Gergely-Lutz equation Carck width prediction, Indian code provision for crack width, Design crack width, AS 3600, AS 5100, EC-2, BS 8110, BS 5400, CEB-FIP 1990 (MC90), ACI 318-89,99

1. Comparison of Crack Width
Provisions
Given In
IS: 456, ACI:318, EC-2, AS:5100, CEB-FIP-90
Prof. Samirsinh P Parmar
Asst. Prof. DDUniversity, Nadiad, Gujarat, India
Mail: samirddu@gmail.co

2. Prediction of Cracking
Why is it important?
 Load distribution and transfer
 Durability
 Code compliance
 Contract conditions
 Client expectations
 Aesthetics
 Clearances, ponding etc.
Samirsinh
P
Parmar,
Asst.Prof.
DDU,
Nadiad,
Gujarat,
India

3. Why is it difficult to predict
crack width?
Uncertain or unknown material properties
Inconsistent and incomplete code provisions
Inherently random nature of cracking
Variations in curing procedures and environmental effects
Complex loading history
Samirsinh
P
Parmar,
Asst.Prof.
DDU,
Nadiad,
Gujarat,
India

4. Indian Code Provisions(IS 456)
 Strain in tension reinforcement is limited to 0.8 Fy / Es
 Design surface crack width should be in accordance with
the values specified in 35.3.2. of IS456
 Concrete and steel are both considered to be fully elastic in both tension and compression
 Elastic modulus of steel can be taken as 200 kN/m2
 Design surface crack width can be calculated from the
following equation :
…contd.
Samirsinh
P
Parmar,
Asst.Prof.
DDU,
Nadiad,
Gujarat,
India

5. Samirsinh
P
Parmar,
Asst.Prof.
DDU,
Nadiad,
Gujarat,
India

6.  For, rectangular tension zone, average strain can be calculated as :
Samirsinh
P
Parmar,
Asst.Prof.
DDU,
Nadiad,
Gujarat,
India

7. Provisions for crack width :
Cracking of concrete should not adversely affect the
appearance or durability of structure.
 Surface width of cracks should not exceed in general 0.3 mm.
 In members which are continuously exposed to moisture or in
contact soil or ground water, an upper limit of 0.2 mm has
been suggested for maximum width of cracks.
 For structures in aggressive environmental conditions, the
assessed surface width of cracks should not exceed 0.1 mm.
Samirsinh
P
Parmar,
Asst.Prof.
DDU,
Nadiad,
Gujarat,
India

8. Code provisions for stress limits
 AS 3600, AS 5100 and EC2 :
 Crack control by stress limits governed by bar diameter and spacing
 AS 5100 has much lower stress limits applicable to stresses due to permanent
loads in exposure classifications B2, C or U
 AS 3600 limits similar to EC2 limits for 0.4 mm crack width for bar diameter,
and 0.3 mm for bar spacing
 AS 5100 limits for exposure classification B2 and higher similar to EC2 limits
for 0.2 mm crack width
 The specified stress limits will result in substantially higher design crack
widths with increased cover.
Samirsinh
P
Parmar,
Asst.Prof.
DDU,
Nadiad,
Gujarat,
India

9. Code provisions for crack
widths
Samirsinh
P
Parmar,
Asst.Prof.
DDU,
Nadiad,
Gujarat,
India
 EC2
....contd.

10. Samirsinh
P
Parmar,
Asst.Prof.
DDU,
Nadiad,
Gujarat,
India

11. Code provisions for crack widths
EC2 - Notes:
 Crack spacing is mainly related to cover depth
 Crack width is directly proportional to crack spacing
 Tension stiffening is limited to 40% of steel strain without
stiffening
 Coefficient for long term tension stiffening is reduced by 1/3 (0.6 to
0.4)
Samirsinh
P
Parmar,
Asst.Prof.
DDU,
Nadiad,
Gujarat,
India

12. Code provisions for crack widths
Design surface crack width:
BS 5400 BS 8110
Samirsinh
P
Parmar,
Asst.Prof.
DDU,
Nadiad,
Gujarat,
India











c
cr
m
cr
d
h
c
a
a
min
2
1
3 
 
  


























 9
1 10
1
8
.
3
g
q
c
s
s
c
t
m
M
M
d
h
A
d
a
h
b












x
h
c
a
a
cr
m
cr
min
2
1
3 
  
  











x
d
A
E
x
a
x
h
b
s
s
t
m
3
1



13. Code provisions for crack widths
 
cs
sr
s
s
k l
w 

 

 2
2
max
 CEB-FIP 1990 (MC 90)
Design crack width:
2
s

2
sr

cs

max
s
l Length over which slip between concrete and steel
occurs
Steel strain under a force causing stress equal to concrete
tensile strength over concrete tension area x empirical
coefficient
Free shrinkage of concrete (generally negative)
Steel strain at the crack
Samirsinh
P
Parmar,
Asst.Prof.
DDU,
Nadiad,
Gujarat,
India

14. Code provisions for crack widths
 ACI 318 - 89, 99, Gergely-Lutz equation
 ACI requirements based on stress limits derived from the Gergely-Lutz equation
:
Samirsinh
P
Parmar,
Asst.Prof.
DDU,
Nadiad,
Gujarat,
India
x)
-
x)/(d
-
(h


3 A
d
f
z c
s

   
units
m
N
z
w 

 

12
max 10
11

15. Crack Width vs Steel Stress
Spacing 125 mm
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0 50 100 150 200 250 300 350
Steel Stress, MPa
Crack
Width,
mm
EC2 BS5400 BS5400 BS8100 CEB_FIP_1990 ACI318_99
Samirsinh
P
Parmar,
Asst.Prof.
DDU,
Nadiad,
Gujarat,
India

16. Crack Width vs Cover
Spacing 125 mm
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
20 30 40 50 60 70 80 90 100
Cover, mm
Crack
Width,
mm
EC2 BS5400 BS5400 BS8100 CEB_FIP_1990 ACI318_99
Samirsinh
P
Parmar,
Asst.Prof.
DDU,
Nadiad,
Gujarat,
India

17. Crack Width vs Spacing
(constant area, constant stress)
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0 50 100 150 200 250 300 350
Bar Spacing, mm
Crack
Width,
mm
EC2 BS5400 BS5400 BS8100 CEB_FIP_1990 ACI318_99
Samirsinh
P
Parmar,
Asst.Prof.
DDU,
Nadiad,
Gujarat,
India

18. References :
 IS 456
 ACI 318
 AS 5100, AS 3600
 EC 2, CEB-FIP (MC 90)
 BS 5400, BS 8110
 www.interactiveds.com.au
Samirsinh
P
Parmar,
Asst.Prof.
DDU,
Nadiad,
Gujarat,
India

19. Thank You!!
Samirsinh
P
Parmar,
Asst.Prof.
DDU,
Nadiad,
Gujarat,
India