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INTRODUCTION

Buildings constitute a part of the definition of civilizations, a way of life advanced by the

people. The construction of buildings should be looked upon as a process responded to human

requirements rather than as a product to be designed and built a great expense.

Due to rapid increase in the urban population in last two decades, it has been noticed during

recent years, there has been a sharp increase in the construction of multi - storied building for

residential purpose, schools, offices etc in big and developing cities. In India buildings of four

stories and higher are often considered as multi – storied structures. One of the important reasons

given in favour of vertical development is the increasing land price in urban areas.

This project concerns with the structural analysis and designing a residential complex

proposed to be built in Rajahmundry town.

This complex has G+4 floors. Each floor is divided into five flats and each flat having two

bedrooms, one hall, dining and kitchen and will cater people of same income groups, the

following table shows the area wise break-up of each room.

Master bed room = 12.87 m2

Bed room = 10.24 m2

Dining room = 10.81 m2

Living room = 11.84 m2

Kitchen = 10.25 m2

Parking facilities are provided in the ground floor separately.

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Each that is provided with all the basic amenities and requirements like two bedrooms

with attached baths, a living cum dining room and a kitchen, as described above, corridor is to be

provided to each bedroom and also the back of every kitchen room. Sufficiently large doors and

windows in good number are provided for better ventilation. A special feature of this building is

the provision of ventilation from all sides as possible i.e., from bath rooms and bed rooms. Each

flat has got main entrance from a common entrance lobby thus take care not to isolate any flat as

a protection against burglary at the same time maintaining sufficient privacy. The building is

provided with a spacious staircase to avoid over – crowding.

All the exterior walls are one brick-wall while all the partition walls are half brick walls.

We propose use M20 concrete for slabs and columns and Foundation and Fe415 bars for the main

reinforcement and fe250 bars for the distribution reinforcement.

Regarding its structural features, it is rectangular building. All the columns are arranged

in such a way that they form typical frames in length and width direction. The longitudinal and

transverse frames are analyzed using the substitute frame method of analysis.

The limit state method of collapse using IS:456-2000 has been adopted for the design

of all structural components like slabs, beams, columns and foundations.

Thus we feel that structure fulfils the basic requirements of good designing and

planning by using effectively every inch of space available and also justifies its name by

increasing the ‘BEAUTY’ of landscape.

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INTRODUCTION TO LIMIT STATE DESIGN

Before the last two decades the structural designers of reinforced concrete were

concerned more with safety against failure of the structure than with durability under service

conditions. The theoretical calculations for design of R.C.C structure were based on classical

elastic theory, fictitious modulus of Elasticity of concrete and permissible working stresses,

recent developments lead to limit state design otherwise called strength and performance criteria

based on the recommendation of International code of practice different countries started

changing their codes introducing limit state design for the design of reinforced concrete

structures.

India introduced limit state design for the design during the revised IS:456-2000 along

with working stress method of design. IS:456-2000 permits design of R.C.C structural design by

both working stress method and limit state method. As has happened in the other scientific field

new ways of thinking replace old ways. In scientific circles this is generally referred as Paradigm

shift limit state design should there fore looked upon as a paradigm a better way of explaining

certain aspects reality and new way us of thinking about old problems. Thus the design should be

learnt and taught with own philosophy and not as an extension of old elastic theory.

Since the rational approach to design of reinforced concrete did not mean simply

adopting the existing method of elastic and ultimate theories. New concepts with a semi

probabilistic approach to design were found necessary the proposed new method had to provide a

framework, which would allow a design to be economical and safe. The new philosophy of

design was called the limit state method of design.

CONCEPT OF LIMIT STATES

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In the method of design based on limit state concepts the structure shall be designed to

withstand safely all loads to act on it throughout its life, it shall also satisfy the serviceability

requirements such as limitations on deflection and cracking. The acceptable limit for the safety

and serviceability requirements before failure occurs is called limit state. The aim of the design is

to achieve acceptable probabilities that the structure will not become unfit for the use for which it

is intended, i.e., that it will not reach a limit state.

All relevant limit state shall be considered in design to ensure an 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.

For ensuring above objective, the design should be based on characteristic values for

material strengths and in the loads to be supported, the characteristic values should be based on

statistical data; if available where such data are not available they should be based on experience.

The design values are derived from the characteristic values through the use of partial safely

factors, one for material strengths and other for load. In the absence of special consideration

these factors have values given is IS:456 – 2000 according to the material the type of loading and

the limit state being considered.

Design basis:

Limit state method based on IS:456-2000 using design aids SP: SI Units. Emphasis

is given on Limit state design method in this project work (a brief description on LSD

method is appended in this project).

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LOAD FACTORS AND PARTIAL SAFETY FACTOR

Ultimate load theory is based on the assumption that a structure reaches a collapse

condition forming a mechanism when a certain load is applied. The load factor has been

judiciously selected giving due considerations to the various factors contributing the failure. The

load factor is used in estimating ultimate loading.

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PARTIAL SAFETY FACTORS:

Partial safety factor for material, strength should account for,

Possibility of deviation of the strength of material.

Deviation of structural dimensions.

Deviation of structural dimensions.

Accuracy of the calculations procedure.

Risk to like and economic consequences.

When assuming the strength of a structure for limit state of collapse.

Value of partial safety factors should be taken into account for,

Partial safety factor for concrete = 1.5

Partial safety factor for steel = 1.15

Partial safety factors for loads should account for

Unusual increasing loads beyond that using for deriving characteristic values.

Unforeseen stress distribution.

In accurate assessment of the effect of loading.

Partial safely factors of loads under different conditions are given in clause 35.4 of

IS:456 – 2000.

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LIMIT STATE OF COLLAPSE:

The limits state of collapse of collapse or the structure or part of the structure could be

assumed from rupture of one more critical section and from backing due to elastic or plastic

instability (including the effects of sway where appropriate) or overturning. The resistance to

bending, shear, torsion and axial loads at every section produced by the probable most

unfavourable combination of loads on the structure using the appropriate partial safety factors.

LIMIT STATE OF SERVICEABILITY

Control of deflection:

The deflection of a structure or part there of shall not adversely affect the appearance or

efficiency of the structure or finished or finished partitions the deflection shall generally be

limited to the following.

a. The final deflection due to all loads including the 4 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.

c. Occurring after erection of partitions and the application of finished.

d. Should not normally exceed “span/350 or 20mm” whichever is less.

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LIMIT STATE OF CRACKING:

Cracking of concrete should not adversely affect the appearance or durability of structure.

The surface for width of cracks should not, in general, exceed 0.3mm surface width of cracks at

points nearest to main reinforcement should not exceed 0.004 times the nominal cover the main

reinforcement.

CHARACTERISTICS, DESIGN VALUES AND PARTIAL SAFETY FACTORS:

Characteristic strength of materials:

The term ‘characteristic strength’ means that value of the strength of material below which, not more than 5% of the test results are expected to fall.

Characteristic loads:

The term ‘characteristic loads’ means that value of load, which has a 95% probability of not being exceeded during the life of structure.

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DESIGN VALUES:

Materials Used:

The design strength of materials, fd = (f/Ym)

Where f : characteristic strength of material and

Ym : Partial safety factor appropriate to the material and the limit

State being considered.

Loads : The design load ‘f’ is given by

Fd = F (Yf)

Where F : characteristic load and

Y : Partial safety factor appropriate to the nature of loading and

the limit state being considered.

Partial safety factors:

1. Y = 1.5 for concrete

2. Y = 1.15 for steel

LoadCombination

Limit state ofcollapse

Limit state ofserviceability

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

D.L + L.L 1.5 1.5 1.0 1.0 1.0 ---

D.L + W.L 1.5 --- 1.5 1.0 --- 1.0

D.L + L.L + W.L 1.2 1.2 1.2 1.0 0.8 0.2

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LIMIT STATE OF COLLAPSE:

Flexure:

Assumptions:

1. Plane sections normal to the axis remain plane after bending.

2. The maximum strain in concrete at the outermost compression fiber is taken as 0.0035

in bending.

3. For design purposes, the compressive strength of concrete in the structure shall be

assumed to be 0.67 times the characteristic strength.

4. The partial safety factors Ym shall be applied in addition to this.

Stress-Strain curve in Limit State Design

Stress block parameters

Area of stress block = 0.36 fck Xu

Depth of cement of compressive force from the extreme fiber in compression = 0.42 X

Xu : Depth of neutral axis.

Fck : characteristic compressive strength of concrete.

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The tensile strength of concrete is ignored.

The limiting values of depth of neutral axis for different grades of steel are given by

Fy (Xu max/d)

250 0.53

415 0.48

500 0.46

MATERIALS:

Concrete: We propose to use M mix concrete for slabs and beams, columns and foundations.

Steel: We proposed to use HYSD bars for main and distribution reinforcement. M.S. bars for shear reinforcement.

Details of materials adopted.

Dead loads:

1. Unit weight of concrete 25KN/m3

2. Unit weight of brick work 19KN/m3

3. Floor finishes 1 KN/m2

Live loads:

1. Living area 2 KN/m2

2. Corridor 2 KN/m2

3. Stair case 5 KN/m2

4. Safe bearing capacity of soil 150 KN/m2

INTRODUCTION TO STRUCTURAL ANALYSIS:

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Structural analysis deals with the behaviour of structure in the given loading conditions.

Depending upon the nature offloading, the structure may respond in number of ways. The

structure may deform statistically, might yield and may vibrate or buckle. Structures carrying

static loading can be classified as statically determinate and statically indeterminate structure. If

all reactions and internal forces in a structure can be found using the equilibrium conditions

along that is,

∑Fx =0, ∑Fy =0, ∑Fz=0, ∑My =0, ∑Mz =0.

Then the structure is statically determinate, if not it is statically indeterminate of

redundant various methods popularly used for analysis includes

Moment distribution method

Kani’s method

Substitute frame method

Slope d/eflection method

Matrix method

In this project two-step moment distribution method is used for the analysis of structure.

In moment distribution method only apart of the frame that is a floor connected above and below

with columns is considered. The columns may be assumed to be fixed, hinged or partially

restrained depending upon the rigidly.

The bending moments can be determined by using any one of the following methods.

Slope deflection method.

Moment distribution method

Building frame formulae

Kani’s method.

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MOMENT DISTRIBUTION METHOD:

The moment distribution method also called as the Hardy cross method, provides

convenient means of analyzing statically indeterminate beams and frames by simple hand

calculations. This general, involves artificially restraining temporarily all the joints against

rotation and writing down the fixed end moments for all the members. The joints are then

released one by one in succession at each released joint. The unbalanced moments are distributed

to all the ends of the members meeting at that joint. A certain fraction of these distributed

moments are carried over to the far end of the members. The released joint is again restrained

temporarily before proceeding to the next joints completed. This completes one cycle of

operations. The process is repeated for number of cycles till the values obtained within the

desired accuracy.

POSITIONING OF BEAMS

Following are some of the guiding principles for positioning of beams:

Beams shall normally, be provided under the walls or below a heavy concentrated load

to avoid these loads directly coming on slabs.

Since beams are primarily provided to support slabs, its spacing shall be decided by the

maximum spans of slabs.

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DESIGN OF BEAMS

Introduction:

Beams are structural elements carrying transverse external loads that cause

bending moment and shear force along their span. These are general supported on bearing walls

or columns and are subjected to roof or floors loads and are reinforced to take up stresses.

The reinforced concrete breams in which the steel reinforced is placed only on

tension side are known as singly reinforced beams. The failure of singly reinforced beams many

be caused in one of the two ways either in compression or in tension. In case the cross-sectional

area of the steel bars provided for reinforcement is moderate or small, at some values of the load,

the steel bars will attain their yield point. When it yields, the depth of neutral axis reduces. That

is the strength increases in the lever arm and the moment of resistance in the remaining

compressions zone of the concrete increases to such a degree that the crushing of the concrete

(the secondary compressions failure) begins only at a load only slightly larger than that which

caused the steel bars to yield. Such a yield failure at the steel bars is preferred as it is gradual

with adequate working of collapse.

In case the cross-sectional area of steel reinforcing bars is large or the normal

cross-sectional area of steel reinforcing bars of high strength is provided, the compression

strength of concrete will be exhausted prior to the steel bars start yielding. In such a case, the

depth at neutral axis increases considerably. It causes an increase in the compressive force. The

failure of concrete in compression occurs by crushing. The crushing failure of concrete is

sudden, explosive in nature and occurs without warning and hence it is not preferred.

If a beam is limited in cross-section and ending moment is more than the moment

of resistance of the singly reinforced section, the concrete can develop the compressive force to

resist the given bending moment. In such a case, the beams are strengthened by providing

reinforcement in compression zone and the resulting section is called doubly reinforced beam.

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For Beam (B1):

1. Load on beam per metre run = 49KN/m

2. Effective span = 7m

3. Effective width of flange:

bf = ( lo /6) + bw +6Df

Here lo = 7m

bw = 23mm

Df = 100mm

bf =7000/6 +230+ 6(100) = 1166.6 +230 +600 = 1996.66

≈ 2000mm

Maximum c/c of beam width= 5820mm

So, Effective width of flange=2000mm is satisfactory.

4. d= Depth =span/ 15 =7000/15 =466mm ≈ 450mm

Overall depth =d + cover =450 + 40 = 490mm

So, effective depth =450mm, b = 250mm

5. Maximum bending moment =wl2 / 8

= 49x72/ 8 =1300.12 KN-m

Bending moment = 81.03KN-m from analysis.

6. Let us assume the neutral axis lies in the flange,

0.36 fck bf X = 0.87fy Ast

X = (0.87.yf .Ast ) / ( 0.36 fck bf )

= (0.87x450xAst ) / (0.36x20x2000) = 0.0271Ast

7. Tension:

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B.M. = 0.87 fy Ast (d – 0.42X)

81.03x106 = 0.87x450xAst (450- (0.42x0.0271Ast ))

= 391.5Ast (450 – 0.0113 Ast )

Ast = 465.37 mm

X = 0.0271Ast =0.0271x465.37 =12.6mm < 216mm OK.

And Neutral axis lies in the flange.

Use 6 – 10mm ϕ bars (A=st =471 > 465)

8. Checks:

Minimum area of tension steel = Ao = (0.85. bw .d)/fy

Ast = 0.85x230x450/415 = 211.98mm2 < 471mm2 Ok

Maximum area of tension steel

At =0.04 bw D

= 0.04 x230x490 = 4508mm2 >471mm2

Hence safe.

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For Beam (B2):

1. Load on beam per meter width =45.28KN/m

2. Effective span = 7.01m

3. Effective width of flange

bf = lo / 6 + bw + 6Df

Where lo = 7.01m = 7010mm

bw = 230mm

Df = 100mm

bf = 7010/6 +230 + 6(100) = 1998.33 ≈ 2000mm

Maximum c/c of beam width =5820mm

So, effective width of beam =2000mm safe.

4. Depth required:

d = depth = Span/15 = 7010/15 = 467.33 ≈ 450mm

Overall depth = 450mm + 40mm cover = 490mm

5. Maximum bending moment = wl2 / 8.

= 45.28x(7.01)2 / 8Bending moment = 78.72 KN-m from analysis.

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6. Let us assume that neutral axis lies in the flange.

0.36 fck bf X = 0.87 fy Ast

= 0.87 fy Ast / 0.36 fck bf

= ( 0.87x450xAst ) / (0.36x20x2000)

X =0.0271 Ast

7. Tension:

Bending moment = 0.87fyAst (d-0.42x)78.72 x 106 = 0.87 x 450 x Ast [ 450 – (0.42 x 0.027Ast) = 391.5 Ast [450-0.0113Ast]Ast = 451.9 mm2

X = 0.0271 Ast

= 0.0271 x 451.9mm2

= 12.24 < 216

Neutral axis lies in the flange.

Use 6 -10 mm. ф bars

Ф (Ast = 471 > 451.9 mm2)

8. Check:

Minimum area of tension steel

Ao = 0.85 bw d/fy

= 0.85 x 230 x 450 / 415

= 211.98 mm2 < 477 mm2

Maximum area of tension steel

At = 0.04 bw D

= 0.04 x 230 x 490

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= 4508 mm2 > 471 mm2 OK

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For Beam (B3):

1. Load on beam per meter run = 39 kN/m

2. Effective span = 3.96 m

3. Effective width of flange

bf = lo/6 + bw + 6Df

lo = 3960 mm

bw = 230mm

Df = 100mm

bf = 3960/6 + 230 + 6(100)

= 1490 ≈ 1500 mm

Maximum center to centre of beam width = 5820mm

So, effective flange width = 1500mm

4. Depth, (d) = span/15

= 3960/15 = 264mm ≈ 260mm

Overall depth = d + cover

= 260 + 40 = 310mm ≈ 300mm.

So effective depth = 260mm, b = 230mm

5. Maximum bending moment = wl2/8

= (39 x 3.962)/8

= 76.44 kN-m

Bending moment from analysis = 54.14 kN-m

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6. Let us assume the neutral axis lies in the flange

0.36 fck bf X = 0.87 fy Ast

X = (0.87 x 450 x Ast) / (0.36 x 20 x 4500)

= 0.03625 Ast

7. Tension:

Bending moment = 0.87fyAst (d-0.42x)

54.14 x 106 = 0.87 x 415 x Ast [ 260 – (0.42 x 0.03625 Ast)

Ast = 549.56 mm2

X = 0.03625 Ast

= 0.03625 x 549.6mm2

= 19.923 < 216 OK

Neutral axis lies in the flange.

Use 8 -10 mm. ф bars Ast = 628.31 mm2

8. Check:

Minimum area of tension steel

Ao = 0.85 bw d/fy

= 0.85 x 230 x 260 / 415

= 122.4 mm2 < 628.31mm2 OK

Maximum area of tension steel

At = 0.04 bw D

= 0.04 x 230 x 300

= 2760 mm2 OK

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For Beam (B4):

1. Load on beam per meter run = 49 kN/m

2. Effective span = 5.82 m

3. Effective width of flange

bf = lo/6 + bw + 6Df

lo = 5820 mm

bw = 230 mm

Df = 100 mm

bf = 5820/6 + 230 + 6(100)

= 1800 mm

Maximum center to centre of beam width = 5820mm

So, effective flange width = 1800mm

4. Depth, (d) = span/15

= 5820/15 = 388 mm ≈ 400mm

Overall depth = d + cover

= 400 + 40 = 440mm

So effective depth = 440mm, b = 230mm

5. Maximum bending moment = wl2/8

= (49 x 5.822)/8

= 207.46 kN-m

Bending moment from analysis = 89.49 kN-m

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6. Let us assume the neutral axis lies in the flange

0.36 fck bf X = 0.87 fy Ast

X = (0.87 x 415 x Ast) / (0.36 x 20 x 1800)

= 0.0278 Ast

7. Tension:

Bending moment = 0.87fyAst (d-0.42x)

89.49 x 106 = 0.87 x 415 x Ast [ 400 – (0.42 x 0.0278 Ast)

Ast = 631 mm2

Use 6 -12 mm. ф bars Ast = 678.50 mm2

8. Check:

Minimum area of tension steel

Ao = 0.85 bw d/fy

= 0.85 x 230 x 400 / 415

= 188.43 mm2 OK

Maximum area of tension steel

At = 0.04 bw D

= 0.04 x 440 x 230

= 4048 mm2 OK

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SYMBOLS USED

A : Area

Ast : Area of Tensile reinforcement

Asc ; Area of Compression reinforcement

b : Breadth of beam/shorter dimension of a rectangular column

D : Overall depth of the beam/sla/longer dimension of rectangular column

d : Effective depth of a beam/slab

dc : Depth of compression steel from highly compressed face

d' : Effective cover in Beams and Columns

e : Eccentricity

fck : Characteristic strength of concrete

fy : Characteristic strength of steel

Ld : Development length

l : Length of column

lef : Effective span of beam/slab

M : Bending moment

Mu : Factored bending moment

P : Axial load on a compression member

Pu : Factored axial load

S : Spacing of stirrups

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V : Shear force

Vu : Factored shear force

Vus : Net factored shear force to be resisted by the stirrups

W : Distributed load per unit area

Wd : Distributed imposed load per unit area

Wl : Distributed load per unit area

τc : Allowable shear stress of concrete

τcmax : Maximum allowable shear stress of concrete

τv : Nominal shear stress of concrete

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BIBLIOGRAPHY

1. Limit State Design - A.K.Jain

2. Theory of Structures - S. Ramamrutham

3. Design of Multi-Storey

Residential Building - Karve & Shah

4. Handbook of Reinforced

Concrete Design - Karve

5. I.S.Code 456-2000 - BIS Publication

6. SP – 16 Design Aids for - BIS Publication

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