1. 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

2. Introduction
 Significance of the study
Modeling of Deep Girders Supporting Shear
Walls
Transfer
Girder
Shear wall
Simply supported deep beam with
applied load and moment

3. • 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).
Modeling of Deep Girders Supporting Shear
Walls
Introduction
Compatibility of strains Equilibrium of stresses Stress-strain relationship
FE analysis by VecTor2-Flow of stresses STM for the same deep beam

4. • 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]
Modeling of Deep Girders Supporting Shear
Walls
Shear Strength components of a deep
beam (Mihaylov, et al., 2013)
Introduction
Key Shear strength
Providing component

5. • Comparison of shear strength predictions made by 2PKT and
strut-and-tie method
Modeling of Deep Girders Supporting Shear
Walls
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
Vexp/Vpred
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

6.  7 beams with different loading column/wall sizes and eccentricity cases
Modeling of Deep Girders Supporting Shear
Walls
Description of beams to-be- investigated
f y = 550 MPa
f u = 594 MPa
fc’ = 70 MPa
Varying
Eccentricity
Varying
column/wall
size
Name h(mm) e
DB400CF
800
0
DB400E-0.2-F 0.25h
DB400E-0.4-F 0.5h
DB800CF
1600
0
DB800E-0.4-F 0.25h
DB800E-0.8-F 0.5h
DB1800CF
3600
0
DB1800E-0.9-F 0.25h
DB1800E-1.8-F 0.5h
DB2800CF
5600
0
DB2800E-1.4-F 0.25h
DB2800E-2.8-F 0.5h
DB3800CF
7600
0
DB3800E-1.9-F 0.25h
DB3800E-3.8-F 0.5h
DB4800CF
9600
0
DB4800E-2.4-F 0.25h
DB4800E-4.8-F 0.5h
DB5800CF
11600
0
DB5800E-2.9-F 0.25h
DB5800E-5.8-F 0.5h
Details of the variables

7.  Modeling Details
Modeling of Deep Girders Supporting Shear
Walls
Description of beams to-be- investigated
Infinitely
Rigid Layer
Infinitely
Rigid Layer
DB2800E-2.8-F-Material Types DB2800E-2.8-F-Eccentric loading

8.  Load-displacement response and failure load predictions from VecTor2
Modeling of Deep Girders Supporting Shear
Walls
Results & Discussion on Behavior of Deep Beams

9.  Concentrically Loaded beams
Modeling of Deep Girders Supporting Shear
Walls
Cracking Pattern-DB400CF Cracking Pattern-DB2800CF
Cracking Pattern-DB5800CF
Results & Discussion on Behavior of Deep Beams

10.  Concentrically Loaded beams
Modeling of Deep Girders Supporting Shear
Walls
Results & Discussion on Behavior of Deep 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

11.  Eccentrically Loaded Beams
Modeling of Deep Girders Supporting Shear
Walls
Results & Discussion on Behavior of Deep 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

12.  Comparison of results between VecTor2 and 2PKT predictions
 For deep beams loaded with very wide walls, the failure load predictions
by 2PKT are unrealistic.
Modeling of Deep Girders Supporting Shear
Walls
Comparison of Results
V CLZ = k f avg b lb1e sin2 α
c
DOF t,avg DOF c
kl =l0
V
Pb1(V/P)l
b1l
c

r
t,min t,max
A
CLZ
=0
b1el =
d
B
t,avg
x
z

h

1
v
b2l
slip
w
A
1
a+ d cott,avg
x z 
x
z c
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
LoadP(KN)
Width of the Column Lb1 (mm)
Comparison of Failure loads obtained from VecTor2 and 2PKT
C
0.25h
0.5h
2PKT
VecTor2

13.  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.
Modeling of Deep Girders Supporting Shear
Walls
Extension for 2PKT
Lb1e,a= Most Stressed
Portion

14.  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.
Modeling of Deep Girders Supporting Shear
Walls
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-LeftSupport(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-LeftSupport(KN
Column/Wall Size(Lb1)-mm
Results with Lb1e,a
VCLZ
Vs
Vci
Vd
V
Vs
Vd

15.  Comparison of results between VecTor2 and strut-and-tie method
 Failure load predictions from STM are highly un-conservative as compared to
VecTor2 predictions.
Modeling of Deep Girders Supporting Shear
Walls
Comparison of Results
0
10000
20000
30000
40000
50000
60000
70000
80000
0 2000 4000 6000 8000 10000 12000 14000
LoadP(KN)
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

16.  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.
Modeling of Deep Girders Supporting Shear
Walls
Comparison of Results
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
Shearstress-V/bd-MPa
Effective depth(d)-mm
Demonstration of size effect for DB800CF and
its scaled model
VecTor2
2PKT
Strut-
and-tie
method
Scaled
Model
DB800CF
Unsafe

17. 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.
Modeling of Deep Girders Supporting Shear
Walls

18. THANK YOU FOR YOUR
PATIENCE
Modeling of Deep Girders Supporting Shear
Walls