Unit 8 ( SERVICEABILITY LIMIT STATE (SLS) )

REINFORCED CONCRETE STRUCTURAL DESIGN C4301/UNIT8/

UNIT 8

SERVICEABILITY LIMIT STATE (SLS)

GENERAL OBJECTIVE

To appreciate how the SLS design of reinforced concrete element is

performed according to the requirements of BS 8110.

At the end of this unit, you will be able to: -

1. determine the ratio from table 3.10, BS 8110

2. calculate the modification factors for tension reinforcement.

3. calculate the modification factors for compression reinforcement.

4. check that the deflection of beams do not exceed the allowable values.

5. calculate clear horizontal distances between bars in tension.

6. calculate allowable distances from table 3.30,BS 8110.

7. calculate the clear distances between the corner of beams and the

nearest longitudinal bars in tension.

8. provide additional reinforcement for deep beam.

9. check that all clear and allowable distances are within limits.

1

OBJECTIVES

SPECIFIC OBJECTIVES:


8.1 Deflection

Excessive deflection in member can cause defect of the finishes, partition wall

etc. BS 8110: Part 2, Clause 3.2 states that the amount of deflection in

reinforced concrete member should be limited to: -

For normal structure, which can be seen, the deflection is limited to .

For structure supporting brittle finishes, the deflection should not exceed

or 20mm.

The detailed calculation of deflection is elaborated in BS 8110: Part 2.

However, this method of calculating deflection is not needed except in certain

circumstances. A more practical way used to control deflection is by limiting

the ratio as stated in BS 8110: Part 1, clause 3.4.6

8.2 Method of checking the deflection

This is done by comparing,

2

INPUT 1


<

Where

= obtained from Table 3.10, BS 8110: Part 1

Table 3.10, BS 8110 is given below:

Type of support Rectangular section Flange section

Cantilever beam 7.0 5.6

Simply supported beam 20.0 16.0

Continuous beam 26.0 20.8

The values of in this table are based on the allowable deflection of .

For spans greater than 10m, has to be multiplied by .

3

Table 3.10: Basic span/effective depth ratios for rectangular flange beams.


m.f.t.r = modification factor for tension reinforcement

=

Where,

fs = service stress

=

As,req = required area of tension reinforcement.

As,prov = provided area of tension reinforcement.

b = redistribution

M = imposed bending moment

b = width of beam

d = effective depth

m.f.c.r = modification factor for compression reinforcement

=

4


Where,

As’,prov = area of compression reinforcement provided

Please note that,

If , the following precautions may be taken: -

add more reinforcement so that the service stress, fs will

decrease and resulting in increased m.f.t.r.

calculate the actual deflection using the detailed method in BS

8110: Part 2 (mentioned earlier)

increased the effective depth of the beam.

The third precaution is usually used; i.e. increase d.

8.2.1Example :

A simply supported rectangular beam spanning 8 m is designed to carry a

bending moment of 80 kNm. The required area of tension reinforcement is

1725 mm2, while the steel reinforcement provided is shown in Figure 8.1

below: You are asked to check the deflection of the beam.

5


Solution:

(From Table 3.10)

Service stress, fs =

= 265 N/mm2

6

8 m

80 kNm

M = 80 kNm

2T25(982 mm2)

3T25 + 2T16(1872 mm2)

350 mm

200 mm

Figure 8.1: Cross-Section Of Beam


m.f.t.r. =

= 0.97

m.f.c.r =

= 1.32

, therefore the beam is satisfactorily free from

deflection.

7


Fill in the blanks: -

8.1 Deflection of reinforced concrete element is to check in order to satisfy the

_________________ limit state requirement.

8.2 The checking regarding to the deflection of beams should be done in

accordance with clause __________________, BS 8110: Part 1

8.3 Excessive deflection of reinforced concrete element can cause cracking

and may destroy ________________ and partitions.

8.4 For spans up to 10 m, the deflection that occurs after construction of

finishes and partition will be limited to ________________________.

8

ACTIVITY 8a


8.5 Table ________________, BS 8110: Part 1 has given the basic ratio.

8.6 The value in Table (in question 5) should be multiplied by __________

from Table 3.11 and Table 3.12, BS 8110.

8.7 For rectangular simply supported beam, the basic ratio is

_____________.

8.8 For spans greater than 10 m, the basic ratio should be multiplied by

__________________.

Check your answers: -

8.1 serviceability

8.2 3.4.6.1

8.3 finishes

8.4 or 20 mm, whichever is the lesser

8.5 3.10

8.6 modification factors

8.7 20

8.8

9

FEEDBACK 8a


8.3 Cracking

Excessive cracking of reinforced concrete element can affect its durability and

aesthetic value. A very wide and deep crack can cause water to penetrate into

the concrete and soon the reinforcement will corrode. Under normal

conditions, it is very difficult to construct crack-free structures because cracks

are caused by various factors such as thermal expansion and contraction, heat

from hydration of cement, creep etc. Some of these factors are not easily

controlled and monitored.

10

If you are satisfied with your answers, you may proceed to the next input, otherwise you should go through this input once again.

INPUT 2


For ordinary structures, it is adequate to check the cracking by limiting the

width of crack so that it will not more than 0.3 mm. For more critical

structures such as water tank, the crack width allowed is up to 0.2 mm. There

are two methods that can be used to check that the cracks do not exceed the

limit. They are as follows: -

calculating the width of cracks

limiting the clear distance between bars.

In this unit, we are going to discuss the second method. The first method is

only used for particular cases and is seldom carried out.

8.4 Spacing of reinforcement

Limiting the maximum distance between bars in tension controls cracks. The

rules regarding these, as specified in clause 3.12.11.2, BS 8110: Part 1 are as

follows: -

i) The clear distance between bars, S1 should not be greater than the

stated values in Table 3.30, BS 8110. This value is also dependent on

the percentage of moment redistribution and steel’s strength.

ii) The corner distance, S2 should not exceed 0.5 times the stated values

in Table 3.30, BS 8110.

iii) If the effective depth of beam is greater than 750 mm, steel

reinforcement to control cracking should be provided near both sides

of the beam. This reinforcement should be at a depth; effective

depth of beam.

11


The distance between bars, Sb should not exceed 250 mm and that the

size of bar should not be less than

Please refer to Clause 3.12.5.4, BS 810 for more clarifications.

The distances denoted by S1, S2 and Sb as shown in Figure 8.2 below: -

12

h

b

S1

S2


8.4.1 Example: -

For the given beam sections in Figure 8.3 and Figure 8.4. Check that cracks

are within limits: -

a) Refer to Figure 8.3

b = 250 mm

h = 500 mm

Cover = 30 mm

13

h>750mm

S1 S1

S2

Figure 8.2: Distance denoted by S1, S2, S3

Sb

Sb

R10-100

2T16

S1

2T20

Figure 8.3: Cross-section of beam


Solution: -

Referring to Clause 3.12.11.2.3, BS 8110, the clear distance between

bars in tension is

S1 = b – 2(cover) – 2(link) – 2(bar)

= 250 - 2(30) - 2(10) - 2(20)

= 130mm

Allowable clear distance,

= 160 mm (From Table 3.30, BS 8110 for fy=460N/mm2 and

zero moment redistribution)

This shows that S1 < 160 mm and therefore cracks are satisfactory.

According to Clause 3.12.11.2.5, BS 8110, clear distance between the

corner of the beam and the nearest longitudinal bar in tension,

S2 =

= 60.7 mm

Allowable corner distance = 80 mm

= 0.5 x values in Table 3.30

S2 < 80 mm

Cracks do not exceed the stated limit.

14


b) Refer to Figure 8.4: -

b = 250 mm

h = 1000 mm

Cover = 30 mm

Solutions:-

Clear distance between bars in tension,

S1 = [b – 2(cover) - 2link - 3bar] 2

= [250 – 2(30) – 2(10) – 3(25)] 2

15

2T20

R8-100

5T25

Figure 8.4: Cross-section of beam


= 47.5 mm < 160 mm o.k

The clear distance of corner bar,

S2 =

= 61.7 mm < 80 mm o.k

h > 750 mm

additional reinforcement to control cracks are required.

The distance between these bars to control crack is,

Sb = 200 mm (Sb maximum = 250 mm)

The size of this bar is,

>10.4 mm

We can provide T12 at a distance of 200 mm from centre to centre.

16


Fill in the blanks with the correct answers: -

8.9 Cracks in reinforced concrete elements are controlled by limiting the

______________ between bars in tension.

8.10 The guidelines to the spacing of reinforcement are given in Clause

____________________ of the BS 8110.

8.11 The clear horizontal distance between bars in tension should not be

greater than the values given in Table _________________, BS 8110.

8.12 The clear distance between the corner of beam and the nearest

longitudinal bar in tension should not exceed _______________ the

values given in Table in Question 3.

8.13 Additional reinforcement to control cracks should be provided near

side faces of beams exceeding _________________ in overall depth.

17

ACTIVITY

8b


.

Check your answers. They should be as follows: -

8.9 maximum distance

8.10 3.12.11.2

8.11 3.30

8.12 0.5 times

8.13 750 mm

18

Before doing the Self

Assessment, read the

summary of this unit.

FEEDBACK 8b


1. Deflection and checking of cracks are done to satisfy the Serviceability

Limit States (SLS).

2. Limiting the spans effective depth ratio can control deflection.

3. Deflection check is done according to Clause 3.4.6, BS 8110

4. Excessive cracks in reinforced concrete elements can be controlled by

limiting the maximum horizontal distance between bars and the corner

distance of the nearest longitudinal bar in tension.

5. For deep beams i.e. the overall depth is greater than 750 mm, additional

reinforcement to control cracks are provided near side faces of the

beam.

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SUMMARY


Figure 8.5 shows a rectangular section of a simply supported beam.

Given that: fcu = 30 N/mm2

fy = 460 N/mm2

fy = 250 N/mm2

Questions:

20

5T16

2T16

455

200 mm

SELF-ASSESSMENT

Figure 8.5: Cross-section of rectangular beam


1. If the span of the beam is 8.0 m, imposed moment, M = 15 kNm and

the area of reinforcement required, Asreq = 950mm2, check this beam

for deflection. (8 marks)

2. Check this beam for crack if the nominal cover, c = 30 mm.

(7marks)

Check your answers given below and then total up your marks.

1. Span = 8.0 m

M = 150 kNm

Asreq = 950 mm2

Service stress, fs =

= 271 N/mm2 …………………………

………………………………

Modification for tension reinforcement,

m.f.t.r =

= 0.55 + 0.38 <2.0

= 0.93 < 2.0 ………………………………………

21

1

1

1

FEEDBACK ON SELF-ASSESSMENT


Modification factor for compression reinforcement,

m.f.c.r =

= 1.13 …………………………………………

………………………………….

= 21.02……………………………..

………………………..

<

Therefore deflection is satisfactory………………

22

Total = 8 marks

1

1

1

1

1


2. Overall depth, h = 455 + 16 + 3.0 mm

= 501 mm……………………………….

Clear distance between bar in tension,

S1 = [200 – 3(16) – 2(30)] 2

= 46 mm …………………………………………………

Allowable clear distance (from Table 3.30, fy= 460N/mm2)

= 160 mm………………………………………………..

Since S1 = 46 mm < 160 mm, therefore check for crack is

satisfactory…………………………………………………

23

S1 S1

1

1

Figure 8.6: Clear distance between bar

1

1


Clear distance between the corner of beam and nearest longitudinal bar in

tension,

Allowable corner distance = 0.5 x 160 mm

= 80 mm …………………

S2 < 80 mm ……………

Therefore cracks do not exceed the limit

24

1

2

Total = 7 marks

Calculate your total marks

What is your score? You should calculate like this: -

Marks obtained x 100% 15

REINFORCED CONCRETE STRUCTURAL DESIGN C4301/UNIT8/ 25

You should score 80% or better to pass this unit.

You may proceed to the next unit if you have got

80% or more.

You should go through this unit or part of this

unit again until you pass. Do not give up.

Proceed on! Congratulations! You have

completed unit 8

END OF UNIT 8


GLOSSARY

ENGLISH MALAY

serviceability limit state had bolehkhidmat

deflection pesongan

modification factor faktor pengubahsuai

clear distance jarak bersih

moment redistribution pengagihan semula momen

service stress tegasan khidmat

cracking keretakan

creep rayapan

thermal expansion pengembangan haba

corner distance jarak sudut

allowable clear distance jarak bersih izin

spacing of reinforcement penjarakkan tetulang

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Documents

Unit 8 ( SERVICEABILITY LIMIT STATE (SLS) )