METHODS OF RCC Chapter DESIGN 1 · 2019. 12. 12. · Design of RCC structures can be done either by...

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METHODS OF DESIGN

A reinforced concrete structure should be so designed that it fulfils it intended purpose during its entire

life time with:

(A) adequate safety in terms of strength and stability

(B) adequate serviceability in terms of durability.

(C) reasonable economy.

Therefore, all the designed structures must be safe, serviceable and economical for its intended life span.

Design of RCC structures can be done either by using theoretical method (i.e., the procedure laid down by

IS codes) or by experimental investigations on models or prototype (full size) structure/ elements.

Mostly the design of structures and structural elements are based upon theoretical methods. The following

design methods are commonly used for RCC structures.

(i) Working Stress Method (WSM)

(ii) Ultimate Load Method (ULM)

(iii) Limit State Method (LSM)

(a) Working stress method of design: In this method, the structures are analyzed by the classical elastic

theory. The stresses in the members are considered for normal working load condition, and no attention is

given to the conditions that arise at the time of structural collapse. The working loads are fixed by

limiting the stresses in concrete and steel to a fraction of the stresses at which the material fails when

tested as cubes and cylinders of concrete and bars of steel.

(b) Ultimate load method of design: An altertnative method of design that was developed was the

ultimate load method or the load which the structure is likely to carry. The ratio of the collapse load to the

working load is known as load factor. The load factor gives exact margin of safety against collapse.

Since the method utilizes a large reserve of strength in plastic region (inelastic retion) and of ultimate

strength of member, the resulting section is very slender or thin. This gives rise to excessive deformations

and cracking. Also, the method does not take into consideration the effects of creep and shrinkage.

(c) Limit state method of design: We have seen that while the working stress method gives satisfactory

performance of the structure at working load, It is unrealistic at ultimate state of collapse. Similarly, while

the ultimate load method provides realistic assessment of safety, it does not guarantee the satisfactory

serviceability requirements at service loads. An ideal method is the one which takes into account not only

Chapter

1 METHODS OF RCC

DESIGN Syllabus: Introduction to WSM, LSM – Limit State of collapse, limit state of

serviceability, Defection, Cracking. Characteristic, strength of concrete & steel,

Partial safety factor for concrete & steel. Characteristic or working load, partial

safety factor for load, Limit state or factor load. Weightage : 10%


2

RCC

the ultimate strength of the structure but also the serviceability and durability requirements. The newly

emerging ‗limit state method‘ of design is oriented towards the simultaneous satisfaction of all these

requirements. This new method makes a judicious combination of the working stress philosophy as well

as the ultimate load philosophy, thus avoiding the demerits of both. The acceptable limit of safety and

serviceability requirements, before failure occurs is called a limit state. Two prominent types of limit

states are considered in the design:

1. Limit state of collapse (strength limit state)

2. Limit state of serviceability

In India IS Code has completely replaced the ultimate load method by the limit state method.

WORKING STRESS METHOD (WSM)

1. This is a traditional method of design which is used for RCC, steel and timber structures.

This method is based upon linear elastic theory. It is also known as ―Elastic Stress Method” or

“Modular Ratio Method”.

2. In this method, the moment and forces acting on a structure are calculated from the actual values of

working loads (service loads) but the stresses, so developed, in concrete and steel are restricted to

only a fraction of their true strengths in order to provide an adequate Factor of Safety (FOS).

FOS = 3 For concrete (with respect to cube strength)

FOS = 1.78 to 1.80 For steel (with respect to yield strength of steel)

3. The permissible (allowable) stresses are kept much below the ultimate strength of the materials.

4. All the forces such as bending moments, shear forces, axial loads etc. can be easily calculated by

assuming the materials to behave perfectly elastic.

5. Structures are proportioned to develop stresses upto a fraction of the ultimate stress of concrete and

yield stress of steel.

Advantages of WSM : Following are the advantages of working stress method:

1. Being simple in concept, it can be easily applied.

2. Under working loads, structures give better serviceability performance (i.e., less cracks and deflection)

Disadvantages of WSM : Following are the disadvantages of working stress method :

1. Since the reinforced concrete is not a perfectly elastic material, therefore, this method does not give

real behaviour of the structure. Highly stressed parts of the structure start deforming

unproportionately to the loading and distribution of moment is not same as or a perfectly elastic

material.

2. This method neither shows the actual strength nor gives the true FOS of the structure under failure.


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RCC

3. This method fails to discriminate between different types of loads that act simultaneously but have

different uncertainties in behaviour.

4. The modular ratio based design results in larger percentage of compression steel than that given by

LSM, thus leading to uneconomical design.

5. In this method, there is no guarantee that a structure designed by elastic method, keeping the

maximum stress in steel, at working load to 1

2the yield stress and maximum stress in concrete to

1

3

the ultimate stress, will be able to carry an ultimate load of twice the working load which means the

actual safety against ultimate loads is not known.

6. WSM of result in comparatively larger sections of structural member with higher quantities of steel

reinforcement.

7. Effect of creep and shrinkage, which are time dependent, are not taken care by WSM.

Ultimate Load Method (ULM)

1. This method was evolved as a alternative to WSM

2. This method is based on the ultimate strength of reinforced concrete at ultimate load.

Ultimate Load = Service Load Load Factor.

Where, Service Load = Design Load

and load factor is taken for desired margin of safety.

Therefore, it is also known as Load Factor Method or Ultimate Strength Method.

3 Different load factors under combined loading conditions can be used to design a particular

structural member.

4. But it may be noted that satisfactory strength performance of structure, at ultimate loads, does not

guarantee satisfactory serviceability performance at normal service loads.

5. It becomes the duty of the designer to ensure that under full working load, no part of the structure is

excessively cracked, none of the member have suffered excessive deflection and the structure will

not vibrate or oscillate excessively under moving or varying loads.

6. It is based upon the results obtained from the experimental investigations showing exact behaviour

of the structures.

7. This method permits the use of lower load factor for loads exactly known (e.g., dead loads) and a

higher load factor for unpredictable loading.


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RCC

Advantages of ULM : Following are the advantages of ULM :

1. Different load factors for different types of loads can be used.

2. Reserve strength in the plastic stage is being utilized by this method.

3. Load factors used in this method gives sufficient margin of safety.

Disadvantages of ULM : Following are the disadvantages of ULM :

1. It ensures safety at ultimate loads but does not satisfy the serviceability requirements at service

(working) loads.

2. There is increase in deflection and crack width due to use of high strength reinforcing steel and

concrete.

3. It does not take into account the effect of creep and shrinkage.

Limit State Method (LSM)

Salient features of this method are :

1. We have so far studied that while Working Stress Method (WSM) gives satisfactory performance of

the structure at working loads but it becomes unrealistic at ultimate state of collapse. On the other

hand, Ultimate Load Method (ULM) provides realistic assessment of safety, it does not guarantee the

satisfactory serviceability at working loads.

2. The best suitable method is that which not only takes into account the ultimate strength but also the

serviceability and durability requirement.

3. In this method, the structure shall be designed to withstand safely all loads which are expected to act

on it throughout its life span.

4. It shall also satisfy the serviceability requirements such as prevention of excessive deflection,

cracking and vibrations.

5. This method of design is based upon safety at ultimate loads and serviceability requirements.

6. The ―Limit State‖ may be defined as the acceptable limit for the safety and serviceability

requirements.

7. In LSM, design values are obtained by multiplying working loads with partial factor of safety and

the design strength of materials is obtained by dividing characteristic strengths (ultimate strength)

with partial FOS.

8. To make sure that the above objectives are satisfied, the design should be based upon characteristic

values for material strengths and applied loads, taking into accounts the variation in the material

strength and loading.


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RCC

DIFFERENT TYPES OF LIMIT STATES

Limit state is a state of impending failure beyond which a structure ceases to perform satisfactorily in

terms of safety and serviceability.

Different types of limit states which are to be considered in design are :

(a) Limit State of Collapse (or Ultimate Limit State).

(b) Limit State of Serviceability.

(c) Other Limit States.

(a) Limit State of Collapse

1. Limit State of Collapse (or failure) depends upon ultimate strength.

2. Limit State of Collapse have been introduced from safety requirements.

3. Limit State of Collapse occur when the structure as a whole or part of the structure collapses under

following conditions :

(i) Limit State of Collapse in Flexure.

(ii) Limit State of Collapse in Compression.

(iii) Limit State of Collapse in Shear.

(iv) Limit State of Collapse in Torsion.

(v) Limit State of Collapse in Bond.

(b) Limit State of Serviceability

1. The limit state of serviceability relates to the performance and behaviour of structure at service loads

(working loads).

2. This limit state is introduced to prevent objectionable deflection and cracking.

3. Generally, design is based upon limit state of collapse at ultimate loads and serviceability (in

excessive cracking and deflection) at working loads.

The two important limit state of serviceability are :

(i) Limit State of Deflection (ii) Limit State of Cracking

(c) Other Limit States (As per IS : 456 – 2000, Clause 35–4): Structures designed for unsual or

special functions shall comply with any relevant additional limit state considered appropriate to that

stretches such as limit states of vibrations, impact resistance, durability, fire resistance etc.

All above mentioned limit states should be considered in design to ensure adequate degree of

safety and serviceability. In general, the structure shall be designed on the basis of the most

critical limit state and shall be checked for other limit states.


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RCC

COMPARISION BETWEEN WORKING STRESS METHOD (WSM) AND LIMIT STATE

METHOD (LSM)

S.No. Working Stress method (WSM) Limit State Method (LSM)

1. It is based on the behavior of structure

under service load (working loads).

The structure shall be designed on the basis of

most critical limit state and checked for other

limit states.

2. This method is assumed to be deterministic

because all loads, stresses and factor of

safety are known.

This method is non-deterministic because

loads and stresses are predicted based upon

experience and field datas.

3. Safety against ultimate loads is not known. It satisfies all the limit states of collapse and

serviceability.

4. This method is based upon linear stress

distribution.

It is based upon non-linear stress distribution

taking inelastic strain into consideration.

5. Structures are proportioned to develop

stresses upto a fraction of the ultimate stress

of concrete and yield stress of steel by

applying FOS.

In this method, the design values are obtained

by applying partial safety factors.

6. WSM leads to comparatively larger

sections of structural members with higher

quantities of steel reinforcement.

LSM results in lesser quantities of steel

reinforcement as compare to WSM

CHARACTERISTIC STRENGTH, DESIGN LOADS AND PARTIAL SAFETY FACTORS

Characteristic Strength of Materials

(As per IS ; 456 – 2000, Clause 36.1)

The term characteristic strength means that strength value of material below which not more than 5% of

the test results are expected to fall. In other words, there is only 5% probability of the actual strength

being less than the characteristic strength. Characteristic strength of material is designated by f.

(a) Characteristic Strength of Concrete (fck) : The characteristic strength of concrete is denoted by

(fck). It is expressed in N/mm2. The value of characteristic strength for different grades of concrete.


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RCC

Characteristic strength (fck) for various grad of concrete

(As per IS : 456 - 2000, Clause 6.1.1)

Group Grade Designation Specified Characteristic Compressive Strength

of 150 mm cube after 28 days of curing (fck)

(N/mm2)

Ordinary concrete M 10

M 15

M 20

10

15

20

Standard Concrete M 25

M 30

M 35

M 40

M 45

M 50

M 55

25

30

35

40

45

50

55

High Strength Concrete M 60

M 65

M 70

M 75

M 80

60

65

70

75

80

Therefore, characteristic strength of concrete (fck) may be defined as the compressive strength of 150 mm

cube after 28 days of curing expressed in N/mm2 below which not more than 5% of test specimens are

expected to fall. The design values should be based on 28 days characteristic strength of concrete. The

design strength should be lower than the mean strength (fm).

Characteristic Strength = Mean Strength - K Standard deviation

fck = fm – K Sd

Where, fM = Mean Strength

K = Constant = 1.645 = 1.65

Sd = Standard deviation

The value of K corresponding to 5% are of the curve is 1.645. BIS has adopted the value of K = 1.65


8

RCC

5%Resultsbelowfck

Fre

qu

ency

of

Resu

lts Mean Strength

1.84 Sd

Characteristic Strength

S = Standard Deviationd

Area of Curve = 5% of total Area

Strength

fck fm

Frequency distribution curve for strength.

(b) Characteristic Strength of Steel (fy) : It is designated by the symbol ‗fy‘ (in N/mm2). The

characteristic strength of steel (fy) is defined as that value of yield stress (N/mm2) or 0.2 percent

proof stress, as specified in the relevant Indian Standard Specifications, below which not more than

5% of the test specimens are expected to fall.

CHARACTERISTIC LOADS (As per, IS : 456 – 2000, Clause 36.2)

The term ―Characteristic load― means that value of load which has a 95 percent probability of not being

exceeded during the life of the structure. These are also termed as service loads.

Since data are not available to express loads in statistical terms, for the purpose of this standard, dead

loads (D.L.) given in IS : 87.5 (Part-l), imposed loads (I.L.) or live loads given in IS 875 (part-2), wind

loads (W.L.) given in IS 875 (Part-3), Snow load as given in IS 875 (part -4) and seismic force (E.L.)

given in IS : 1893 shall be assumed the characteristic loads.

5% of Resultsabove F

Fre

quen

cy o

f R

esu

lts

Mean Load 1.84 Sd

Characteristic Load

Load

Fm F

Area of Curve =5% of Total Area

95% Area

Frequency distribution Curve for Load.

Characteristic load is shown by the ordinate upto which the area of frequency distribution curve for load

is 95% of total area.

F = Fm + K.Sd


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RCC

Where, F = Characteristic Load

Fm = Mean Load

K = constant = 1.645 1.65

Sd = Standard deviation

PARTIAL SAFETY FACTORS OR (PARTIAL FACTOR OR SAFETY)

(a) Partial Safety factor for Strength Materials (As per IS : 456 – 2000, Clause 36.4.2):

It is designated as ‗m‘. The partial factor of safety for strength of material is the factor, which when

multiplied by characteristic strength of material gives the design values for materials. The values of

m, for each material will be different for different states and are given in Table :

Partial safety factor (m) for strength of materials

Material Limit State of collapse Limit state of serviceability

Deflection Cracking

Concrete 1.5 1.0 1.3

Steel 1.15 1.0 1.0

Higher value of m is taken for concrete (i.e., 1.5) than steel (i.e., 1.15) because it is expected that the

strength of concrete may vary from the test results because of improper performance of concrete

operations (like mixing, transportation, placing compaction etc.) whereas chances of deviation for

steel from expected strength are less as compared to concrete.

As the values of design strength are same as that of characteristic strengths, therefore the value for

concrete and steel is taken as 1.0

(b) Partial Safety factor for Leads (As per IS .- 456 - 2000, Clause 36.4.1) : It is designated as ‗f. The

partial factor of safety for loads may be defined as the factor, which when multiplied with

characteristic loads gives the value of design loads. It depends upon type of load (i.e., D.L. or L.L. or

W.L.) and the type of limit state.

Values of partial factor of safety (f) for loads

Load combinations Limit State of Collapse Limit State of Serviceability

D.L. L.L. W.L. D.L. L.L. W.L.

D.L. + L.L. 1.5 1.5 – 1.0 1.0 –

D.L. + W.L. 1.5 or 0.9* – 1.5 1.0 – 1.0

D.L. + L.L. + W.L. 1.2 1.2 1.2 1.0 0.8 0.8


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RCC

e.g., For load combination D.L. + L.L. and limit state of collapse the values of D.L. and L.L, so

calculated, are to be multiplied with 1.5 (i.e., partial safety factor).

DESIGN VALUES: (As IS : 456 – 2000, Clause 36.3)

Design values characteristics are obtained when partial safety factors are applied to the characteristic

strength of material and characteristic loads.

(a) Design Values for Materials : Design strength of material is designated by (fd).

Mathematically, it is represented as below:

d

m

ff

Where, fd = Design strength of the material

f = Characteristic strength of the material =

m = Partial safety factors for concrete and steel for different limit state conditions

= 1.5 for concrete (For Limit State of Collapse)

= 1.15 for steel (For Limit State of Collapse)

(b) Design Values for Loads : Design load values are designated as (Fd) and mathematically

represented as below :

Fd = F f

Where , Fd = Design Load

F = Characteristic load

and f = Partial safety factor for various load combinations for different limit states.

Design loads are sometimes also referred as “factored load,” which is obtained by multiply load by a

appropriate factor (generally taken as 1.5). The factored load is used to calculate factored shear force and

factored bending moment.

DESIGN STRESS STRAIN CURVES (As per IS : 456 - 2000, Clause 38)

(a) Stress – Strain Curve for Concrete (In Flexural Compression) : The IS code permits the use of

any appropriate curve for relationship between the compressive stress and strain distribution in

In Table

(i) When (E.L.) are considered then substitute (W.L.) with E.L.

(ii) The value of (D.L.) is to be multiplied by 0.9* for the load combination of (D.L. +

W.L.) for limit state of collapse, only when stability against overturning or stress

reversal is critical.


11

RCC

concrete. The relationship between the compressive stress distribution in concrete and the strain in

concrete may be assumed to be rectangular, trapezoid, parabola or any other shape which results-in

prediction of strength in substantial agreement with the test result.

An acceptable stress strain curve is given in Fig. The curve for concrete is a parabola in its initial

stage upto a strain valve 0.002 (where slope becomes zero). Beyond strain valve of 0.002, the stress

remains constant with increasing load until a strain valve of 0.0035 is reached i.e. when concreted is

said to have failed. For design purpose, the compressive strength of concrete in structure shall be

assumed to be 0-67 times the characteristic strength (fck)

IS code 456 – 2000 recommends that partial safety factor, m = 1.5 shall be applied

fck

0.67 fck

Idealised Curve

0.67 f ..... (i)ck

fck

CharacteristicCurve

DesignCurveStr

ess

0.67 f ck

m

0.67 f ck

1.5=

= 0.45 f ..... (ii)ck

ParabolicCurve

0 0.002

Strain

0.0035

Fig. Design Stress Strain Curve for concrete

e.g. For M 25 concrete

Ideal value = 25 N/mm2

Acceptable limit = 0.67 fck

i.e, characteristic value = 0.67 25 = 16.75 N/mm2

Where as Design value = ck0.67f

1.5

= 0.45 fck = 0.45 25 = 11.25 N/mm2

Note: Ideal value is actually 0.33 times greater than fck i.e, = (0.33 25) + 25 = 33.25

N/mm2

The maximum stress in the characteristic curve is restricted to 0.67 fck (i.e. 2

3 times

the strength of cube). The 0.67 factor is introduced to take into account for the

difference in strength indicated by a standard cube test and strength of concrete in

structure.


12

RCC

(b) Design Stress Strain Curve for Reinforcing Material

(i) For Mild Steel Reinforcement (Having Definite Yield Point) : Mild Steel reinforcement conforms to

Fe 250 grade with characteristic strength, fy, = 250 N/mm2. For mild steel, the stress is proportional

to strain upto yield point and after that the strain increases at constant stress. The change from elastic

to plastic condition is abrupt therefore it shows a definite yield point.

The partial factor of safety m = 1.15. Therefore a design stress of y

y

f0.87f

1.15 is used for mild

steel reinforcement.

Str

ess

E = 2 10 N/mmS 5 2

Design Curve

Characteristic Curve

fy

fy

m

= fy

1.15= 0.87 fy

S = 0.001 p s = 10 to 15 times

StrainWhere,

= Elastic Strains

= Plastic Strainp

Design stress strain curve for mild steel.

(ii) For High Strength Deformed Reinforcement (i.e., HYSD Bars or Cold Worked bars): HYSD

bars conforms to Fe 415, Fe 500, grades and having characteristic strengths of 415 N/mm2 and 500

N/mm2 respectively. These type of bars do not show a definite yield point and hence taken as 0.2

percent proof stress

500

450

400

350

300

250

200

150

100

50

00.001 0.002 0.003 0.004 0.005

Strain

CharacteristicCurve

Design Curve

Str

ess

(N

/mm

)2

500

= 0.87 fy

500

1.15415

= 0.87 f or y

400

1.15

Design stress strain curves for (HYSD) High Yield Strength Deformed steel)


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RCC

e.g. For Fe 415 Grade of Steel,

Characteristic valve = 415 N/mm2

Design valve = yf

1.15 [ FOS = 1.15]

= 0.87 fy

Design valve = 0.87 415

= 361 N/mm2


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RCC

1. Partial safety factors for concrete and steel

respectively may be taken as:

(A) 1.5 & 1.15 (B) 1.5 & 1.78

(C) 3 & 1.78 (D) 3 & 1.2

2. The characteristic strength of concrete in the

actual structure is taken as:

(A) fck (B) 0.85 fck

(C) 0.67 fck (D) 0.447 fck

3. The characteristic strength of concrete is

defined as that strength below which not more

than ___________ of the test results are

expected to fall.

(A) 10 percent (B) 5 percent

(C) 15 percent (D) 20 percent

4. The minimum grade of reinforced concrete in

sea water as per IS 456:2000 is:

(A) M15 (B) M20

(C) M30 (D) M40

5. Characteristic strength of concrete is measured

at:

(A) 14 days (B) 28 days

(C) 91 days (D) 7 days

6. Ordinary concrete is not used for concrete

grade

(A) M 100 (B) M 150

(C) M 250 (D) M 400

7. Characteristic compression strength of M20

concrete is

(A) 30N/sqmm (B) 27N/sqmm

(C) 28N/sqmm (D) 20N/sqmm

8. Water cement ratio is the ratio of

(A) Weight of water to weight of cement

(B) Weight of cement to weight of water

(C) Volume of cement to volume of water

(D) Volume of water to volume of cement

9. The total no. of grades as specified by IS 456-

2000 are

(A) 5 (B) 10

(C) 15 (D) 25

10. Compressive strength of concrete is

_________ tensile strength

(A) More than (B) Less than

(C) Equal (D) None

11. Reinforced Cement Concrete (RCC) was

evolved because plain concrete has

(A) High tensile strength

(B) Low tensile strength

(C) Tensile strength

(D) None of the above

12. The size of cube to determine characteristic

compressive strength of concrete is

(A) 150 150 150 mm

(B) 300 300 300 mm

(C) 200 200 200 mm

(D) 450 450 450 mm

Practice Problems


15

RCC

13. A slump cone is used primarily to provide

indication of which of following in concrete

(A) Durability and finish

(B) Air entrainment and chemical resistance

(C) Strength and workability

(D) Appearance and color

14. For the construction of RCC slabs, columns,

beams etc the minimum recommended grade

of concrete mix is

(A) M 10 (B) M 15

(C) M 20 (D) M 25

15. The modules of elasticity of M-25 grade

concrete (in N/mm2) as per IS: 456-2000 is

assumed as

(A) 36,00 (B) 30,00

(C) 28,500 (D) 25,000

1. (A)

2. (A)

3. (B)

4. (C)

5. (B)

6. (D)

7. (D)

8. (A)

9. (C)

10. (A)

11. (B)

12. (A)

13. (C)

14. (C)

15. (D)

Ans. 15.D

EC = 5000 fck

= 5000 × 25

= 25,000

Explanation Level - 1

Answer key


Beams are the flexural members which are provided in the structures to resist bending, caused due to

external loading. Beams can be either rectangular in section or flanged beams.

1. Rectangular beams e.g, Singly or Doubly Reinforced.

2. Flanged beams e.g., T and L beams

SINGLY REINFORCED BEAM.

A singly reinforced beam is a beam provided with longitudinal reinforcement in the tension zone only.

n

b

d

Ast

D

c

Let b = Breadth of a rectangular beam

d = Effective depth of the beam ( i.e depth form compression edge to the centre

of the tensile reinforcement)

n = Depth of neutral axis below the compression edge

D = Overall depth of beam i.e distance between top most edge to the bottom edge

of beam

Ast = Cross-sectional area of steel in tension

C = Effective Cover = Distance between centre of steel bars and bottom most edge of beam

Clear cover = distance between the bottom of bars and bottom most edge of beam.

ASSUMPTIONS IN LIMIT STATE OF COLLAPSE IN FLEXURE

(As PER is : 456–2000, CLAUSE 38.1)

Design for the limit state of collapse in flexure shall be based on the assumptions given below:

(i) Plane sections normal to the axis remain plane after bending i.e., strain developed in any part of the

cross –section is proportional to its distance from the neutral axis.(Strain is linear)

Chapter

2 BEAMS

Syllabus: Analysis & Design of singly Reinforced, Doubly

reinforced Beams. Sections balanced, under Reinforced section &

Over reinforced section flanged beams T Beams, L-Beams.

Weightage : 20%


17

RCC

(ii) The maximum strain in concrete at the outermost compression fibre is taken as 0.0035 in bending.

(iii) The relationship between the compressive stress distribution in concrete and the strain in concrete

may be assumed to be parabolic.

ParabolicCurve

Str

ess

fck

0.67 fck

0.67fck

m

Strain0.002 0.0035

Stress-Strain Curve for Concrete.

For design purpose, the compressive strength of concrete in the structure shall be assumed to be 0.67

times the characteristic strength (fck). The partial factor of safety m = l.5 shall be applied in addition to

this

i.e., Design compressive stress = ckck

0.67f0.45f

1.5

Where, fck = Characteristic compressive strength of concrete.

(iv) The tensile strength of concrete is ignored.

(v) The stresses in the reinforcement are derived from representative stress-strain curve for the type of

steel used.

For design purpose, the partial safety factor (m) = 1.15 shall be applied.

(vi) The maximum strain in tension reinforcement in the section at failure shall not be less than

y

s

f0.002

1.15E

or y

s

0.87f0.002

E

Where, fy = Characteristic strength of steel

Es = Modulus of elasticity of steel.


18

RCC

Str

ess

E = 200000S

fy

0.975 f y

0.95 fy

0.90 fy

0.85 fy

0.80 fy

fy

f /1.15y

.0001.0003.0007

.002

.001

.004

.003Strain

fy

Str

ess

fy

f / 1.15y

E = 200000 N/mmS

2

Cold Worked Deformed Bar Steel Bar with Definite Yield Point

Representative Stress –Strain Curves for Reinforcement.

CONCEPT OF NEUTRAL AXIS (N.A)

It is an imaginary axis which divides the cross-section of a beam into two zones i.e, compression and

tension zone. The stresses are zero at this axis. Neutral axis is always situated at the centre of gravity of

the given section.

In case of a simply supported beam the neutral axis divide the beam section into compression zone (top

portion) and tension zone (bottom portion). But in case of cantilever beams, the stresses are reverse i.e.,

top portion is tension zone and bottom portion is compression zone.

The location of N.A. in case of RCC beam, depends upon the amount of steel provided in the tension

zone. The depth of neutral axis from the top most, compression edge, increases with the increase in

amount of steel.

DEPTH OF NEUTRAL AXIS (Xu)

Depth of neutral axis from the top compression edge is designated as (xu). The location of N.A. can be

determined from the stress strain diagram of a beam section

Where, b = Width of beam section

d = Effective depth of beam

Ast = Area of steel in tension

xu = Depth of neutral axis from top edge

c = Strain in concrete


19

RCC

fck, = Characteristic strength of concrete (Nfmmz)

fy, = Yield stress of steel (Nfmmz)

C = Resultant compressive force

T = Resultant Tensile force

Z = Lever arm, (distance separating two forces T and C)

Es = Modulus of elasticity of steel '

At limit state of collapse. considering the equilibrium of forces (tensile and compressive.)

i.e., Resultant compressive force (C) = Resultant tensile force (T)

0.36 fck b xu = 0.87 fy Ast

Mathematically, y st

u

ck

0.87f .Ax

0.36f .b

b

N.A

Ast

xu d

C = 0.0035

C = 0.002

0.45 fck

T = 0.87 f Ay st

Lever arm (Z) = d – 0.42 xu

C = 0.36 f b xck u

0.42 xu

Section a Beam Strain Diagram

0.87 fy

Es

+ 0.002

Strain Distribution Diagram

Stress and Strain across a RCC beam section.

MAXIMUM DEPTH OF NEUTRAL AXIS [Xu(max.)]

(As per Clause 38.1)

Maximum depth of neutral axis is designated as xu(max). It is necessary to limit the depth of axis because

greater depth of neutral axis, resulting from higher percentage of tensile steel, will lead to design of over

reinforced sections.

In over reinforced sections, steel reaches its peak value of stress later than concrete hence results in brittle

failure. Therefore xu(max.) is limited to ensure that tensile steel reaches its yield stress earlier than concrete

to avoid brittle failure.

The limiting (maximum) values of depth of neutral axis is dependent upon two factors i.e.,

effective depth of the section (d) and grade of steel used (i.e. value of fy).

From strain diagram, the value of maximum depth neutral of axis


20

RCC

b

0.002

0.0035

0.42 x (max.)u

d

xu(max.)

N.A

Beam Section Strain Diagram

0.87 f y

S

+ 0.002

Strain Diagram of Singly Reinforced Beam Section

In above figure, from similar triangles

u(max.)

yu(max.)

s

x 0.0035

0.87fd X0.002

E

or u(max.)

y

s

X 0.0035

0.087fd0.0055

E

Substituting the value of Es = 2 105 N/mm

2 and fy = 250 N/mm

2 (For mild steel)

We get, u(max.)

5

X 0.0035

0.87 250d0.0055

2 10

= 0.531 0.53

xu(max.) = 0.53d

Similarly, for other grades of steel, the value of xu(max.) can be calculated and are shown in Table.

Table: Maximum (Limiting ) Depth of Neutral Axis (xumax.)

Grade of Steel Yield stress fy (N/mm2) Xu(max.)

Fe 250 250 0.53 d

Fe 415 415 0.48 d

Fe 500 500 0.46 d

LEVER ARM

0.45 fck

C

Z = (d – 0.42 x )u

0.42 xu

T


21

RCC

The distance between the resultant compressive force (C) and tensile force (T) is called the lever arm It is

denoted by z..

Total compression in Concrete (C) = Total Tension in Steel (T)

From Fig. Z = d – 0.42 xu

Mu = C Z or T Z

Ultimate moment of resistance, Mu = C Z

= 0.36 fck . b. xu (d – 0.42 xu)

As the maximum depth of neutral axis is limited to xu(max), therefore the maximum value of moment is

also limited.

Put xu = xu(max) and Mu = Mu (lim)

Mulim = 0.36 fck b xu(max) (d – 0.42 xumax.)

TYPES OF BEAM SECTIONS

The beam sections can be of three types:

1. Balanced Section

2. Under-reinforced section

3. Over-reinforced section

1. Balanced section or Critical section or Economical section.

A section is known as a balanced section in which the compressive stress in concrete (in compressive

zone) and tensile stress in steel will both reach the maximum permissible values simultaneously.

The neutral axis of such a section is known as critical neutral axis (𝑛𝑐). The area of steel provides is

known as economical area of steel.

Balanced Section: This section in which the tensile steel reaches the yield strain

y

s

0.087fi.e, 0.002

E

simultaneously as the concrete reaches the failure strain (Es = 0.0035) is

known as balanced section.

Conditions applicable for balanced section are;

(i) (max.) u

u u(max.)

xu xor x x

d d

(ii) pt = pt(lim.)

(iii) The moment of resistance will be maximum (or limiting moment)

Mu(lim.) = C Z

or Mu(lim.) = 0.36 fck b x umax . (d – 0.42 xu(max.))


22

RCC

(where Z = lever arm, Z = d – 0.42 xu and xu = xumax)

b

c = 0.0035

d

xu(max.)

N.A


0.87 f y

S

+ 0.002Ast s =

Strain diagram of a balanced section

2. Under-reinforced section.

If the area of steel provided is less than that required for a balanced section, it is known as under-

reinforced section. Due to less reinforcement the position of actual N.A. (n) will shift above the

critical. N.A. (nc) i.e n<nc. In under-reinforced section steel is fully stressed and concrete is under

stressed. Under such conditions, the beam will fail initially due to over stress in the steel.

b

c = 0.0035

d

ActualN.A


0.87 f y

S

+ 0.002Ast s =

xu xu max.

BalancedN.A

d

Conditions applicable for under – reinforced section are:

(i) percentage of steel in under reinforced section is less than as required for balanced section i.e.,

pt < pt(lim.)

(ii) xu < xu(max.)

(iii) Ultimate moment of resistance will be governed by steel (i.e, Tensile force T) because it will reach its

peak value of strain earlier than concrete.

Mu = T Z

Mu = 0.87fy Ast (d – 0.42 xu)

[ xu < xu(max.) value of xu is used.


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RCC

OVER REINFORCED SECTION

In over reinforced sections, concrete fails first and hence such failures are brittle and does not give

enough time or warning. IS : 456–2000 code recommends that such sections may be redesigned. By

limiting the percentage of tensile steel, we can restrict the use of over reinforced sections.

b

c = 0.0035

ActualN.A


0.87 f y

ES

+ 0.002Ast s =

xuxu max.

BalancedN.A

Strain diagram for a over reinforced section

Conditions applicable for over reinforced sections are:

(i) percentage of tensile steel is more than that in balanced section

i.e, pt > pt(lim.)

(ii) xu > xu(max.)

(iii) Moment of resistance is governed by concrete (i.e, compressive force C)

Mu = C Z

Mu = 0.36 fck.b.xu(max.) (d – 0.42 xu(max))

[ value of xu should not exceed xu(max.)]

BASIC RULES FOR DESIGN OF BEAMS:-

1. Effective span.

Unless otherwise specified, the effective span of a member shall be as follows:

(a) Freely supported, beam or slab: The effective span is taken as smaller of the :

(i) distance between the centres of supports

(ii) clear distance plus the effective depth of beam or slab

(b) Cantilever beam or slab: the effective span is the portion projecting beyond fixed end upto free

endi.e, length of over hang.

(c ) Continuous beam or slab: If the width of support is less than 1

12 of the clear span, the effective

span shall be same as given in (a) ( i.e. as in case freely supported beam or slab). If the width of

support is greater than1

12 of the clear span or 600 mm whichever is less, the effective span shall be

taken as under:


24

RCC

(i) For the end of span with one end fixed and the other continuous or for intermediate spans, the

effective span shall be the clear span between the supports.

(ii) For end span with one end free and other continuous, the effective span shall be the clear span

plus half the effective depth of the beam or the clear span plus half the width of the

discontinuous support, whichever is less.

SLENDERNESS LIMITS FOR BEAMS TO ENSURE LATERAL STABILITY.

A simply supported or continuous beam shall be so proportioned that the clear distance between the

lateral restraints does not exceed 60b or 250 𝑏2

𝑑 whichever is less, where, d is the effective depth of the

beam and b the breadth of the compression face midway between the lateral restraints.

REINFORCEMENT.

(a) Minimum reinforcement: the minimum area of tension reinforcement shall not be less than that

given by the following:

As = 0.85 bd

𝑓𝑦

where A s= minimum area of tension reinforcement,

b = breadth of the beam or the breadth of the web of T-beam

d = effective depth, and

fy = characteristic strength of reinforcement.

(b) Maximum reinforcement : The maximum area of tension reinforcement shall not exceed 0.04bD

Where D = overall depth of beam.

(c ) Compression reinforcement: The maximum area of compression reinforcement shall not exceed

0.04 bD.

(d) Side face reinforcement: When the depth of web in the beam exceeds 750mm, side face

reinforcement shall be provided along two faces. The total area of such reinforcement shall not be

less than 0.1 % of the web area and shall be distributed equally on two faces at a spacing not

exceeding 300mm or web thickness whichever is less.

SPACING OF REINFORCEMENT.

(a) Minimum horizontal distance between bars

(i) Diameter of bar if diameters are equal

(ii) Diameter of largest bar if diameters are unequal

(iii) 5mm more than the nominal size of aggregate.

When bars in rows, the minimum vertical distance should be greater of the following:


25

RCC

(i) 15 mm

(ii) 2

3 Nominal size of bar.

COVER TO REINFORCEMENT.

Reinforcement shall have concrete cover and the thickness of such cover (excluding plate or other

decorative finish) shall be as follows:

(i) The clear cover for longitudinal reinforcing bar in a beam shall not be less than 25mmm or the

diameter of the reinforcing bar whichever is more.

(ii) For reinforced concrete members totally immersed in sea water, the cover shall be 40mm more than.

DOUBLY REINFORCED BEAMS:-

Beams reinforced with main steel both in tension and compression zones are called doubly reinforced

beams. In order to prevent the compressive stress in concrete from exceeding its safe permissible value,

steel must be provided in the compression zone to take up extra compressive stress. Thus the beam gets

doubly reinforced.

Conditions under which doubly reinforced beams are used:-

A doubly reinforced section is generally provided under the following conditions:

1. When the depth of beam is restricted due to headroom considerations, architectural or some other

such reason e.g. basement floors and stair cases.

2. When the B.M due to external loading is large compared with resisting moment (Qbd2) and the size

of the beam is restricted.

3. When the member is subjected to eccentric loading.

4. The external live leads may alternate i.e. may occur on either face of the member.

5. When the member is subjected to shocks, impact or accidental laternal thrust.

6. When the beam is continuous over several supports, the section of the beam at the supports is usually

designed as a doubly reinforced section.

The maximum area of compression reinforcement shall not exceed 0.04 b D (As per clause 26.5.1.2 of IS

456 – 2000).

A doubly reinforced beam section with tension and compression steel may consist of two sections i.e,

section (1) and section (2)

Doubly reinforced beams are considered as uneconomical, as the strength of compression

reinforcement is not fully utilized.


26

RCC

Doubly Reinforced beam section subjected to moment (M )u

b

Ast

Asc

d

d´

=

b

Ast

d

+

Section (A)

resisting moment =

Mu = M (lim)1 u

b

Ast2

Ascd

d´

Section (B)

Balance Resisting =

Moment = M u

(M =M - M )u u u 2 1

2

d – d´

Doubly Reinforced Beam Section.

Section (A) represents the limiting moment (Mu lim.) . resisted by singly reinforced beam with 1stA area of

tensile steel).

Section (B) represents the balance moment of resistance, which exceed Mu lim., is to be carried by

additional tensile steel 2stA and compression steel (Asc).

Section (A) indicates a singly reinforced section, with tensile steel 1stA , which reaches its limiting value

of moment of resistance Mu lim.

i.e., 1u u lim.M M

Section (B) indicates a section with compression steel Asc and additional tensile steel 2stA to resist the

balance moment 2uM

Where, 2 1u u uM M M

In, fig. d = Effective depth (mm)

d = Effective cover to compression (mm)

Asc = Area of steel in compression (mm2)

Ast = Area of steel in tension (mm2)

b = Width of the beam section (mm)

1stA = Area of tensile steel required for singly reinforced beam to resist Mu lim. (mm2)

2stA = Area of additional steel intention required to resist 2uM

= 1

2

u uM M (mm )

Note: Mu lim. for Fe 250 = 0.148 fck bd2

Fe 415 = 0.138 fck bd2

Fe 500 = 0.133 fck bd2


27

RCC

DEPTH OF NEUTRAL AXIS (N.A.) OF DOUBLY REINFORMCED BEAM

A doubly reinforced, section having compression reinforcement at a depth d‘ below the outermost

compression fibre.

b

Ast

xu

0.0035 0.45 fck

T = T + T1 2

= 0.87 f Ay st

Lever arm (Z) = d – 0.42 xu

0.42 xu

(1) Section a doublyreinforced beam

(2) Section Diagram

0.87 fy

Es

+ 0.002

(3) Section Diagram

Asc

d

d´

d – d´

d´

0.0035( 1 – )d´xu

N.A

C2

C1

Where, C = 0.36 f b x1 ck u

C = (f f )Asc2 sc cc

d´

Where, T = 0.87 fy Ast1 1

T = 0.87 fy Ast2 2

Stress Strain diagram of Doubly Reinforced Beam Section.

Let xu = Ultimate depth of N.A.

fsc = Stress in steel in compression

fcc = Compressive stress in concrete at the level of compression steel

= 0.446 fck = 0.45 fck [For d '

0.2d ]

d = Effective cover to compression reinforcement

Total compression force, C = C1 + C2

Where C1 = Compressive force contributed by concrete

= 0.36 fck b.xu

C2 = Compressive force contributed by steel in compression zone.

= (fsc Asc) – (fcc Asc) [ Stress = Force

Area

C2 = (fsc – fcc)Asc Force = Stress Area]

Total compressive force, C = 0.36 fck b xu + Asc (fsc – fcc)

Similarly, total tensile force, T = T1 + T2

Where, T1 = Tensile force produced by 1stA

= 2y st0.87f A

and T2 = Tensile force produced by 2stA

= 2y st0.87f A


28

RCC

Total tensile force, T = T1 + T2

= 1 2y st y st0.87f A 0.87f A

= 1 2y st st0.87f (A A )

T = 0.87 fy Ast

For equilibrium of forces at the limit state of collapse,

Total tensile force (T) = Total compressive forces (C)

or 0.87 fy Ast = 0.36fck b xu + (fsc – fcc)Asc

Therefore, the value of y st sc cc sc

u

ck

0.87f A (f f )Ax

0.36f b

Assuming that the loss of concrete area occupied by compression steel is neglected (i.e., fcc = 0)

y st sc sc

u

ck

0.87f A f Ax

0.36f b

SOME IMPORTANT FORMULAE TO CALCULATE THE FOLLOWING PARAMETERS

1. Area of tensile steel (Ast)

Where, Area of tensile steel, 1 2st st stA A A

1stA = Area of tension steel corresponding to a balanced singly reinforced section.

1

u lim

st

y u max.

MA

0.87f (d 0.42x )

[where

1u lim uM M ]

2stA = Area of additional tension streel

2

2

u

st

y

MA

0.87f (d d ')

[Where

2 1u u uM M M ]

2. Area of compression steel (Asc)

Asc = 2u

sc

sc

MA

f (d d ')

3. Ultimate moment of resistance (Mu) (As per IS : 456 – 2000, ANNEX ‗G‘ Clause 38.1 – G : 1.2)

Ultimate moment of resistance may be defined as the resistance offered by beam to the moments

developed due to applied loads. In the ultimate moment of resistance of a doubly reinforced section

can be obtained by taking moments of forces C1 and C2 about the C.G. of tensile steel.

The above equation clearly shows that the depth of N.A. decreases with increase in

compression steel.


29

RCC

We know that, 1 2u u uM M M

Also 1u u limM M

= C1 Lever arm

[ Distance between force C1 and C.G. of tensile steel]

1u ck u uM 0.36f bx (d 0.42x )

Similarly, 2u 2M C Leverarm

2u sc cc scM (f f )A (d d')

Ultimate moment of resistance, Mu = 0.36 fck b x u (d – 0.42 xu) + (fsc – fcc) Asc (d – d)

Assuming that the loss of concrete area occupied by compressive steel is neglected (i.e, fcc = 0)

Mu = 0.36 fck b xu (d – 0.42 xu) + fsc Asc (d – d)

T-BEAM

When slabs and beams are cast monolithically and if the beam deflects under applied loads it drags along

with it a portion of slabs. This portion of the slab assists in resisting the effects of the loads and is called

the ‗flange‘ of the T-beam. The portion of the beam below the slab is called ‗Web‘ or ‗Rib‘.

T-beams are more common than rectangular beams because when slabs and hanging beams are cast

monolithically, they automatically forms a T-beam. Under the action of externally applied loads the beam

along with some portion of slab deflects simultaneously

Flange

Web (Rib)

Astbw

Df

Slab

DIMENSIONS OF A T-BEAM

(D) Overalldepth

(d) Effectivedepth

b (Effective width of flange)f

D (Depth of flange)f

A (Area of steel in Tension)st


30

RCC

1. Thickness of the flange (Df):- This is equal to the overall depth of the slab forming the flange of the

T-beam.

2. Breadth of web (bw). This is the breadth of the beam projecting below the slab. The breadth of web

should be sufficient to accommodate the tensile reinforcement in the beam with suitable spacing

between the bars.

3. Effective width of flange (bf). A certain portion of the slab on either side of the beam can be

considered as forming the compression flange. The effective width of flange mainly depends upon

the span, breadth of web and the thickness of slab acting as flange.

The width of a flange, effective for taking compression, may be taken as follows, but in no case it

should be greater than the breadth of web plus half the sum of clear distances to the adjacent beams

on either side.

Effective width of flange:

(a) For T-beams Bf = 𝐼0

6+ bW+ 6Df

(b) For L-beams Bf = 𝐼0

12+ bW+ 3Df

(c) For isolated beams, the effective flange width shall be obtained as below but in no case greater than

the actual width.

T-beam, bf = 𝑙0

𝑙0𝑏 + 4

+ 𝑏𝑤

L-beam, bf = 0.5 𝑙0

𝑙0𝑏 + 4

+ 𝑏𝑤

where bf = effective width of flange

bw = breadth of web

Df = thickness of flange

b = actual width of flange

and I0 = distance between the points of zero moments.

For continuous beams, I0 may be assumed as 0.7 times the effective span.

ULTIMATE MOMENT OF RESISTANCE OF A SINGLE REINFORCED T-BEAM

(As per IS : 456 – 2000, ANNEX ‗G‘, Clause (38.1)G-2

Ultimate moment of resistance is the resistance offered by T-beam to the externally applied loads. The

ultimate moment of resistance is dependent upon the position of neutral axis. Depending upon the

size of the cross section, the area of steel reinforcement provided in tensile zone and characteristic

strength of materials, the position of neutral axis may be

First Case within the flange portion of T-beam.

Second Case outside the flange (i.e., within the rib portion of T-beam).


31

RCC

First Case Neutral axis lies within the flange thickness or just at the bottom of the flange (i.e., xu Df).

xuN.A.

0.45 fck0.42 xu

C = 0.36 f b xck f u

z = d – 0.42 xu

T = 0.87 f Astybw

Ast

Df

d

bf

(a) T - beam Section (b) Stress distribution Diagram

Where, d = Effect depth of beam

xu = depth of N.A. from top of flange

Df = Depth of flange

Z = Lever arm

C = Resultant compressive force

T = Resultant tensile force

fck = Characteristic strength of concrete

fy = Yield strength of steel

Location of xu : Depth of neutral axis (xu) can be obtained by considering the compression and

tensile forces to be in equilibrium

i.e, Total compression (C) = total tension (T)

0.36fck b xu = 0.87 fy Ast

y st

u

ck

0.87f Ax

0.36f b

i.e., xu xu max. This will automatically restricts the use of over reinforced sections. Ultimate

Moment of Resistance.:

Depending upon the values of xu < xu(max.), there conditions arise:

Note: The value of xu as obtained from above equation should not exceed the maximum depth

of neutral axis (xu max.)

i.e., xu(max.) = 0.53 d [For Fe 250 steel]

= 0.48 d [For Fe 415 steel]

= 0.46 d [For Fe 500 steel]


32

RCC

(i) When xu < xu(max) (i.e, The T-beam section is under reinforced)

Then the value of ultimate moment of resistance can be obtained by the equation .

Mu = T Z

Mu = 0.87 fy Ast (d – 0.42 u)

Where, T = Resultant tensile force

and Z = Lever arm distance separating compression and tensile force

or Mu = C Z

Where C = Resultant compressive force

Mu = 0.36 fck bxu (d – 0.42 xu)

(ii) When xu = xu(max.) (i.e, The T-beam is balanced section)

Mu = 0.36 fck b xu (max.) bf (d – 0.42 xu (max.))

(iii) When xu > xu (max.) (i.e, The T-beam section is over reinforced)

Mu = 0.36 fck xu(max.) bf (d – 0.42 xu(max.))

Second Case: When neutral axis (N.A.) lies outside the flange (i.e, xu > Df).

When the neutral axis of a T-beam lies outside the flange, which means that it lies in web (rib) of T-beam.

xu < xu(max.) (i.e, T-beam is under reinforced section)

1. Neutral axis lies outside the flange in the range of f

u

D0.43

x

bf

0.45 fck

0.42 xu

C

Tbw

d =

d

xu

N.A.

0.45 fck

bw

z = d 0.42 x1 u +T1

Df

xu

N.A.

bw

b – bf w

2

b – bf w

2

C2

D1

2

0.45 fck

z = d – 2

D1

2

[T + T = T1 2

= 0.87 f Ay st

T2

d

Stress Distribution When Xu > Df and 1

u

D0.43

X


33

RCC

(a) Location of Depth of Neutral axis (xu)

xu can be obtained equating the compressive and tensile forces.

Total tension = Total Compression

Where total compression = Compressive force in Flange + Compression force in web

i.e., T = C1 + C2

0.87 fy Ast = [0.36 fck bw xu) 9d – 0.42 xu) + 0.45 fck Df (bf – bw)

(b) Ultimate Moment of Resistance (Mu)

Therefore, ultimate moment of resistance (Mu) can be obtained by taking moment of compressive forces

about the centroid of tension steel.

Mu = (0.36 fck bw xu) (d – 0.42 xu) + 0.45 fck Df (bf – bw)

2. Neutral axis lies outside the flange f

u

D0.43

x

Ast

d

N.A.

Df

xu

bf

d

0.45 fck

0.42 xu

C

bw

T

=

d

bw

0.45 fck

xu

N.A.

z x = d – 0.42 x1 u +

0.42 xu

C1

xu

yf

N.A.

b – bf w

2

b – bf w

2

d

T2

C2

z = d – 2

y1

2

[T + T = T1 2

= 0.87 f A ]y st

0.45 fck

yf

2

Stress Distribution when xu > Df and 1

u

D0.43

X

(a) Location of Depth of Neutral axis (xu)

From diagram xu can be obtained by equating the compressive and tensile forces.


34

RCC

i.e., Total compression = Total Tension

or C1 + C2 = T

or 0.36 fck xu bw + 0.45 fck yf (bf – bw) = 0.87 fy Ast

Where, yf = 0.15 xu + 0.65 Df and (yf Df)

(b) Ultimate moment of resistance (Mu)

Therefore, Ultimate moment of resistance (Mu) can be determined by taking moments of

compressive forces about centroid of tension steel.

Mu = 0.36 fck bwxu (d – 0.42 xu) + 0.45 fck yf (bf – bw) (d – 0.5 yf)

Third Case When reduced xu = xu max. (i.e, T – beam is a balanced section)

(a) Neutral axis lies outside the flange fD

0.20d

Location of Depth of neutral axis (xu)

0.36 fck bw xu + 0.45 fck Df (bf – bw ) = 0.87 fy Ast

Ultimate moment of resistance (xu = xu(max.))

Mu = 0.36 fck bw xu(max.) (d – 0.42 xu(max.)) + 0.45 fck Df (bf – bw) (d – 0.5 Df)

Fourth case Neutral axis lies outside the flange fD

0.20d

Location of Depth of N.A. (xu)

0.36 fck bw xu + 0.45 fck yf (bf – bw) = 0.87 fy Ast

Ultimate moment of resistance (xu = xu max.)

Mu = 0.36 fck bw xu(max.) (d – 0.42 xu(max.)) + 0.45 fckyf (bf – bw) (d – 0.5 yf)

Where yf = 0.15 xu(max.) + 0.65 Df

f(y fD )


35

RCC

1. What is the Limiting Value of neutral axis

depth ratio (Xu, max. /d) for Fe-415 HYSD Steel

Bars?

(A) 0.53 (B) 0.48

(C) 0.46 (D) 0.43

2. What is the required minimum area of tension

reinforcement in beams as per IS 456-2000?

(A) 0.85bd/fy (B ) 0.65bd/fy

(C) 0.80bd/fy (D) 0.95bd/fy

3. In a cantilever beam, main reinforcement is

provided:

(A) Above the neutral axis

(B) As vertical stirrups

(C) As helical reinforcement

(D) Below the neutral axis

4. A simply supported beam is considered as a

deep beam if the ratio of effective span to

overall depth is less than:

(A) 1 (B) 4

(C) 3 (D) 2

5. In a singly reinforced beam, the effective depth

is measured from its extreme compression

edge to

(A) Tensile edge

(B) Tensile reinforcement

(C) Neutral axis of the beam

(D) Longitudinal central axis

6. The final deflection due to all loads including

the effects of temperature, creep and shrinkage

and measured from the as – cast level of

support, roof and all other horizontal member

members should not exceed

(A) Span/350 (B) Span/300

(C) Span/250 (D) Span/200

7. The assumption that the plane sections normal

before bending remain normal after bending is

used

(A) Only in working stress method of design

(B) Only in limit state method of deign

(C) In both working stress and limit state

methods of design

(D) Only in ultimate load method of design

8. Doubly reinforced beam is provided when

(A) Depth is restricted

(B) B.M is very low

(C) Superimposed load is small

(D) None

9. In balanced section beam the moment of

resistance of concrete is given by

(A) Qb2d (B) Qbd

(C) Qbd2

(D) None

10. In over reinforcement section area of tensile

steel provided is________ the Area of steel

provided in balanced section.

(A) More than (B) Less than

(C) Equal (D) None

Practice Problem Level -1

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ZPH

ERE

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EIN

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G E

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INEE

RS

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DU

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ERE

Co

pyr

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RSE

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36

RCC

11. Minimum percentage of tension steel in an

RCC beam for Fe 500 steel is

(A) 0.12 (B) 0.17

(C) 0.22 (D) 0.80

12. As per IS 456, the effective length of

cantilever shall be taken as

(A) Clear span

(B) Clear span + effective depth/2

(C) Clear span + effective depth

(D) Clear span + effective width

13. In a singly reinforced beam, if the permissible

stress in concrete reaches earlier than the

permissible stress in steel, the beam section is

called

(A) Under reinforced section

(B) Over reinforced section

(C) Balanced section

(D) Economic section

14. Side face reinforcement shall be provided in

the reinforced concrete beam when depth of

web in the beam exceeds

(A) 500mm (B) 750mm

(C) 1000mm (D) 1200mm

15. The maximum percentage of steel in a RCC

beam is

(A) 1% (B) 2%

(C) 3% (D) 4%

16. The maximum shear stress in a rectangular

beam is

(A) 1.25 times the average

(B) 1.50 times the average

(C) 1.75 times the average

(D) 2.0 times the average

17. The effective depth of R.C.C beam is taken

from topmost compressive fiber to the

(A) Top of the tensile steel reinforcement

(B) Bottom of the tensile steel reinforcement

(C) Center of gravity of the tensile steel

(D) Bottom of the beam

18. If d and n are the effective depth and depth of

the neutral axis respectively of a singly

reinforced beam, the lever arm of the beam is

(A) d (B) n

(C) d + n/3 (D) d – n/3

19. In a T beam the ratio of span to overall depth

should not exceed

(A) 10 (B) 12

(C) 18 (D) 20

20. If the depth of actual neutral axis is more than

critical neutral axis, section is

(A) Balanced

(B) Under – reinforced

(C) Over – reinforced



37

RCC

1. (B)

2. (A)

3. (A)

4. (D)

5. (B)

6. (C)

7. (C)

8. (A)

9. (C)

10. (A)

11. (B)

12. (B)

13. (B)

14. (B)

15. (D)

16. (B)

17. (C)

18. (D)

19. (D)

20. (C)

Ans 1 B Given F4 = 415, Assume E5 = 2×105

Xu(max) .0035

.87fd0.0055

E

y

s

5

Xu .0035

.87 415d0.0055

2 10

0.48

Ans 12 B Minimum percentage of steel in RCC Beams is .85bd

fy

Given Fe 500 steel fy = 500 Mpa

Minimum percentage of steel in RCC Beams is .85

.0017 or .17%500

=> .0017 or .17%


Answer key

EDUZPHERE PUBLICATIONS | ©All Right Reserved | www.eduzpherepublications.com

CLASSIFICATION OF SLABS

(i) One-way slabs (ii) Two-way slabs.

(i) One-way slabs. One-way slabs are provided when the ratio of length of a room to its greater than

or equal to 2. In this case, the bending takes place only in one direction i.e. along shorter span. The

main reinforcement is provided in the direction of the shorter span.

LongSpan2

ShortSpan

(ii) Two –way slabs. Two-way slabs are provided when the ratio of length of a room to its width is less

than 2. The bending takes place in both directions. Therefore, main steel is provided in both the

directions. So, in this case distribution steel may not be provided.

LongSpan2

ShortSpan

(iii) Flat Slabs: they are of generally multispan slabs, which are directly supported on columns at regular

intervals When head room is required (e.g., in basements) the flat slabs can be adopted.

(iv) Edge Supported Slabs: Such slabs are supported on beams or on walls.

ONE WAY SLABS

Slabs which have ratio of longer span to shorter span greater than or equal to 2 are called; as one way

slabs. Such slabs are also categorized as edge supported slabs (i.e.. Slab supported on two edges/side walls).

This type of slab spans in one direction i.e., perpendicular to the supporting edges. That is why they are

also termed one way slabs. The bending in such slabs also takes place in one direction (i.e., perpendicular

to supports). That is why the main reinforcement is also provided along shorter span and distribution steel

along longer span

Sh

ort

Sp

an

Wall/Beam Distribution Steel

Long Span

Short Span

Main Steel

Long Span

Chapter

3 SLABS

Syllabus: Slab, Design & Analyze of one way slab, Two way

slab depth of slab as per deflection checks. Min & Max spacing of

main steel & distribution steel in slabs Weightage : 10%


39

RCC

Slab Spanning Along One Direction (One-way Slab).

Types of Reinforcement in one way slabs : There are two types of reinforcement provided in one way

slabs :

1. Main Steel : Main steel is provided along (parallel to) shorter span. The purpose of this steel is to :

(a) take up the loads

(b) to resist bending

(c) to support the distribution steel.

Generally alternative main bars are bent up at /7 distance from the centre of supports which means

half the number of bars are straight bars and half bars are bent up bars.

2. Distribution Steel : Distribution steel is provided in a. direction perpendicular to the direction of

main steel (i.e., along longer span). The distribution bars are not provided with hooks (Standard U

Shaped) even if mild steel is used.

The distribution steel must be tied above the main steel, otherwise the lever arm (distance Between

C.G‘s. of compressive and tensile areas) will decrease and thus resulting in reduction of moment of

resistance.

Moment of resistance = Compressive or tensile force Lever arm

It is clearly seen from the above relation that moment of resistance is directly proportional to lever

arm.

Purpose of Providing Distribution Steel :

l. It keeps the main reinforcement in position.

2. The most important purpose of providing distribution steel is to distribute the concentrated load

coming over the slab.

3. It helps in resisting shrinkage and temperature stresses and thats why it is also known as ―stress

reinforcement‖.

TWO WAY SLABS

When ratio of longer span shorter span of a slab, supported on four sides, is less than 2, then in it is

known as a two way slab.

In two way slabs, the total load is divided on both the spans instead of one as in case of one way slab.

Therefore, the main reinforcement is provided in both the directions. ‗That means no distribution steel is

provided.

Providing main steel along both spans reduces the shear force, bending and deflection in Slabs. Therefore

resulting in slabs of smaller thickness with less quantity of steel reinforcement.


40

RCC

Hence, two way slabs are considered to be economical.

COMPARISON BETWEEN ONE WAY SLAB AND TWO WAY SLAB

S.No. Item Description One Way slab Two way slab

1. Ratio of

Longspan

Short span

2 < 2

2. Bending of Slab Along shorter span Along both the spans

3. Main Steel Provided along shorter

span

Providing along both the

spans

4. Distribution Steel Provided along longer

span and above the

main steel.

No distribution steel required

and the main steel is provided

along both span

5. Thickness of Slab More Less

6. Quantity of Steel More Less

7. Cost of Slab More Less (i.e, Economical)

General Considerations of design for slabs:-

1. Effective Span:-

a) For simply supported slab: The effective span of a simply supported slab is taken as the

distance between the centre to centre of supports or the clear distance between the supports plus

the effective depth of the slab whichever is smaller.

b) For continuous slab: In case of a continuous slab, where the width of the support is less

than 1

12 of the clear span, the effective span shall be worked out by following the rule given

in (a) above.

In case the supports are wider than 1

12 of the clear span or 600mm whichever less is, the effective

span shall be taken as under:

(i) For end span with one end fixed and the other continuous or for intermediate spans, the effective

span shall be the clear span between supports.

(ii) For end span with one end free and the other continuous the effective span shall be equal to

clear span plus half the effective depth of the slab, or, clear span plus half the width of the

discontinuous support, whichever is less.

2. Deflection Control:-

For slabs , the vertical deflection limits may generally be assumed to be satisfied provided the span

to depth ratios are not greater than the values obtained as below:


41

RCC

a) For spans upto 10m

Cantilever 7

Simply supported 20

Continuous 26

b) For spans above 10m, the values in para (a) may be multiplied by 10/span in metres , except for

cantilevers in which case deflection calculations should be made.

For two-way slabs of small spans (up to 3.5 m) with mild steel reinforcement, the span to overall

depth ratios given below may generally be assumed to satisfy vertical deflection limits for loading

class upto 3000 N/m2.

Simply supported slabs 35

Continuous slabs 40

For high strength deformed bars of grade Fe 415, the values given above should be multiplied by 0.8.

3. Reinforcement in Slabs.

1. Minimum reinforcement. The area of reinforcement in either direction in slabs should not be

less than 0.15 per cent of the total cross-sectional area in case mild steel bars are used as

reinforcement. In case of high strength deformed bars, this value can be reduced to 0.12 per

cent.

2. Maximum diameter. The maximum diameter of the reinforcing bar in a slab should not

exceed 1

8th of the total thickness of the slab.

3. Clear cover to reinforcement. The clear cover for any other reinforcement should not be les

than 15 mm or the diameter of the reinforcing bar whichever is more.

Spacing reinforcement.

(a) Minimum distance between individual bars.

(i) The minimum horizontal distance between two parallel main reinforcing bars shall not less

than the diameter of the bar(in case of unequal diameter bars, the diameter of the larger bar is

considered) or 5mm more than the nominal maximum size of coarse aggregate used in the

concrete, whichever is more.

(ii) In case where it is desired to provide main bars in two or more layers one over the other, the

minimum vertical clear distance between any two layers of the bars, shall normally be 15mm

or two-thirds the nominal maximum size of aggregate or the maximum size of the bar

whichever is the greatest.

(b) Maximum distance between bars in tension.

(i) The pitch of the main tensile bars in slab should not exceed three times the effective depth of

the slab or 450mm whichever is smaller.


42

RCC

1. In case of simply supported slabs with free

edges, what are the design moments as per

code?

(A) Mx = ax wLx2 , My = ay wLy

2

(B) Mx = ax wLx2, My = ay wLx

2

(C) Mx = ax wLy2 , My = ay wLx

2

(D) Mx = ax wLy2 My = ay wLy

2

2. What recommendation is given for basic value

of span/effective depth ratio in IS code 456-

2000 for continuous beams up to 10m span?

(A) 29 (B) 28

(C) 27 (D) 26

3. The minimum cover of a slab should neither be

less than the diameter of bar nor less than

(A) 10 mm (B) 15 mm

(C) 20mm (D) 13mm

4. The minimum reinforcement in slabs should

not be less than ____% of the initial cross –

sectional area when HYSD bars are used in the

either direction.

(A) 0.10 (B) 0.12

(C) 0.15 (D) 0.18

5. The ratio of the diameter of reinforcing bars

and the slab thickness is

(A) 1/4 (B) 1/5

(C) 1/6 (D) 1/8

6. Distribution steel is provided

(A) In one way slab (B) In beam

(C) In column (D) None

7. In case of slabs using Mild Steel bars the

minimum %age of steel recommended is

(A) 1.0% (B) 0.3%

(C) 0.15% (D) 0.12%

8. In case of simply supported beam of span 15m,

the minimum effective depth to satisfy vertical

deflection limit should be

(A) 450 mm (B) 600 mm

(C) 750 mm (D) 900 mm

9. In a two way slab, main reinforcement is

provided along

(A) Width of the slab

(B) Length of the slab

(C) Diagonal of the slab

(D) Length and width of the slab

10. The effective span of a simply supported slab is

(A) Distance between the centres of the

bearings

(B) Clear distance between the inner faces of

the walls plus twice the thickness of the

wall

(C) Clear span plus effective depth of the slab

(D) All of the above



43

RCC

11. For a continuous floor slab supported on

beams, the ratio of end span length and

intermediate span length is

(A) 0.6 (B) 0.7

(C) 0.8 (D) 0.9

12. For cantilever slab, span to depth ratio as per

control of deflection

(A) 7 (B) 20

(C) 25 (D) 30

13. If 1y/1x> 2.0 the slab is

(A) Two way slab (B) Continuous slab

(C) Flat slab (D) One way slab

14. In a two way slab, main reinforcement is

provided along

(A) Width of the slab

(B) Length of the slab

(C) Diagonal of the slab

(D) Length and width of the slab

15. A flat slab is supported on

(A) Beams

(B) Columns

(C) Walls

(D) Columns monolithically built with slab

1. (B)

2. (D)

3. (C)

4. (B)

5. (D)

6. (A)

7. (C)

8. (C)

9. (D)

10. (D)

11. (D)

12. (A)

13. (D)

14. (D)

15. (B)

Ans: 8 C

Vertical deflection limit for simply supported beam is d 𝑠𝑝𝑎𝑛

20

given span 15m or 15000mm

vertical deflection limit for simply supported beam is d 15000

20 = 750mm

Explanation

Answer key


Columns are vertical compression members used to transfer the loads of the structures such as buildings,

factory floors, cinema balconies, auditorium halls, floors of framed buildings etc. to the foundation below.

The transfer of load may be:

(i) direct from the roof or floor slabs through the columns to the foundation.

(ii) Indirect through a beam to the column and then to the foundation.

All vertical members may not be termed as columns. Only those members whose effective length is more

than three times the least lateral dimension are called columns and those members whose effective length

is less than three times the least lateral dimension are called ―pedestals‖.

Effective length of a column;-

The actual length() of the column is the clear distance between the two ends of the columns. The length

or height of a column which takes part in buckling when the columns is subjected to loads is called

effective length (lef) of the column.

Effective Length of Columns as per IS : 456 - 1978

Degree of end restraint of compression

member

Symbol Theoretical value

of effective

length

Recommended

value of effective

length

Effectively held in position and

restrained against rotation at both ends

(i.e., both ends are fixed)

0.5

0.65

Effectively held in position at both ends,

restrained against rotation at one end

(i.e., fixed at one end and hinged at the

other end)

0.7

0.80

Chapter

4 COLUMNS

Syllabus : Analyse & Design of Axially loaded short & long

columns effective length of columns. Eccentricity in column.

Spacing of lateral ties. Min & Max Reinforcement in Columns.

Weightage : 15%


45

RCC

Effectively held in position at both ends,

but not restrained against rotation ( i.e.,

both ends are hinged)

1.00

1.00


restrained against rotation at one end,

and at the other restrained against

rotation, but not held in position.

1.00

1.20


restrained against rotation at one end,

and at the other partially restrained

against rotation but not held in position

----

1.50

Effectively held in position sat one end

but not restrained against rotation, and at

the other end restrained against rotation

but not held in position

2.00

2.00


restrained against rotation at one end but

not held in position nor restrained against

rotation at the other end (i.e., fixed at one

end and free at the other end)

2.00

2.00

CLASSIFICATION OF COLUMNS

Columns can be classified as under

1. Depending upon materials used in construction:

(a) Timber Columns: Timber is used as construction materials for the construction of houses.

Wooden columns are generally named as posts and generally used where load intensity is less.

(b) Steel Columns: in steel structures, the vertical members carrying axial loads are generally

termed as stanchions. The load carrying capacity of steel columns is higher as compared to

timber.

Rolled steel sections like ISHB, ISMB are used as columns.

(c) Masonry Columns: When Columns are made with the help of brick masonry then they are

known are pillars or piers.

(d) Composite Columns: When a rolled steel I – section is embedded in a concrete column it is

known as composite column. It is used for heavy loads and are shown in diagram.


46

RCC

Sectional Elevation

I-Joist

Longitudinal Reinformcement

Composite Column

Sectional Plan

Metal or Cement Pipe

Sectional Elevation

Sectional Plan

Column Concrete Filled Typed

(e) RCC Column: Most commonly used columns are RCC columns, in which steel reinforcement

is used to increase the strength. Steel reinforcement is provided as longitudinal bars (main bars)

and lateral ties (links). Lateral ties can be shape of rings or helical (spiral) reinforcement as

shown in fig.

LongitudinalReinforcement

Lateral Ties


Spiral of helicalReinforcement

Longitudinal Reinforcement

Lateral Ties

(a) Circular Columns with Lateral Ties (Rings)

(b) Circular Column withhelical reinformcment

(c) Square Column with Lateral Ties

2. Depending upon the shape of the column: As per the architectural requirements, the columns may

be casted as :

(a) Rectangular Columns diagram. (b) Square columns diagram.

(c) Circular Columns diagram. (d) Hexagonal Columns diagram.

Rectangular Column Square Column Circular Column Hexagonal Column


47

RCC

3. Deepening upon the length of columns: Depending upon the length, columns can be classified as:

(a) Long columns : When the ratio of effective length of columns to the least lateral dimensional is

greater than 12, it is known as long column.

(b) Short Columns: When the ratio of effective length of column to the least lateral dimension is

less than or equal to 12, it is known as short column.

4. Depending upon the line of action of load:

(a) Axially loaded volumes: If the load coming over the columns is in line with the longitudinal

axis of the column, then the column are known as axially loaded columns.

Load (P)

Plan of a Column

C.G

Longitudinal Axis

Longitudinal Section

Load (P)

Axially loaded columns are subjected stresses only.

(b) Eccentrically loaded columns: Columns in which loads acts away from the longitudinal axis

i.e, at an eccentricity ‗e‘ are known as eccentrically loaded columns.

C.G

Plan of a Column

C.G

P

P

LongitudinalAxis

Eccentricity ( )

Longitudinal Section

These types of columns are subjected to bending stresses, developed due to eccentricity, in

addition to compressive stresses.

Long and short columns

A column is considered to be short when the ratio of the effective length to its least lateral dimension is

less or equal to 12. When the ratio of the effective length of a column to its least lateral dimension

exceeds 12, the column is considered to be a long column.

Slenderness ratio =𝐼𝑒𝑓

𝑏≤ 12 ……….Short column

Slenderness ratio =𝐼𝑒𝑓

𝑏> 12 ……….Long column


48

RCC

Where Ieff = effective length of the column

b = least lateral dimension (for helical reinforcement, least lateral dimension is the core

diameter)

Since a long column buckles more easily, the ratio between the column‘s effective length and its

least lateral dimension have definite relation with the load carrying capacity of the column. On

account of its buckling tendency a long column has less strength than a short column of the same

sectional area and hence can carry lesser loads as compared to a short column.

Comparison between Short and Long Column.

S. No Item Type of Column

Short column Long Column

1.

Effective length of column

Least lateral dimension

≤ 12

> 12

2.

Effective length of column

Least radius of gravity

≤ 40

> 40

3. Tendency to buckle Less More

4. Strength More Less than short column

Reinforcement for columns

The object of stipulating a maximum percentage of steel is to provide reinforcement within such a limit to

avoid congestion of reinforcements which would make it very difficult to place the concrete and

consolidate it. For practical purpose, steel upto 4 – 5% of the gross sectional area is provided.

In square or rectangular columns, a minimum of four bars are provided. In circular columns, a minimum

of six bars are required. In columns with five or more sides, the minimum number of bars is one for each

side.

Recommendations (Is : 456 :2000) regarding longitudinal reinforcements.

(i) The cross-sectional area of longitudinal reinforcement in a column shall not be less than 0.8% nor

more than 6 % of gross cross-sectional area of the column.

(ii) The minimum number of longitudinal bars provided in a column shall be four in rectangular column

and six in circular columns.

(iii) A columns having helical reinforcement must have at least six bars of longitudinal reinforcement

within the helical reinforcement.

(iv) The bars shall not be less than 12 mm in diameter.


49

RCC

(v) Spacing of longitudinal bars measured along the periphery of the column shall not exceed 300 mm.

(vi) Where it is necessary to splice the longitudinal reinforcement, the bars shall over-lap for a distance

of not less than 24 times the diameter of the smallest bar.

(vii) The cover shall be 40 mm or the diameter of the longitudinal bar, whichever is greater. In case of

columns of 200 mm or under, whose bars do not exceed 12 mm, cover of 25 mm may be used.

(viii) In case of pedestals in which the steel reinforcement is not taken into account in strength

considerations, nominal longitudinal reinforcement not less than 0.15% of the cross sectional area

shall be provided.

Transverse Reinforcement

The diameter of the transverse reinforcement is one-fourth of the diameter of the largest longitudinal bar

or 5 mm, whichever is greater. The diameter of the transverse reinforcement should not be more than 20

mm and the internal angle of the link should not be more than 135°.

Functions of transverse reinforcement: Following are the functions of transverse reinforcement:

1. It helps in confining the concrete and helps in taking circumferential tension.

2. It holds the main bars in position.

3. It prevents buckling of longitudinal steel.

(a) Buckling ofLongitudinal Steel

(b) Longitudinal Splittingof Concrete

(c) Diagonal Tension

4. It prevents longitudinal splitting of concrete.

5. It helps in resisting the diagonal tension.

The transverse reinforcement may be provided in columns as:

(a) Lateral ties (i.e, Links or Rings)

(b) helical reinforcement (Spirals)


50

RCC


Lateral Ties

Sectional Elevation

Sectional Plan

Lateral Ties


Sectional Elevation

Sectional Plan(b)


Spiral of helicalReinforcement

Sectional Elevation

Sectional Plan(b)

IS : 456–2000 Specifications for lateral ties

Arrangement of transverse reinforcement:

1. If the longitudinal bars are not spaced more than 75 mm on either side, transverse reinforcement

need only to go round corner and alternate bars for the purpose of providing effective lateral support

as shown in diagram.

All dimensions millimeters

2. If the longitudinal bars spaced at a distance of not exceeding 48 times the diameter of the tie are

effectively tied in two directions, additional longitudinal bars in between these bars need to be tied in

one direction by open ties .

If the distance between corner bar in one face is more than 48 times the diameter of the tie, then

additional longitudinal bars in between these bars should be tied .

> 48 tr

tr

All dimensions in millimeters

(a)

135°Maximum

> 48 tr

All dimensions in millimeter

(b)

> 48 tr


51

RCC

3. When the longitudinal reinforcing bars in a compression member are placed in more than one row,

effective lateral support to the longitudinal bars in the inner rows may be provided if

(i) transverse reinforcement in accordance with (2)

(ii) no bar of the inner row is closer to the nearest compression face than three times the diameter of

the largest bar as shown in diagram.

3

Diameter

All dimensions in millimeters 4. Where the longitudinal bars in a compression member are grouped (not in contact) and each group

adequately tied with transverse reinforcement in accordance to (2). The transverse reinforcement for

the compression member as a whole may be provided on the assumption that each group is a single

longitudinal bar for purpose of the transverse reinforcement in accordance to (2) .

The diameter of such transverse reinforcement need not, however, exceed 20 mm as shown in

diagram.

Transverse Reinforcement

Individual Groups

Arrangement Transverse Reinforcement 5. Diameter and Pitch of lateral ties (As per clause 26.5.3.2 (c))

(i) Diameter: The diameter of the polygonal links (lateral ties) shall be greater of the followings:

(a) 6 mm

(b) 1

4 times the largest diameter of longitudinal bar.

Pitch or Spacing of lateral ties.

Pitch or spacing of lateral ties should not be more than the least of the following:

(i) The least lateral dimension of the column

(ii) 16 times the diameter of the smallest longitudinal bar

(iii) 48 times the diameter of the transverse reinforcement.


52

RCC

I.S. Specifications for helical (spiral) reinforcement (As per clause 26.5.3.2 (d))

(i) Diameter of helical reinforcement: Diameter of bars for helical reinforcement should be greater

than the followings:

(a) 6 mm

(b) 1

4 times the diameter of largest longitudinal bar.

Pitch or helical reinforcement:

Pitch of helical reinforcement shall not be more than 75 mm, nor more than one-sixth of the core diameter

of the column. Pitch of helical reinforcement shall not be less than 25 mm, norles than 3 times the

diameter of steel bar forming the helix.

Pitch ≯ 75mm

Or ≯ 1

6 Diameter of core

Pitch ≮ 25mm

Or ≮ 3 Diameter of helix bar.

Uses of Helical Reinforced Columns: use of helical reinforced columns are as follows:

1. The columns with helical reinforcement are more effective in providing lateral restraint and also

resist some compressive load. Thus the chances of buckling of longitudinal steel, longitudinal

splitting of concrete and diagonal tension gets reduced.

2. Spiral reinforcement increases the ductility and toughness of the reinforced column and hence are

useful in earthquakes prone areas.

3. Load carrying capacity of columns, reinforced with helical reinforcement, is more than that of

columns, provides with lateral ties.

MINIMUM ECCENTRICITY (As per Clause 25.4)

The ideal condition of axial loading hardly ever exist. In general practice, a truly axially loaded column is

safely found. There is always certain inherent minimum eccentricity in the columns due to the following

reasons.

1. Lateral deflection of the column.

2. Inaccurate construction practices.

3. Inaccurate loading on columns.

Columns with lateral ties and preferred because they are simple, economical and are widely

used.


53

RCC

As per IS 456 – 2000 recommendations: All columns shall be designed for minimum eccentricity (emin) as

under.

Minimum eccentricity in x – direction (ex min.) = x D

500 30

= 20 mm whichever is greater

Minimum eccentricity in y-direction (ey min.) = y b

500 30

or = 20 mm whichever is greater

Where, x and y = unsupported length with respect to major and minor axis respective

D = Depth of column section with respect to major axis

b = Width of column section with respect to minor axis.

AXIAL LOAD CARRYING CAPACITY OF SHORT COLUMNS (As per clause 39.3)

1. For short columns with lateral ties (Rings)

Columns are said to be short when

(a) Both the slenderness ratios are less than or equal to 12.

i.e, eyex 12and 12

D b

(b) Minimum eccentricities: xx min.

De

500 30

or 20 mm whichever is greater

y

y min

be

500 30

Or 20 mm whichever is greater .

As per IS specifications:

(i) Each axially loaded column should be designed for axial load plus biaxial moments,

developed due to eccentricities in two principal directions.

(ii) As per clause 39.2, if the calculated eccentricity is larger than the minimum, then the

minimum eccentricity is neglected.

(iii) If the applied moments, on the column, are larger than the moments due to minimum

eccentricity then the columns shall be designed for applied loads plus moments.


54

RCC

2. For Short columns with helical (spiral) reinforcement (As per clause 39.4) ; Ultimate axial load

carrying capacity of columns (with helical reinforcement) = 1.05 (Pu)

Ultimate axial strength = 1.05 (0.4 fck Ac + 0.67 fy Asc)

The above formula holds good only if the following condition is satisfied.

i.e., Volumeof helicalreinforcement

Volumeof Core

g ck

k y

A f0.36 1

A f

Where, Ag = Gross cross – sectional area of column (mm2).

Ak = Area of core of helically reinforced column measured upto the outside diameter of helix (mm2).

fck = Characteristic yield strength of helical steel (N/mm2) but not exceeding 415 N/mm

2

LONG COLUMNS SUBJECTED TO AXIAL LOADS (SLENDER COMPRESSION MEMBERS)

(As per clause 39.7)

When either or both the slenderness ratio are more than 12, then column is considered as long column.

i.e, For long columns: eyex 12 or 12

D b

Axially loaded long columns have more tendency to buckle as compared to short columns.

Deflected Shape

Load Load

= 0(i.e, no Deflection)

(a) Long Column (b) Short Column

If exmin < 0.05 D and eymin. < 0.05 b, then as per IS 456-2000 specification, formula for ultimate

load carrying capacity (Pu) of axially loaded short column may be expressed as under:

Pu = 0.4fck Ac + 0.67 fy Asc

Where, Pu = Ultimate load carrying capacity (or Factored axial load in N or kN)

fck = Characteristic compressive strength of concrete (N/mm2)

Ac = Area of concrete excluding steel

= Gross area of column – Area of steel (i.e, Ag – Asc)

fy = Characteristic tensile strength of steel (N/mm2)

Asc = Area of longitudinal (main0 steel in column)


55

RCC

Tendency of deflection in long and short columns.

In long columns additional members are produced due to deflection and hence should be taken into

account for the design.

Additional moments are expressed as under.

2

u exa(x)

P DM

2000 D

and

2

eyua(y)

P DM

2000 b

Where, Ma(x) and Ma(y) = Additional moments developed in respect to major axis (x-axis) and minor axis

(y-axis) respectively.

Pu = factored axial load

ex and ey = Effective length in respect of major axis and minor axis respectively

D = Depth of cross section at right angles to the major axis (x-axis)

b = Breadth of the cross – section

The value of additional moments i.e, Ma(x) and Ma(y) are further reduced by a factor (k) given by the

following relation.

uz u

uz u

P Pk

P P

Factor (k) is always less than or equal to 1.

Where, k = Reduction factor 1

Puz = Load carrying capacity of column under pure axial loading.

Pu = Factored axial load

Pb = Balance axial load corresponding to condition of maximum compressive strain of 0.00035 in

concrete of tension steel tensile strain of 0.002 in the outer most layer.


56

RCC

1. The design ultimate load on the short axially

loaded column is computer by which of the

following equation?

(A) 0.3fck Ac+0.57fyAsc

(B) 0.3fckAc+0.67fyAsc

(C) 0.4fckAc+0.67fyAsc

(D) 0.4fckAc+0.87fyAsc

2. What should be the Effective length of

compression members effectively held in

position & restrained against rotation at both

ends as per IS code?

(A) 0.75 L (B) 0.65 L

(C) 0.55L (D) 0.45 L

3. According to IS : 456 – 2000, the maximum

reinforcement in a column is:

(A) 4% (B) 2%

(C) 6% (D) 8%

4. A column is regarded as a long column if the

ratio of its effective length and lateral dimension,

exceeds

(A) 10 (B) 12

(C) 20 (D) 30

5. Min. diameter of rod in RCC column as per IS

456 is

(A) 14mm (B) 16mm

(C) 12mm (D) 10mm

6. In an RCC column the minimum number of bars

in a square column are

(A) 2 (B) 3

(C) 4 (D) 5

7. A long column fails in

(A) Compression (B) Buckling

(C) Tension (D) None

8. In case of circular column the minimum number

of bars recommended by IS: 456

(A) 10 (B) 8

(C) 6 (D) 4

9. The load carrying capacity of column designed

by working stress method is 500 kN.s The

collapse load of the column is

(A) 500.0kN (B) 662.50kN

(C) 750.0kN (D) 1100.0kN

10. Columns may be made of plain concrete if their

unsupported length does not exceed their least

lateral dimension by

(A) Two times (B) Three times

(C) Four times (D) Five times

11. The effective width of a column strip of a flat

slab is

(A) One-fourth the width of the panel

(B) Half the width of the panel

(C) Radius of the column

(D) Diameter of the column

12. The minimum cover provided in the column is

(A) 35mm (B) 40mm



57

RCC

(C) 50mm (D) 30mm

13. The pitch of lateral ties in column should not be

more than

(A) 200mm (B) 250mm

(C) 300mm (D) 100mm

14. If a column of length ―L‖ is restrained against

horizontal & vertical displacement and is free to

rotate at both ends, its equivalent length will be

(A) 2L (B) L

(C) 0.5L (D) 0.707L

15. All R.C. columns must be designed for a

minimum eccentricity of

(A) l/50 + D/3 (B) l/25 + D/30

(C) l/500 + D/30 (D) l/30 + D/500

16. Maximum spacing of longitudinal bars measured

along the periphery of the RC column shall not

exceed

(A) 200mm (B) 250mm

(C) 300mm

(D) 20 times dia. Of longitudinal bar

17. A compression member is termed as column or

strut if the ratio of its effective length to the length

to the least lateral dimension is more than

(A) 2 (B) 3

(C) 5 (D) 1

18. The purpose of lateral ties in short concrete

columns is:

(A) To avoid buckling of longitudinal bars

(B) To facilitate construction

(C) To facilitate compaction of concrete

(D) To increase the load carrying capacity

19. Axial load carrying capacity of a RC column of

gross area of concrete Ac, area of steel As, and

permissible stresses c in concrete and s in

steel, m –modular ratio is given as

(A) cAc + (m –1)cAs (B) sAs + mcAs

(C) cAs + cAs (D) c(Ac – As) + cAs

20. The lateral ties in a reinforced concrete

rectangular column under axial compression are

used to

(A) avoid the buckling of the longitudinal steel

under compression

(B) provide adequate shear capacity

(C) provide adequate confinement to concrete

(D) reduce the axial deformation of the column

21. In a reinforced concreted beam column, the

increase in the flexural strength along with the

increase in the axial strength occurs

(A) beyond the elastic limit of the material

(B) when the yielding of the tension

reinforcement governs the strength

(C) when the crushing of the concrete in the

compression zone governs the strength

(D) never

22. Is 456 : 1978 recommends to provide certain

minimum steel in a RCC beam

(A) to ensure compression failure

(B) to avoid rupture of steel in case a flexural

failure occurs

(C) to hold the stirrup steel in position

(D) to provide enough ductility to the beam

23. In an axially loaded spirally reinforced short

column, the concrete inside the core is subjected

to

(A) bending and compression

(B) biaxial compression

(C) triaxial compression

(D) uniaxial compression


58

RCC

24. Which of the following are the additional

moments considered for design of slender

compression member in lieu of deflection in x

and y directions?

(A)

22u eyu ex

PPand

2000D 2000D

(B) u eyu ex

PPand

2000D 2000D

(C)

22u eyu ex

PPand

2000D 2000b

(D)

22u eyu ex

PPand

200D 200b

25. An axially loaded column is of 300 mm 300

mm size. Effective length of column is 3m. What

is the minimum eccentricity of the axial load for

the column ?

(A) 0 (B) 10 mm

(C) 16 mm (D) 20 mm

1. (C)

2. (B)

3. (C)

4. (B)

5. (C)

6. (C)

7. (B)

8. (C)

9. (C)

10. (C)

11. (B)

12. (B)

13. (C)

14. (B)

15. (C)

16. (C)

17. (B)

18. (A)

19. (A)

20. (A)

21. (B)

22. (D)

23. (C)

24. (C)

25. (D)

Ans: 9 C Collapse load = Load factor X

Working load

Given Working load 500 KN

for columns load factor = 1.5

Collapse load = 1.5 500 750KN

Ans: 25 D emin (minimum eccentricity)

Max. of =

unsupported length of column

500

lateral dimension

30

or 20mm

Max. of = 3000 300

16mm500 30

or 20mm

mine 20mm


Answer key


Shear force is present in beams where there is a change in bending moment along the span. It is equal to

the rate of change if bending moment. The various modes of failure.

A

C

III II I II III

N45°

CracK

Regions of Cracks in Flexural members

L

Diagonal tension failure.

This type of failure occurs when magnitude of shear force is large in relation to bending moment. Such

cracks are normally at 45° with the horizontal.

Flexural shear failure.

This type of failure occurs when bending moment is large relation to the shear force. Such cracks are

normally at 90° with the horizontal.

Diagonal compression failure.

This type of failure takes place by crushing of concrete in the compression zone near the load as the

diagonal crack formed independently penetrates in that zone.

Shear reinforcement is essentially provided to prevent formation of crack and failure of the beam due to

shear. To guard against diagonal compression failure, the code has fixed the upper limit for maximum

allowable shear stress in a member.

Inclination of cracks at different locations in simply supported beams are given below :

(i) At near the supports of a simply supported beam (where BM. = 0) the inclination of cracks shall be

at 45°.

(ii) At or near the centre of Span of simply supported beam (where B.M = Maximum), we cracks will be

vertical.

(iii) In between the supports and centre of span, the inclination of cracks will vary from 45° to 90° with

respect to bottom face of beam.

Chapter

5 SHEAR, BOND &

TORSION Syllabus: Shear reinforcement Types of shear failure minimum

shear provided in structures. Design of shear reinforcement Bond

development length bond stress in Tension & compression Torsion.

Moment produced by torsion in structure. Weightage : 15%


60

RCC

Prevention of Cracks : The above mentioned cracks can be prevented by properly designing the shear

reinforcement. The most important part of designing the shear reinforcement is to provide reinforcement

for diagonal tension. Reinforcement can be provided in the following forms :

1. Vertical or inclined shear stirrup

2. Bent up bars

3. Combination of vertical stirrups and bent up bag

FACTORS AFFECTING THE SHEAR RESISTANCE FOR RCC MEMBERS

The shear resistance of a rectangular RCC beam, without shear reinforcement is dependent upon the

following factors :

1. Grade of concrete : Higher the grade of concrete, more is the shear resistance.

2. Grade of tensile steel reinforcement : Higher the grade of tensile steel reinforcement, less is the

shear strength i.e., Grade of steel is inversely proportional to shear strength. Mild steel reinforcement

gives better shear resistance.

3. Percentage of tensile steel reinforcement (pt) : Increase in percentage of tensile reinforcement

increases the shear strength.

4. Compressive force : Axial compression force (if present) helps in increasing the shearing resistance.

5. Compressive reinforcement : More the percentage of compression steel, more is the shear

resistance.

6. Tensile Force : It reduces, partially, the shear strength of concrete.

7. Shear reinforcement : The shear resistance of RCC beams increases with increase in shear

reinforcement.

CRITICAL SECTION FOR SHEAR DESIGN

Generally, the critical section for shear is considered as the junction portions (i.e., either between wall and

beam or beam and column). Following cases may be considered for calculating line critical sections :

1. If the support offers compressive reaction e.g., in case of beams resting on walls (or columns) then

the sections between the support and a distance equal to the effective depth (d) of the member from

the face of support, is considered as critical portion and hence should be designed properly for shear.

dBeam

d

Brick MasonrySupport Critical

Section

Critical Section for shear


61

RCC

2. If the support is offering tensile reaction e.g. in case of bottom slab supporting the side walls of a

tank.

Critical Section

R.C.C. TankWall

R.C.C. Slab of Water Tank

Fig. Critical Section for Shear

Beam

Failu

re P

lane

= 30°

aV

X

SupportingWall

av

Where av = Shear SpanShear Failure is acting at plane X – X

Where av = shear span

Shear failure is acting at plane X – X.

Nominal Shear Stress.

In Is:456-1978 the equation for shear stress q=𝑣

𝑏 𝑗 𝑑 has been simplified by dropping the lever arm

factor(j) and by changing the terms shear stress (q) by the term nominal shear stress (𝜏 ).

The formula for calculating nominal shear stress in beams or slabs of uniform depth specified in the code is

𝜏𝑣 = 𝑣

𝑏𝑑

Where v = nominal shear stress

V = maximum shear force in beam at critical section

b = breadth of the member

(For flnged sections b = bw= Breadth of web)

D = effective depth.

Shear strength of Concrete.

Shear strength of concrete is to be considered in design. For beams, the shear strength of concrete varies

according to the grade of concrete and the percentage of steel.


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RCC

SHEAR REINFORCEMNT (WITH LIMIT STATE DESIGN) (As per Is: 456–2000, Clause 40.1)

1. Normal Shear Stress uv

V

bd

Where, y = Nominal shear stress

Vu = Factored shear force in beam at critical section

b = width of the beam

d = Effective depth of beam

2. Shear strength of concrete without shear reinforcement (As per IS : 456–2000, Clausen 40.2.1):

As per IS:456 the magnitude of the design shear strength of concrete in beams without shear

reinforcement shall be as given in the Table

Table: Design Shear strength of Concrete, c, (N/mm2)

stt

Ap 100

bd

Permissible shear Stress of Concrete, c (N/mm2) for Various Grades of

Concrete

M15 M 20 M 25 M 30 M 35 M 40 and above

0.15 0.28 0.28 0.29 0.29 0.29 0.30

0.25 0.35 0.36 0.36 0.37 0.37 0.38

0.50 0.46 0.48 0.49 0.50 0.50 0.51

0.75 0.54 0.56 0.57 0.59 0.59 0.60

1.00 0.60 0.62 0.64 0.66 0.67 0.68

1.25 0.64 0.67 0.70 0.71 0.73 0.74

1.50 0.68 0.72 0.74 0.76 0.78 0.79

1.75 0.71 0.75 0.78 0.80 0.82 0.84

2.00 0.71 0.79 0.82 0.84 0.86 0.88

2.25 0.71 0.81 0.85 0.88 0.90 0.92

2.50 0.71 0.82 0.88 0.91 0.93 0.95

2.75 0.71 0.82 0.90 0.94 0.96 0.98

3.00 and

above

0.71 0.82 0.92 0.96 0.99 1.01

Design shear Strength for Solid Slabs (As per IS: 456–2000, Clause 40.2.1.1): for solid slabs, the

design shear strength for concrete shall be equal to v .k, where k is a constant

Overall

Depth of

slab, mm

300 or

more

275 250 225 200 175 150 or

less

k 1.00 1.05 1.10 1.15 1.20 1.25 1.30


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RCC

3. Maximum Shear Stress (c(max.)): The value of c (max) is limited to the value given in Table to

prevent cracks in concrete.

Table: Maximum Shear Stress, c (max), (N/mm2)

Grade of concrete M 15 M 20 M 25 M 30 M 35 M 40 and above

c max, (N/mm2) 2.5 2.8 3.1 3.5 3.7 4.0

4. Minimum shear Reinforcement (Nominal Shear Reinforcement) (As per IS ; 456–2000 clause 40.3)

(As per IS : 456–2000 clause 40.3)

When the value of nominal shear stress (v) is less than or equal to the shear strength of concrete (c),

then there is no need to design shear reinforcement but under such conditions, minimum shear

reinforcement (Nominal shear reinforcement) in the form of stirrups shall be provided (As per IS :

456–2000, Clause 26.5.1.6)

sv

v y

A 0.4

bS 0.87f

Where, Asv = total cross – sectional area of stirrup legs effective in shear.

b = breadth of the beam or breadth of the web of flanged beam

Sv = Stirrup spacing along the length of the member

(Maximum spacing of stirrups shall be least among 0.75 d or 300 mm)

fy = Characteristic strength of the stirrups reinforcement in N/mm2 which shall not be taken

greater than 415 N/mm2.

DESIGN OF SHEAR REINFORCEMENT (As per IS : 456–2000, Clause B–5.4)

When v exceeds c shear reinforcement is provided in the beam. Shear reinforcement shall be provided

in the following forms:

(a) Vertical stirrups

(b) Bent up bars

(c) Combination of (a) and (b).

Spacing of vertical stirrups is given by:

Sv = 𝜎𝑠𝑣 𝐴𝑠𝑣 𝑑

𝑉𝑠

Sv = Spacing of stirrups

Asv = Total cross-sectional area of stirrup legs

Shear reinforcement shall be provided for the following shear force (Vs),

Where Vs = V - 𝜏𝑐bd.


64

RCC

D = Effective depth of beam

𝜎𝑠𝑣 = Permissible tensile stress in shear reinforcement

Vs = Shear force to be resisted by shear reinforcement.

If 𝜏𝑣 <𝜏𝑐 , no shear reinforcement is required. Provide nominal stirrups throughout the beam.

Thus, 𝐴𝐴𝑠𝑣

𝑏𝑆𝑣≥

0.4

𝑓𝑦

(a) Vertical Stirrups:

CompressionReinforcement

TensionReinforcement

Vertical Stirrups

Support

Bearing onWall

C of Bearing

Vertical Stirrups in beams.

1. When shear reinforcement is provided vertically in the form of stirrups (rings), it is known as vertical

stirrups.

2. The diameter of the steel used for making stirrups varies from 6 mm to 10 mm.

3. Stirrups are bent around the tension reinforcement and the compression reinforcement in the form of

a loop. This reduces the chances of slippage during tension.

4. The hook forming the free ends of stirrups are always provided in the compression zone.

5. The magnitude of shear force (V1), to he resisted, decides the number of legs of stirrups e.g., stirrups

can be single legged, two legged, four legged

Single Legged Stirrup Two Legged Stirrup

Four Legged Stirrups Six Legged Stirrups

Vertical Stirrups


65

RCC

6. Use of closely spaced stirrups of smaller diameter bars gives better control over cracks than using

stirrups of larger diameter reinforcement bars placed relatively for apart.

7. Spacing of vertical stirrups (As per IS : 456-2000, Clause B-5-4)

sv sv

s

.A .dS

V

Where, Sv = Centre to centre spacing of stirrups (in mm)

s = Permissible tensile stress in shear reinforcement which shall not be greater than

230 N/mm2.

As, = Total cross-sectional area of stirrup legs

d = Effective depth

Vs = Net design shear force to be resisted by shear reinforcement

(b) Bent up bars along with stirrups :

Bentup-barCL

Width of Support

Vertical Stirrups

TensionReinforcement

CompressionReinforcement

Combination of Bent up Bare and Vertical Stirrups.

1. In case of simply supported beams, the bending moment is maximum at centre and ‗gradually

reduces to zero at the supports.

2. Tensile reinforcement (longitudinal bars) can be bent up near the support where they are no longer

required to resist the bending moment. Bars can be bent up at the same cross section or at different

cross sections along the length of the beam.

3. Combination of vertical stirrups and bent up bars is generally used in case of heavily loaded beams.

Both bent up bars and vertical stirrups are used for resisting the shear forces or stresses.

4. The bent up bars are inclined at an angle (generally taken as 45° to the horizontal).

5. As per IS : 456-2000, clause B-5.4, where bent up bars are provided, their contribution towards shear

resistance shall not be more than half that of the total shear reinforcement (i.e., sV

2), where

Vs = Total shear force for shear reinforcement.


66

RCC

6. Shear reinforcement shall be provided to carry a shear equal to Vs and shear taken by bent up bars is

calculated as

Vs = sv Asv sin

Where, Vs (for bent up bar) = Shear taken by bent up bar and is limited to sV

2

s = permissible tensile stress in steel 230 N/mm2

Asv = Area of bent up bars

= Angle between bent up bars and the axis of member, but not less than 45°.

Maximum spacing of shear reinforcement:

This should not exceed least of the following:

(i) 0.75 d or 450mm, whichever is les.

(ii) Sv (spacing of stirrups from consideration of minimum shear reinforcement in the beam)

Sv =

𝐴𝑠𝑣 𝑓𝑦

0.4 𝑏

For inclined strirrups at 45° spacing should be at d distance.

Bond and development length:-

The main assumption in the theory of reinforced concrete design is that there us a perfect bond of

reinforcement with concrete i.e, there is no slipping of reinforcement bars whenever some forces are

acting on it. This bond develops due to shrinkage of concrete drying. Without this bond, the

reinforcement will not serve any purpose to arrest the widening of cracks in the tension zone.

Development length of bars in tension.

The development length Ld for bars in tension is given by

Ld = ∅ 𝜎𝑠

4 𝜏𝑏𝑑

Where ∅ = Nominal diameter of the bar

𝜎𝑠 = stress in bar at the section considered at design load(Generally taken as .87fy)

𝜏𝑏𝑑 = Permissible stress in bond.

Design bond stress(bd) (As per IS : 456 – 2000, Clause 26.2.1.1)

Values of design bond stress, in limit state method, for plain and deformed bars are given below.

(A) Bars in Tension

(i) For Plain steel bars


67

RCC

Table: Design bond stress for plain bars in tension.

Grade of Concrete M 20 M 25 M 30 M 35 M 40 and above

Design bond stress, bd, (N/mm2) 1.2 1.4 1.5 1.7 1.9

(ii) For deformed bars (Tor Steel): As per IS : 456-2000, the values of bd for deformed bars (in

tension) are 60% greater than the values for plain bars. The values are shown in Table 3.9.

Table: Design bond stress for deformed bars (Tor steel) in tension

Grade of Concrete M 20 M 25 M 30 M 35 M 40 and above

Design bond stress, bd, (N/mm2) 1.92 2.24 2.4 2.72 3.04

(B) Bars in compression: IS : 456 – 2000 has recommended that the values of bd for plain bars in tension

may be increased by 25% to get the values of bd for steel in compression.

POSITIVE MOMENT REINFORCEMENT (As per IS : 456 – 2000, clause 26.2.3.3)

Following recommendations have been made in IS code for positive moment reinforcement:

(i) At least 1

rd3

the positive moment reinforcement in simple members and 1

th4

the positive moment

reinforcement in continuous members shall extend along the same face of the member into the

support, to a Length equal to dL

3 [i.e, one third of the development length (Ld)].

(ii) When a flexural member is part of the primary lateral load resisting system, the positive

reinforcement required to be extended into the support as described in (i) shall be anchored to

develop its design stress in tension at the face of the support.

(iii) At simple supports and at points of inflection, positive moment tension reinforcement shall be

limited to a diameter such that Ld computed for s (with the help of relation)

Development length, st

d

bd

.L

4

does not exceed 1

0

ML

V

or In other words, 1d 0

ML L

V . This condition must be satisfied

Where, M1 = moment of resistance of the condition assuming all reinforcement at the section to be

stressed to st

M1 = st . Ast . j. d

V = Shear force at that section due to design load


68

RCC

L0 = Sum of the anchorage beyond the centre of the support and the equivalent anchorage value of any

hook or mechanical anchorage simples support and the point of which even is greater inflection, L0c

is limited to the affective depth of the members or 12, which ever is greater (where = nominal

diameter of the bar).

The value of 1M

V in the above expression may be increased by 30%, when the ends of the

reinforcement are confined by a compressive reaction. Therefore, the above expression will

become

1d 0

1,3ML L

V


69

RCC

1. Shear reinforcement is provided in the form of:

(A) Vertical bars

(B) Inclined bars

(C) Combination of vertical and inclined bars

(D) Any one of the above

2. Tension bars in a cantilever beam must be

enclosed in the support up to:

(A) Ld (B) Ld /3

(C) 12 (D) D

3. The propagation of Shear Crack in prestressed

concrete member depends on

(A) Tensile Reinforcement

(B) Compression Reinforcement

(C) Shear reinforcement

(D) Shape of the Cross – section of beam

4. The shear reinforcement has to be designed

when nominal shear stress is________

permissible shear stress

(A) Less than (B) Equal than

(C) More than (D) None

5. In the absence of shear stirrups, where do you

think the cracks in a RCC beam constructed in

a frame would come first:

(A) Center of the beam (B) Near the supports

(C) Point of inflection (D) None of these

6. As per IS:456-2000, the shear strength

variation along the section is assumed

(A) Constant (B) Linearly varying

(C) Parabolic (D) Non uniform

7. The minimum spacing of the vertical stirrups

to resist shear in beam , in terms of effective

depth ―d‖ is restricted to

(A) D (B) 0.5d

(C) 0.75d (D) 3d

8. The development length in tension in HYSD

bars when used with M20 grade of concrete is

(A) 68 times the nominal dia. Of bar

(B) 51 times the nominal dia. Of bar

(C) 46 times the nominal dia. Of bar

(D) 78 times the nominal dia. Of bar

9. The anchorage value of a 45o bend in

reinforcing bar embedded in concrete is

assumed to be

(A) 2 times the diameter of bar

(B) 4 times the diameter of bar

(C) 8 times the diameter of bar

(D) 16 times the diameter of bar

10. Shear reinforcement is provided to resist

(A) Diagonal compression

(B) Diagonal bending

(C) Diagonal tension




70

RCC

11. For deformed bar, bond stress is

(A) More than plane bar

(B) Less than plane bar

(C) Equal to plane bar


12. The spacing of nominal shear reinforcement is

given by

(A) 0.8fyAsv /0.4d

(B) 0.80fyAsv /0.25b

(C) 0.87fyAsv /0.25d

(D) 0.87fyAsv /0.4b

13. When the shear stress exceeds the permissible

limit in a slab, then to bring the shear stress

within limits

(A) Its depth should be increased

(B) Shear reinforcement should be provided

(C) Torgue steel should be used

(D) Steel should be provided on compression

side

14. When HYSD bars are used in place of mild

steel bars, the bond strength

(A) Increases (B) Decreases

(C) Dose not change (D) Becomes zero

15. In limit state method of design , for HYSD

bars the values of bond stress shall be

(A) Decreased by 50% (B) Increased by 60%

(C) Decreased by 60% (D) Increased by 50%

16. The main reason for providing number of

reinforcing bars at a support in a simply

supported beam is to resist in that zone

(A) compressive stress

(B) shear stress

(C) bond stress

(D) tensile stress

17. Torsion resisting capacity of a given RC

section

(A) decreases with decrease in stirrup spacing

(B) decreases with increase in longitudinal

bars

(C) does not depend upon stirrup and

longitudinal steels

(D) increases with the increase in stirrup and

longitudinal steels

18. If the nominal shear stress (v) at a section

does not exceed the permissible shear stress

(c)

(A) minimum shear reinforcement is still

provided

(B) shear reinforcement is provided to resist

the nominal shear stress

(C) no shear reinforcement is provided

(D) shear reinforcement is provided for the

difference of the two.

19. In limit state design, permissible bond stress in

the case of deformed bars is more than that in

plain bars by

(A) 60% (B) 50%

(C) 40% (D) 25%


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20. Shear span is defined as the zone where

(A) bending moment is zero

(B) shear force is zero

(C) shear force is constant

(D) bending moment is constant

1. (D)

2. (A)

3. (A)

4. (C)

5. (B)

6. (C)

7. (C)

8. (C)

9. (B)

10. (C)

11. (A)

12. (D)

13. (B)

14. (A)

15. (B)

16. (C)

17. (D)

18. (A)

19. (A)

20. (C)

8. Ans. (c)

ys

bd bd

.87fLd

4 4

For HYSD = 415 Fe

For M–20 bd 1.2 1.6 [For HYSD value is increase by 60%]

.87 415Ld 47.01 or 46

4 1.2 1.6

Explanations Level - 1

Answer key


A GUIDE TO IS 456:2000 LIMIT STATE APPROACH CODE

MATERIALS

Clause: 5.1Cement

The cement used shall be any of the following and the type selected should be appropriate for the

intended use:

a) 33 Grade ordinary Portland cement conforming to IS 269 => 33 MPA

b) 43 Grade ordinary Portland cement conforming to IS 8 112 => 43 MPA

c) 53 Grade ordinary Portland cement conforming to IS 12269 => 53 MPA

5.3.3 Size of Aggregate

For most work, 20 mm aggregate is suitable. Where there is no restriction to the flow of concrete into

sections, 40 mm or larger size may be permitted.

5.3.3.1

For heavily reinforced concrete members as in the case of ribs of main beams, the nominal maximum size

of the aggregate should usually be restricted to 5 mm less than the minimum clear distance between the

main bars or 5 mm less than the minimum cover to the reinforcement whichever is smaller.

5.4.2 The pH value of water shall be not less than 6.

5.4.3 Sea Water

Table 1 Permissible Limit For Solid

(clauses 5.4)

S.No. Tested as per Permissible Limit, Max

(i) Organic IS 3025 (Part 18) 200 mg/I

(ii) Inorganic IS 3025 (Part 18) 3000 mg/I

(iii) Sulphates (as SO2) IS 3025 (Part 24) 400 mg/I

Chapter

6 IS CODE PROVISIONS Syllabus: IS:456:2000 codal provisions, amendments

Weightage : 20%


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(iv) Chorides (as CI) IS 3025 (Part 32) 2000 mg/I

for concrete not containing

embedded steel and 500 mg/I

for reinforced concrete work

(v) Suspend matter IS 3025 (Part 17) 2000 mg/I

5.6.3 The modulus of elasticity of steel shall be taken as 200 kN/mm2. The characteristic yield strength of

different steel shall be assumed as the minimum yield Stress/O.2 percent proof stress specified in the

relevant Indian Standard.

6.1.1 The characteristic strength is defined as the strength of material below which not more than 5

percent As per IS456:2000 there are 15 grades of concrete of the test results are expected to fall.

Table 2 Grades of Concrete

Group Grade Designation Specified characteristic compressive Strength

of 150 mm Cube at 28 Days in N/mm2

(1) (2) (3)

Ordinary concrete M10

M15

M20

10

15

20

Standard concrete M25

M30

M35

M40

M45

M50

M55

25

30

35

40

45

50

55

High Strength concrete M60

M65

M70

M75

M80

60

65

70

75

80

Note: 1) In the designation of concrete mix M refers to the mix and the number to the specified

compressive strength compressive strength of 150mm size cube at 28 days, expressed in N/mm2.


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6.2.2 Tensile Strength of Concrete

Flexural strength, tf .7 fck where fck where fck is in N/mm2

6.2.3.1 The modulus of elasticity of concrete can be assumed as follows:

CE 5000 fck

where Ec is the short term static modulus of elasticity in N/mm2. Actual measured values may differ by

20 percent from the values obtained from the above expression.

Creep Coefficient

Age of Loading Creep Coefficient

7 days 2.2

28 days 1.6

1 year 1.1

6.2.6 Thermal Expansion

Type of Aggregate Coefficient of Thermal Expansion

for concrete /°C

Quartzite 1.2 to 1.3 10–5

Sandstone 0.9 to 1.2 10–5

Granite 0.7 to 0.95 10–5

Limestone 0.6 to 0.9 10–5

WORKABI LITY OF CONCRETE

Placing conditions Degree of Workability Slump (mm)

(1) (2) (3)

Blindingconcrete;

shallow sec tions;

Pavementsusing pavers

Very low See 7.1.1

Massconcrete;

Lightly reinforced

sec tionsin slabs,

beams,walls,columns;

Floors;

Hand placed pavements;

Canallining;

Stripfootings

Low 25–75


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Heavily reinforced

Sec tion in slabs,

beams,walls,columns;

Slipform work;

Pumped concrete

Medium 50–100

75–100

Trench fill;

In situ piling

tremieconcrete

High

Very high

100–50

See 7.1.2

Note: For most of the placing conditions, internal vibrators (needle vibrators) are suitable. The

diameter of the needle shall be determined based on the density and spacing of reinforcement bars

and thickness of sections. For tremie concrete, vibrators am not rewired to be used (see &SO 13.3).

7.1.1 In the ‗very low‘ category of workability where strict control is necessary, for example pavement

quality concrete, measurement of workability by determination of compacting factor will be more

appropriate than slump (see IS 1199) and a value of compacting factor of 0.75 to 0.80 is suggested.

Table 3 Environmental Exposure Conditions

(Clauses 8.2.2.1 and 35.3.2)

S.No. Environment Exposure Conditions

(1) (2) (3)

(i) Mild Concrete surfaces protected against weather or aggressive

conditions, except those situated in coastal area.

(ii) Moderate Concrete surfaces sheltered from severe rain or freezing

whilst wet

Concrete exposed to condensation and rain

Concrete continuously under water

Concrete in contact or buried under non aggressive

soil/ground water

Concrete surfaces sheltered from saturated salt air in

coastal area

(iii) Server Concrete surfaces exposed to severe rain, alternate

wetting and drying or occasional freezing whilst wet or

severe Condensation.


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(iv) Very severe Concrete completely immersed in sea water Concrete

exposed to coastal environment Concrete surfaces

exposed to sea water spray, corrosive fumes or severe

freezing conditions whilst wet

(v) Extreme Concrete in contact with or buried under aggressive sub-

soil/ground water

Surface of members in tidal zone

Members in direct contact with liquid/solid aggressive

chemicals

8.2.2.3 Freezing and thawing

Nominal Maximum size

Aggregate (mm)

Entrained Air Percentage

20 5 1

40 4 1

8.2.4.2 Maximum cement content

Cement content not including fly ash and ground granulated blast furnace slag in excess of 450 kg/m3

should not be used unless special consideration has been given in design to the increased risk of cracking

due to drying shrinkage in thin sections, or to early thermal cracking and to the increased risk of damage

due to alkali silica reactions.

Table : Minimum Cement Content, Maximum Water-Cement Ratio and Minimum Grade of

Concrete for Different Exposures with Normal Weight Aggregates of 20mm Nominal

Maximum Size

(Clauses 6.1.2, 8.2.4.1 and9.1.2)

S.No. Exposure Plain Concrete Reinforced concrete

Minimum

cement

Content

Kg/m3

Maximum

Free

Water-

Cement

Ratio

Minimum

Grade of

Concrete

Minimum

Cement

Content

kg/m3

Maximum

Free

Water –

Cement

Ratio

Minimum

Grade of

concrete

(1) (2) (3) (4) (5) (6) (7) (8)

(i) Mild 220 0.60 …. 300 0.55 M 20

(ii) Moderate 240 0.60 M 15 300 0.50 M 25

(iii) Servere 250 0.50 M 20 320 0.45 M 30


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(iv) Very

Severe

260 0.45 M 20 340 0.45 M 35

(v) Extreme 280 0.40 M 25 360 0.40 M 40

Notes 1. Cement content prescribed in this table is irrespective of the grades of cement and it is

inclusive of ad & ones mentioned in 5.2. The additions such as fly ash or ground granulated blast

furnace slag may be taken into account in the concrete composition with respect to the cement

content and water-cement ratio if the suitability is established and as long as the maximum amounts

taken into account do not exceed the limit of pozzolona and slag specified in IS 1489 (Part I) and IS

455 respectively.

2. Minimum grade for plain concrete under mild exposure condition is not specified.

8.2.8 Concrete in Sea-water

Concrete in sea-water or exposed directly along the sea-coast shall be at least M 20 Grade in the case of

plain concrete and M 30 in case of reinforced concrete. The use of slag or pozzolana cement is

advantageous under such conditions.

Table 8 Assumed Standard Deviation (Clauses 9.2.4.2 and Table 11)

Grade of concrete Assumed Standard Deviation N/mm2

M10

M15

3.5

M 20

M25

4.0

M30

M35

M40

M45

M50

5.0

Note :The above values correspond to the site control having proper storage of cement; weigh

batching of all materials; controlled addition of water; regular checking of all materials, aggregate

gradings and moisture content; and periodical checking of workability and strength. Where there is

deviation from the above the values given in the above table shall be increased by INmm2.


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11 FORMWORK

(a) Deviation from specified dimensions

of cross –section of columns and

beams

+12 mm

–6 mm

(b) Deviation from dimensions of footings

(1) Dimensions in plan

+50 mm

–12 mm

(2) Eccentricity 0.02 times the width of the footing in the

direction of deviation but not more than 50mm

(3) Thickness 0.05 times the specified thickness

Types of Formwork Minimum Period Before Striking Formwork

(a) Vertical formwork to columns, walls,

beams

16 – 24 h

(b) Soffit formwork to slabs (Props to be

refixed immediately after removal of

formwork)

3 days

(c) Soffit formwork to beam (Props to be

refixed immediately after removal of

formwork)

7 days

(d) Props to slabs:

(1) Spanning up to 4.5m

(2) Spanning over 4.5 m

7 days

14 days

(e) Props to beams and arches:

(1) Spanning up to 6 m

(2) Spanning over 6m

14 days

21 days

Tolerances on Placing of Reinforcement

Unless otherwise specified by engineer-in-charge, the reinforcement shall be placed within the following

tolerances:

a) for effective depth 200mm or less ± 10mm

b) for effective depth more than 200 mm ± 15mm


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As a general guidance, the maximum permissible free fall of concrete may be taken as 1.5 m.

14.2.2 Under-water concrete should have a slump recommended in 7.1. The water-cement ratio shall not

exceed 0.6 and may need to be smaller, depending on the grade of concrete or the type of chemical

attack. For aggregates of 40mm maximum particle size, the cement content shall be at least 350

kg/m3 of concrete

Quantity of Concrete in the Work, m3 Number of Samples

1–5

6–15

16–30

31–50

51 and above

1

2

3

4

4 plus one additional sample for each additional

50m3 or part thereof

Note: At least one sample shall be taken from each Shift. Where concrete is produced at continuous

production unit, such as ready-mixed concrete plant, frequency of sampling may be agreed upon

mutually by suppliers and purchasers.

Clause: 15.4 Test Results of Sample

The test results of the sample shall be the average of the strength of three specimens. The individual

variation should not be more than 15 percent of the average. If more, the test results of the sample are

invalid.

Clause: 17.8 Non-destructive Tests

Non-destructive tests are used to obtain estimation of the properties of concrete in the structure. The

methods adopted include ultrasonic pulse velocity [see IS 133 11 (Part l)] and rebound hammer [IS 13311

(Part 2)], probe penetration, pullout and maturity.

Clause: 19.2 Dead Loads

Unless more accurate calculations are warranted, the unit weights of plain concrete and reinforced

concrete made with sand and gravel or crushed natural stone aggregate may be taken as 24 kN/m3 and 25

kN/m3 respectively.

Clause: 19.3 Imposed Loads, Wind Loads and Snow Loads

Imposed loads, wind loads and snow loads shall be assumed in accordance with IS 875 (Part 2), IS 875

(Part 3) and IS 875 (Part 4) respectively.


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Clause: 19.4 Earthquake Forces

The earthquake forces shall be calculated in accordance with IS 1893.

Clause: 20.5 Lateral Sway

Under transient wind load the lateral sway at the top should not exceed H/500, where H is the total height

of the building. For seismic. Loading, reference should be made to IS 1893.

Clause: 22.2 Effective Span

a) Simply Supported Beam or Slab: - The effective span of a member that is not built integrally with

its supports shall be taken as clear span plus the effective depth of slab or beam or centre to centre of

supports, whichever is less.

b) Cantilever:- The effective length of a cantilever shall be taken as its length to the face of the support

plus half the effective depth except where it forms the centre of a support shall be taken.

Table 12 Bending Moment Coefficients

(Clauses 22.5.1)

Type of Load

(1)

Span Moments

Near Middle At Middleof

of EndSpan InteriorSpan

(2) (3)

Span Moments

AtSupport At other

next to the Interior

End Support Supports

(4) (5)

Dead load and imposed load

(fixed)

1

12

1

16

1

10

1

12

Imposed load (not fixed) 1

10

1

12

1

9

1

9

Note: For obtaining the bending moment, the coefficient shall be multiplied by the total design load

and effective span.

a) For T-beams, 0f w fb b 6D

6

b) For L-beams, 0f w fb b 3D

12

c) For isolated beams, the effective flange width shall be obtained as below but in no case greater than

the actual width:

T-beam, 01 w

0

b b

4b


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L-beam, 01 w

0

.5b b

4b

Where,

bf = effective width of flange,

0 = distance between points of zero moments in the beam.

bw = breadth of the web,

Df = thickness of the flange, and

b = actual width of the flange.

Note- For continuous beams and frames, '0' may be assumed as 0.7 times the effective span.

a) The final deflection due to all loads including the effects of temperature, creep and shrinkage and

measured from the as-cast level of the, supports of floors, roofs and all other horizontal members,

should not normally exceed span/250.

b) The deflection including the effects of temperature, creep and shrinkage occurring after erection of

partitions and the application of finishes should not normally exceed span/350 or 20 mm whichever

is less.

23.2.1 The vertical deflection limits may generally be assumed to be satisfied provided that the span to

depth ratios are not greater than the values obtained as below:

a) Basic values of span to effective depth ratios for spans up to 10 m:

Cantilever 7

Simply supported 20

Continuous 26

Clause: 23.3 Slenderness Limits for Beams to Ensure Lateral Stability

Restraints does not exceed 60 b or 2250b

dwhichever is less, where d is the effective depth of the beam

and b the breadth of the compression face midway between the lateral restraints.

For a cantilever, the clear distance from the free end of the cantilever to the lateral restraint shall not

exceed 25b or 2100b

d whichever is less.


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24 SOLID SLABS

Clause: 24.1 General

1) For two-way slabs of shorter spans (up to 3.5 m) with mild steel reinforcement, the span to overall

depth ratios given below may generally be assumed to satisfy vertical deflection limits for loading

class up to 3 kN/m2.

Simply supported slabs 35

Continuous slabs 40

For high strength deformed bars of grade Fe 415, the values given above should be multiplied by 0.8.

25 COMPRESSION MEMBERS

Clause: 25.1 Definitions

25.1.1 Column or strut is a compression member, the effective length of which exceeds three times the

least lateral dimension.

25.1.2 Short and Slender Compression Members

A compression member may be considered as short when both the slenderness ratios eyex and

D b

are less

than 12:

Clause: 25.3 Slenderness Limits for Columns

25.3.1 The unsupported length between end restraints shall not exceed 60 times the least lateral dimension

of a column.

25.3.2 If, in any given plane, one end of a column is unrestrained, its unsupported length, l, shall not

exceed

2100b

D

Where

b = width of that cross-section, and

D= depth of the cross-section measured in the plane under consideration.

Clause: 25.4 Minimum Eccentricity

All columns shall be designed for minimum eccentricity, equal to the unsupported length of column/

500 plus lateral dimensions/30, subject to a minimum of 20 mm. Where bi-axial bending is

considered, it is sufficient to ensure that eccentricity exceeds the minimum about one axis at a time.


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RCC

26.2.1 Development Length of Bars

The development length Ld is given by

= s

d

bd

L4

where,

= nominal diameter of the bar,

s= stress in bar at the section considered at design load, and

bd= design bond stress given in 2.6.2.1.1.

26.2.1.1 Design bond stress in limit state method for plain bars in tension shall be as below:

Grade of concrete M 20 M 25 M 30 M 35 M 40 and above

Design bond stress,

bdN/mm2

1.2 1.4 1.5 1.7 1.9

For deformed bars conforming to IS 1786 these values shall be increased by 60 percent.

For bars in compression, the values of bond stress for bars in tension shall be increased-by 25 percent.

1) Bends-The anchorage value of bend shall be taken as 4 times the diameter of the bar for each 450

bend subject to a maximum of 16 times the diameter of the bar.

2) Hooks-The anchorage value of a standard U-type hook shall be equal to 16 times the diameter of

the bar.

26.2.5.1 Lap splices

a) Lap length including anchorage value of hooks for bars in flexural tension shall be Ld (see 26.2.1)

or 30ф whichever is greater.

b) The lap length in compression shall be equal to the development length in compression, calculated

as described in 26.21, but not less than 24 ф.

26.3.2 Minimum Distance Between Individual Bars

The following shall apply for spacing of bars:

a) The horizontal distance between two parallel main reinforcing bars shall usually be not-less than the

greatest of the following:

1) The diameter of the bar if the diameters are equal,

2) The diameter of the larger bar if the diameters are unequal, and

3) 5 mm more than the nominal maximum size of coarse aggregate.


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26.4.2.1 However for a longitudinal reinforcing bar in a column nominal cover shall in any case not be

less than 40 mm, or less than the diameter of such bar. In the case of columns of minimum dimension of

200 mm or under, whose reinforcing bars do not exceed 12 mm, a nominal cover of 25 mm may be used.

26.4.2.2 For footings minimum cover shall be 50 mm.

26.5.1 Beams

26.5.1.1 Tension reinforcement

a) Minimum reinforcement-The minimum area of tension reinforcement shall be not less than-that

Given by the following:

= s

y

A 0.85

bd f

Where

As = minimum area of tension reinforcement,

b = breadth of beam or the breadth of the web of T-beam,

d = effective depth, and

f = characteristic strength of reinforcement in N/mm2

b) Maximum reinforcement--The maximum area of tension reinforcement shall not exceed 0.04 bD.

26.5.1.3 Side face reinforcement

Where the depth of the web in a beam exceeds 750 mm, side face reinforcement shall be provided along

the two faces. The total area of such reinforcement shall be not less than 0.1 percent of the web area and

shall be distributed equally on two faces at a spacing not exceeding 300 mm or web thickness whichever

is less.

26.5.1.5 Maximum spacing of shear reinforcement

The maximum spacing of shear reinforcement measured along the axis of the member shall not exceed

0.75 d for vertical stirrups and d for inclined stirrups at 45°, where d is the effective depth of the section

under consideration. In no case shall the spacing exceed 300 mm.

26.5.1.6 Minimum shear reinforcement

Minimum shear reinforcement in the form of stirrups shall be provided such that:

sv

sv y

A 0.4

b 0.87f

26.5.2.1 Minimum reinforcement

The mild steel reinforcement in either direction in slabs shall not be less than 0.15 percent of the total

cross sectional area. However, this value can be reduced to 0.12 percent when high strength deformed

bars or welded wire fabric are used.


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RCC

26.5.2.2 Maximum diameter

The diameter of reinforcing bars shall not exceed one eight of the total thickness of the slab.

26.5.3 Columns

26.5.3.1 Longitudinal reinforcement

a) The cross-sectional area of longitudinal reinforcement shall be not less than 0.8 percent nor more

than 6 percent of the gross cross sectional area of the column.

b) The minimum number of longitudinal bars provided in a column shall be four in rectangular

Columns and six in circular columns.

c) The bars shall not be less than 12 mm in diameter.

d) Spacing of longitudinal bars measured along the periphery of the column shall not exceed 300 mm.

e) Pitch and diameter of lateral ties

1) Pitch-The pitch of transverse reinforcement shall be not more than the least of the following

distances:

i) The least lateral dimension of the compression members;

ii) Sixteen times the smallest diameter of the longitudinal reinforcement bar to be tied; and

iii) 300 mm.

2) Diameter-The diameter of the polygonal links or lateral ties shall be not less than one fourth of

the diameter of the largest longitudinal bar, and in no case less than 6 mm.

Clause: 27.2

Temperature, exposure to weather, the time and season of the laying of the concrete, etc. Normally

structures exceeding 45 m in length are designed with one or more expansion joints.

29 DEEP BEAMS

Clause: 29.1 General

a) A beam shall be deemed to be a deep beam when the ratio of effective span to overall depth, is less

than:

1) 2.0 for a simply supported beam; and

2) 2.5 for a continuous beam.

31.6.1 The critical section for shear shall be at a distance d/2 from the periphery of the column/capital/

drop panel, perpendicular to the plane of the slab where d is the effective depth of the section (see

Fig. 12).

c ck0.25 f in limit state method of design,


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The minimum thickness of walls shall be 100 mm.

Section 5 Structural Design (Limit State Method)

36 CHARACTERISTIC AND DESIGN VALUES AND PARTIAL SAFETY FACTORS

Clause: 36.1 Characteristic Strength of Materials

The term ‗characteristic strength‘ means that value of the strength of the material below which not more

than 5 percent of the test results are expected to fall. The modified to include the concept of characteristic

strength, the characteristic value shall be assumed as the minimum yield stress/0.2 percent proof stress

specified in the relevant Indian Standard Specifications.

Clause: 36.2 Characteristic Loads

The term ‗characteristic load‘ means that value of load which has a 95 percent probability of not being

exceeded during the life of the structure.

Clause: 36.3 Design Values

36.3.1 Materials

The design strength of-the materials, fd is given by d

m

ff

Clause: 36.4.2.1

values of partial safety factor γm should be taken as 1.5 for concrete and 1.15 for steel.

Table 18 Values of Partial Safety Factor γl for Loads

(Clauses 18.2.3.1.36.4.1 and B.4.3)

Load Combination Limit State of collapse

DL IL WL

Limit Stated of

Serviceability

(1) (2) (3) (4) DL IL WL

DL + IL 1.5or 1.0

1.50.9 1.5

1.0 1.0 –

1.0 – 1.0

DL + IL + WL 1.2

1.0 0.8 0.8

1) While considering earthquake effects, substitute EL for WL

2) For the limit states of serviceability, the values of γl given in this table m applicable for short

tern effects. While assessing the long term effects due to creep the dead load and that part of the

live load likely to be permanent may only be considered.

3) This value is to be considered when stability against overturning or stress reversal is critical.


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RCC

38 LIMIT STATE OF COLLAPSE: FLEXURE

Clause: 38.1 Assumptions

a) Plane sections normal to the axis remain plane after bending.

b) The maximum strain in concrete at the outermost compression fiber is taken as 0.0035 in bending.

f) The maximum strain in the tension reinforcement in the section at failure shall not be less than:

Y

s

f0.0002

1.15E

Es =200000 N/mm2

fΥ max/ d

250 0.53

415 0.48

500 0.46

Clause: 39.3 Short Axially Loaded Members in Compression

Pu = 0.4 fck .Ac + 0.67 fy .Asc

Clause: 39.4 Compression Members with Helical Reinforcement

The strength of compression members with helical reinforcement satisfying the requirement of 39.4.1

shall be taken as 1.05 times the strength of similar member with lateral ties.

Clause: 39.6 Members Subjected to Combined Axial Load and Biaxial Bending

uyuxa a

ux1 uy1

MM1.0

M M

Where Puz = 0.45 fck . Ac + 0.75 fy .Aαc

For values of Pu / Puz = 0.2 to 0.8, the values of αn vary linearly from 1 .0 to 2.0. For values less than 0.2,

αn is 1 .0; for values greater than 0.8, αn is 2.0.

40 LIMIT STATE OF COLLAPSE: SHEAR

Clause: 40.1 Nominal Shear Stress

u

v

d

V

b

Clause: 40.4 Design of Shear Reinforcement

When exceeds shear reinforcement shall be provided in any of the following


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RCC

Where bent-up bars are provided, their contribution towards shear resistance shall not be more than half

that of the total shear reinforcement. Shear reinforcement shall be provided to carry a shear equal to Vu -

c bd The strength of shear reinforcement Vus, shall be calculated as below:

y sv

us

v

0.87f A dV

S

Clause: 41.3 Shears and Torsion

41.3.1 Equivalent Shear

uc u

TV V 1.6

b

Clause: 41.4 Reinforcement in Members Subjected to Torsion

41.4.2 Longitudinal Reinforcement

Mel = Mu+ Mt

t u

1 D / bM T

1.7

ANNEX B

(Clauses 18.2.2, 22.3.1, 22.7, 26.2.1 and 32.1)

STRUCTURAL DESIGN (WORKING STRESS METHOD)

B-l GENERAL

B-2.1.2 Bond Stress for Deformed Bars

Clause: B-2.3 Increase in Permissible Stresses

d) The modular ratio m has the valuecbc

280

3

Grade of Concrete Permissible Stress in Compression

Bending Direct

Permissible Stress in

Bond (Average) for Plain

Bars in tension

(1) (2)

cbc

(3)

ac

(4)

bd

M 10 3.0 2.5 ---

M 15 5.0 4.0 0.6

M 20 7.0 5.0 0.8

M 25 8.5 6.0 0.9

M 30 10.0 8.0 1.0

M 35 11.5 9.0 1.1

M 40 13.0 10.0 1.2

M 45 14.5 11.0 1.3

M 50 16.0 12.0 1.4


89

RCC

1

333

percent wind and seismic forces need not be considered as acting simultaneously.

ANNEXURE D

(Clauses 24.4 and 37.1.2)

SLABS SPANNING IN TWO DIRECTIONS

D-1 RESTRAINED SLABS

Clause: D-l.1

Mx = x w (x)2

My = y w (x)2

D-l.11

Torsion y / x is greater than 2, the slabs shall be designed as spanning one way.

AMENDMENT NO. 4 – MAY 2013 TO

IS 456: 2000 PLAIN AND REINFORCE CONCRETE - CODE OF PRACTICE

No. Clause Before Amendment After Amendment

1. 5.3

Aggregates

Aggregates shall comply with the

requirements of IS 383. As far as

possible preference shall be given to

natural aggregates.

Aggregates shall comply with the

requirements of IS 383.

2. 5.3.4 Coarse and fine aggregate shall be

batched separately. All-in-aggregate

may be used only where specifically

permitted by the engineer-in-charge.

Coarse and fine aggregate shall

be batched separately.

3. 5.4

Water

Water used for mixing and curing shall

be clean and free from injurious

amounts of oils, acids, alkalis, salts,

sugar, organic materials or other

substances that may be deleterious to

concrete or steel.

Water, natural or treated, used

for mixing and curing shall be

clean and free from injurious

amounts of oils, acids, alkalis,

salts, sugar, organic materials or

other substances that may be

deleterious to concrete or steel.

4. 5.4.3

Sea Water

Mixing or curing of concrete with sea

water is not recommended because of

presence of harmful salts in sea water.

Under unavoidable circumstances sea

water may be used for mixing or curing

in plain concrete with no embedded

steel after having given due

consideration to possible disadvantages

and precautions including use of

appropriate cement system.

Sea water shall not be used for

mixing or curing of concrete

because of presence of harmful

salts. Under unavoidable

circumstances sea water may be

used for mixing or curing in plain

concrete with no embedded steel

after having given due

consideration to possible

disadvantages and precautions

including use of appropriate

1. The values of permissible shear stress in concrete are given in Table 23.

2. The bond stress given in co1 4 shall be increased by 25 percent for bars in compression.


90

RCC

cement system.

5. 5.5.7 –

New clause

added

- The amount of admixture added

to a mix shall be recorded in the

production record. Redosing of

admixtures is not normally

permitted. In special

circumstances, if necessary,

additional dose of admixture may

be added at a project site and

mixed adequately in mixer itself

to regain the workability of

concrete with the mutual

agreement between the

producer/supplier and the

purchaser/user of concrete.

However the producer/supplier

shall assure the ultimate quality

of concrete supplied by him and

maintain record of quantity and

time of addition.

6. Table 2 –

Grades of

Concrete

IS 456 : 2000

Table 2 Grades of concrete

(Clause 6.1, 9.2.2, 15.01.1 and 36.1) Group Grade

Designation

Specified

Characteristic

Compressive Strength of

150mm Cube

at 28 Days in N/mm2

(1) (2) (3)

Ordinary

Concrete

M10

M15

M20

10

15

20

Standard

Concrete

M 25

M30 M35

M40

M45 M50

M55

25

30 35

40

45 50

55

High Strength

Concrete

M60 M65

M70

M75 M80

60 65

70

75 80

Note:

1. In the designation of concrete mix M

refers to the mix and the number to

the specified compressive strength

of 150 mm size cube at 28 days,

expressed in N/mm2.

(Page 16, Table 2) – Substitute

the following table for the

existing table:

Table 2 Grades of Concrete

(Clauses 6.1, 9.2.2, 15.1.1 and

36.1)

Group Grade

Designation

Specified

Characteristic Compressive

strength of

150 mm Cube at 28 days

N/mm2

(1) (2) (3)

Ordinary

Concrete

M10

M15

M20

10

15

20

Standard

Concrete

M25

M30

M35 M40

M45

M50 M55

M60

25

30

35 40

45

50 55

60

High Strength

concrete

M65 M70

M75

M80 M85

M90

M95 M100

65 70

75

80 85

90

95 100

Notes:


91

RCC

2. For concrete of compressive strength

greater than M55, design parameters

given in the standard may not be

applicable and the values may be

obtained from specialized literatures

and experimental results.

1. In the designation of concrete

mix M refers to the mix and the

number to the specified

characteristic compressive

strength of 150 mm size cube at

28 days, expressed, in N/mm2 .

2. For concrete of grades above

M60, design parameters given in

the standard may not be

applicable and the values may be

obtained from specialized

literatures and experimental

results.

In this amendment, Classification

of Concrete has been changed.

M60Gr. has been shifted to Standard

concrete and from Grades M85 to

M100 are added to High strength

concretes. In note to M55 is

replaced with M60.

7. 8.1

General

A durable concrete is one that performs

satisfactorily in the working

environment during its anticipated

exposure conditions during service.

The materials and mix proportions

specified and used should be such as to

maintain its integrity and, if applicable,

to protect embedded metal from

corrosion.

A durable concrete is one that

performs satisfactorily in the

working environment during its

anticipated exposure conditions

during service life. The materials

and mix proportions specified

and used should be such as to

maintain its integrity and, if

applicable, to protect embedded

metal from corrosion.

8. NOTES to

Table 5

Minimum

Cement

Content,

Maximum

Water-

Cement Ratio

and Minimum

Grade of

Concrete for

Different

Exposures

with Normal

Weight

Aggregates of

20 mm

Nominal

Maximum

Size

Cement content prescribed in this table

is irrespective of the grades of cement

and it is inclusive of additions

mentioned in 5.2. The additions such as

fly ash or ground granulated blast

furnace slag may be taken into account

in the concrete composition with

respect to the cement content and

water-cement ratio if the suitability is

established and as long as the

maximum amounts taken into account

do not exceed the limit of pozzolona

and slag specified in IS 1489 (Part I)

and IS 455 respectively.

Cement content prescribed in this

table is irrespective of grades and

types of cement and is inclusive

of mineral admixtures mentioned

in 5.2. The mineral admixtures

such as fly ash or ground

granulated blast furnace slag

shall be taken into account in the

concrete composition with

respect to the cement content and

water-cement ratio not exceeding

the limit of fly ash and slag

specified in IS 1489(Part I) and

IS 455 respectively, beyond

which these additions though

permitted, shall not be

considered for these purposes.


92

RCC

9. NOTES to

Table 5 – Note

3 added

Only 2 note items mentioned. 3. The minimum cement content,

maximum free water-cement

ratio and minimum grade of

concrete are

10. 8.2.5.4

Alkali-

aggregate

reaction

b) Use of low alkali ordinary Portland

cement having total alkali content not

more than 0.6 percent (as Na2O

equivalent).

Further advantage can be obtained by

use of fly ash (Grade 1) conforming to

IS 3812 or granulated blast furnace slag

conforming to IS 12089 as part

replacement of ordinary Portland

cement (having total alkali content as

Na2O equivalent not more than 0.6

percent), provided fly ash content is at

least 20 percent or slag content is at

least 50 percent.

b) Use of low alkali ordinary

Portland cement having total

alkali content not more than 0.6

percent (as Na2O equivalent).

Further advantage can be

obtained by use of flyash

conforming to IS 3812 (Part I) or

ground granulated blast furnace

slag conforming to IS 12089 as

part replacement of ordinary

Portland cement (having total

alkali content as Na2O equivalent

not more than 0.6 percent),

provided fly ash content is at

least 25percent or slag content is

at least 50 percent.

11. 8.2.6.2

Drainage

At sites where alkali concentrations are

high or may become very high, the

ground water should be lowered by

drainage so that it will not come into

direct contact with the concrete.

Additional protection may be obtained

by the use of chemically resistant stone

facing or a layer of plaster of Paris

covered with suitable fabric, such as

jute thoroughly impregnated with

bituminous material.

At sites where alkali

concentrations are high or may

become very high, the ground

water should be lowered by

drainage so that it will not come

into direct contact with the

concrete.

Additional protection may be

obtained by the use of suitable

impermeable barriers.

12. 9.2

Design Mix

Concrete

9.2.1

As the guarantor of quality of concrete

used in the construction, the

constructor shall carry out the mix

design and the mix so designed (not the

method of design) shall be approved by

the employer within the limitations of

parameters and other stipulations laid

down by this standard.

As the guarantor of quality of

concrete used in the construction,

the constructor shall carry out the

mix design and the mix so

designed (not the method of

design) shall be approved by the

employer within the limitations

of parameters and other

stipulations laid down by this

standard. If so desired, the

employer shall be provided with

supporting data including graphs

showing strength versus water

cement ratio for range of

proportions, complete trial mix

proportioning details to

substantiate the choice of cement

content, fine and coarse

aggregate content, water, mineral

admixtures, chemical admixtures


93

RCC

etc.,

13. 9.2.2 The mix shall be designed to produce

the grade of concrete having the

required workability and a

characteristic strength not less than

appropriate values given in Table 2.

The target mean strength of concrete

mix should be equal to the

characteristic strength plus 1.65 times

the standard deviation.

The mix shall be designed to

produce the grade of concrete

having the required workability

and a characteristic strength not

less than appropriate values

given in Table 2.

Proportion/grading of aggregates

shall be made by trial in such a

way as to make densest possible

concrete. The target mean

strength of concrete mix should

be equal to the c

14. Table 8

Assumed

Standard

Deviation

Table 8: Assumed Standard Deviation

(Clause 9.2.4.2 and Table 11) Grade of

Concrete

Assumed

Standard

Deviation N/mm2

M10

M15

3.5

M 20

M 25

4.0

M30

M35

M40

M45

M50

5.0

Note: The above values correspond to

the site control having proper storage

of cement; weight batching of all

materials; controlled addition of water,

regular checking of all materials,

aggregate gradings and moisture

content; and periodical checking of

workability and strength. Where there

is deviation from the above the values

given in the above table shall be

increased by 1N/mm2.

(Page 23, Table 8) – Substitute

the following for the existing

table:

Table 8 Assumed Standard

Deviation

(Clause 9.2.4.2 and Table 11) Grade of

concrete

Assumed

Standard

Deviation

N/mm2

M10

M15

3.5

M 20

M 25

4.0

M30

M35

M40

M45

M50

M 55

M60

5.0

Note:

1. The above values correspond

to the site control having proper

storage of concrete , weigh

batching of all materials,

controlled addition of water,

regular checking of all materials,

aggregate grading and moisture,

content, and period checking of

workability and strength. Where

there is deviation from the above,

the value given in the above table

shall be increased by 1 N/mm2 .

2. For grades above M 60 , the


94

RCC

standard deviation shall be

established by actual trials based

on extend properties, before

finalizing the mix.

In this amendment, M55 and

M60 has been added in the

amended version to the Grade of

Concrete. Also note 2 is added.

15. 10.2

Batching

To avoid confusion and error in

batching, consideration should be given

to using the smallest practical number

of different concrete mixes on any site

or in any one plant. In batching

concrete, the quantity of both cement

and aggregate shall be determined by

mass; admixture, if solid, by mass;

liquid admixture may however be

measured in volume or mass; water

shall be weighed or measured by

volume in a calibrated tank (see also IS

4925). Ready-mixed concrete supplied

by ready-mixed concrete plant shall be

preferred. For large and medium

project sites the concrete shall be

sourced from ready mixed concrete

plants or from on site or off site

batching and mixing plants (see IS

4926).

To avoid confusion and error in

batching, consideration should be

given to using the smallest practical

number of different concrete mixes

on any site or in any one plant. In

batching concrete, the quantity of

both cement and aggregate shall be

determined by mass; admixture, if

solid, by mass; liquid admixture may

however be measured in volume or

mass; water shall be weighed or

measured by volume in a calibrated

tank (see also IS 4925).

For large and medium project sites,

the concrete shall be sourced from

Ready mixed concrete plants or

from captive on site or off site

automatic batching and mixing

plants. The concrete produced and

supplied by ready-mixed concrete

plants shall be in accordance with IS

4926. In case of concrete from

captive on site or off site automatic

batching and mixing plants, similar

quality control shall be followed.

16. 10.2.1 Except where it can be shown to the

satisfaction of the engineer-in-charge

that supply of properly graded

aggregate of uniform quality can be

maintained over a period of work, the

grading of aggregate should be

controlled by obtaining the coarse

aggregate in different sizes and

blending them in the right proportions

when required, the different sizes being

stocked in separate stock-piles. The

material should be stock-piled for

several hours preferably a day before

use. The grading of coarse and fine

aggregate should be checked as

frequently as possible, the frequency

for a given job being determined by the

engineer-in charge to ensure that the

specified grading is maintained.

The grading of aggregate shall be

controlled by obtaining the

coarse aggregate in different

sizes and blending them in right

proportions, the different sizes

being stocked in separate stock

piles. The material should be

stock-piled for several hours

preferably a day before use. The

grading of coarse and fine

aggregate should be checked as

frequently as possible, the

frequency for a given job being

determined by the engineer-in

charge to ensure that the

specified grading is maintained.


95

RCC

17. 10.2.2 The accuracy of the measuring

equipment shall be within + 2 percent

of the quantity of cement being

measured and within + 3 percent of the

quantity of aggregate, admixtures and

water being measured.

The accuracy of measuring

equipment shall be within ±2

percent of the quantity of cement

and mineral admixtures being

measured and within ±3percent

of the quantity of aggregate,

chemical admixtures and water

being measured. In a batching

plant, the concrete production

equipment shall be calibrated

initially at the time of installation

or reconditioning of the

equipment and subsequently at

the following intervals:

a)Mechanical/knife edge systems

: At least once every two months

b)Electrical / load cell systems :

At least once every three months

18. 10.2.3 Proportion/Type and grading of

aggregates shall be made by trial in

such a way so as to obtain densest

possible concrete. All ingredients of the

concrete should be used by mass only.

All ingredients of concrete shall

be used by mass except water

and chemical admixtures which

may be by volume.

19. 10.2.5 It is important to maintain the water-

cement ratio constant at its correct

value. To this end, determination of

moisture contents in both fine and

coarse aggregates shall be made as

frequently as possible, the frequency

for a given job being determined by the

engineer-in-charge according to

weather conditions. The amount-of the

added water shall be adjusted to

compensate for any observed variations

in the moisture contents. For the

determination of moisture content in

the aggregates, IS 2386 (Part 3) may be

referred to. To allow for the variation

in mass of aggregate due to variation in

their moisture content, suitable

adjustments in the masses of

aggregates shall also be made. In the

absence of -exact data, only in the case

of nominal mixes, the amount of

surface water may be estimated from

the values given in Table 10.

It is important to maintain the

water-cement ratio constant at its

correct value. To this end,

determination of moisture

contents in both fine and coarse

aggregates shall be made as

frequently as possible, the

frequency for a given job being

determined by the engineer-in-

charge according to weather

conditions. The amount-of the

added water shall be adjusted to

compensate for any observed

variations in the moisture

contents. For the determination

of moisture content in the

aggregates, IS 2386 (Part 3) may

be referred to. Where batching

plants are used, it is

recommended to determine

moisture content by moisture

probes fitted to the batching

plants. To allow for the variation

in mass of aggregate due to

variation in their moisture

content, suitable adjustments in

the masses of aggregates shall

also be made. In the absence of -

exact data, only in the case of


96

RCC

nominal mixes, the amount of

surface water may be estimated

from the values given in Table

10.

20. 10.3 Mixing

Concrete shall be mixed in a

mechanical mixer. The mixer should

comply with IS 1791 and IS 12119.

The mixers shall be fitted with water

measuring (metering) devices. The

mixing shall be continued until there is

a uniform distribution of the materials

and the mass is uniform in colour and

consistency. If there is segregation after

unloading from the mixer, the concrete

should be remixed.

Concrete shall be mixed in

mechanical mixer (see also IS

1791 and IS 12119). It shall be

ensured that stationary or central

mixers and truck mixers shall

comply with the performance

criteria of mixing efficiency as

per IS 4634. Mixing efficiency

test shall be performed at least

once in a year. The mixers shall

be fitted with water measuring

(metering) devices. The mixing

shall be continued until there is a

uniform distribution of the

materials and the mass is uniform

in colour and consistency. If

there is segregation after

unloading from the mixer, the

concrete should be remixed.

21. 10.3.1 For guidance, the mixing time shall be

at least 2 min. For other types of more

efficient mixers, manufacturers‘

recommendations shall be followed; for

hydrophobic cement it may be decided

by the engineer-in-charge.

As a guidance, the mixing time

shall be at least 2min for

conventional free fall (drum)

batch type concrete mixers. For

other types of more efficient

mixers, manufacturers‘

recommendations shall be

followed.

22. 10.3.3 Dosages of retarders, plasticisers and

superplasticisers shall be restricted to

0.5, 1.0 and 2.0 percent respectively by

weight of cementations‘ materials and

unless a higher value is agreed upon

between the manufacturer and the

constructor based on performance test.

Dosages of retarders, plasticisers

and superplasticisers shall be

restricted to 0.5, 1.0 and 2.0

percent respectively by mass of

cementitious materials; however,

the dosages of polycarboxylate

based admixtures shall not

exceed 1.0percent. A higher

value of above admixtures may

be used, if agreed upon between

the manufacturer and the

constructor based on

performance test relating to

workability, setting time and

early age strength.

23. 11.1

General

General

The framework shall be designed and

constructed so as to remain sufficient

rigid during placing and compaction of

(Page 25, Clause 11.1, informal

table)–Substitute the following

for the existing table:


97

RCC

concrete, and shall be such as to

prevent loss of slurry from the

concrete. For further details regarding

design, detailing, etc, reference may be

made to IS 14687. The tolerances on

the shapes, lines and dimensions shown

in the drawing shall be within the limits

given below: (a) Deviation from

specified dimensions of

cross-section of

columns and beams

12mm6

(b) Deviation from

dimensions of footings

(1) Dimensions in plan 50mm12

(2) Eccentricity 0.02 times

the specified

thickness

(a) Deviation from

specified

dimensions of cross – section

of columns and

beams

10mm5

(b) Deviation from dimensions of

footings:

(1) Dimension in plan

50mm10

(2) Eccentricity 0.02 times the

width of the

footing in the direction of

deviation but

not more than

50 mm

(3) Thickness 50mm10

Or

0.05 times

the specified thickness,

whichever is

less

In this amendment, The

tolerances on shapes, lines and

dimensions are revised.

24. 13.4

Construction

Joints and

Cold Joints

Joints are a common source of

weakness and, therefore, it is desirable

to avoid them. If this is not possible,

their number shall be minimized.

Concreting shall be carried out

continuously up to construction joints,

the position and arrangement of which

shall be indicated by the designer.

Construction joints should comply with

IS 11817.

Joints are a common source of

weakness and, therefore, it is

desirable to avoid them. If this is

not possible, their number shall

be minimized. Concreting shall

be carried out continuously up to

construction joints, the position

and arrangement of which shall

be indicated by the designer.

25. Table 11 Table 11 Characteristic Compressive Strength

compliance Requirement

(Clauses 16.1 and 16.3)

Specified

Grade Mean of the Group of 4 Non-

Overlapping

consecutive Test Results in N/mm2

Individual Test

Results in

N/mm2

(1)

M 15

(2)

fck + 0.825

established standard deviation

(rounded off to

nearest 0.5 N/mm2) Or

fck + 3 N/mm2,

whichever is greater

(3)

fck –3 N/mm2

M 20 Or

above

fck+ 0.825 established

standard deviation

9rounded off to nearest 0.5 N/mm2

) or

fck–4 N/mm2

[Page 30, Table 11 (See also Amendments

No. 1 and 3)] – Substitute the following for

the existing Table11: Table 11 Characteristic Compressive Strength

Compliance requirement (Clause 16.1 and 16.3)

(1)

M 15 and above

(2)

fck + 0.825

established

standard deviation

(rounded off

to nearest 0.5 N/mm2)

Or

Which ever is greater

(3)

fck – 3 N/mm2

Note:

(1) In the absence of established

value of standard deviation , the

value given in Table 8 may be


98

RCC

fck + 4N/mm2 ,

whichever is

greater

assumed, and attempt should be

made to obtain results of 30

samples as early as possible to

establish the value of standard

deviation.

(2) For concrete of quantity up to

30 m3 9where the number of

samples to be taken is less than

four as per the frequency of

sampling given is 15.2.2), the

mean of test results of all such

samples shall be fck + 4N/mm2,

minimum and the requirement of

minimum individual test result

shall be fck – 2 N/mm2 ,

minimum. However, when the

number of sample is only one as

per 15.2.2, the requirement shall

be fck + 4 N/mm2 , minimum.

In this amendment, The

characteristic compressive

strength compliance

requirements are revised. In the

revision it is same for M15 and

above grades. Note 2 is added.

26. 24.4.1

Restrained

Slab with

Unequal

Conditions at

Adjacent

Panels

In some cases the support moments

calculated from Table 26 for adjacent

panels may differ significantly. The

following procedure may be adopted to

adjust them.

a) Calculate the sum of moments at

midspan and supports (neglecting

signs).

In some cases the support

moments calculated from Table

26 for adjacent panels may differ

significantly. The following

procedure may be adopted to

adjust them.

a) Calculate the sum of the

midspan moments and the

average of the support moments

(neglecting signs) for each panel.

27. 26.2.1

Development

Length of

Bars - NOTES

– Note 3 added

Only 2 Note items mentioned. 3) For plain cement concrete of

M15grade with nominal

reinforcement, the design bond

stress may be taken as 1.0

N/mm2.

28. 26.2.1.1

Design bond

stress in limit

state method

for plain bars

in tension

shall be as

below:

For deformed bars conforming to IS

1786 these values shall be increased by

60 percent. For bars in compression,

the values of bond stress for bars in

tension shall be increased-by 25

percent.

For deformed bars conforming to

IS 1786 these values shall be

increased by 60 percent. For bars

in compression, the values of

bond stress for bars in tension

shall be increased-by 25 percent.

For fusion bonded epoxy coated

deformed bars, design bond


99

RCC

stress values shall be taken as 80

percent of the values given in the

above table.

29. 35.3.2

Cracking – 3rd

para

The surface width of the cracks should

not, in general, exceed 0.3 mm in

members where cracking is not harmful

and does not have any serious adverse

effects upon the preservation of

reinforcing steel nor upon the

durability of the structures. In members

where cracking in the tensile zone is

harmful either because they are

exposed to the effects of the weather or

continuously exposed to moisture or in

contact soil or ground water, an upper

limit of 0.2 mm is suggested for the

maximum width of cracks. For

particularly aggressive environment,

such as the ‗severe‘ category in Table

3, the assessed surface width of cracks

should not in general, exceed 0.1 mm.

The surface width of the cracks

should not, in general, exceed 0.3

mm in members where cracking is

not harmful and does not have any

serious adverse effects upon the

preservation of reinforcing steel nor

upon the durability of the structures.

In members where cracking in the

tensile zone is harmful either

because they are exposed to the

effects of the weather or

continuously exposed to moisture or

in contact soil or ground water, an

upper limit of 0.2 mm is suggested

for the maximum width of cracks.

For particularly aggressive

environment, such as ‗very severe‘

and ‗extreme‘ categories given in

Table 3, the assessed surface width

of cracks should not in general,

exceed 0.1 mm.

30. 40.5.2

Shear

Reinforcement

for Sections

Close to

supports

If shear reinforcement is required, the

total area of this is given by:

As = avb(Ԏv-2dԎc/aV)/0.87fy ≥0.4

avb/0.87fy

If shear reinforcement is

required, the total area of this is

given by:

ΣASV = avb(Ԏv-2dԎc/aV)/0.87fy

≥0.4 avb/0.87fy

31. B-2.1.1 Direct

Tension

For M50, Tensile stress – 5.2

For M55, Tensile stress – 5.6

For M50 and above, Tensile

stress – 5.2

32. Table 21

In this amendment, The change

to the table is

a)Substituting the entries against

M55

b)Insertion of a new row for M60

33. ANNEX E

(Clause 25.2)

EFFECTIVE

LENGTH OF

COLUMNS

E-l : In the absence of more exact

analysis, the effective length of

columns in framed structures may be

obtained from the ratio of effective

length to unsupported length lef/l given

in Fig. 26 when relative displacement

of the ends of the column is prevented

and in Fig. 26 when relative lateral

displacement of the -ends is not

E-l : In the absence of more exact

analysis, the effective length of

columns in framed structures

may be obtained from the ratio of

effective length to unsupported

length lef/l given in Fig. 26 when

relative displacement of the ends

of the column is prevented and in

Fig. 27 when relative lateral


100

RCC

prevented. In the latter case, it is

recommended that the effective length

ratio Ief /l may not be taken to be less

than 1.2.

displacement of the -ends is not

prevented. In the latter case, it is

recommended that the effective

length ratio Ief /l may not be taken

to be less than 1.2.


101

RCC

1. The minimum thickness of a reinforced

concrete wall should be :

(A) 7.5 cm (B) 10 cm

(C) 15 cm (D) 12.5 cm

2. The minimum head room over a stair must be:

(A) 200 cm (B) 205 cm

(C) 210 cm (D) 220 cm

3. Minimum thickness of load bearing RCC wall

should be

(A) 5 cm (B) 10 cm

(C) 15 cm (D) 20 cm

4. Modular ratio ‗m‘ for M25 grade of concrete is

(A) 16.67 (B) 13.33

(C) 10.93 (D) None

5. Permissible deviation from specified

dimensions of cross – section of column &

Beams as per IS Standard is _____ mm

(A) +10mm -4mm (B) +12mm -6mm

(C) +14mm -8mm (D) None

6. Expansion joints are provided if the length of

concrete structure exceeds

(A) 10m (B) 15m

(C) 35m (D) 45m

7. For avoiding the limit state of collapse, the

safety of RC structure is checked for

appropriate load combinations of dead (DL),

imposed load or live load (LL), wind load

(WL) and earthquake load (EL). Which of the

following load combinations is NOT

considered?

(A) 0.9DL + 1.5WL

(B) 1.5DL + 1.5WL

(C) 1.5DL + 1.5WL + 1.5EL

(D) 1.2DL + 1.2IL + 1.2WL

8. Various types of load on a building are

(A) D.L (B) C.L

(C) W.L (D) All

9. Retrofitting is

(A) Redesigning whole building

(B) Fitting new door

(C) Fitting new windows

(D) To upgrade earthquake resistance existing

building to make it safer

10. Minimum admissible water – cement ratio for

mild environmental exposure should be

(A) 0.55 (B) 0.50

(C) 0.45 (D) 0.40

11. A cantilever retaining wall should not be used

for heights more than

(A) 4m (B) 6m

(C) 8m (D) 10m



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RCC

12. For the modern box-girder bridges deployed in

the flyovers nowadays

(A) The depth of the box girder in the middle

is maximum

(B) The depth of the box girder on the support

is maximum

(C) The depth of the box girder remains same

along the length

(D) The depth of the box girder does not

matter

13. The minimum cement content recommended

by IS: 456 for reinforced cement concrete with

normal weight 20mm size aggregates subjected

to moderate exposure in Kg/m3

(A) 300 (B) 320

(C) 340 (D) 360

14. The concrete having a slump of 6.5 cm is said

to be

(A) Dry (B) Earth moist

(C) Semi – plastic (D) Plastic

15. Minimum spacing between horizontal parallel

reinforcement of different size should not be

less than

(A) One diameter of thinner bar

(B) One diameter of thicker bar

(C) Sum of the diameter of thinner and

thicker bars

(D) Twice the diameter of thinner bar

16. The modular ratio for M15 grade concrete,

according to IS : 456 is

(A) 14 (B) 15

(C) 18 (D) 19

17. The minimum clear distance between main

reinforcement bar is

(A) Equal to the diameter of the reinforcing

bar

(B) Equal to the size of the aggregate

(C) 5mm more than the maximum size of

coarse aggregate

(D) Greater of (A) and (C) above

18. Expansion joint in masonary walls are

provided in wall lengths more than

(A) 10m (B) 20m

(C) 30m (D) 40m

19. In any case the bearing of a lintel should not be

less than

(A) 10cm (B) 15cm

(C) 20cm (D) 30cm

20. For good quality cement the specific surface of

cement should not be less than__________.

(A) 2250cm2 /gm (B) 2500cm

2 /gm

(C) 2750cm2 /gm (D) None of these


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RCC

1. (B)

2. (C)

3. (B)

4. (C)

5. (B)

6. (D)

7. (C)

8. (D)

9. (D)

10. (A)

11. (B)

12. (C)

13. (A)

14. (D)

15. (B)

16. (D)

17. (D)

18. (D)

19. (B)

20. (A)

Ans 4 C Modular ratio m = 280

3𝜎𝑐𝑏𝑐

For M 25 grade of concrete σcbc = 8.5

Modular ratio m =>280

3𝑋8.5 = 10.98

Explanations Level - 1

Answer key


CONCEPT OF FOOTINGS

―Footing is that portion of the foundation which ultimately delivers the load to the soil, and thus is in

contact with it‖.

Functions of Footings: The major functions of footings are as under:

1. To distribute the load of superstructure to a wider area so that maximum pressure on soil does not

exceeds the bearing capacity of soil.

2. To limit the settlement of structure with in the permissible values.

Foundations may be broadly classified under the two categories:

(i) Shallow foundations : (e.g. Strip footing, isolated footing, spread footing etc.)

(ii) Deep foundations (e..g, pile foundation, well foundation etc.)

As per Terzaghi, a foundation is said to be shallow when it depth is equal to or less than its width. In case

of deep foundations, the depth is much greater than its width.

The shallow footings are of the following types:

1. Isolated footing 2. Combined footing 3. Strap footing 4. Mat or raft footing

Mat foundation Trapezoidal Footing Strip Footing

Wall

Str

ip F

oo

tin

g

Sp

read

Fo

oti

ng

Sp

read

Foo

tin

g

Co

mbin

ed F

oo

tin

gs

Types of shallow foundations.

The load of the superstructure is transmitted to the foundation or substructure through either

walls or columns. Hence, footing plays an important role in effective load transfer mechanism .

Chapter

7 PRESTRESS & FOOTINGS

Syllabus: Footings, Types of footing, check for one way &

punching shear. Prestressing, Methods of presstressing losses in

presstressing. Weightage : 10%


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RCC

1. Isolated footing : A footing that supports a single column is known as isolated footing. It is used

generally provided where intensity of load is less and columns are not closely spaced.

Elevation Elevation Elevation Elevation

Plan

Circular Footing(for Circular Column)

PlanSquare Footing

(for Square Column)

PlanRectangular Footing

(for Rectangular Column)

PlanSquare Footing

(for square Column)

Isolated Footings of Uniform Thickness

Isolated footings may be square, rectangular, or circular in plan as shown in fig. square footings are

more economical for square or circular columns. Under rectangular shaped columns, rectangular

footing is used.

(i) Isolated footing of uniform thickness: When load on column is not large or the size of footing

works out to be small requiring lesser depth of footing then the thickness of footing is kept

uniform.

(ii) Isolated footing of varying thickness (Sloped footing): When depth of the footing works out

to be more, it is common practice to reduce the depth of footing towards the outer edges to

make the footing economical.

Elevation

Plan

Isolated Footing (Sloped Type)

2. Combined footing: A footing which supports two or more columns is termed as combined footing.

Such footings are provided when

(i) Individual footings lie very near to each other.

(ii) When two nearby footings overlap.


106

RCC

(iii) When bearing capacity of soil is so low that the isolated footing work out to be of uneconomical

size.

Combined footings may either be rectangular or trapezoidal

Elevation Elevation

Plan Plan

Combined Rectangular footing Combined Trapezoidal Footing

Combined Rectangular footing Combined trapezoidal Footing

3. Strap or Cantilever footing: A strap footing consists of spread footings of two columns connected

by a strap beam. The strap beam does not remain in contact with soil and thus does not transfer any

pressure to the soil.

Strap Beam

Elevation

PlanStrap Footing

This type of footing is generally used:

(i) To combined the footing of outer column to the adjacent one so that the footing of the former does

not extend in the adjoining property.

(ii) When the distance between the columns is so large that a combined rectangular or trapezoidal

footing works out to be uneconomical.

4. Mat or Raft Footing: A mat or raft is a combined footing that covers the entire area beneath the

structure and supports all the walls and columns (As shown in fig.) it is provided when:

(i) The loads on the columns is very large.

(ii) The available bearing capacity of soil is very low that independent column footings are

impracticable.

When the use of spread footings would cover more than one-half of the plan area, then it

is economical to use mat or raft footing.


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RCC

INDIAN STANDARD CODE RECOMMENDATIONS FOR DESIGN OF FOOTINGS (IS : 456–

2000)

1. In sloped or stepped footings, the effective cross – section in compression shall be limited by the

area above the neutral plane, and the angle of slope or depth and location of steps shall be such that

the design requirements are satisfied at every section. Sloped and stepped footings that are designed

as a unit shall be constructed to assure action as a unit.

2. Thickness at the edge of footing. In reinforced and plain concrete footings, the thickness at edge

shall be not less than 15 cm for footings on soils nor less that 30 cm above the tops of piles for

footings on piles.

3. In the case of plain concrete pedestals, the angle between plane passing through the bottom edge of

the pedestal and the corresponding junction edge of the column with pedestal and the horizontal

plane Shall be governed by the expression:

PlainConcretepadestal

Column

tan 0

ck

100q0.9 1

f

Where q0 = calculated maximum bearing pressure at the base of the pedestal in N/mm2, and

fck = characteristic strength of concrete at 28 days in N/mm2

Check for Shear:

One way Shear: the critical section will be located at distance d (d-effective depth) from the face of the

column.

Two Way Shear: The critical section will be located at d/2 (d-effective depth) from the distance face of

the column.

PRESTRESSING

When the pre-stressed concrete member is subjected-to external loads, the already induced Compressive

stress in concrete will neutralize the tensile stresses developed in the member on loading. As a result, the

resultant stresses ―in concrete, in tensile zone, will be totally eliminated or get reduced to a great extent.

Pre-stressing is commonly introduced by tensioning the steel reinforcement.


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RCC

Assumptions in the design of pre-stressed concrete members: Pre-stressed concrete members are

designed on the basis of the assumptions given below :

1. A transverse plane section of the member will remain plane after bending.

2. Hook's law is applicable to concrete and steel.

3. The stress in the reinforcement does not change along the length of the reinforcement. Variation of

stress in the reinforcement due to change in the external loading is ignored.

PRINCIPLE OF PRE-STRESING (ANALYSIS BY STRESS CONCEPT)

A simply supported pre-stressed concrete beam of rectangular section pre- stressed by a tendon provided

through its centroidal longitudinal axis.

External Loading

Tendon

P

Supports

P

PA

+ +

MZ

PA

MZ

+

PA

MZ

PA

MZ

–

=+

+

–

Stress due to Prestressing

Force

Stress due to B.M

FinalStresses

Simply Supported Pre-stressed Concrete Beam.

Let the beam be subjected to external loading system and P = Pre-stressing force supplied by the tendon.

Due to this pre-stressing force, the compressive stress induced in concrete = P

A

where A = cross-sectional area of the member.

Stress induced after loading = M

Z

Where M = B.M. due to the dead load and external loading.

Z = Section modulus of the beam section.

At extreme ends, the final stresses on beam section = P M

A Z

Stress at top most edge = P M

A Z

Stress at extreme bottom edge = P M

A Z


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RCC

This clearly shows that the entire cross-section of the member becomes effective for resisting bending

moment and at the same time the danger of development of cracks (in tension zone) gets minimized or

eliminated.

ADVANTAGES AND DISADVANTAGES OF PRE-STRESSED CONCRETE

Advantages of Pre-stressed concrete: Pre-stressed concrete has the following advantages over RCC

members :

1. The technique of pre-stressing eliminates cracking of concrete under all stages of loading and the

entire section of the structure takes part in resisting the external load.

Where as in RCC members only portion of concrete above the neutral axis is effective.

2. The concrete does not crack and the possibility of corrosion of steel gets minimized.

3. Pre-stressing needs about 1

rd3

the quantity of steel and 1

rd4

the quantity of concrete as compared

to RCC.

4. Lighter and slender members are possible with the use of high strength concrete and steel.

5. In pre-stressed concrete beams, dead loads are practically neutralized. Hence, long span structures

are possible because of reduction of self weight of the structure.

6. Pre-stressed concrete can be safely recommended for structures subjected to heavy loads, impact and

vibrations e.g., railway sleeper and gantary girders in bridges, etc.

7. Pre-stressed concrete members like electric poles, railway sleepers, etc. can be produced in factories

under controlled working conditions where as RCC members have to be cast in situ.

8. Diagonal tension can be reduced to a greater extent by using pre-stressed concrete.

9. Pre-stressed precast members can be tested before use where as RCC structural members can not be

tested as such. X

10. It is possible to construct large size liquid retaining structures with the help of pre-stressed concrete

which were not economical to build otherwise with RCC.

Such structures are economical and are safe against cracking and subsequent leakage?

11. Pre-stressed concrete members deflect significantly before ultimate failure, thus giving enough

warning. Whereas in RCC structures no such indication is noticed.

Disadvantages of Pre-stressed Concrete : Pre--stressed concrete has the following disadvantages :

l. It requires perfect supervision at all stages and technical know how.

2. It requires high quality dense concrete of high strength. Perfect quality control in production,

placement and compaction is required.

3. Cost of high strength materials is very high.

4. Initial cost of equipments required for pre-stressing is very high.

5. Very long and slender members are difficult to transport.

6. It requires high tensile steel, which is 2-5 to. 3-5 times costlier than mild steel.


110

RCC

7. High tensile strength steel have high carbon content and hence it is brittle. Therefore, the pre-stressed

sections are brittle.

8. Pre-stressed sections are less fire resistant.

I.S. SPECIFICATIONS FOR MATERIALS USED IN PRE –STRESSED CONCRETE

As per the Indian Standard code of practice for pre—stressed concrete (IS : 1343), the

following specifications for materials must be kept in mind.

The two main materials in pre-stressed concrete are :

(a) Concrete

(b) Steel

(a) Concrete : The concrete to be used in pre-stressed concrete member should be strong enough so that

full strength can be utilized.

As per IS : 456-2000, a minimum grade of M 40 for pre-tensioned systems and M 30 for post-

tensioned system should be used. High strength concretes are preferred for pre-stressing works

because :

1. Small cross– sections are possible by using high strength concretes. It reduces the dead weight and

consequently longer spans become technically and economically feasible.

2. Rich concrete mix has high value of modulus of elasticity which helps in reducing deflection and

early release of pre-stressing equipment.

3. Creep and shrinkage is less in high strength concrete and causes less loss of pre-stressing force.

Water cement ratio for most of the pre-stressed concrete works should be about 0.45.

To ‗achieve a slump value of 75 mm with 0-45 water cement ratio would require 10 bags of cement

per cubic metre of concrete.

Use of admixture is not generally recommended but they can be used only with the approval of

engineer in charge based upon the evidence, that with the passage of time, neither the compressive

strength of concrete nor other desired properties of concrete and steel are affected.

(b) Pre-stressing steel : High tensile strength steel is used for pre-stressing. The steel used for pre-

stressing the concrete shall be one of the following :

(i) Single wires (also called as tendons).

(ii) Group of wires (also termed as strands or cables).

(iii) Alloy steel round bars.

(i) Single wires (tendons) : Hard drawn high tensile steel wire of diameter ranging from 1.5 mm

to 8 mm and having tensile and other properties as specified in the following clauses.

(ii) Wire strands (cables) : Hard drawn steel wires may be used in the form of cables known as

wire strands. Stress is produced by spinning six individual wires around a central straight wire.


111

RCC

Stranded cables is made up of seven or more individual high strength wires. The diameter of the

stranded cable varies generally from 7 mm to 17 mm. These types of standard cables are

generally used in post tensioning works.

(iii) Round bars : High tensile alloy steel bars are used in pre-stressing systems. It is available in 10

mm to 32 nun diameter.

Loss of pre-stress resulting due to creep and shrinkage of concrete and relaxation of steel

generally amounts to 15% to 20% of the initial stresses.

In RCC works steel used is of Fe 250 grade or Fe 415 grade but if such steel is used in pre-

stressed works, then very less amount of pre-stress is left after the losses. That is the reason why

high tensile steel is used in pre-stress works.

Some of the important properties of high tensile steel are mentioned below :

1. Ultimate tensile strength : Cold drawn high tensile strength steel wires used for pre-stressed

concrete shall conform to the specifications shown in table

Minimum ultimate tensile strength of high strength steel wires.

Diameter (in mm) 1.5 2.0 2.5 3.0 4.0 5.0 7.0 8.0

Minimum ultimate

strength (N/mm2)

2350 2200 2050 1900 1750 1600 1500 1400

2. Surface condition of wire : The wires shall be free from rust, scaling and other deleterious material

liable to affect proper tensioning or bonding with concrete.

PRE-STRESSING EQUIPMENT

The equipment needed for the construction of pre-stressed concrete are mentioned below :

1. Tensioning Equipment :

(i) Tensioning equipments are required for both pre-tensioned and post-tensioned method of pre-

stressing concrete.

(ii) High tensile strength steel is pre-stressed by means of levers, screw jacks, hydraulic jack and

other similar mechanical jacks. But I.S. specifications recommends hydraulic or mechanical

jack only.

The diameter of the steel wire increases the minimum Ultimate strength decrease.


112

RCC

(iii) Tensioning equipment must apply a controlled force and shall not induce dangerous stresses or

torsional effect on steel or concrete.

(iv) The variation in applied force shall not exceed 5%.

2. Temporary gripping device : Pre-stressing tendons may be gripped with the help of double cone,

wedges etc. The gripping device shall be strong enough having good anchorage so that the wires

does not slip.

Gripping device shall be such that in a tensile test, the wire or wires fixed by them would break

before the failure of the grip itself.

3. Releasing device: The releasing device shall be so designed that it is able to transfer the pre-stress,

to be carried out, gradually so as to avoid large differences between wires in a tension, severe

eccentricity of pre-stress or sudden application of stress to the concrete.

The release of pressure should be gradual and uniform in all wires.

4. End Anchorage :

(i) The anchoring device shall be capable of holding, without more than nominal slip, the pre-stressing

tendon subjected to a load midway between proposed initial pre-stressing load and the ultimate

strength‗ of the pre-stressing tendon.

(ii) The anchoring device shall be capable of holding the pre-stressing tendons without giving a nominal

slip.

(iii) It should be strong enough to resist, in all respects, a force equal to at least-the breaking strength of

the tendons.

(iv) The end anchorage shall transfer, effectively and evenly, the entire force from the pre- stressing

tendons to the concrete without inducing undesirable stress.

(v) Anchorage shall be safe and secure against both dynamic and static loads.

METHODS OF PRE-STRESSING

The commonly used method for internal pre-stressing are :

1. Pre-tensioning method

2. Post-tensioning method.

Depending upon whether the steel is tensioned before or after the casting of concrete.

Pre-tensioning method

In this method of pre-stressing, the tendons are pre-stressed before the concrete is placed. This is a simple

method used in factories production.


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RCC

The following steps are followed in pre-tensioning method :

1. Steel tendons (cables, strands or wires) are first placed in pre-determined position in the form work

(casting bed).

2. One end of tendons (reinforcement) is secured to an abutment while the other end of the

reinforcement is pulled by using a jack for a pull (P) of desired magnitude and this end is then fixed

to another .

3. The concrete is then poured in the form work. and is cured and gets hardened. Steam curing can be

used to get 28 days concrete strength in a shorter time span.

4. Ends of the reinforcement are now cut at the abutments and in between the members casted on the

same bed .

The reinforcement which tends to resume its original length will compress the concrete surrounding

it by bond action.

The pre-stress is thus transmitted to concrete entirely by the action of bond between the

reinforcement and the surrounding concrete.

P

Abutment

Pull(P)

HydraulicJack

(a)

(b) (a) The tendon has been tensioned and then concreting has been done.

(b) After the concrete has hardened the tendon is cut off at the ends. The beam gets pre-stressed

by bond action.

AnchorsTendon

AbutmentCasting Bed

Concrete Member

Pull (P)

Hydraulic Jack

Several members can be manufactured at one time.

In this casting bed is very long and hence several members can be manufactured

simultaneously.


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RCC

Advantages and Disadvantages of Pre-tensioning Method .

Advantages

1. This method is quite simple.

2. This method is advantageous for factory production.

3. Members casted by this method are quite durable.

4. Several members can be casted at one time on same casting beds.

Disadvantages:

1. Abutments to hold the tendons should be very strong. At site such arrangements –are difficult to

construct and hence suitable for factory production.

2. Size of member is restricted because heavier and slender members are more difficult to transport.

3. Loss of pre-stress is more in pre-stressing due to creep and shrinkage. Even when wires are cut, they

get shorten and stress induced in steel is lost to some extent.

Uses of pre-stressing : This method is best suitable for pre-stressing small size members such as railway

sleepers, boundary concrete pillars, electric poles, fence posts, beams, simply supported slabs, piles etc.

Post-tensioning Method

(i) Post-tensioning is a method of pre-stressing in which the tendon is tensioned after concrete has

hardened.

(ii) The beam is casted leaving conduct pipes for placing the tendons.

(iii) The ducts can be made in a number of ways by leaving corrugated steel tube in the concrete, by

providing steel spirals, sheet metal tubing, rubber hose etc. This duct remains in the structure.

(iv) Another procedure is that tendons are coated with grease or a bituminous material to prevent them

from becoming bonded with concrete.

Steps to be followed in post-tensioning method :

1. The metal hose generally referred to as the sheath or duct is placed inside the form work where

tendons are to be placed.

2. Concrete is poured in the form work and allowed to harden after curing.

3. After that tendons are placed in the ducts and anchored on one side.

4. Tendons are stressed by pulling with the help of jacks, the void between the tendon and the sheath

(or duct) is filled with cement grout under pressure. The tendons are now cut and tension is released.


115

RCC

DuctAnchors

Tendon

P

Hydraulic Jack

Duct Filled With Cement Grout

Arrangement in post –tensioned method

Advantages and Disadvantages of Post-Tensioning Method :

Advantages :

1. Both cast in situ and precast members can be constructed with this method.

2. Loss of pre-stress is less (15 %) as compared to pre-tensioning method (25%).

3. There is no limit of casting as the method can be applied at site also.

Disadvantages :

1. This method is costly because of added cost of sheathing and grouting.

2. Complications arise from friction of wires in the ducts, at the anchorage and in the jack itself at the

time of pre-stressing. '

Uses : Cast in situ or precast. construction can be done with post-tensioning method. Large span bridges

and buildings are possible.

DIFFERENCES BETWEEN PRE-TENSIONING AND POST TENSIONING METHODS

S.No. Pre-tensioning method Post-tensioning method

1. Method is best suitable for factory

production under controlled conditions.

Both cast in situ and pre-cast members can be

made.

2. Loss of pre-stress is more (i.e., 25 %). Loss of pre-stress is less (i.e., 15%) as compared

to pre-tensioning method.

3. Size of member is restricted because long

slender members are more difficult to

transport.

As the method is applicable for cast in situ

therefore any size of member can be casted.


116

RCC

4. This method is simple and economical. This method involves cost of sheathing and

grouting hence costly than pre-tensioning

method.

5. Minimum grade of concrete to be used is M

40.

Minimum grade of concrete to be used is M 30.

SYSTEMS OF PRE-STRESSING

A pre-stressing system comprises essentially a method of stressing the steel along with a method of

anchoring it to the concrete. The procedure of pre-stressing is same in ‗all the systems but difference

exists in providing tendons and end anchorage. A number of different systems and their patents for

tensioning and anchoring of tendons exists. The most commonly used post tensioning systems of pre-

stressing the concrete are :

1. Freyssinet system

2. Magnel Blaton system

3. Lee - Mc Call system

1. Freyssinet system : The Freyssinet system was the first to be introduced among the post tensioning

systems. It was developed by French engineer Freyssinet and is most widely used post-tensioning

method of pre-stressing.

High tension steel wires 5 mm to 8 mm diameter 8, 12 or 16 in number are arranged to form a group

into a cable with a spiral spring inside. The spiral spring provides the means for a proper spacing

between wires and thus provides a channel which can be cement grouted.

The complete arrangement is enclosed in a flexible tube or sheating of 32 gauge metal sheet . The

cable projects about 80 mm beyond the ends of the tube to have a grip of Wires in the tensioning

hydraulic jack.

The end anchorage consists of a cylinder of ordinary good quality concrete and is provided with

corrugations on the outer surface. It has a central conical hole and is provided with heavy loop

(spiral) reinforcement. This cylinder is called female cone .

Metal Sheathing

Wires

Helical Spring


117

RCC

View X-X

Corrugated Surface

Female Cone

Y

Y

X

X

Male Cone

View Y–Y

High Tension

Steel Wire

Tube for GroutingMale Cone

Female Cone

Sheathing

Prestressing Cable

End Anchorage in Freyssinet system

These cylinders are kept in position and the conical plugs are pushed into the conical holes after the cable

is tightened. The central hole passing axially through the plug permits cement grout to be injected through

it. Grout prevents the wires from slipping.

The conical plugs are pre cast reinforced concrete cast round a steel tube. The conical plug known as male

cone .

Advantages of Freyssinet System

1. The desired pre-stressing force is obtained quickly.

2. Securing the wires (tendons) is not expensive.

3. The precast reinforced concrete plugs may be left in the concrete and they do not project beyond the

ends of the member.

Disadvantages of Fryssinet System

1. The jacks required for post tensioning are heavy and expensive.

2. The greatest tensile force applied to a cable varies from 250 KN to 500 kN, which may not be

sufficient.

3. All the wires (tendons) are stretched simultaneously, hence the stresses in all the wires may not be

exactly the same.

2. Magnel Blaton System : This system of pre-stressing was developed by Prof. Magnel and

contractor Blaton, of Belgium.


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RCC

This method is based upon the following principles :

(i) Wires must be placed in a definite order and not at random.

(ii) At a time only two wires must be stretched to obtain uniformity of stress in all wires.

(iii) Equal spacing between all the wires in cable must be maintained to allow easy injection of cement

grout. Cement grout protect the wires from corrosion.

In this system, a cable of rectangular section is provided, which contains even number of wires upto 64,

using high tensile steel wires of 5 mm – 7 mm diameter.

These wires are arranged four in a group in a horizontal line. Horizontal and vertical spacing is

maintained by providing horizontal and vertical spacers @ 1-5 m c/c to keep the wires in correct position.

These spacers do not offer any appreciable frictional resistance to the wires.

(b) Horizontal Spacer (a) Vertical Spacer

The wires are anchored by wedging, two at a time into sandwich plates. The sandwich plates (or locking

plates) are about 25 mm thick and are provided with two wedge shaped grooves on its two faces. The

wires are taken in each groove and tightened. Then a steel wedge is driven between the tightened wires to

anchor them against the plate. Each plate can anchor upto eight wires.

Tendon

Wedge

Sandwich Plate

Steel Wedge

Distribution PlateSteelWedge

Steel Wedge

A complete anchorage system may consist of one to eight sandwich plates. The various sandwich plates

are arranged one above the other against a distribution plate.

Regular ducts can be casted at suitable places along the length of the member by introducing rubber cores

in the mould. The rubber cores are pulled out after 6-8 hours of concreting thus making ducts. The wires

are inserted in these ducts only at the time of pre-stressing.


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Advantages:

1. This method saves the cost of sheathing as ducts are formed by rubber cores.

2. Wires are placed in layers with proper horizontal and vertical spacing by providing spacers:

3. Only two wires are stretched at a time thus uniform stress is induced in every wire.

3. Lee-Mc Call System : This is a system of pre-stressing in which high tensile alloy steel bars (silico

magnesia steel) are used instead of wires with tensile strength varying from minimum 950 N/mm2 to

maximum of 2100 N/mm2. These rods (steel bars) are provided in 22 mm, 25 mm, 28 mm and 30

mm, diameter and in length upto 20 metres.

The anchoring of the bars is done by screwing special threaded units

End PlateConcreteMember

Washer

Nut

High Tensile Steel Rod

Nut

Bar

Enlarged detail of thread

Ducts are made in the member by means of rubber core, which are pulled out when concrete is still in

plastic stage. When the concrete gets hardened, steel rods are induced in the duct.

After a desired stress level, a nut is tightened at its screwed end to prevent its return to original length.

In this system, the member can be stressed and unstressed as required. Thus, the early losses due to

shrinkage and creep of concrete can be overcome by re-stressing the rod. This system is best suitable for

spans 12 m to 15 m.

Advantages :

1. This system is very simple.

2. The member can be stressed and de-stressed as desired.

3. Loss of pre-stress can be overcome by re-stressing the steel rods.

4. Equal stressing in bar is possible than using number of wires.

5. Stressing can be done in stages in this system by tightening the nut at any stage.

Disadvantages :

1. Large sized members can not be stressed. This method is best suitable for 12 m to 15 m span.

2. High pre-stressing intensities cannot be employed.

3. Large sized bars cannot be used in all members.

4. To stress a bar of greater diameter, heavy jacks are required.


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LOSS IN PRE-STRESS

The pre-stressing force applied to the member does not remain constant, but decreases with the passage of

time. The amount of pre-stressing force which gets reduced with the passage of time is known as loss of

pre-stress.

A loss of pre-stress will affect the stress distribution on the section of the member. The loss of pre-stress

may vary from 15% to 20% of the initial pre-stressing force. Loss of pre-stress is 18 - 20% in pre-

tensioning- system and 15-18% in post tensioning system. It is, therefore, necessary to estimate the

probable loss of pre-stress that may be incurred in a pre-stressed member.

Loss of pre-stress may take place in a pre-stressed concrete member due to many reasons.

Causes for loss of pre-stress :

1. Loss of pre-Stress [during the tensioning process) due to friction : There always exists a certain

amount of friction in the jacking anchoring system and on the walls of the ducts. The actual stress on

tendon is less than what is indicated by the pressure gauge. This type of loss occurs only in the post

tensioned members. The major losses clue to friction occur between the tendons and its surrounding

material (i.e., duct or spacer). These losses are due to length and curvature effect.

Length effect means friction met with in a straight tendon due to slight imperfection of the duct.

Curvature effect is due to the curved ducts.

To reduce the loss due to friction cables can be lubricated, metal tubes may be provided at ends and

stress may be applied from both ends.

2. Loss due to elastic deformation (shortening) of concrete : This loss takes place only in pre-

tensioned members. When pre-stress is transferred to concrete, elastic stress and strains are induced

it. Due to this, the concrete member gets shortened, along with shortening of steel, there by reducing

the pre-stress in steel.

The loss due to elastic shortening of concrete may range from 3% to 6% in pre-tensioned members

and 4% in post-tensioned members.

3. Loss due to shrinkage of concrete : Shrinkage in concrete is its contraction due as drying and

chemical changes. It is dependent upon quantity of water, type of aggregates used in the mix and

surrounding atmospheric conditions.

The loss of pre-stress due to shrinkage of concrete may range from 4% to 6% for post-tensioned

members and 3% to 4% for pre-tensioned members.


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RCC

4. Loss due to relaxation of steel : Under a constant strain, there is a loss of stress in steel which is

called relaxation. The amount of relaxation is dependent upon time, temperature and level of stress.

Loss of pre-stress due to relaxation of steel amounts to 2% to 8% of the initial stress.

5. Loss due to creep of concrete : Creep is a time dependent deformation which takes place due to

presence of stress in concrete or it may be defined as shortening of concrete due to continued

compression in concrete. Amount of creep shortening is concrete may be several times its initial

elastic shortening.

Pre-tensioned member experiences more loss of pre-stress due to creep of concrete than post-

tensioned members because transfer of pre-stressing generally takes place earlier in pre-tensioned

members.

Loss of pre-stress due to creep of concrete amounts to 5-10% .

6. Loss due to slippage of tendons and anchorage system : Pre-stressing force is transferred when

the jacks are released. Due to this a slight loss of pre-stress occur due to slippage of tendon and end

anchorage system. This slippage generally varies from 2 to 5 mm


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RCC

1. The critical section for two – way shear of

footing is at the

(A) Face of the column

(B) Distance d from the column face

(C) Distance d/2 from the column face

(D) Distance 2d from the column face

2. As per IS:456 – 2000 recommendations the

thickness of footing edge on soils should not

be less than

(A) 100mm (B) 120mm

(C) 150mm (D) 200mm

3. For a number of column constructed in a row

the type of foundation provided is

(A) Footing (B) Raft

(C) Strap (D) Strip

4. Normally counter forts in a retailing wall are

spaced at an interval of:

(A) 6 to 8m (B) 4 to 6m

(C) 2 to 3 m (D) 1 to 3m

5. Most commonly used method of pre-stressing

in industries is

(A) Hoyer‘s Method

(B) Freyssinet Method

(C) Magnel Method

(D) Lee McCall Method

6. The critical section for two way shear in an

isolated spread footing is at the

(A) Face of the column

(B) Distance 1.5d from column face

(C) Distance d from column face

(D) Distance d/2 from column face

7. Critical section for calculating bending

moment for a spread concrete footing of

effective depth d is gives by the plane at

(A) 75mm from column face

(B) (d/2) from column face

(C) D from column face

(D) column face

8. In reinforced and plain concrete footing resting

on soils, the thickness at edge shall not be less

than

(A) 25cm (B) 30cm

(C) 50cm (D) 15cm

9. Counter fort retaining wall is generally

constructed when height of the earth to be

retained exceeds

(A) 3 m (B) 8 m

(C) 6 m (D) 10 cm

10. The loss of prestress due to elastic shortening

of concrete is least in

(A) one wire pre-tensioned beam

(B) one wire post – tensioned beam



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RCC

(C) multiple wire pre-tensioned beam with

sequential cutting of wires

(D) multiple wire post –tensioned beam

subjected to sequential prestressing.

11. IS : 1343 : 1980 limits the minimum

characteristic strength of pre-stressed concrete

for post tensioned work and pretension work as

(A) 25 MPa, 30 MPa respectively

(B) 25 MPa, 35 MPa, respectively

(C) 30 MPa, 35 MPa respectively

(D) 30 MPa, 40 MPa respectively

12. In a reinforced concrete retaining wall, a shear

key is provided, if the

(A) shear stress in the vertical stem is

excessive

(B) shear force in the toe slab is more than

that in the heel slab

(C) retaining wall is not safe against sliding

(D) retaining wall is into safe against

overturning

13. A buttress in a wall is intended to provide

(A) lateral support to roof slab only

(B) lateral support to wall

(C) to resist vertical loads only

(D) lateral support to roof beams only

14. In a combined footing for two columns

carrying unequal loads, the maximum hogging

moment occurs at

(A) inside face of the heavier column

(B) a section equidistant from both the

columns

(C) a section having maximum shear force

(D) a section having zero shear force

15. The critical section for maximum bending

moment in the footing under masonary wall is

located at

(A) the middle of the wall

(B) the face of the wall

(C) mid-way between the face and the middle

of the wall

(D) a distance equal to the effective depth of

footing from the face of the wall

16. In case of pre-tensioned RC beams

(A) Shrinkage of concrete is of the order of

3 10–4

(B) relaxation of steel can be ignored

(C) only one wire can be stretched at a time

(D) even mild steel can be used for

prestressing

17. Prestressed concrete is more desirable in case of

(A) cylindrical pipe subjected to internal fluid

pressure

(B) cylindrical pipe subjected to external fluid

pressure

(C) cylindrical pipe subjected to equal

internal and external fluid pressures.

(D) cylindrical pipe subjected to end pressures

18. In a load – balanced prestressed concrete beam

under self load the cross – section is subjected

to

(A) axial stress

(B) bending stress

(C) axial and shear stress

(D) axial and bending stress


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RCC

19. Which one of the following statements is

correct?

(A) Web shear cracks start due to high

diagonal tension in case of beams with

their webs and high presetressing force.

(B) Shear design for a prestressed concrete

beam is based on elastic theory.

(C) In the zone where bending moment is

dominant and shear is insignificant,

cracks occur at 20° to 30°.

(D) After diagonal cracking, the mechanism

of shear transfer in a prestressed concrete

member is very much different from that

in reinforced concrete members.

20. The magnitude of loss of prestress due to

relaxation of steel is in the range of

(A) zero to 1% (B) 2 to 8%

(C) 8 to 12% (D) 12 to 14%

21. The ultimate strength of the steel used for

prestressing is nearly

(A) 250 N/mm2 (B) 415 N/mm

2

(C) 500 N/mm2 (D) 1500 N/mm

2

22. In post – tensioned prestressed concrete beam,

the end block zone is the zone between the end

of the beam and the section where

(A) no lateral stresses exist

(B) only longitudinal stresses exist

(C) Only shear stresses exist

(D) the shear stresses are maximum

23. The propagation of a shear crack in

presetressed concrete member depends on

(A) tensile reinforcement

(B) compression reinforcement

(C) shear reinforcement

(D) shape of the cross – section of the beam

24. In pre –tensioning scheme, pre-stress load is

transferred in

(A) a single stage process

(B) multi stage process

(C) either single stage or multi –stage process

depending upon the magnitude of load

transfer

(D) the same manner as in post – tensioning

scheme

25. In the conventional prestressing, the diagonal

tension in concrete

(A) increases

(B) decrease

(C) does not change

(D) may increase or decrease


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RCC

1. (C)

2. (C)

3. (D)

4. (C)

5. (B)

6. (D)

7. (D)

8. (D)

9. (C)

10. (B)

11. (D)

12. (C)

13. (B)

14. (D)

15. (C)

16. (A)

17. (A)

18. (A)

19. (B)

20. (B)

21. (D)

22. (B)

23. (D)

24. (A)

25. (B)

Answer key

METHODS OF RCC Chapter DESIGN 1 · 2019. 12. 12. · Design of RCC structures can be done either by...

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