnt from the UCSD Full-scale Shake Table

Testing on a 7-Story Residential Building Slice, SEAOC Convention, September 2007, under

publication.

Portland Cement Association (PCA), 2006, Design of a Seven-Story Reinforced Concrete

Bearing Wall Building Located in an Area of High Seismic Risk. Personal Communication.

Vecchio, F.J., Collins, M.P.,1986, The Modified Compression Field Theory for Reinforced

Concrete Elements Subjected to Shear, Journal of the American Concrete Institute, vol. 83, No.

2, pp. 219-231.

PCA Report SN2961 Walls Restrepo

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