12745472 analysis design of strong column weak beam sni 0328472002

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3.1 INTRODUCTION Moment resistant ductile frame of reinforced concrete structure is designed for strength and

ductility. Strength related to the maximum capacity of the structural member to resist the

earthquake load, ductility related to the maximum deformation beyond the yield stress without

loss of strength. To prevent the failure during strong earthquake the column member is designed

stronger than the beam member it is called as strong column and weak beam concept.

This chapter describes the analysis and design of flexural member and column member using the

strong column and weak beam concept.

3.2 BEHAVIOR OF STRONG COLUMN & WEAK BEAM 3.2.1 GENERAL

During the strong earthquake the reinforced concrete structure is designed so it can provide the

energy dissipation as well as possible. The only method can be used to follows the requirement

above is strong column and weak beam design method.

The followings are the major aspect of the strong column and weak beam concept, as follows :

The overall structure is designed so it can develop inelastic structural behavior.

Column is designed stronger than beam it means during strong earthquake column member

remain elastic so it can provide stability and strength of the stories above.

The development of plastic hinge is forms at the end of beam, so the energy dissipation is

occurs in the plastic hinge.

To ensure the perfect energy dissipation at plastic hinge, plastic hinge region required special

reinforcement detailing (confinement) to improve ductility, energy absorption capacity and

perform inelasticity.

3.2.2 PLASTIC HINGE FORMATION

In the strong column and weak beam concept the beam is permitted to yields but the column

remains elastic. The behavior of reinforced concrete beam is more ductile than the reinforced

concrete column, so it is safer to design the location of plastic hinge forms at the end of beam

rather at the column.

The figure below shows the formation of plastic hinge at the end of reinforced concrete beam, as

follows :

CHAPTER

03 ANALYSIS & DESIGN OF STRONG COLUMN & WEAK BEAM – SNI 03-2847-2002


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FIGURE 3.1 FORMATION OF PLASTIC HINGE

3.2.3 DUCTILITY

In general meaning the ductility is the ability of the structural member to deform beyond its yield stress several times without significant losses of its strength. As already known concrete

material is a brittle material so during the strong earthquake this material may fail suddenly.

To provide the ductility of the plastic hinge region which at the end of beam special reinforcement

detailing is required so during the earthquake the plastic hinge can deform beyond its yield stress

without failure.

3.3 STRENGTH REDUCTION FACTOR The following is the strength reduction factor used in the reinforced concrete design based on the SNI

code, as follows :

TABLE 3.1 STRENGTH REDUCTION FACTORS – SNI 03-2847-2002

NO ACTIONS φ

1 Flexure 0.80

2 Shear 0.75

3 Torsion 0.75

4 Axial Tension 0.80

5 Axial Compression – Tie 0.65

6 Axial Compression – Spiral 0.70

7 Bearing on Concrete 0.70

3.4 ANALYSIS & DESIGN OF FLEXURAL MEMBER 3.4.1 GENERAL The design procedure of flexural member / beam using the strong column – weak beam concept is

almost similar to the original reinforced concrete design.


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The followings are the major basic of flexural member design with strong column – weak beam

concept, as follows :

Design of flexural reinforcement due to gravity load, earthquake load is similar to the original

reinforced concrete design.

The shear strength is calculated based on the probable moment resistance, not due to factored

shear force.

Special reinforcement detailing for longitudinal reinforcement, shear reinforcement,

confinement reinforcement and development length and splie of reinforcement.

3.4.2 LIMITATION OF DIMENSION

The followings are the minimum limits of reinforced concrete beam dimension, as follows :

Minimum beam width = 250 mm.

Maximum beam width = width of supporting column + 1.5 depth of beam.

Width to depth ratio ≥ 0.3.

Span to depth ratio ≥ 4 to prevent the deep beam action.

3.4.3 PROBABLE MOMENT RESISTANCE During the strong earthquake the end of beam will yields, if the shear strength is not strong

enough the beam will fail due to shear which is brittle. Based on the requirement the shear design

must be done based on the probable moment resistance of the end of beam. The shear capacity of

the plastic hinge region must be over and above that corresponding flexural failure.

The probable moment resistance is calculated based on the following assumption, as follows :

The flexural reinforcement is enters into the strain hardening area.

The ratio of ultimate tensile strength to yield strength is taken as 1.25.

The strength reduction factor is taken as φ=1.0.

The figure below shows the free body diagram of calculation of probable moment resistance.

T

C

FIGURE 3.2 PROBABLE MOMENT RESISTANCE

The steel stress of the tensile reinforcement is taken as (1.25fy) rather than fy.

The probable moment resistance is calculated, as follows :

⎥⎦

⎤⎢⎣

⎡⎟⎠

⎞⎜⎝

⎛ −=φ2adfA25.10.1M yspr [3.1]


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where :

φMpr = probable moment resistance

As = area of tensile reinforcement

fy = yield strength of tensile reinforcement

d = effective depth

a = depth of compressive block

The depth of compressive block is calculated, as follows :

b'f85.0fA25.1

ac

ys= [3.2]

3.4.4 SHEAR DESIGN

The design shear force for flexure member is calculated based on the shear force due to gravity load

and reversible side sway bending moment (hinging of end of beam).

The figure below shows the shear force diagram due to gravity load and hinging at beam end, as

follows :

FIGURE 3.3 DESIGN SHEAR FORCE

The seismic shear force is :

⎟⎠

⎞⎜⎝

⎛+

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ +=

+−

2Lw

LMM

V u

n

prRprLL

⎟⎠

⎞⎜⎝

⎛−

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ +=

−+

2Lw

LMM

V u

n

prRprLR

LL0.1DL2.1wu +=

[3.3]


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where :

VL = shear force at left side

VR = shear force at right side

MprL = probable moment resistance at left side

MprR = probable moment resistance at right side

DL = uniform gravity load of DL

LL = uniform gravity load of LL

Ln = clear span length

The shear reinforcement is designed with the concrete shear strength at the plastic hinge region

taken as zero :

0Vc = [3.4]

Design of shear reinforcement outside the plastic hinge region is similar to the original


The concrete shear strength Vc is taken zero if :

The axial compressive force is less than 20

'fA cg

3.4.5 REINFORCEMENT DETAILING

A. General

The most important of the earthquake resistant design of reinforced concrete building is the strength

and the ductility. Strength provided by the maximum capacity of the member and ductility is

provided by the good reinforcement detailing especially at the plastic hinge region.

B. Longitudinal Reinforcement

The figure below shows the detailing requirement for longitudinal reinforcement.

FIGURE 3.4 DETAILING REQUIREMENT – LONGITUDINAL REINFORCEMENTS

The followings are the requirements of longitudinal reinforcement detailing for flexural member, as

follows :


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Minimum 2 bars are continuously top and bottom.

Minimum and maximum reinforcement ratio is :

ymin f

4.1=ρ

025.0max =ρ [3.5]

The ductility is decrease if the amount of tensile reinforcement is increase so we need to

limit the reinforcement ratio.

The positive moment strength at the face of beam – column must follows :

( ) ( )−+ ≥ ENDnENDn M5.0M [3.6]

At every section the positive and negative moment strength must follows :

( ) ( ) ( )+−+ ≥ ENDnENDnSPANn M25.0/M25.0M

( ) ( ) ( )+−− ≥ ENDnENDnSPANn M25.0/M25.0M

[3.7]

C. Shear Reinforcement

Shear reinforcement must be designed to resist the seismic design force as explained before. Shear

reinforcement is designed due to shear force from the probable of plastic hinge development at

the end of member not used the factored shear force from lateral structural analysis.

The followings are the basic function of the shear reinforcement in the earthquake resistant building, as

follows :

Provide sufficient shear strength so full flexural strength can be developed.

Ensure the adequate rotation capacity in plastic hinge region.

Provide lateral support to longitudinal reinforcement.

D. Confinement Reinforcement

Confinement reinforcement is used to prevent the buckling of longitudinal reinforcement.

ACI divide to types of confinement reinforcement, as follows :

Hoop, hoop is a closed tie having seismic hook at one end.

Cross Tie, cross tie is continuous reinforcing bar having seismic hook at one end and hook not

less than 90o at other end.

The figure below shows the confinement reinforcement.


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FIGURE 3.5 HOOP & CROSS TIES

The following are the requirements for confinement reinforcement, as follows :

Confinement reinforcement is placed over a length equal to 2h from the face of support / at any

location where the plastic hinge developed.

First rein is place not less than 50 mm from the face of support.

Confinement reinforcement is placed at the lap splice.

Maximum spacing is taken the minimum of :

d/4

8 x of longitudinal reinforcement

24 x confinement reinforcement

300 mm

The figure below shows the confinement reinforcement detailing.

FIGURE 3.6 CONFINEMENT REINFORCEMENT DETAILING

E. Development Length & Splice

The development length and splice of reinforcement must not provided for earthquake resistant

building, as follows :

Within joint.

Within 2h from the face of support.

In location where plastic hinge developed.


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3.5 ANALYSIS & DESIGN OF COLUMN MEMBER 3.5.1 GENERAL

The column member is a compression member which is has lower ductility than the flexural member.

Because it is more difficult to control the ductility in column member so the concept of strong

column – weak beam is used. The column member is designed remain elastic due to strong

earthquake and the flexural member is permitted to yield with special confinement reinforcement to

ensure the ductility. During the earthquake the column member is the only structural member must

keep the stability of the structure.

3.5.2 LIMITATION OF DIMENSION

The followings are the minimum limits of reinforced concrete column dimension, as follows :

Minimum column dimension = 300 mm.

Ratio of shortest dimension to perpendicular dimension ≥ 0.4.

3.5.3 STRONG COLUMN – WEAK BEAM CONCEPT

The column member must be designed to behave remain elastic due to earthquake. To ensure the

column member is still elastic so it must be designed stronger than the flexural member.

The strong column – weak beam concept stipulate the design bending moment for column member is :

( )∑ ∑≥ beamcol M56M [3.8]

where :

∑ colM = sum of moment at joint corresponding to the flexural strength of column at that joint

(sum of column bending strength above & below the beam)

∑ beamM = sum of moment at joint corresponding to the flexural strength of beam at that joint

The figure below shows the explanation of the equation above.

FIGURE 3.7 DESIGN MOMENT FOR STRONG COLUMN


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So the design bending moment at joint of the corresponding column can be written, as follows :

( ) ( )beamnncolnn MM56MM +−+− φ+φ≥φ+φ

( ) ( )beamnncolnn MM56MM −+−+ φ+φ≥φ+φ

[3.9]

where :

φ = strength reduction factor as used

in original reinforced concrete design which is less than 1.0

The column must be designed also due to factored axial load which result in the lowest flexural

strength.

3.5.4 SHEAR DESIGN

The same with the flexural member the shear strength must be designed based on the probable

moment resistance at the plastic hinge region.

hMM

V prBprTe

+= [3.10]

where :

Ve = design shear force of column

MprT = probable moment resistance at op of column

MprB = probable moment resistant at bottom of column

h = clear height of the column

The design shear force must not less than factored shear force from the lateral structural

analysis.

The shear reinforcement is designed with the concrete shear strength at the plastic hinge region (l0

region) taken as zero if the axial compressive force is 20

A'fP gc

u < :

0Vc = [3.11] Design of shear reinforcement outside the plastic hinge region is similar to the original



A. General

The most important of the earthquake resistant design of reinforced concrete building is the strength

and the ductility. Strength provided by the maximum capacity of the member and ductility is

provided by the good reinforcement detailing especially at the plastic hinge region.


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The followings are the requirements of longitudinal reinforcement detailing for column member, as

follows :

Minimum and maximum reinforcement ratio is :

01.0min =ρ

06.0max =ρ [3.12]

Practical reinforcement ratio is between 3.5% and 4.0%.

C. Shear Reinforcement

Shear reinforcement must be designed to resist the seismic design force as explained before. Shear

reinforcement is designed due to shear force from the probable of plastic hinge development at the end of member but shall not less than the factored shear force from lateral structural

analysis.

The followings are the basic function of the shear reinforcement in the earthquake resistant building, as

follows :

Provide sufficient shear strength so full flexural strength can be developed.

Ensure the adequate rotation capacity in plastic hinge region.

Provide lateral support to longitudinal reinforcement.

D. Confinement Reinforcement

The following are the requirements for confinement reinforcement for column member, as follows :

Minimum ratio of spiral confinement is :

yv

cs f

'f12.0≥ρ

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛−≥ρ

yv

c

ch

gs f

'f1AA

45.0 [3.13]

where :

ρs = ratio of volume of spiral reinforcement to core volume

Ag = gross cross section of column

Ach = core area measured from outside of transverse reinforcement

fyv = yield strength of confinement reinforcement

Minimum area of rectangular hoop is :

⎟⎟⎠

⎞⎜⎜⎝

⎛≥

yv

ccsh f

'fsh09.0A [3.14]


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⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛−≥

yv

c

ch

gcsh f

'f1AA

sh3.0A

where :

Ash = area of transverse reinforcement perpendicular to hc

hc = dimension of column core from c – c of transverse reinforcement

FIGURE 3.8 RECTANGULAR HOOP

Confinement reinforcement must be in the form of closed hoop.

Confinement reinforcement is placed over a length equal to l0 from the end of column. The

height l0 is taken as the greater of :

Depth of column at the face of joint.

1/6 of height of column.

500 mm.

Spacing of confinement reinforcement at the l0 region shall not more than :

¼ minimum dimension of column.

1/6 of longitudinal reinforcement.

⎟⎠

⎞⎜⎝

⎛ −+=

3h350100s x , 150s100 ≤≤ where hx is the spacing of confinement legs.

The figure below shows the typical detailing for column member.


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FIGURE 3.9 TYPICAL DETAILING OF CONFINEMENT REINFORCEMENT

E. Development Length & Splice

The development length and splice of reinforcement must follows :

Lap splice are to be used within the center half of column height, it is designed as tension

splice.

Welded splice / mechanical connector can be used at any section, used for alternate

longitudinal reinforcement.


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FIGURE 3.10 SPLICE OF LONGITUDINAL REINFORCEMENT

3.6 ANALYSIS & DESIGN OF JOINT 3.6.1 GENERAL

The most critical location of the structural strength is the joint between beam and column. Due to the

development of plastic hinge at the end of beam the joint will suffer to the shear force acting at the

effective area of joint. The joint must has enough shear strength to resist this force.

Minimum dimension of column parallel to the longitudinal reinforcement of beam is taken as :

φ⋅20 [3.15]

3.6.2 HORIZONTAL SHEAR FORCE Horizontal shear force at the joint is calculated based on the probable moment resistance at the end

of beam (Mpr is calculated with 1.25 fy and φ=1.0).


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The figure below shows the free body diagram of joint.

FIGURE 3.11 FREE BODY OF JOINT

The horizontal force is calculated, as follows :

ulruh VCTV −+= [3.16]

where :

Vuh = horizontal force at joint

Tr = tensile force of longitudinal reinforcement (right side)

Cl = compressive force of concrete (left side)

Vu = shear force of column

3.6.3 SHEAR STRENGTH OF JOINT

The horizontal shear force as above must be less than the shear strength of the joint, as follows :

TABLE 3.2 SHEAR STRENGTH OF JOINT

CONDITION SI

Confined on all faces of beam jcn A'f70.1V =

Confined on three faces / two opposite faces jcn A'f25.1V =

Other case jcn A'f00.1V =

where :

Vn = nominal shear strength of joint


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f’c = concrete compressive strength

Aj = effective area of joint (parallel to the reinforcement generate shear)

For light weight concrete the factor 0.75 is applied.

The strength reduction factor is taken as φ = 0.85.

The effective joint width is taken as the minimum of :

hb +≤

x2b +≤ [3.17]

where:

b = beam width perpendicular to the shear

h = dimension of column parallel to the shear

The effective area of joint is shown in the following figure.

FIGURE 3.12 EFFECTIVE AREA OF JOINT

The strength of the joint based on the test result is just provided by the concrete, it is not too

sensitive to the amount of transverse reinforcement at joint. If the factored shear force is bigger

than the shear strength then just increase the column size / increase the beam width.

The column dimension parallel to the beam reinforcement which is generate shear force at joint

must not less than 20 x maximum diameter of longitudinal reinforcement of beam.


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A. General The detailing of reinforcement in the joint also very important because this area is the critical section

during earthquake.


The longitudinal reinforcement of beam can be anchored to the column with standard 90o hook. There

is small different with the original reinforced concrete design which is in the ldh.

FIGURE 3.13 STANDARD HOOK

The development length ldh beyond the column face is taken as :

TABLE 3.3 DEVELOPMENT LENGTH LDH

SI

c

bydh

'f4.5

dfl ≥

bdh d8l ≥

"6ldh ≥

where :

db = diameter of longitudinal reinforcement

The development length Ldh must not less than 8db or 150 mm.

For straight bar the development is taken as :

TABLE 3.4 DEVELOPMENT LENGTH LD

CONDITION ld

Depth of concrete beneath the reinforcement ≤ 12” dhd l5.2l =

Depth of concrete beneath the reinforcement > 12” dhd l5.3l =

The development length ld must not less than 2.5 ldh(depth of concrete below reinforcement is less

than 300mm), 3.5 ldh(depth of concrete below reinforcement is more than 300mm).

12745472 analysis design of strong column weak beam sni 0328472002

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