seismic design of reinforced concrete...

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Chapter 6 Seismic Design of Reinforced Concrete Buildings

Chapter 6

6.1 Introduction

6.2 Earthquake Damage in Reinforce Concrete Buildings

6.3 Structural System and Seismic Grading for Structures

6.4 Seismic design of RC frames

6.5 Seismic design of RC walls

6.6 Detailing

6.7 Dual system *

6.8 Case Study

The appropriate maximum height for R/C buildings (m)

(Table 6.1.1 in GB50011-2010)

Notes: the height in () is the value listed in GB 50011-2008

Structure Types System Seismic Fortification Intensity

6 7 8 (0.2g) 8 (0.3g) 9

Frame System 60 50 (55) 40 (45) 35 24 (25)

Frame-Wall System 130 120 100 80 50

Structural Wall System 140 120 100 80 60

Frame supported Wall System

120 100 80 50 N.A

Frame- Tube System 150 130 100 90 70

Tube in Tube System 180 150 120 100 80

Slab-Column and Wall System

80(40) 70(35) 55(30) 40 N.A

Seismic grading for reinforced concrete buildings

(Table 6.1.2 in GB50011-2010)

Types of structure Seismic fortification intensity

6 7 8 9

Fram structure

Height (m) ≤24 >24 ≤24 >24 ≤24 >24 ≤24

Frames 4th 3rd 3rd 2nd 2nd 1st 1st

Large span frames

3rd 2nd 1st 1st

Wall-Frame

structure

Height (m) ≤60 >60 ≤24 25~60 >60 ≤24 25~60 >60 ≤24 25~60

Frames 4th 3rd 4th 3rd 2nd 3rd 2nd 1st 2nd 1st

Structural walls

3rd 3rd 2nd 2nd 1st 1st

Structural wall

structure

Height (m) ≤80 >80 ≤24 25~80 >80 ≤24 25~80 >80 ≤24 25~60

Structural walls

4th 3rd 4th 3rd 2nd 3rd 2nd 1st 2nd 1st

be continued

Types of structure Seismic fortification intensity

6 7 8 9

Frame -supported

wall structure

Height (m) ≤80 >80 ≤24 25~80

>80 ≤24 25~80

Struc-tural walls

General 4th 3rd 4th 3rd 2nd 3rd 2nd

Streng-thening

3rd 2nd 3rd 2nd 1stI 2nd 1st

Frames that supporting

walls 2nd 2nd 1st 1st

Framed-tube structure

Frame 3rd 2nd 1st 1st

Tube 2nd 2nd 1st 1st

Tube in tube structure

Exterior tube 3rd 2nd 1st 1st

Interior tube 3rd 2nd 1st 1st

Slab-column-wall structure

Height (m) ≤35 >35 ≤35 >35 ≤35 >35

Columns 3rd 2nd 2nd 2nd 1st

Walls 2nd 2nd 2nd 1st 2nd 1st

(Table 6.1.2 in GB50011-2010)

Flow Chart of seismic design

simplified

m4

m3

m2

m1

K4

K3

K2

K1

Calculation of Eq. Action

Floor 1

Floor 2

Floor 3

Floor 4

D value I-Point

Shear force distribution

Response Eq. Action

Unfavorable Combinations of Some Responses

6.4 Seismic design of RC frames

Three Methods to calculate the Eq. Action

2

Design of Element

Flexural Strength

Shear Strength

Flexural Strength

Shear Strength

The strength of Shear shall be stronger than flexural

columns shall be stronger than beams

Joint shear strength

joint shall be stronger than connected beams and columns

Mc,up

Mc,low

Mb,r

Mb,l

Vc,up

Vb,l

Vb,r

Nc,up

Nc,low

Vc,low Vc,low

Vc,low

Beam

Column

The strength of Shear shall be stronger than fexual

Flow Chart of seismic design 6.4.5 Design of beam-column joints

Principle: strong joints-weak members

The design of beam-column joints is primarily

aimed at:

(i) preserving the integrity of the joint so that the strength

and deformation capacity of the connected beams and

columns can be developed and substantially maintained.

(ii) preventing significant degradation of the joint stiffness

due to cracking of the joint and loss of bond between

concrete and the longitudinal column and beam

reinforcement or anchorage failure of beam reinforcement.

(1)Schematic Diagram

bc

sbo

sb

bjb

jhH

ah

ah

MV

/

/

0

1 (5.41)

bc

sbo

sb

bua

jhH

ah

ah

MV

/

/

0

115.1

(5.42)

(2) Design value of shear force

=1.5,1.35, 1.2 corresponding to grade 1, 2 and 3 for frame structurej

(6.42)

(6.43)

For Grade 1 frame structure at Intensity 9 area, it should also comply with:

strong joints - weak members

s

ahAf

b

bNhbfV sb

svjyv

c

j

jjjtj

RE

j05.01.1

1

(3) Seismic shear strength checking of joint core

s

ahAfhbfV sb

svjyvjjtj

RE

j09.0

1

( .3 )j c c j j

RE

1V 0 f b h

(6.39)

(6.40)

(6.41)

For Grade 1 frame structure at Intensity 9 area, it should also comply with:

6.5 Seismic design of reinforced concrete structural walls

Structural wall system

• Reinforced-concrete structural walls

(commonly referred to as shear walls)

are being used more and more for

resisting earthquake forces, either alone

or in conjunction with ductile moment

resisting frames.

• The reason is that shear walls stiffen a

building, and this reduces nonstructural

damage.

3

• When walls are situated in advantageous position in building, they

can form an efficient lateral-force-resisting system, while

simultaneously fulfilling other functional requirements.

• The extent to which a wall will contribute to the resistance of

overturning moments, story shear forces, and story torsion depends

on its geometric configuration, orientation, and location within the

plane of the building.

6.5.1 Structural wall system

Construction of

RC-Shear Wall

Colum

Slab

Beam

Colum Beam

Main reinforcement of the colum

Stirrup

Main reinforcement of the beam

Longitudinal reinforcement of the wall

horizontal reinforcement of the wall

Strengthening rebar of the opening

• Boundary elements (边缘约束构件) are often present to

allow effective anchorage of transverse beams.

• Boundary elements are often provided

• to accommodate the principal flexural reinforcement,

• to provide stability against lateral buckling of a thin-

walled section and,

• to enable more effective confinement of the compressed

concrete in potential plastic hinges.

Boundary elements 6.5.2 Structural Analysis

Equivalent stiffness of member

• a cantilever model is used for simplicity, to derive the equivalent

flexure stiffness of structural walls.

• For structural walls with regular and uniform stiffness along the vertical

direction, the equivalent flexure stiffness E c Ieq can be obtained.

single wall

Wall with

small openings Coupled wall

a. Walls under vertical load

Where is the coefficient considering construction error

allowance, is the coefficient considering out-plane buckling.

6.5.3 Seismic design of structural walls

)( /

ysc fAAfN (5.67) (6.93)

b. Walls under combination of seismic and gravity loading


(6.97a) 2.5 )2.0(1

wwcc

RE

hbfV

(5.68)

)15.0(1

wwcc

RE

hbfV

(5.69)

(6.98) = /( )c c

0M V h

Where the shear-span-ratio is :

(6.97b)

4

• The design shear force at bottom section in strengthened regions

（底部加强区）of a structural wall

For structure walls in grade 1,2,3 frames, is 1.6, 1.4 and 1.2.

For those with Grade 1 at Intensity 9,

• Design shear force at end section of a coupling beam （连梁）

with a span depth ratio greater than 2.5

• Where is 1.3, 1.2, 1.1 for Grade 1, 2, 3

wvwVV

Gbn

r

b

l

bvb VlMMV /)(

vw


1.1 ( / ) wua w wV M M V

vw

Load carrying capacity of normal cross section of wall under

eccentric axial loading

Walls under eccentric compressive force

)(1 //

cswssys

RE

NNAfAN

(5.74)

)

2()

2(

1/

0

// fw

csw

f

wys

RE

hhNMM

hhfAM

(5.75)

(6.105)

(6.106)

6.5.4 Shear Capacity checking of wall section

Walls with a rectangular section, subjected to a large

eccentric tensile force

wu

u

RE M

eNN 0

0

1

(5.88)

2

2/)

2(

/

0

/

0

fw

ywsw

f

wyswu

hhfA

hhfAM

(5.90)

(6.119)

(6.121)

6.5.4 Shear Capacity checking of wall section Diagonal shear resistance of structural walls under eccentric

compressive loading

Diagonal shear resistance of structural walls under eccentric

tensile loading

Seismic shear resistance of coupling beams

00 8.0)1.04.0(

5.0

11w

shyh

wwwt

RE

hs

Af

A

ANhbfV

(5.91)

00 8.0)1.04.0(

5.0

11w

shyh

wwwt

RE

w hs

Af

A

ANhbfV (5.92)

00 7.005.0

1b

svyvbbc

RE

b hs

AfhbfV

(5.93)

(6.122)

(6.123)

(6.124)

Shear strength check on the construction joints （施工缝） of structural walls

Horizontal construction joints （水平施工缝） are potential planes of weakness for structural walls.

If shear resistance of a construction joint fails to satisfy this requirement, additional steel reinforced bars are needed perpendicular to the horizontal joint, with sufficient anchorage length each side of the joint.

NAfV sy

RE

wj 8.06.01

(5.94)

6.5.5 Design of Structural Wall

Plane layout

Vertical layout

Axial-force ratio

Boundary element

Strengthening region at the bottom

Minimum ratio of reinforcement of wall

Construction requirement of tie beam

5

Plane Layout

Principle：

Increase the integral lateral stiffness, but not too high;

Try to make the stiffness center superpose upon the

centric to reduce eccentricity and avoid torsion;

Avoid short-width wall;

The length of wall should be shorter than 8m and the

height-to-width should be lager than 2;

Wall should be arranged in two ways along the main axis

and the axis of wall should align to the axis of frame.

It’s inappropriate to set the frame beam onto the tie beam.

Vertical Layout

Principle：

The shear wall should be arranged continuously from bottom to

top;

Openings should be lined up in the same place. Irregular

openings should be strengthened;

Pay attention to the situation that the shear wall is set upon

beams. These beams are frame-supported beams, so their

seismic intensity should be upgraded. ;

Try to avoid weak layer. The shear force of weak layer should

multiply the amplification coefficient 1.15;

The out-of-plane stiffness should be controlled.

Bottom Strengthening Region

Purpose：

To ensure draw ability after plastic hinges appear in

the shear walls, the strengthening region at the

bottom should be reinforced.

Principle：

1/8 of the total height of shear wall，

When H>150m, 1/10

Or reinforce the two stories at the bottom

Limit of Axial-Load Ratio

principle：

Increase wall’s drawability to make the shear walls at

the bottom form plastic hingles when facing rare

earthquake, avoiding brittle failure.

Axial pressure N based on representative value of

gravity load. (different from colums)

Axial-load ratio

Ⅰ（9 degree） Ⅱ（7,8 degree） Ⅱ

N/fcA 0.4 0.5 0.6

Boundary Member

Restraining boundary member

Constructing boundary member

Principle

Restraining boundary member：the ends of Grade 1 and 2’s shear wall’ bottom-

strengthening region and the first story above;

Constructing boundary member：the rest

ends of Ⅰ,Ⅱ shear wall. The ends of Ⅲ,Ⅳ shear wall and non-seismic design wall.

Restraining Boundary Member

Length of wall: lc

Volume stirrup ratio:

Characteristic value of stirrup: v

Item Ⅰ（9 degree） Ⅰ（7,8 degree） Ⅱ

v 0.20 0.20 0.20

lc (embedded

column) 0.25hw 0.20hw 0.20hw

lc (flanking column

or column at the

end of wall)

0.20hw 0.15hw 0.15hw

cv v

yv

f

f

6

Diameter of stirrup: 8mm;

Stirrup spacing value: 100mm（Ⅰ）

150mm（Ⅱ）

Longitudinal reinforcement:

range—shaded area A;

Area—1.4%， 1.2%， 1.0%；

（ special Ⅰ,Ⅰ,Ⅱ shear wall respectively ）

Diameter： 616, 614;

Restraining Boundary Member

约束边缘构件

约束

边缘构件截面及配筋


Length of wall, minimum of stirrup, maximum stirrup

spacing

Strengthening portion at the bottom Other locations

Stirrups or tie bar Stirrups or tie bar

Seismic

grade of

structure

s

Minimum

amount of

longitudinal

reinforcements

(the greater value

should be used)

Minimu

m

diameter

(mm)

Max.

spacing

(mm)

Minimum

amount of

longitudinal

reinforcements

(the greater value

should be used)

Minimu

m

diameter

(mm)

Max.

spacing

(mm)

1 0.010Ac, 616 8 100 0.008Ac, 614 8 150

2 0.008Ac, 614 8 150 0.006Ac, 612 8 200

3 0.006Ac, 612

（0.005Ac, 412）

6 150 0.005Ac, 412 6 200

4 0.005Ac, 412 6 200

（150）

0.004Ac, 412 6 250

（200）


Minimum Dimension of Shear Wall

Strength of concrete ≥C20；

Thickness of shear wall

Seismic

intensity region Embedded column Non-embedded column

Ⅰ,Ⅱ

Strengthening

region at the

bottom

H/16 200 h/12 200

The rest H/20 160 h/15 180

Ⅲ, Ⅳ

Strengthening

region at the

bottom

H/20 160 H/20 160

The rest H/25 160 H/25 180

Non-

seismic

design

all H/25 160 H/25 180

1. Non-seismic action：

2）Seismic action：

Shear-span ratio>2.5：

Shear-span ratio≤2.5：

.w c c w w0V 0 25 f b h

( . )w c c w w0

RE

1V 0 20 f b h

( . )w c c w w0

RE

1V 0 15 f b h

c

c

w0

M

V h

Minimum Dimension of Shear Wall

7

Distributing reinforcements

Lateral and vertical reinforcemens：

swsw

w

A

b s

Shear wall

Seismic

intensity

Minimum ratio of

reinforcement

Maximum

spacing value

Minimum

diameter

Normal

height Ⅰ, Ⅱ, Ⅲ 0.25% 300 8

Normal

height

Ⅳ, non-seismic

design 0.20% 300 8

B height Special Ⅰ

Strengthening

region: 0.40%

The rest: 0.35%

300 8

Temperature

-stress-

increase

region

Seismic and

non-seismic

0.25%

200 ——

Design of Tie Beam

principle：

Similar to the design of RC beam;

According to the design of double-tendon section beam;

Moment and shear force should be adjusted：

Ideal elastic：6,7 degree： ×0.8，

8,9 degree： ×0.5，

Not consider the function of tie beams when meeting

rare earthquake.

Flexure capacity：

'( )y s b0M f A h a

1. non-seismic action：

2. seismic action：

Span-to depth ratio>2.5:

Span-to-depth ratio<=2.5:

. svw t b b0 yv b0

AV 0 7 f b h f h

s

( . )svb t b b0 yv b0

RE

A1V 0 42 f b h f h

s

( . . )svb t b b0 yv b0

RE

A1V 0 38 f b h 0 9 f h

s

Design of Tie Beam---Shear Capacity

Minimum dimension：

1. non-seismic action：

2. seismic action：

Shear-span ratio>2.5：

Shear-span ratio≤2.5：

.w c c w w0V 0 25 f b h

( . )w c c w w0

RE

1V 0 20 f b h

( . )w c c w w0

RE

1V 0 15 f b h

Design of Tie Beam

Strong-shear-weak-bending

Ⅰ,Ⅱ,Ⅲ,Ⅳ seismic：

9 degree：

l r

b bb vb Gb

n

M MV V

l

.l r

bua buab Gb

n

M MV 1 1 V

l

Design of Tie Beam Reinforcement of tie beams

8

Exercises

Given: A 12-storey office building will be built in the area, which seismic

fortification is 7. The building is designed to use concrete (C35, fc＝

16.7N/mm2）. The length of the plane of the building is 48m, with the

spacing of columns is 8.0m, the width is 24m, with spacing of columns is

6.0m, meanwhile, the height for ground floor is 5.5m, and for the other floors

are all as 3.9m. The dead loads and live loads for every storey is 5.5kN/m2 and

2.5kN/m2 respectively.

Ask: 1. Please use the limitation of axial-force ratio to evaluate the section

dimension of column at bottom story.

2. Check the dimension of column according to the minimum requirement for

shear resistant.

3. According to GB 50011,2010, please give the limitation value of drift,

torsion action, minimum reinforcement ratios and maximum reinforcement

ratios of column and beam respectively.

Review this chapter !

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