Progressive Collapse Resistance of Reinforced Concrete Frame Structures Prof. Xianglin Gu College of Civil Engineering, Tongji University 28/12/2012

Progressive Collapse Resistance of Reinforced Concrete Frame Structures

Prof. Xianglin Gu

College of Civil Engineering, Tongji University

28/12/2012

Acknowledgements

This research project is sponsored by the National

Natural Science Foundation of China (No.

90715004) and the Shanghai Pujiang Program (No.

07pj14084).

Outline

Introduction

Experimental Investigation

Testing Specimens Test Setup and Measurements Test Results

Simplified Models for Nonlinear Static Analysis of RC Two-bay Beams

Conclusions

Introduction

Ronan Point (1968 )

Alfred P. Murrah (1995)

World Trade Center (2001)

Important buildings may be subjected to accidental loads, such as explosions and impacts, during their service lives. It is, therefore, necessary not only to evaluate their safety under traditional loads and seismic action (in earthquake areas), but also the structural performance related to resisting progressive collapse.

http://news.jnzc.net/world/200609/142902.shtml

Introduction

For a reinforced concrete (RC) frame structure, columns on the first floor are more prone to failure under an explosion or impact load, compared with other components. The performance of a newly formed two-bay beam above the failed column determines the resistance capacity against progressive collapse of the structure.

an extetior column failed

an extetior column failed

an intetior column failed

Previous Experimental Work

At present, experimental studies have mainly focused on RC beam-column subassemblies, each of which consists of two end-column stubs, a two-bay beam and a middle joint, representing the element above the removed or failed column.

Su, Y. P.; Tian, Y.; and Song, X.S., “Progressive collapse resistance of axially-restrained frame beams”, ACI Structural Journal, Vol. 106, No.5, September-October 2009, pp. 600-607.Yu, J., and Tan, K.H., “Experimental and numerical investigation on progressive collapse resistance of reinforced concrete beam column sub-assemblages”, Engineering Structures, 2011, http://dx.doi.org/10.1016/j.engstruct.2011.08.040.

Choi H., and Kim J., “Progressive collapse-resisting capacity of RC beam–column sub-assemblage”, Magazine of Concrete Research, Vol.63, No.4, 2011, pp.297-310.

Yi, W.J., He, Q.F., Xiao, Y, and Kunnath, S.K., “Experimental study on progressive collapse-resistant behavior of reinforced concrete frame structures”. ACI Structural Journal. Vol.105, No.4, 2008, pp. 433-439.1

Previous Experimental Work

From the above experiments, it can be concluded that the compressive arch and catenary actions were activated under sufficient axial constraint and that the vertical capacities of two-bay beams were improved due to the compressive arch action.

However, the mechanism of the onset of catenary action was not sufficiently clear and needed to be further studied. Meanwhile, the contribution of the floor slab in resisting progressive collapse has largely been ignored, and the influence of the space effect on the performance of a frame structure is not studied deeply.

What does this study examine

• This study has investigated the mechanisms of progressive collapse of RC frame structures with experiments on two-bay beams, where the space and floor slab effects were considered. • Based on the compressive arch and catenary actions and the failure characteristics of the key sections of the beam observed in the test, simplified models of the nonlinear static load-displacement responses for RC two-bay beams were proposed.

Experimental Investigation

Testing Specimens

Test Setup and Measurements

Test Results

Testing Specimens

420

0

7800 7800 7800 7800

1 2 7 4 3 6 5

A

B

C

D

E

600×600 400×600

400×400

Region to be tested

7800 7800

420

0 42

00

420

0

Plane layout of a prototype structure

Plan View of XB7 (B1A, B1, B2, TB3, TB4, TB5 and XB6)

B2 (XB6)

150

125

12

5

150

0.5w

0.5w

ln

b 125

125

150

150

the longitudinal direction

the

tran

sver

se d

irec

tion

b

l n

100

2C8

100 2C6

100

150

2C8

2C8

B1A and B1 (XB6)

Elevation View of B1A, B1, B2 and XB6 Splice of B1A

TB3, TB4 and TB5 (XB7) Elevation View of TB3, TB4, TB5 and XB7

h

A6@65

ln

100

100

150 350

250

2C8 or 2C6

2C8

250 50 50

gauges

ln

A6@65

A10@80 #12@100

150

100

350

2C8

250

250

2C10

2C10

100

h t

50 50

100

100 1

50

100 gauges

40

#12@100

100

2C8

2C8 h 50

gauges

Test subassemblies and reinforcement layout

The test specimens contained 1/4-scaled RC structures: rectangle beam-column subassemblies (named B1A, B1, B2 respectively), T-beam-column subassemblies (named TB3, TB4 and TB5 respectively), a substructure with cross beams (named XB6) and a substructure with cross beams and a floor slab (named XB7).

Testing Specimens

Table 1 Specimen properties

Specimen No.Section, b×h for beam and

w×t for flange, mm

*ln,mm

Top bars and reinforcement ratios

Bottom bars and reinforcement ratios

*fc ,kN/mm2

*Ec(×104),kN/mm2

B1A 100×150 1800 28(ρ=0.86%) 28(ρ=0.86%) 25.6 2.82

B1 100×150 1800 28(ρ=0.86%) 28(ρ=0.86%) 21.8 2.73

B2 100×100 900 28(ρ=1.49%) 26(ρ=0.83%) 25.8 2.80

TB3Beam 100×150

180028(ρ=0.86%) 28(ρ=0.85%)

28.9 2.86Flange 450×40 #12@100(ρ=0.31%)

TB4Beam 100×150

180028(ρ=0.84%) 28(ρ=0.84%)

26.5 2.86Flange 450×40 #12@100(ρ=0.31%)

TB5Beam 100×150

180028(ρ=0.85%) 28(ρ=0.86%)

29.8 2.86Flange 450×40 #12@100(ρ=0.31%)

XB6Longitudinal beam 100×150 1800 28(ρ=0.85%) 28(ρ=0.86%)

32.3 2.87Transverse beam 100×100 900 28(ρ=1.41%) 26(ρ=0.80%)

XB7

LongitudinalBeam 100×150

180028(ρ=0.86%) 28(ρ=0.85%)

31.5 3.02Floor 1950×40 #12@100(ρ=0.31%)

TransverseBeam 100×100

90028(ρ=1.45%) 26(ρ=0.83%)

Floor 3750×40 #12@100(ρ=0.31%)

* ln represents the net span of a beam. fc represents the compressive strength of concrete. Ec represents the Young's modulus of concrete.

Testing Specimens

Table 2 Reinforcement properties

typeDiameter,

mm Yield strength fy ,

kN/mm2 Ultimate strength fu ,

kN/mm2

Elongation,(%)

Young's modulus Es(×105),kN/mm2

6 5.75 569 714 14.9 2.34)

8 7.60 537 670 14.0 1.92

#12 2.80 238 319 24.0 1.46

6 6.60 329 523 22.1 2.18

bolts 19.63 561 671 - 1.86


Boundary conditions and test setup of specimens

Bolts

RC reaction wall

End column stab Roller Torque angle indicator

Bolts

Hydraulic actuator

ln

Strain gauges

LDVT

BE,FC *BM,FT *BE,FC BM,FT

Constraint beam P

h

150

ln

N N

350 150 400


Test Results

Failure modes of specimens

(a) Specimen B1A (b) Specimen B1 (c) Specimen B2

(d) Specimen TB4 (e) Specimen TB5 (f) Specimen XB6

(h) Specimen XB7: Bottom view(g) Specimen XB7: Top view

Test Results

Compressive arch action and catenary action

BM Failed column

P N N

(b) catenary action for top bars in beam

BM Failed column

P N N

BE BE

BM

(c) catenary action for top and bottom bars in beam

BE

Failed column

P N N

(d) catenary action for bottom bars in beam

(a) compressive arch action

BE

BM

BE

BM Failed column

N N

P

B2

B1A,B1

Test Results

The details of the test results are presented by

dividing the specimens into 4 types:

• RC Beam-column subassemblies

• RC T-beam-column subassemblies

• RC Cross-beam systems without floor slab

• RC Cross-beam systems with a floor slab

RC Beam-column Subassemblies

It can be seen that the failure process can be divided into three stages: an elastic stage, a compressive arch stage and a catenary stage.

-60

-40

-20

0

20

40

60

0 50 100 150 200 250 300

Ver

tica

l L

oad

P (

kN

)

Middle Joint Deflection Δ (mm)

Specimen B1ASpecimen B1

Ho

rizo

nta

lRea

ctio

n N

(k

N)

Elestic Stage

Compressive Arch Stage Catenary Stage

Yielding at BE and BM Peak Load

Vertical load P and horizontal reaction force N versus middle joint deflection Δ for B1A and B1

Vertical load P and horizontal reaction force N versus middle joint deflection Δ for B2

-30

-20

-10

0

10

20

30

40

0 50 100 150 200 250

Ver

tica

l Loa

d P

(kN

)

Middle Joint Deflection Δ (mm)Hor

izon

tal

Rea

ctio

n N

(kN

)

Compressive Arch Stage

Catenary Stage

Elestic Stage

Peak Load

Yielding at BE and BM

(a) Specimen B1A (b) Specimen B1 (c) Specimen B2


Strain of rebars in B1A

(a) at BM for B1A

-4000

-2000

0

2000

4000

6000

8000

0 50 100 150 200 250 300 Middle Joint Deflection Δ (mm)

Top rebar 1Top rebar 2Bottom rebar 1Bottom rebar 2Yield Strain

Yield Strain

Stra

in o

fB

ars

at B

M

Middle Joint Deflection Δ (in.)

0 9.87.95.93.92.0 11.8

(×10

-6)

(b) at BE for B1A

-6000

-4000

-2000

0

2000

4000

6000


Top rebar 1Top rebar 2Bottom rebar 1Bottom rebar 2

Yield Strain

Yield Strain

Stra

in o

fB

ars

BE


0 9.87.95.93.92.0 11.8

(×10

-6)


The shapes of the curves for B1A and B1 were similar, and no indication of splice failure was observed in B1A, implying that the lap splice according to GB50010-2010 can meet the continuity requirements in progressive collapse resistant design.

-60

-40

-20

0

20

40

60

0 50 100 150 200 250 300

Ver

tica

l Loa

d P

(kN

)


Specimen B1ASpecimen B1

Hor

izon

tal

Rea

ctio

n N

(kN

)

Elestic Stage


Yielding at BE and BM Peak Load

Vertical load P and horizontal reaction force N versus middle joint deflection Δ for B1A and B1

(Definitions of BE and BM are given in Table 3)

RC T-Beam-column Subassemblies

-10

0

10

20

30

0 50 100 150 200 250 300

Ver

tica

l Loa

d P

(kN

)


Specimen B1Specimen TB3Specimen TB4Specimen TB5

Elestic Stage


Peak Load

Yielding at BE and BM

Vertical load P versus middle joint deflection Δ for B1, TB3, TB4 and TB5


Specimen TB4 Specimen TB5


Ps

NN N NPs

TB3,TB4,TB5

(a) Compressive arch action (b) catenary action

Considering the effect of floor slabs, there was only one mechanism that activated the catenary action, that is, the bottom beam bars fractured at BM.


-2000

0

2000

4000

6000


Flange rebar 1Flange rebar 2Flange rebar 3Flange rebar 4

Yield strain

Str

ain

ofB

ars

at F

C

from inside to outside:1,2,3,4

(×1

0-6

)


0 2.42.01.61.20.80.4

-2000

0

2000

4000

6000


Flange rebar 1Flange rebar 2Flange rebar 3Flange rebar 4

Yield strain

Stra

in o

fBar

s at

FT

from inside to outside:1,2,3,4

(×10

-6)


0 2.42.01.61.20.80.4

Strain of steel bars at FT for TB5 Strain of steel bars at FC for TB5

RC Cross-beam system without a floor slab


Vertical load P versus middle joint deflection Δ for B1, B2 and XB6

-20

0

20

40

60

80

0 50 100 150 200 250 300

Ver

tica

l Loa

d P

(kN

)


Specimen B1Specimen B2Specimen XB6

Compressive Arch Stage

Elestic Stage

Catenary Stage

Peak LoadYielding at BE and BM

-30

-15

0

15

30

45

60

0 50 100 150 200 250Hor

izon

tzl r

eact

ion

N (k

N)

Middle joint deflection Δ (mm)

Specimen B2

Transverse of XB6

(a) longitudinal direction (b) transverse direction

-60

-45

-30

-15

0

15

30

45

60

0 50 100 150 200 250 300

Hor

izon

tzl r

eact

ion

N (k

N)

Middle joint deflection Δ (mm)

Specimen B1

Longitudinal of XB6

Horizontal reaction N versus middle joint deflection Δ for two directions of XB6

RC Cross-beam system with floor slab


Vertical load P versus middle joint deflection Δ for XB6 and XB7

-20

0

20

40

60

80

100

0 50 100 150 200 250

Ver

tica

l L

oad

P (

kN

)


Specimen XB7Specimen XB6

Elestic Stage


Peak LoadYielding at BE and BM

Simplified Models for Nonlinear Static Analysis

For the simplicity, the models of the nonlinear static analysis of RC two-bay beams were derived by linking the critical points.

0

Compressive arch stage

Catenary stage Elastic stage

u s

tr

a

sP

yP

cuP

auP

trP

y

0


Catenary stage

Elastic stage

'u

a 'tr a

sP

yP 'cuP

auP

ttrP

y

btrP

Static load-deflection response for two-bay beams (the catenary action was activated by the concrete crushing)

Static load-deflection response for two-bay beams (the catenary action was activated by the beam bars fracture)

失效柱

Ps 1

ts LA

1t

y Lf

1t

u Lf

1bs LA

1b

y Lf

1b

u Lf

0ts LA

0t

y Lf 0t

u Lf

0bs LA

0b

y Lf

0b

u Lf

1ts RA

1t

y Rf 1t

u Rf

1bs RA

1b

y Rf

1b

u Rf

0bs RA

0b

y Rf

0b

u Rf

0ts RA

0t

y Rf 0t

u Rf

BE BE BM BM

The areas and the yielding and ultimate strengths for the continuous top beam bars were t

sA , tyf and

tuf , and for the continuous

bottom beam bars were bsA , b

yf and buf

Areas and yielding and ultimate strengths for the top and bottom bars in beams


0



u s

tr

a

sP

yP

cuP

auP

trP

y

0


Catenary stage

Elastic stage

'u

a 'tr a

sP

yP 'cuP

auP

ttrP

y

btrP



The yielding load, which was the load of the ending of the elastic stage, could be determined not considering the influence of the axial constraint.

1 0 1 0

1 2

y L y L y R y Ry

n n

M M M MP

l l

失效柱

Ps 1

ts LA

1t

y Lf

1t

u Lf

1bs LA

1b

y Lf

1b

u Lf

0ts LA

0t

y Lf 0t

u Lf

0bs LA

0b

y Lf

0b

u Lf

1ts RA

1t

y Rf 1t

u Rf

1bs RA

1b

y Rf

1b

u Rf

0bs RA

0b

y Rf

0b

u Rf

0ts RA

0t

y Rf 0t

u Rf

BE BE BM BM tsA

tyf t

uf

bsA

byf b

uf

Areas and yielding and ultimate strengths for the top and bottom bars in beams

3 3 2 3 22 23 2

3 2

3 2 32

6 16 2y

ys

n l ml m m nP n l m mnm m m

B nl l

the stiffness of the most unfavorable section of beam (BM)

the yielding moment of two beam ends, respectively

the yielding moment of the left and right sections of beams near the middle column, respectively

'1 0.5nm l b '

2 0.5nn l b


0



u s

tr

a

sP

yP

cuP

auP

trP

y

0


Catenary stage

Elastic stage

'u

a 'tr a

sP

yP 'cuP

auP

ttrP

y

btrP



To determine the ultimate bearing capacity of the RC two-bay beam considering the compressive arch action, it was assumed that: 1) the beam between the plastic hinges is elastic; 2) the stress distribution block of concrete in compressive zone at BE and BM can be equivalent to the rectangular block; 3) the axial reactions N applied on BE and BM have the same value and the applied points of N are all on the middle of the sections;4) the tensile strength of concrete is neglected.

Δs

Ps

b' ln1 ln2

Pu

t t

BE

BM BM

BE

Deformation mode of two-bay beams under ultimate state considering the compressive arch action


BE

BM

BE

BM Failed column

N N

P


11 1 1 0 1

1cosn

n L L

l tl e z tg z tg

0


Catenary stage

Elastic stage

'u

a 'tr a

sP

yP 'cuP

auP

ttrP

y

btrP



From the Deformation made of two-bay beams under ultimate state considering the compressive arch action, the deformation compatibility of the RC two- bay beams can be derived.

Deformation made of two-bay beams under ultimate state considering the compressive arch action

the drift of BE

Δs

ln1+t

ln1-e

z1L

z0L

BE

N

N

BM

θ1

xn1L

xn0L

Geometrical relationship of BE and BM for the left bay of two-bay beams

Δs

Ps

b' ln1 ln2

Pu

t t

BE

BM BM

BE

1 /ne N l EA

0 0 0 10.5 0.5 /L n L Lz h x h x

1 1 1/ /s n s nl e l

For the left bay: 2

1 01 2s s

L L s Lx x h B N

2

1 01 2s s

R R s Rx x h B N

21 0 1 0

1

2sL L R R s s L Rx x x x h B B N

For the right bay:

For the two- bay beam: 2 2

2 2

2n n s

Rs

l lB

EA k EA

2 21 1

2n n s

Ls

l lB

EA k EA

0



u s

tr

a

sP

yP

cuP

auP

trP

y


0



u s

tr

a

sP

yP

cuP

auP

trP

y

0


Catenary stage

Elastic stage

'u

a 'tr a

sP

yP 'cuP

auP

ttrP

y

btrP



x1L, x0L, x1R and x0R can be determined by the equilibrium conditions of the internal forces at BE and BM.

Stress and strain distribution of BE in the left bay

N

1 1b bs L s LA

1 1t ts L y LA f

cu1

bs L

1 cf

1Lx

1u LM

11 1 1

1

1 1 1 1

1b

b b bss L s cu s L y L

Lb b b bs L y L s L y L

aE f

xf f

The stress of bottom bars can be derived.

1 11 1 1 1 1

1 1

bb b L ss L y L L L Lb b

L s s

x af D x C

a a

11

1 1

by L

L b bL s s

fD

a a

1 11

1 1

by L

LL

fC

11

11L b

y L

s cu

f

E

simplified


BE

BM

BE

BM Failed column

N N

P


0



u s

tr

a

sP

yP

cuP

auP

trP

y

0


Catenary stage

Elastic stage

'u

a 'tr a

sP

yP 'cuP

auP

ttrP

y

btrP



x1L, x0L, x1R and x0R can be determined by the equilibrium conditions of the internal forces at BE and BM.

Accordingly, the bending moment of BE can be determined as

In a similar way, x0L, x1R and x0R can be determined and Mu0L, Mu1R and Mu0R can also be calculated accordingly.

According to the equilibrium condition of the internal forces at BE, x1L can be determined.

1 1 1 1 1 1t t b by L s L c L s L s Lf A N f bx A

11 1 1 1 1 1 1 02 2 2 2

b b b t tLu L c L s L s L s y L s L

xh h hM f bx A a f A h


BE

BM

BE

BM Failed column

N N

P


N and are quadratic functions of Δs and there is always a Δs that makes become the maximum. and the corresponding vertical deflection can be determined by trial and error method.

auP a

uPmax

auP '

s

Given the stiffness of the axial constraint and the properties of the two-bay beam .

Assume all rebars at BE and BM are yielded and the expressions of x1L, x0L, x1R and x0R can be determined.

Set a starting value for Δs.

Determine N.Calculate x1L, x0L, x1R and x0R. Judge whether the rebars are yielded or not.

Choose the appropriate expressions of x1L, x0L, x1R and x0R , determine N again.

Calculate x1L, x0L, x1R , x0R and the bending moment s Mu1L, Mu0L, Mu1R and Mu0R .

Calculate . auP

1

a au un n

P P

0

Δs ＝ Δs +dΔs

become the maximum , and ， .

auP max

a au uP Pmax

auP

0'

a s y


0



u s

tr

a

sP

yP

cuP

auP

trP

y


The load and deflection at the transition point of the compressive arch stage and the catenary stage can be determined on the base of the mechanism activated the catenary action.

Concrete is deactivated at the transition point,

So, Loadings working on the two-bay beam at the catenary stage

1 2

1 1t t b bs y s y s s

n n

P f A f Al l

ln1 b'

Δs

Ps T

ln2

θ1 θ2 T

Ps

tr yP P

1 2

1 2

tr n ntr t t b b

y s y s n n

P l l

f A f A l l

BM Failed column

P N N

BE BE

BM


When the catenary action is activated by the concrete crushing, the relationship of Ps and Δs at the catenary stage can be expressed as


0



u s

tr

a

sP

yP

cuP

auP

trP

y


Loadings working on the two-bay beam at the catenary stage

ln1 b'

Δs

Ps T

ln2

θ1 θ2 T

Ps

BM Failed column

P N N

BE BE

BM


The vertical deflection at the ending of the catenary stage is depended on the elongations of the top and bottom bars.

According to GSA2003, the acceptance criterion of the rotation degree for beam is 12°.

So,

1 212 0.2 min( , )u n n n n nl tg l l l l

1 2

1 1c t t b bu y s u s u

n n

P f A f Al l

1 2

1 1c t t b bu u s y s u

n n

P f A f Al l

or



ln1 b'

Δs

Ps T

ln2

θ1 θ2 T

Ps

0


Catenary stage

Elastic stage

'u

a 'tr a

sP

yP 'cuP

auP

ttrP

y

btrP


1 2

1 1t ts y s s

n n

P f Al l

BM Failed column

P N N



BE

Failed column

P N N


1 2

1 1b bs y s s

n n

P f Al l

When the catenary action is activated by the fracture of bottom bars at BM, the relationship of Ps and Δs at the catenary stage can be expressed as

When the mechanism is the fracture of the top bars at BE, the relationship of Ps and Δs at the catenary stage can be expressed as



ln1 b'

Δs

Ps T

ln2

θ1 θ2 T

Ps

0


Catenary stage

Elastic stage

'u

a 'tr a

sP

yP 'cuP

auP

ttrP

y

btrP


BM Failed column

P N N



1 2

1 1t ts y s s

n n

P f Al l


0 0' '

1 2

y yb u u

trn n

M MP

l b l b

' 1 2

1 2

btr n n

tr b by s n n

P l l

f A l l

The vertical load was carried by the top beam bars after the bottom bars fracture. So the bottom value of the vertical load at the transition point can be determined as

So,


Due to the load-deflection response for the mechanisms of concrete crushing and rebars fracture being coincident before fracture of bars , the top value of the vertical load at the transition point can be determined by the descending branch in the compressive arch stage for the mechanism of concrete crushing.


ln1 b'

Δs

Ps T

ln2

θ1 θ2 T

Ps

0


Catenary stage

Elastic stage

'u

a 'tr a

sP

yP 'cuP

auP

ttrP

y

btrP


BM Failed column

P N N



The top value of the vertical load at the transition point can be determined as

'a

t a u trtr u tr a

tr a

P PP P

sP

0 a tr s

ttrP

auP

trP

'tr

Static load-deflection responses for two-bay beams



ln1 b'

Δs

Ps T

ln2

θ1 θ2 T

Ps

0


Catenary stage

Elastic stage

'u

a 'tr a

sP

yP 'cuP

auP

ttrP

y

btrP

Static load-deflection response for two-bay beams (the catenary action was activated by the beam bars fracture)1 2

1 1t ts y s s

n n

P f Al l

BM Failed column

P N N



The carrying capacity at the catenary stage is depended on the ultimate strength of the top bars.

1 2

1 1c t tu u s u

n n

P f Al l





ln1 b'

Δs

Ps T

ln2

θ1 θ2 T

Ps

0


Catenary stage

Elastic stage

'u

a 'tr a

sP

yP 'cuP

auP

ttrP

y

btrP


1 2

1 1c t tu u s u

n n

P f Al l


BE

Failed column

P N N


1 2

1 1b bs y s s

n n

P f Al l

When the mechanism is the fracture of the top bars at BE, the relationship of Ps and Δs at the catenary stage can be expressed as

0 0' '

1 2

y yb u u

trn n

M MP

l b l b

' 1 2

1 2

btr n n

tr b by s n n

P l l

f A l l

The vertical load was carried by the top beam bars after the bottom bars fracture.

'a

t a u trtr u tr a

tr a

P PP P


0

5

10

15

20

25

30

0 100 200 300 400

Ver

tical

load

P(k

N)

Middle joint deflection Δ(mm)B1A

Ps-ex Ps-cal

0

5

10

15

20

25

30

0 100 200 300 400

Ver

tical

load

P (k

N)

Middle joint deflection Δ(mm)B1

Ps-ex Ps-cal

0

5

10

15

20

25

30

0 50 100 150 200 250

Ver

tical

load

P (k

N)

Middle joint deflection Δ(mm)B2

Ps-cal Ps-ex

0

50

100

150

200

0 50 100 150 200 250 300

Ver

tical

load

P (k

N)

Middle jiont deflection Δ(mm)A1

Ps-ex Ps-cal

0

50

100

150

200

250

0 50 100 150 200 250 300

Ver

tical

load

P (k

N)

Middle jiont deflection Δ(mm)A5

Ps-ex Ps-cal

0

30

60

90

120

150

0 100 200 300 400 500

Ver

tical

load

P (

kN)

Middle jiont deflection Δ(mm)B3

Ps-ex Ps-cal

(a) Static load-deflection response for test specimens

(b) static load-deflection response for test specimens carried by Su et al [1]

static load-deflection response for test specimens

It can be seen that the shapes of the calculated load-deflection response curves have good match with the tested curves.

Conclusions

• Based on the test results, it can be concluded that the failure process for the specimens can be divided into an elastic stage, a compressive arch stage and a catenary stage, regardless of floor and/or space effects.

• The ultimate carrying capacity of a beam or cross-beam system in the compressive arch stage increases when considering the effect of a floor slab, and the ultimate carrying capacity for unidirectional beams increases with increased floor slab width.

• The ultimate bearing capacity of a cross-beam system in the compressive arch stage is enhanced by the space effect, larger than that of the longitudinal or transverse direction, but not the sum of the ultimate bearing capacities of these two directions.

Conclusions

• Mechanisms to activate the catenary action were discussed, which yielded that the elongations of beam bars are an important factor in determining the mechanism.

• When considering the effect of floor slabs for unidirectional beams, there is only one mechanism to activate the catenary action, which is the fracture of the bottom steel bars in beams at BM. The ultimate carrying capacity in the catenary stage depends on the top bars.

• When considering the space effect and effect of floor slabs at the same time, there are two probable mechanisms to activate the catenary action fracture of the bottom bars at BM in the either longitudinal direction or the transverse direction.

• The lap splice of the bottom bars according to GB50010-2010 can meet the continuity requirements in progressive collapse resistant design.

Conclusions

• The simplified models of the nonlinear static load-deflection response for RC two-bay beams were proposed based on the test results. They were verified to be effective by comparing the calculated and test results.

Thank You !

Documents

Progressive Collapse Resistance of Reinforced Concrete Frame Structures Prof. Xianglin Gu College of Civil Engineering, Tongji University 28/12/2012