SLS requirement

1. Design of Reinforced
Concrete Structures to
BS8110
5-SERVICEABILITY LIMIT STATES
Eng. Sunil Jayawardena
BSc Eng (Hons)., PGDip(CPM)., Ceng.,MIE(SL)

2. Satisfaction of SLS
 These states are checked by observing satisfaction of simplified rules(empirical) –”deemed to
satisfy” or by the satisfaction of physical requirements by actual condition of the member.
Limits states are the limiting of deflection (control of section dimensions) and limiting crack
width (control of rebar arrangement).
Limit States Physical Requirement Simplified Rules
Deflection Deflection
For appearance
For finishes
Deflection should not be greater than span/250
Deflection shall note be greater than span/350 or 20mm
for non brittle finishes
Deflection shall not be greater than span/500 for brittle
finishes.
Cracking Crack Width Crack width not greater than 0.3mm

3. Span/Depth Ratios
Basis
M=wl2/8 = fbh2/6 ------------- (1) f is the permissible stress
δ = 5/384. wl2/EI --------------(2)
From (1) w=4/3.bh2/l2.f
Then (20 δ =
5
384
(
4
3
)
𝑏ℎ2
𝑙4
𝑙2
𝐸(
𝑏ℎ3
12
)
δ
𝑙
= k(
𝑙
ℎ
) hence δ/l can be controlled by controlling l/h ratio
K is depend on support condition hence different l/h ratios

4. Design Procedure
STEP 1:
Determine basic
𝑠𝑝𝑎𝑛
𝑒𝑓𝑓.𝑑𝑒𝑝𝑡ℎ
ratio (Table 3.9 BS8110: prt 2)
-depend on -1)support condition 2) whether rectangular or flanged beam
-if span > 10m ratios obtain from table 3.9 should be multiflied by
10
𝑠𝑝𝑎𝑛(𝑚)
STEP 2:
To find allowable span/depth ratio above should be modified by two modification factors.
F1 –modification factor for tension r/f (Table 3.10 of BS8110: prt 2)
F2-modification factor for compression r/f (Table 3.11 of BS8110: prt 2)

5. Design Procedure

6. Design Procedure
STEP 4:
Find allowable
𝑠𝑝𝑎𝑛
𝑑𝑒𝑝𝑡ℎ
=
𝐵𝑎𝑠𝑖𝑐
𝑑𝑒𝑝𝑡ℎ
F1.F2
STEP 5:
Check that
𝑎𝑐𝑡𝑢𝑎𝑙 𝑠𝑝𝑎𝑛
𝑒𝑓𝑓𝑒.𝑑𝑒𝑝𝑡ℎ
= allowable
𝑠𝑝𝑎𝑛
𝑑𝑒𝑝𝑡ℎ
Note:
If creep & shrinkage are expected to be significant, allowable span/depth ratio should be
reduced by up to 15% (Cl 3.4.6.7 of BS8110: prt1).

7. Detailing requirements
Structure should have satisfactory durability, serviceability performance under
normal circumstances.
BS8110 recommends simple rules based on
Cover to reinforcements
Minimum member dimensions
Limits to reinforcements quantity
Limiting reinforcement spacing
Reinforcement detailing may also affected by stability considerations, rules
concerning anchorage and lapping of bars.

8. Flexural Cracking
Members subjected to bending generally exhibit a series of distributed flexural
cracks, even at working loads.
These cracks are not a issue unless width become excessive which effect
appearance and durability of r/f concrete member.
BS 8110 recommend maximum acceptable value of 0.3mm at any position of
the surface under normal condition.
Crack width calculation is performed based on working loads and partial safety
factors of 1.0. BS8110 recommends effective modulus of elasticity should be
taken as half of instantaneous values to allow creep effects.

9. Mechanism of Flexural Cracking
M M
𝞊cc
𝞊ct
strain
 When moment of the section (M) is increased gradually,
cracking of concrete initiated when tensile strain of concrete
in tensile zone reached limiting value.
 This cracking will propagate upward until distance between
cracks not allow to develop sufficient tensile stresses to
cause further cracking.
 These initial cracking are called “primary crakes” and
spacing of these crack are experimentally shown to be
approximately 1.67(h-x) and is independent of
reinforcement detailing.
 Beyond above point development of cracks are governed by reinforcement to a large extend.
 Bonding between steel and concrete cause to development of strain in concrete and this strain is high approximately
mid way between primary crack and reinforcement. Hence further cracks developed in between.
 These cracks are propagate with increasing of moment until bonding between steel and reinforcement is incapable to
develop sufficient tensile stresses to form cracks within the length between cracks.

10. Maximum Spacing of R/f
Basis of concept
Design surface crack width, wcr=
3𝑎𝑐𝑟𝞊𝑚
1+2(
𝑎𝑐𝑟
−𝐶𝑚𝑖𝑛)
ℎ−𝑥
)
Cmin -cover to r/f
x -N.A depth
𝞊m -average strain at level where cracking is being considered
acr -distance from nearest bar to point considered
acr
Cmin
Likely point of
maximum crack width

11. Maximum Spacing of R/f
Maximum value of wcr= 3acr.𝞊m
Now wcr<= 0.3mm (limiting value)
Then, acr <= 0.3/3𝞊m
Also we have service stress
fs =
5
8
fy
1
β𝑏
(assuming As req=As prov)
𝞊s =
5
8
fy
1
β𝑏
1
𝐸𝑠
Assuming 𝞊m=𝞊s substituting in above eqn we have
acr <= 3200βb/fy as above we have acr≈0.5 Clear spacing
Clear spacing <= 6400βb/fy
acr
Cmin
Likely point of
maximum crack width

12. Code Requirements of Max.Spacing
h>750mm
b
ab ab
sb
sb
2
3
ℎ
Clear horizontal distance between
bars in tension, ab<= Table 3.28
When h>750mm
Provide rebars of which φ <
𝑠𝑏.𝑏
𝑓𝑦
where b >
500mm
at spacing > 250mm
Over a depth of
2
3
h from tension face.
Cl 3.12.11.2.6 & 3.12.5.4

13. Code Requirement on Minimum Spacing
1) Individual bars
≥ hagg+5
≥ 2/3 hagg
Gaps vertical in line
1) bars in pairs
≥ hagg+5
≥ hagg+5
≥ hagg+5
≥ 2/3 hagg
Note
1. This is required to facilitate good compaction of concrete around reinforcements and for insertion of poker
vibrator
2. Vertical gaps should be in line
3. When bar size > hagg+5, spacing > bar diameter or equivalent bar diameter (φe = 𝑛𝜙2 )
Cl 3.12.11.1