US Air Force Warehouse, Ohio, USA(August,1955)

Kayani (2014)

Johnson M K (1989)

Taylor

Angelakos (2001)

Zararis (2003)

Kani G (1964)

AC Scordelis

Collins M P (2008)

Placas A (1971)S Mindess (2003)

Z P Bazant (1984)

Z Zheng (2000)

R Malm (2009)

C Juarez (2007)

JCM Ho FTK Au (2005)

L Vandewalle (2000)A Buuml (2010)

J Thomas (2007)

S Colombo (2005)

MZ Jumaat (2010)

L Li Y Guo (2008)

K Chansawat (2009)

KS Elliott (2002)

E Ahmad (2011)

CM Belgin (2008)

O Adwan B Bose (1999)

J Ruis J Planes (1998)

S Yuyama (1995)

P Rao SK Sekar (2011)

OVER 2000REPORTED

SHEAR TESTS IN PAST 60 YEARS

Reference: Collins et all. (2007)

INVESTIGATION OF SHEAR BEHAVIOUR OF SLENDER BEAMS

USING FINITE ELEMENT ANALYSIST H E T H I N G S W E D O F O R Y O U

PROJECT ADVISOR

DR. WASIM KHALIQ

ASSOCIATE PROFESSOR

GROUP MEMBERS

1. USMAN MAHMOOD

2. AAKIF SAEED

3. ASAD ULLAH MALIK

4. FAIZAN HAMEED

Research Scope

Why Finite Element Analysis?

Modelling procedure in ABAQUS®

Benchmark Analysis - Material Calibration

Parametric Analysis

Comparison with ACI predicted Strength

An expression for minimum shear reinforcement

OVERVIEWF I N A L Y E A R P R O J E C T

PROJECT SCOPE

Successfully modelled RC beam in shear and flexure.

Analytically studied different beams with varying

shear reinforcement and shear span ratios which

closely depicts experimental response

Validated modified equation for Ultimate Shear

Strength proposed by Kayani et al. (2014)

Proposing a modified equation for Minimum Shear

Reinforcement

F I N A L Y E A R P R O J E C T

TIME ALLOCATION

F I N A L Y E A R P R O J E C T

LEARNING PHASE

BENCHMARK ANALYSIS

PARAMETRIC ANALYSIS

5%

RESULT EXTRACTION & INTERPRETATION

15%

15%

20%

60%

Pie chart: Percentage time allocated

FINITE ELEMENT MODELLING

Can FEM serve as a replacement for experimental

testing?

Software we used?

ABAQUS 6.13 ®

F I N A L Y E A R P R O J E C T

FOUR POINT BEND TEST

WHY FOUR POINT BEND TEST?

Reference: Collins et all. (2007)

Analysed full scale – 20 beams

Benchmark Analysis - 8 beams

Parametric Analysis - 12 beams

BEAMS ANALYZED

N-SERIES BEAM

Length = 3658 mm ~ 12 ft.

Breath = 254 mm ~ 10 inches

Depth = 457 mm ~ 18 inches

N-Series – Beams without web reinforcement

A-Series- Beams with ACI minimum shear reinforcement

A-SERIES BEAM

Length = 3658 mm ~ 12 ft.

Breath = 254 mm ~ 10 inches

Depth = 457 mm ~ 18 inches

Z-Series- Beams with Zararis minimum shear reinforcement

Z-SERIES BEAM

Length = 3658 mm ~ 12 ft.

Breath = 254 mm ~ 10 inches

Depth = 457 mm ~ 18 inches

M-Series- Beams with minimum shear reinforcement

proposed by Kayani et al.

M-SERIES BEAM

Length = 3658 mm ~ 12 ft.

Breath = 254 mm ~ 10 inches

Depth = 457 mm ~ 18 inches

M’-Series- Beams with minimum shear reinforcement

proposed by Usman et al.

M’-SERIES BEAM

Length = 3658 mm ~ 12 ft.

Breath = 254 mm ~ 10 inches

Depth = 457 mm ~ 18 inches

ABAQUS ®F I N I T E E L E M E N T

M O D E L L I N G S T R A T E G Y

MODELLING GUIDE

MODELLING

x

y

z

XSYMM

𝑈1 = 𝑈𝑅2 = 𝑈𝑅3 = 0

ZSYMM

𝑈3 = 𝑈𝑅1 = 𝑈𝑅2 = 0

*Where 1, 2 and 3 denote the x, y and z axis respectively

USE OF SYMMETRY

MODELLING MESH DENSITY

MODELLING

0

2

4

6

8

10

12

14

16

18

0 5000 10000 15000 20000 25000 30000

Fie

ld O

utp

ut

Vari

ab

le U

2

(mm

)

Element Number

Stable Displacements

after 10,000 elements Element Number as

29,000

MESH DENSITY

Graph: Field Output Variables vs. Element Number

MODELLING SUMMARY MODULE ABAQUS/STANDARD

ANALYSIS TYPE NON-LINEAR STATIC ANALYSIS

SOLUTION TECHNIQUE NEWTON-RAPHSON METHOD

FAMILYBEAM CONTINUUM/SOLID

REINFORCEMENT WIRE/TRUSS

ELEMENT TYPE

BEAM

C3D8R WITH

HOURGLASS

CONTROL

REINFORCEMENT T3D3

LOADING DISPLACEMENT CONTROL

PLA

TE

SR

OLL

ER

SREAL TIME SNAPSHOTS

FULL ASSEMBLY

Beam tested at NICE Same beam modelled in ABAQUS®

SIMULATION

BENCHMARK ANALYSISM A T E R I A L

C A L L I B R A T I O N

ELASTIC PROPERTIES

• Young’s Modulus = 200𝑮𝑷𝒂/29000ksi

• Poisson’s Ration = 0.3

• Type = Isotropic

PLASTIC PROPERTIES

Grade 40 Steel (𝒇𝒚=276 Mpa*)

INPUT MATERIAL PROPERTIES (STEEL)

Grade 60 Steel (𝒇𝒚=414 Mpa*)

0

100

200

300

400

500

600

0 0.01 0.02 0.03 0.04 0.05 0.06

Yie

ld S

tre

ss

(M

Pa)

Plastic Strain*

ELASTIC PROPERTIES

• Young’s Modulus =200 GPa /29000 ksi

• Poisson’s Ration = 0.3

• Type = Isotropic

PLASTIC PROPERTIES

0

100

200

300

400

500

600

700

0 0.01 0.02 0.03 0.04 0.05 0.06

Yie

ld S

tre

ss

(M

Pa)

Plastic Strain*

*Courtesy: Fazal Steel Mills, Industrial Area I-9 , Islamabad

INPUT MATERIAL PROPERTIES (CONCRETE)

Normal Strength Concrete (NSC)

Compressive Strength ( ) = 4000 psi (27.6 MPa)

Density of concrete 𝑤𝑐 = 2300-2500 kg/m3 for NSC

Poisson’s ratio vc = 0.18

Klink (1985)

Young’s Modulus Ec = 26000 MPa

(ACI 8.5.2)

1.5 0.043 'c c c

E w f

5.075.17105.4 ccc fw

BASIC CONCRETE ELASTIC INPUT PROPERTIES

cf

ANALOGY

Tension

Stiffening

Bond Slip

&

Dowel ActionPost Failure Stress–

strain

Response

Vd

F

Inelastic Behavior Of Concrete In

Compression

0

5

10

15

20

25

30

0.000 0.002 0.004 0.006 0.008 0.010

Yie

ldS

tress

(M

Pa

)

Inelastic Strain

0

0.5

1

1.5

2

2.5

3

0 0.001 0.002 0.003

Yie

ld S

tress

(M

Pa)

Cracking Strain

3

( )'

'1 ( )

'

'1.55

4.7

c c

c

c

f

f

f c

Carreira and Chu (1985) Wang and Hsu (1994)

0.4( )cr

t cr

t

f

CONCRETE PLASTIC INPUT PROPERTIES

INPUT MATERIAL PROPERTIES (CONCRETE)

Inelastic Behavior Of Concrete In

Tension

55.14.32

cf

510)16871.0( xfcc

)(4 psiff ccr

el

tt

ck

tcr 0~

ν = 0.005

ν = 0.01

MATERIAL CALLIBRATION

33%24%15%40%18%43% ѱ = 2 5 ° ν = 0.01

ѱ = 31° ν = 0.01

ѱ = 35°

ѱ = 35°

ѱ = 38° ν = 0.01

ѱ = 38° ν = 0.005

PERCENTAGE ERROR

V i sc os i ty Pa r a meter

(ν )

Dilation Angle

(ѱ)

LOA

D C

AR

RYI

NG

CA

PAC

ITY

AN

D

DIS

PLA

CEM

ENT

AT

FAIL

UR

ELO

AD

CA

RR

YING

CA

PAC

ITY AN

D

DISP

LAC

EMEN

T AT FA

ILUR

E“One test on a good sample is better than 10 tests on a poor sample”

J. Michael Duncan

LOAD DEFLECTION CURVES

*Z-series represent beams designed for Zararis minimum reinforcement

Comparison of Experimental and FEM determined Mid Point Deflections for Z1* Beam

Graph: Beam Z1 - Load vs. Deflection at midpoint

0

10

20

30

40

50

60

70

80

0 4 8 12 16 20 24 28 32 36

Lo

ad

(to

n)

Deflection (mm)

Model

Experimental

Linear

Graph: Beam Z1 - Load vs. Deflection at Quarter Point midpointComparison of Experimental and FEM determined Quarter Point

Deflections for Beam Z1*

*Z-series represent beams designed

for Zararis minimum reinforcement

LOAD DEFLECTON CURVES

0

10

20

30

40

50

60

70

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34

Lo

ad

(to

n)

Deflection (mm)

QP1

Model

MID POINT QUARTER POINT

N-Series

A-Series

Z-Series

M-Series

SIMULATION OF BEAM WITHOUT SHEAR REINFORCMENT

NO SHEAR REINFORCEMENT

ACI BEAM ZARARIS’S BEAMMODIFIED

ZARARIS BEAM a

/d=

2.5

a/d

= 3

.0a

/d=

3.5

a/d

= 4

.0

PARAMETRIC ANALYSIST H E C O M P A N Y B A C K G R O U N D SB E A M S W I T H S H E A R

R E I N F O R C E M E N T

PARAMETRIC ANALYSIS

B E A M S W I T H S H E A R R E I N F O R C E M E N T

To analyze the relation between shear span-to-depth

ratio (𝒂/𝒅) and the Ultimate Shear Strength (𝑉𝑢)

Comparison between ACI and Finite Element

Analysis predicted strengths.

Validation of Kayani et al. (2014) Modified

Equation for Ultimate Shear Strength (𝑉𝑢) using

Finite Element Analysis

Proposing a modified equation for Minimum Shear

Reinforcement to attain full flexure capacity

PARAMETRIC ANALYSIS

𝑉𝑢 R E L A T I O N T O 𝑎 / 𝑑

0.9

1

1.1

1.2

1.3

1.4

2 2.5 3 3.5 4 4.5 5

a/d

ACI PREDICTED STRENGTH

TREND LINE

*RSSV = Relative Shear

Strength Value

fail

predicted

V

V

B E A M S W I T H S H E A R R E I N F O R C E M E N T

𝑉𝑢 𝒂/𝒅

PARAMETRIC ANALYSISC O M P A R S I O N O F U L T I M A T E S H E A R

E Q U A T I O N S

ACI CODE

KAYANI et al. (2014)

PARAMETRIC ANALYSISC O M P A R S I O N O F U L T I M A T E S H E A R

E Q U A T I O N S

1.2 0.2     0.21 0.25   du ct v yv

la c aV d f

d d d df bd

Size effect Splitting Tensile Strength

Development Length

Reference - ACI Code 318-11-2, 11-5, 11-15

Reference – Kayani et al Modified Equation (2014)

0.9

1

1.1

1.2

1.3

1.4

2 2.5 3 3.5 4 4.5 5

RS

SV

a/d

ACI PREDICTED STRENGTH

STRENGTH PREDICTED BYMODIFIED EQUATION

PARAMETRIC ANALYSISV A L I D A T I O N O F M O D I F I E D

E Q U A T I O N

G r a p h – C o m p a r i s o n b e t w e e n A C I a n d M o d i f i e d E q u a t i o n p r e d i c t e d s t r e n g t h

PARAMETRIC ANALYSISB E A M S W I T H S H E A R

R E I N F O R C E M E N T

1

11.7

v c

c

y y

yv

f f

ff

a fd

M I N I M U M S H E A R R E I N F O R C E M E N T R A T I O T O A T T A I N F U L L F L E X U R E C A P A C I T Y

PARAMETRIC ANALYSISB E A M S W I T H S H E A R

R E I N F O R C E M E N T

1

11.7

v c

c

y y

yv

f f

ff

a fd

M I N I M U M S H E A R R E I N F O R C E M E N T R A T I O T O A T T A I N F U L L F L E X U R E C A P A C I T Y

(min)

500.75

yv y

c

v

vf f

f

Reference - ACI Code 318 - 11.4.6.3

Longitudinal reinforcement ratio

Shear span to depth ratio

PARAMETRIC ANALYSISB E A M S W I T H S H E A R

R E I N F O R C E M E N T

2.15

2.2

2.25

2.3

2.35

2.4

2.45

2.5

2 2.5 3 3.5 4 4.5

α

a/d

G r a p h – R e l a t i o n b e t w e e n α a n d a / d

𝒂/𝒅 α2.5 2.48

3.0 2.35

3.5 2.27

4.0 2.20

PARAMETRIC ANALYSISB E A M S W I T H S H E A R

R E I N F O R C E M E N T

G r a p h – R e l a t i o n o f % N o m i n a l C a p a c i t y t o T r a n s v e r s e R e i n f o r c e m e n t R a t i o .

0

20

40

60

80

100

120

140

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

% N

OM

INA

L FL

EXU

RE

CA

PAC

ITY

TRANSVERSE STEEL RATIO

No Shear Reinforcement

ACI Min Shear Reinforcement

Zararis Min Shear Reinforcement

Kayani Min Shear Reinforcement

Proposed Min Shear Reinforcement

Linear (Nominal Flexure Capacity)

CONCLUSIONSB E A M S W I T H S H E A R

R E I N F O R C E M E N T

Finite Element Modelling (FEM) is a technique

which can be used to better understand shear failure

mechanism.

FEM significantly reduces time and effort in

comparison to experimental testing

The equation devised by Kayani et al. provides a

better shear strength prediction than ACI

The proposed equation provides better prediction for

full flexure capacity of RC beams

THANK YOU!T H E T H I N G S W E D O F O R Y O U