Modeling of Deep Girders Supporting Shear Walls

Modeling of Deep Girders Supporting Shear Walls

Master’s Thesis Defense Presentation

By

Syed Karar Hussain

Members of the Jury

Prof. Boyan Mihaylov, ULg (Promoter)

Prof. Jean-François Demonceau, ULg Prof. Jean-Marc Franssen, ULg

Luc Demortier, GREISCH Yves Duchêne, GREISCH


Introduction

Significance of the study

Transfer Girder

Shear wall

Simply supported deep beam with applied load and moment


• Analysis Techniques for deep beams Strut-and-Tie Method: An easy way to analyze and design deep beams.

Widely used by different design codes (ACI, EC etc). Finite Element Analysis: Relatively complex but accurate method for

analyzing RC members(deep beams). VecTor2-Takes its basis from Modified Compression Field Theory(Bentz

2006) and Distributed Stress Field Model(Collins,1986).

Introduction

Compatibility of strains Equilibrium of stresses Stress-strain relationship

FE analysis by VecTor2-Flow of stresses STM for the same deep beam


• Analysis Techniques for deep beams Two Parameter Kinematic Theory: Predicts the response of a

concentrically loaded deep beam with only two degrees of freedom .[7]

Shear Strength components of a deep beam (Mihaylov, et al., 2013)

Introduction

Key Shear strength Providing component


• Comparison of shear strength predictions made by 2PKT and strut-and-tie method

Introduction

2PKT & CSA sectional

Average=1.10, COV=13.7%

(Mihaylov, et al., 2013)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.5 1.0 1.5 2.0 2.5 3.0

a/d

Vex

p/V

pred

ACI strut-and-tie & sectional

Average=1.30, COV=29.0%

(Mihaylov, et al., 2013)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.5 1.0 1.5 2.0 2.5 3.0

a/d


7 beams with different loading column/wall sizes and eccentricity cases

Description of beams to-be- investigated

f y = 550 MPa f u = 594 MPafc’ = 70 MPa

Varying Eccentricity

Varying column/wall

size

Name h(mm) eDB400CF

8000

DB400E-0.2-F 0.25hDB400E-0.4-F 0.5h

DB800CF1600

0DB800E-0.4-F 0.25hDB800E-0.8-F 0.5h

DB1800CF3600

0DB1800E-0.9-F 0.25hDB1800E-1.8-F 0.5h

DB2800CF5600

0DB2800E-1.4-F 0.25hDB2800E-2.8-F 0.5h

DB3800CF7600

0DB3800E-1.9-F 0.25hDB3800E-3.8-F 0.5h

DB4800CF9600

0DB4800E-2.4-F 0.25hDB4800E-4.8-F 0.5h

DB5800CF11600

0DB5800E-2.9-F 0.25hDB5800E-5.8-F 0.5h

Details of the variables


Modeling Details

Description of beams to-be- investigated

Infinitely Rigid Layer

Infinitely Rigid Layer

DB2800E-2.8-F-Material Types DB2800E-2.8-F-Eccentric loading


Load-displacement response and failure load predictions from VecTor2

Results & Discussion on Behavior of Deep Beams


Concentrically Loaded beams

Cracking Pattern-DB400CF Cracking Pattern-DB2800CF

Cracking Pattern-DB5800CF



Concentrically Loaded beams


Principal compressive stresses-DB400CF Principal compressive stresses-DB2800CF

Principal compressive stresses-DB5800CF f y(MPa) profile at the

top of the loading column f y(MPa) profile at the junction


Eccentrically Loaded Beams


Cracking pattern-DB2800E-2.8-F Principal compressive stresses-DB2800E-2.8-F

f y(MPa) profile at the top of the loading column

f y(MPa) profile at the junction


Comparison of results between VecTor2 and 2PKT predictions

For deep beams loaded with very wide walls, the failure load predictions by 2PKT are unrealistic.

Comparison of Results

V CLZ = k f avg b lb1e sin2 α

c

t

DOF t,avg DOF c

ckl =l0

kl =l0

V

Pb1(V/P)l

b1l

c

t,min

t,max

A

CLZ

b1el =

d

B

t,avg

x

z

h

1l

A1

a+ d cot t,avg

x z

xzc

a+ d cot t,avg

t,minx

z

B

2.5(h-d

)

kl =l0

d

Kinematic Model of 2PKT

0

50000

100000

150000

200000

250000

0 2000 4000 6000 8000 10000 12000 14000

Loa

d P

(K

N)

Width of the Column Lb1 (mm)

Comparison of Failure loads obtained from VecTor2 and 2PKT

C

0.25h

0.5h

2PKT

VecTor2


Iteration of L1e: The effective width of the loading column for the all the beams was iterated in a way that the failure load predictions by 2PKT and VecTor2 became same.

Extension for 2PKT

Lb1e,a= Most Stressed Portion


Comparison of the shear strength contributions by all components obtained by initial(Lb1e) & adjusted(Lb1e,a) predictions.

A suitable method for estimating Lb1e is required to be devised.

Extension for 2PKT

0.0

20000.0

40000.0

60000.0

80000.0

100000.0

120000.0

0.0 2000.0 4000.0 6000.0 8000.0 10000.0 12000.0

V-L

eft

Supp

ort(

KN

)

Column/Wall Size(Lb1)-mm

Results with Lb1e

V(clz)

Vs

Vci

Vd

V

0.0

5000.0

10000.0

15000.0

20000.0

25000.0

30000.0

35000.0

40000.0

0.0 2000.0 4000.0 6000.0 8000.0 10000.0 12000.0

V-L

eft

Su

pp

ort(

KN

Column/Wall Size(Lb1)-mm

Results with Lb1e,a

VCLZ

Vs

Vci

Vd

V

VsVd


Comparison of results between VecTor2 and strut-and-tie method

Failure load predictions from STM are highly un-conservative as compared to VecTor2 predictions.


0

10000

20000

30000

40000

50000

60000

70000

80000

0 2000 4000 6000 8000 10000 12000 14000

Loa

d P

(K

N)

Width of the Column Lb1 (mm)

Failure load comparison of VecTor2 and Strut-and-Tie method predictions

C

0.25h

0.5h

0.25h

0.25h

0.50h

STM

VecTor2


Possible reasons for deviation in predictions by VecTor2 and STM Size Effect in deep beams : A geometrically similar model of DB800CF on a

scale of 1/5 was analyzed by all the approaches. If extrapolated, the predictions by STM will be more un-conservative as compared to

STM and 2PKT.


Size Effect demonstration for Zhang and Tin tests(Mihaylov et al,2013)

STM doesn’t capture size effect of deep beams

Comparison of DB800CF and its 1/5th scale model

0

1

2

3

4

5

6

7

0 1000 2000 3000 4000 5000 6000

Sh

ear

stre

ss-V

/bd

-MP

a

Effective depth(d)-mm

Demonstration of size effect for DB800CF and its scaled model

VecTor2

2PKT

Strut-and-tiemethod

Scaled Model

DB800CF

Unsafe


References

[1]ACI 318-08, 2008. Building Code Requirements for Structural Concrete (ACI 318-08) and Commentary, Farmington Hills, MI 48331: American Concrete Institute.

[2]Hooke, . R., 1678. Lectures de Potentia Restitutiva (Spring Explaining the Power of Springing Bodies), s.l.: John Martyn Printer.

[3]Mihaylov, B. I., Bentz, E. C. & Collins, M. P., 2010. Behavior of Large Deep Beams Subjected to Monotonic. ACI STRUCTURAL JOURNAL, Volume 107, pp. 726-734.

[4]Bentz, E. C., Vecchio, F. J. & Collins, M. P., 2006. Simplified Modified Compression Field Theory for Calculating Shear Strength of Reinforced Concrete Elements. ACI STRUCTURAL JOURNAL, 103(5), pp. 614-624.

[5]Vecchio, . F., 2000. Disturbed Stress Field Model for Reinforced Concrete: Formulation. Journal of Structural Engineering, Volume 126 , pp. 1070-1077.

[6]Mihaylov, B. I., Bentz, E. C. & Collins, M. P., 2013. Two-Parameter Kinematic Theory for Shear Behavior of. ACI STRUCTURAL JOURNAL, Volume 110, pp. 447-445.


THANK YOU FOR YOUR PATIENCE