serviceability limit state

8/3/2019 Serviceability Limit State

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BST 10346, Structural Design, Serviceability Limit State 1

Serviceability limit state

Serviceability limit state of Deflection

The reasonable limits of deflections of beams and slabs for normal reinforced concretebuildings as recommended in BS 8110 are as follows:

1. The final deflection measured below the as-cast level of the supports of floors, roofs andall other horizontal members, should not generally exceed span / 250. i.e. d1 + d2

2. Partitions and finishes will be affected only by such deflection as occurs after theconstruction of the partitions or the application of the finishes. A limit of span / 500, or

20mm, whichever is the lesser, is suggested. i.e. d1

3. According to the BS 8110,

d2 should not exceed span / 500 or 20 mm, whichever is the lesser, and d1 + d2 should not exceed span / 250.

Calculation of Deflection

The defection of an elastic beam is given by the general equation:

CWL / EI

Where C is a constant, depending on the nature of the loading

W is the loading

L is the effective span

E is the modulus of elasticity of the beam, and

I is the second moment of area, or moment of inertia, of the section of the beam

It is difficult to calculate the deflections of a reinforced concrete beam or slab under load

because, although steel behaves elastically under service load conditions, concrete does not.

Also, the combination of two materials when acting as one results in complicated equation

for the E and I values.


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Checking of Deflection

The process of checking the deflections of a reinforced concrete beam or slabs has been

simplified by BS 8110.

In all normal cases, the deflections of a beam will not be excessive if the ratio of its span to

its effective depth is not greater than the appropriate ratios given in BS 8110.

The procedure is as follows:

1. Find the basic span / effective depth ratio.2. Find the modification factors. These are:

Modification factor for tension reinforcement m1, depending on the area of tensionreinforcement which is expressed in terms of M/bd and the service stress, and

Modification factor for compression reinforcement m2, depending on the area ofcompression provided.

3. The maximum allowable span therefore= basic span / effective depth ratio x effective depth x m1 x m2.

4. If the actual span is less than or equal to that found in step 3 above, then the deflection

of that beam or slab will be within the recommended limits.

We shall now discuss further each of the steps outlined above.

Step 1: The basic span / effective depth ratios for rectangular or flanged beams are given in

Table 3.10 of BS 8110. These values are based on limiting the total deflection tospan / 250, which should normally ensure that the part of deflection occurring after

the construction of finishes and partitions will be limited to the lesser of span / 500

or 20 mm for spans up to 10m. For flanged beams with b w/b > 0.3, linear

interpolation between the values for rectangular sections and for flanged beams

with bw/b > 0.3 may be used.

Basic span / effective depth ration for rectangular or flanged beams (BS 8110, Table 3.10)

Support conditions Rectangular sections Flanged beams with bw/b 0.3

Cantilever 7 5.6

Simply supported 20 16

Continuous 26 20.8

For span > 10 m, Table 3.10 should be used only if it is not required to limit the increase of

deflection after the construction of finishes and partitions. If a limit on the increase is

required, the values given in Table 3.10 should be multiplied by 10/span, except for

cantilevers where the design should be justified by calculation.


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The modification factors m1 and m2 are given in Table 3.11 and Table 3.12 of BS 8110

respectively.

Deflection will increase if there is an increase of steel stress. Thus, the use of tension steel

with higher stresses will reduce the ratios of span to effective depth.

The service stress in the reinforcement, fs, can be estimated from the equation

fs = (5 fy Asreq.) / (8 Asprov.)

The use of compression reinforcement will affect the performance of a beam by increasing its

stiffness and by reducing the downward warping of the beam due to shrinkage of the

concrete.

Modification factor for tension reinforcement (BS 8110, Table 3.11)

M/bdService stress

N/mm 0.5 0.75 1.00 1.5 2.0 3.00 4.00 5.00 6.00

100 2 2 2 1.86 1.63 1.36 1.19 1.08 1.01

150 2 2 1.98 1.69 1.49 1.25 1.11 1.01 0.94

(fy = 250) 156 2 2 1.96 1.66 1.47 1.24 1.1 1 0.94

200 2 1.95 1.76 1.51 1.35 1.14 1.02 0.94 0.88

250 1.9 1.7 1.55 1.34 1.2 1.04 0.94 0.87 0.82

(fy = 460) 288 1.68 1.5 1.38 1.21 1.09 0.95 0.87 0.82 0.78

300 1.6 1.44 1.33 1.16 1.06 0.93 0.85 0.8 0.76

Modification factor for compression reinforcement (BS 8110, Table 3.12)

100 As prov./bd Factor 100 As prov./bd Factor

0 1 1 1.25

0.15 1.05 1.5 1.33

0.25 1.08 2 1.4

0.35 1.1 2.5 1.45

0.5 1.14 3 1.5

0.75 1.2 - -


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Work Example 1

Check the deflection for the continuous beam with 8 m span together with the following

details:

Bending moment : 250 kNm

b : 300 mm

d : 425 mm

fy : 460 Mpa

Solution:

From the BS 8110, Table 3.10, the basic span / effective depth ratio for a continuous slab is

26.

Service stress fs, = 5/8 x 460 = 288 N/mm

M/bd = 250 x 106 / (300 x 425) = 4.61 N/mm

From Table 3.11, m1 = 0.84

Actual span / effective depth ratio = 8 / 0.425 = 18.8

Allowable span / effective depth ratio = 0.84 x 26 = 21.8 > 18.8 OK!!

Work Example 2

Check the deflection for the simply supported beam with 8 m span together with the

following details:

Bending moment : 250 kNm b : 300 mm

d : 425 mm

fy : 460 Mpa

Solution:


20.


M/bd = 250 x 106 / (300 x 425) = 4.61 N/mm

From Table 3.11, m1 = 0.84


Allowable span / effective depth ratio = 0.84 x 20 = 16.8 < 18.8 Failed!!


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Work Example 3

Check the deflection for the simply supported beam with 8 m span together with the

following details:

Bending moment : 250 kNm

b : 300 mm

d : 425 mm

fy : 460 Mpa

As : 3T16 (603mm)

Solution:


20.


M/bd = 250 x 106 / (300 x 425) = 4.61 N/mm

From Table 3.11, m1 = 0.84

From Table 3.12, m2 = 1.132


Allowable span / effective depth ratio = 0.84 x 1.132 x 20 = 19 > 18.8 OK!!


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Serviceability limit state of cracking

The cracking of concrete must be such as will not adversely affect the appearance and

increase danger of corrosion of the steel reinforcement.

BS 8110 recommends that the surface widths of cracks should generally not exceed 0.3

mm. This also applies to members which are exposed to particularly aggressive

environments such as sea water.

In tall or long buildings, the effects of temperature, creep and shrinkage may require the

provision of movement joints or expansion joints within both the structure and the cladding.

As calculation of crack width in beams or slabs are tedious and time-consuming works, BS

8110 has provided rules governing the minimum percentages of reinforcement, the minimum

bar size and the maximum spacing of reinforcement, so that the maximum limit of crack

widths will not be exceeded.

Minimum Percentages of Reinforcement

The minimum percentages of reinforcement for the various conditions of loading and types

of members are listed below table.

Table 3.27 of BS 8110


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be provided at the side faces at not greater than 250 mm centers. These bars should be

distributed over a distance of 2/3 of the beams overall depth measured from its

tension face and the bar size should comply with above descriptive section.

Minimum Spacing of Reinforcement

The steel bars in a beam should be so placed that when the beam is being concreted, the

concrete will flow easily around them to achieve proper compaction and so that an adequate

bond between the steel and the concrete will be formed. The bars must therefore be spaced so

that the aggregate can move between them and so prevent the formation of honeycombs

within the beam. The minimum horizontal space between the bars should be the maximumsize of the coarse aggregate plus 5 mm of the diameter of the bar, whichever is the greater.

Another practical consideration is the use of poker vibrators during concreting to ensure the

proper compaction of concrete. The vibrators are about 40 mm in diameter, and sufficient

space should be left between the top bars of a beam to allow the vibrators to pass through.

3.3

3.3


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Slabs

BS 8110 contains a set of rules for the maximum spacing of reinforcement in slabs. In

general, the clear spacing between bars should not exceed the lesser of 3 d or 750 mm.

In addition, unless crack widths are checked by calculation, the following rules should also

be observed to ensure adequate control of cracking.

No further check on bar spacing is required if either:

Grade 250 steel is used and h < 250 mm Grade 460 steel is used and h < 200 mm The reinforcement percentage 100As / bd < 0.3%

Where none of the above conditions apply, the bar spacing should be limited to the values

given in Table 3.30 of BS 8110

Where the reinforcement percentage > 1%,

OR

the values given in Table 3.30 of BS 8110 divided by the reinforcement

percentage for lesser amounts.


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Cover for Fire Resistance and Corrosion

The nominal concrete cover is an important factor to be considered in the design for

serviceability limit states of durability and fire resistance.

Nominal concrete cover is the design depth of concrete cover to all steel reinforcement,

including links. It is the dimension used in design and is indicated on the structural drawings.

The nominal cover should

1. Comply with the recommendations relating to bar size and aggregate size. Theserecommendations are:

A cover to the main bar should be at least equal to the main bar diameter, and The nominal cover should be greater than the nominal maximum size of the

aggregate.

2. Protect the steel against corrosion and fire.Serviceability limit state of durability (Cover for Fire Resistance and Corrosion)

The durability of concrete is ensured in the design by the following considerations:

1. Possible corrosion of the steel reinforcement is prevented by completely protectingit from the weather or contact with moisture. This is achieved by providing a

sufficiently thick nominal cover, depending on the exposure condition and grade of

concrete used.

2. The conditions of exposure affect durability. Concrete used indoors will beattached only very mildly compared with concrete which is buried underground orexposed to sea water.

3. The choice of the grade of concrete also affects durability. The stronger theconcrete, the greater its resistance to the effects of exposure to the weather or to

water.

4. Sufficient concrete is provided around the steel to ensure an adequate bond between the steel bars and concrete thereby enabling the two materials to act as

one.

5. The steel is insulated from the high temperatures caused by fire.


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Exposure conditions (From BS 8110, Table 3.2)

Environment Exposure conditions

Mild Concrete surface protected against weather or aggressive conditions.

Moderate Concrete surfaces sheltered from severe rain or freezing whilst wet.

Concrete subject to condensation.

Concrete surfaces continuously under water. Concrete in contact with

non-aggressive soil.

Severe Concrete surfaces exposed to severe rain, alternate wetting and drying,

or occasional freezing or severe condensation.

Very Severe Concrete surfaces exposed to seawater spray, de-icing salts, corrosive

fumes or severe freezing conditions whilst wet.

Extreme Concrete surfaces exposed to abrasion action

e.g. sea water carrying solid, flowing acidic water, machinery or

vehicles.

Nominal cover to all reinforcement (including links) to meet durability requirements (BS

8110, Table 3.4)

Conditions of exposure Nominal Cover mm

Mild 25 20 20 20 20

Moderate - 35 30 25 20

Severe - - 40 30 25

Very Severe - - 50 40 30

Extreme - - - 60 50


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Serviceability limit state of fire resistance

The whole of a structure, and the elements that go to make it up, must be fire resistant for a

certain period, the length of time in each case being dictated by the particular use of the

structure and the protection that the structure must provide to its occupants in the event of a

fire.

The fire resistance of a structural element is a combination of the following factors:

1. Its retention of the original design strength after exposure to a fire of some duration2. Its resistance to the penetration and spread of fire, and3. Its resistance to the transmission of heat so that the fire can be contained within a local

area.

A structural element is said to have a fire resistance period of one hour when, after having

been exposed to a fire for one hour, it is still capable of supporting the loads that it was

initially designed for. The required number of hours of fire resistance of a structure is based

on the time needed for the occupants of the structure is based on the time needed for the

occupants of the structure to escape and for fire-fighters to be able to control the fire without

themselves being in danger of the structure collapsing. For example, the Hong Kong

Building Regulations require buildings to be separated from any adjoining building by a wall

which has a fire resistance period of not less than four hours.

The fire resistance period required of a structure varies from half an hour to four hours,

depending on the volume of enclosed space and the structures use.

In designing a structure, note that while steel loses a large part of its tensile strength when itstemperature is raised to high heat (about 40% of its strength when the temperature is raised to

400C), concrete loses hardly any. For this reason, the fire resistance of a reinforced concrete

structure element is taken as being the degree of insulation provided by the nominal cover to

the steel, which helps to control the rise in the steels temperature. The aim of design for fire

resistance is therefore to provide the amount of insulation needed to delay, for the prescribed

period, the penetration of high heat to the steel bars.

The nominal cover and the minimum dimensions of reinforced concrete members need to

provide for the appropriate fire resistance periods are given in below tables respectively. The

values in Table 8.4 of BS 8110 can be modified by the addition of different types of surface

finishes.


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Nominal cover to all reinforcement (including links) to meet specified periods of fire

resistance (BS 8110, Table 3.5)

Nominal Cover

Beams Floors Ribs ColumnsFire

resistance

(Hours)

Simply

supported

mm

Continuous

mm

Simply

supported

mm

Continuous

mm

Simply

supported

mm

Continuous

mm mm

0.5 20 20 20 20 20 20 20

1.0 20 20 20 20 20 20 20

1.5 20 20 25 20 35 20 20

2 40 30 35 25 45 35 25

3 60 40 45 35 55 45 25

4 70 50 55 45 65 55 25

Minimum dimensions of reinforced concrete members for fire resistance (BS 8110, Table

3.2)

Column widthFire

resistance

(Hours)

Minimum

beam width

mm

Rib width

mm

Minimum

thickness of

floors

mm

Fully

exposed

mm

50%

exposed

mm

One face

exposed

mm

0.5 200 125 75 150 125 100

1.0 200 125 95 200 160 120

1.5 200 125 110 250 200 140

2.0 200 125 125 300 200 160

3.0 240 150 150 400 300 200

4.0 280 175 170 450 350 240

Work example 4

Determine the nominal cover and the breadth of the web for the beam. The exposure

condition is mild and the period of fire resistance required is 1.5 hours. The maximum size of

the aggregate is 20 mm, and fcu = 30 N/mm.

Solution:

Durability

For mild condition of exposure, nominal cover to all steel = 25 mm (Table 3.4)

Fire resistanceFor fire resistance period of 1.5 hours, nominal cover to all steel = 20 mm (Table 3.5)


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The largest value is 25mm.

On completion of this topic, you should be able to:

1. Design of RC beams and slabs for the SLS of deflection and cracking

serviceability limit state

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