Chapter-1INTRODUCTIONA Multi-storied building consists of multiplefloors with structural elements and non-structural elements. The main aim of the Multi-storied buildings is to increase the floor area of the building without increasing the area of the land that the building is built on, saving land and money.Functional designing of the building is very important since the requirements of dwellers vary from building to building. In view if this, an attempt has been made in this mini-project to know the basic principles involved in the planning, analysis, design and detailing.

1.1 Principal requirements of Structural Design

a) Safety: According to the safety requirement, the structure should be safe in carrying the design loads.b) Serviceability: According to the serviceability requirement, the deflections and cracks developed while carrying the loads should be within the permissible limits.c) Economy: According to this criterion, the structure should be economically built satisfying the safety and serviceability requirements.d) Aesthetic appearance: Complying with all the requirements of safety, serviceability and economy, the structure shall be aesthetically sensible.1.2 Stages in Structural Planning1. Positioning of columns2. Orientation Of Columns3. Location of beams4. Spanning of Slabs5. Layout and Planning of Stairs6. Type of Footings

1.2.1 Guidelines for Positioning of columns

a) Columns should be preferably located at or near the corner of the building and at intersections of walls because basically the function of the column is to support beams, which are normally placed under the walls to support them.

b) When the Centre distance between the intersection of walls is larger or where there are no cross walls, the spacing between the two columns will be governed by the limitations on span of the beam. Hence, large spans of the beam should be avoided for economy reasons and also from the considerations of controlling the deflection and cracks.

c) Columns should be avoided inside a big hall as it disturbs the functional utility and the appearance.

1.2.2 Guidelines for orientation of Columns

Generally, the columns provided in a building are rectangular with width of column not less than the width of supported beam for effective load transfer.a) According to requirements of aesthetics and utility, projection of column outside the wall should be avoided as they not only give bad appearance but also obstruct the usage of corners and create problems in placing furniture. The depth of column shall be in the plane of wall to avoid such offset.

b) In case of rigidly connected beams at rigid angle, moments are to be carried in additional to the axial loads, column should be oriented such that the depth of column is perpendicular to the major axis of building so as to get moment resisting capacity.

c) When the effective length of the column in one plane is greater than that in other plane at right angles, the greater dimension shall be the plane having larger effective length.

1.2.3 Guidelines for positioning of Beamsa) Beams shall be provided under the walls or below heavy concentrated loads to avoid these loads directly coming on to the slabs.

b) Beams are primarily provided to support slabs. Hence their spacing will be decided by the maximum spans of slabs.

1.2.4 Spanning of SlabsThe positions of supporting beams or walls will decide the span of the slab.

1.2.5 Layout of StairsThe type of stair case and its layout will be governed by the available size of staircase room and position of beams and columns along the boundary of staircase.

1.2.6 Choice of Footing TypeSuitable type of footing required for the structure will be chosen based on the applied loads and moments.

1.3 LoadingThis stage involves determination of various types of loads that are acting on the structures. The values of loads are taken from the relevant IS-codes.

Types of loads The loads and their relevant codes are as follows1. Dead loads (IS:875-1987, part-1)2. Live loads (IS:875-1987, part-2)3. Wind loads (IS:875-1987, part-3)4. Snow loads (IS:875-1987, part-4)

1.3.1 Dead Loads The permanent stationary loads are called dead loads. It includes:1. Self-weight2. Weight of floor finishes3. Weight of partition Walls, furniture, etc.,

1.3.2 Live loads or Imposed loadsNon-permanent or moving loads on a structure are called live loads. This type of loads includes traffic loads, weight of furniture, weight of people, etc.

1.4 Loading StandardsBased on IS: 875-1987, the loads considered in the present design are as followsa) The Dead loadsR.C.C: 25 kN/m3P.C.C: 24 kN/m3Brick masonry: 19kN/m3Floor finishes: 1 kN/m3

b) Live Loads On Floors: 4kN/m2On Roofs: 2.5kN/m2On Stairs: 5kN/m2

1.5 Design Standards of various components in a Building

Few thumb rules are followed while designing various rooms of residential buildings.

1.5.1 Living RoomAliving room is also known assitting room orlounge room orFront room is aroomfor entertaining, reading, or other activities. The living room should not be less than 14m2 with a minimum width of 3m to 3.15m.

1.5.2 KitchenAkitchenis aroomor part of a room used forcookingandalso for dining. For kitchen cum dining, minimum area recommended is 9.5 m2.

1.5.3 BedroomAbedroomis a privateroomwhere people usually sleep at night time or relax during the day. Now-a-days, house are with multiple bedrooms and a bathroom may be connected to the bedroom. In any case, the size of the bedroom should not be less than 12m2.

1.5.4 Bathrooms and water closetsAbathroomis aroom forbathingin containing abathtuband/or ashowerand optionally a toilet. A bathroom of size 1.45m X 1.5m is suitable with 1.5mX1.2m as minimum. Minimum size of water closets is 1.2mX0.9m.

Chapter-2ANALYSIS OF BUILDING FRAMESubstitute frame method This method assumes that the moments in the beams of any floor are influenced by loading on that floor alone. The influence of loading on the lower or upper floors is ignored altogether. The process involves the division of multi-storied structure into smaller frames. These sub frames are known as equivalent frames or substitute frames.The substitute frames are usually analyzed by the moment distribution method, using only one cycle of distribution. The substitute frames are formed by the beams at the floor level under consideration, together with the columns above & below with their far ends fixed. The distributed bending moments are not carried over far ends of the columns in this process. The moments in the columns are computed at each floor level independently & retained at that floor irrespective of further analysis.Table 2.1 Shear forces and bending moments in all the columnsColumn no.Shear force (kN)Bending moments (kN-m)

MxMy

1.121.8421.107-7.95

2.251.0834.14519.33

3.170.89-51.811.41

4.266.09-39.65-0.36

5.428.472.74-4.408

6.206.343.0651.34

7.79.611.1911.52

8.283.257.715.09

9.169.32-37.297-1.15

10.189.816.9923.93

11.268.52-3.12816.51

12.127.95-44.442.52

13.231.32-23.950.217

14.437.8-6.8250.069

15.237.3225.31.304

16.960.92-22.0834.62

17.2312.6-67.6534.145

18.860.2526.3211.26

19.298.2222.229.22

20.1456.88-32.9832.56

21.926.32.08-35.407

22.206.343.0651.371

23.428.472.74-4.408

24.266.09-39.65-0.36

25.79.611.1911.52

26.283.257.715.09

27.169.32-37.297-1.97

28.974.4413.17934.62

29.2156.79-64.65-25.518

30.1456.8231.26-22.62

31.237.3225.31.577

32.437.8-6.8250.069

33.231.32-23.950.217

34.189.816.9925.59

35.268.52-3.12816.51

36.127.95-44.442.52

Fig 2.1 Typical floor plan of the building

Chapter-3DESIGN OF STRUCTURAL MEMBERS

3.1 SLABSSlabs are thin flexural members forming floors and roofs of building and carrying distributed loads. A slab may be supported by beams or walls and may be used as the flange of a T or L beam. The common shapes of slabs are square, rectangular, triangular and circular. Slabs are designed by using the theories of bending and shear. The following Methods of analysis are commonly used for the design of slabs.Based on aspect ratio (ratio of longer span to the shorter span) and support conditions of slabs, slabs are classified as one-way slabs and two-way slabs.3.1.1 One-way SlabsIf the aspect ratio is greater than or equal to 2 or if the slab is supported only on two opposite sides, then the slab shall be designed as a one-way slab. In the one-way slab, bending action takes place only along the shorter span. About 95% of load is carried by shorter span and the rest is carried by the longer span. Hence, the main reinforcement is to be provided in the shorter direction. Steel is also provided in the transverse direction to distribute any unevenness that may occur in loading and for temperature and shrinkage effects in that direction. This steel is called distribution steel or secondary reinforcement. The main steel is calculated from the bending moment consideration and under no circumstances should it be less than the minimum specified by the code. The secondary reinforcement provided that, is usually the minimum specified by the code for such reinforcement.

3.1.2 Two-way Slabs

If the aspect ratio is less than 2 and is supported on four sides, then it is to be designed as a two-way slab. In a two-way slab, loads are carried to the supports along both the directions and bending action takes place in both the directions. Hence, reinforcement shall be provided along both the directions. That is why the steel provided in each of the 2 directions is called as main steel. Compared to one-way slab, the spans in a two-way slab are subjected to lesser bending moments since the load is distributed along both the directions. If the aspect ratio is less than 2 but supported on two opposite sides, the slab shall be designed as one-way slab only.

3.1.3 Design of Slab panel S7

Shorter Span, Lx = 3 m Longer Span, Ly = 3.6 mM20 grade concrete and Fe500 grade steel are used.fck = 20 MPa; Fy = 500 MPa => d = 0.1154 mD = 115.4 + 30 = 145.4Taking over all depth, D = 150 mmEdge Condition one short Edge Discontinuous

Loading:Self-Weight of slab = 0.15 x 25 =3.75 KN/M2Live Load =2.5 KN/M2Floor Finishers =1 KN/M2Total Load = 7.25 KN/M2

Factored Load = 1.5 7.25 = 10.875 KN/M2

Bending Moment:The bending moment co-efficients (x & y) for the slab panels are obtained from Table 26 (clauses D-1.1 and 24.1) of IS 456:2000 with respect to corresponding edge conditions.

Shorter Direction:Negative Moment on Continuous Edge, -Mx= x W Lx= 0.0438 10.875 x 32= 4.287 KN-m

Ast Required = 77 mm2 Providing 10mm dia bars, Spacing required = 652mm But Min Spacing to be provided = least of (300mm & 3d) = 300mm Hence Ast Provided = 167.55 mm2

Positive Moment at Mid Span, +Mx= x W Lx= 0.0328 x 10.875 x 32= 3.21 KN-m

Ast Required = 86.63 mm2 Providing 10mm dia bars, Spacing required = 623 mm But Min Spacing to be provided = least of (300mm & 3d) = 300mm Hence Ast Provided = 167.55 mm2

Longer Direction:Negative Moment on Continuous Edge, -My= x W Lx= (0.0486) 10.875 x 3.6652= 7.1 KN-m

Ast Required = 128.8 mm2 Providing 10mm dia bars, Spacing required = 390 mm But Min Spacing to be provided = least of (300mm & 3d) = 300mm Hence Ast Provided = 167.55 mm2

Positive Moment at Mid Span, +My= x W Lx= 0.0366 x 10.875 x 3.6652= 5.34 KN-m

Ast Required = 96.26 mm2 Providing 10mm dia bars, Spacing required = 522 mm But Min Spacing to be provided = least of (300mm & 3d) = 300mm Hence Ast Provided = 167.55 mm2

Check For deflection:Percentage of tension reinforcement, Pt = 100 = 0.13%

fs = 0.58500 = 250.74 MPaCorresponding modification factor from fig.4, clause 23.2.1 of IS 456:2000,K = 2 = 26= 52 d = 69.23mm < 115.4mmHence, slab safe against deflection.Fig 3.1 shows the reinforcement detailing of slab S7.

Table 3.1 Design details of other slabsSlabSpanMoments(in kN-m)Ast Req(in mm2 )Spacing req(in mm)Spacing provided(in mm)Ast provided(in mm2 )

S1Shorter-Mx7.96144.87347300167.55

+Mx6.06109.52459300167.55

Longer-My7.25131.6382300167.55

+My5.4498.1512300167.55

S2Shorter(one-way)+Mx6.352115.25681300167.55

S3Shorter-Mx4.1273.96680300167.55

+Mx3.1155.72902300167.55

Longer-My4.1273.96680300167.55

+My3.1155.72902300167.55

S4Shorter(one-way)+Mx4.784.8593300167.55

S5Shorter-Mx6.53118.22425300167.55

+Mx4.9488.92565300167.55

Longer-My5.03167.53300300167.55

+My3.2167.53300300167.55

S6Shorter (one-way)+Mx6.352115.25436300167.55

S7Shorter-Mx4.28777653300167.55

+Mx86.6386.63580300167.55

Longer-My7.1128.5391300167.55

+My5.4496.26522300167.55

S8Shorter-Mx2.5846.051091300167.55

+Mx1.8332.61541300167.55

Longer-My2.444.681125300167.55

+My1.81311621300167.55

3.2 Beams

A beam is a flexural member which is capable of withstanding its own weight, loads from respective slabs and wall loads by bending action.

Fig 3.3 Bending action of a beam3.2.1 Load calculations for beam B8 1.85mm0.8mm

3.6mm

Fig 3.4 Triangular and trapezoidal load distribution over a beam

Area = ( = 6.21 m2Load from slab = = 11.64 kN/mLoad from beam = 2.59 kN/mLoad from wall = 5.43 kN/mTotal = 29.49 kN/m

Table- 3.2 Details of loading on various beamsBeamLoading (kN/m)

B'131.39

B'228.575

B'334.28

B'427.03

B'531.605

B'632.34

B'744.25

B'829.49

B'929.49

B'1029.49

B'1120.60

B'1217.95

B'1327.50

B'1429.48

B'1528.98

B'1629.49

Vide fig 3.7 for the location of above beams in the plan

3.2.3. Design of beams B7, B16

29.49kN/m44.25kN/m

3.6m3.6m

Fig 3.5

Fixed end moments:FEMAB = = = -31.85 kN/mFEMBA = 31.85 kN/mFEMBC = = = - 47.79 kN/mFEMCB = 47.79 kN/mRelative stiffness:At joint A:KAB = = = 11.5 x mm3KAA1 = KAA2= = 13.8x mm3At joint B:KBA =11.5xmm3KBB1= = 2.02x mm3KBB2 = 2.02x mm3 At joint C:KBC = 11.5xmm3 KCC1 = = 13.8x mm3KCC2 = 13.8x mm3 Distribution factors:DFAB = = 0.294DFAA1 = DFAA2 = = 0.353DFBA = DFBC = = 0.425DFBB1 = DFBB2 = = 0.075DFCB == 0.294DFAB = DFAB = = 0.353

Table 3.3 Substitute frame method

AA1AA2ABBABB1BB2BCCBCC1CC2

Distrib-ution factors

0.3530.3530.2940.4250.0750.0750.4250.2940.3530.353

Fixed end momen-ts-31.8531.38-47.847.8

11.2411.249.3636.771.1951.1956.77-14.1-16.9-16.9

Carry over momen-ts3.384.68-7.033.39

-1.2-1.2-0.990.990.1760.1760.996-0.99-1.2-1.2

Total 10.0410.04-20.144.31.3711.371-47.136.13-18.1-18.1

On calculating net moments acting on AB and BC beams separately, we getNet sagging moment on AB = 15.58kN/mNet sagging moment on BC = 30.09kN/mSo Mu=30.09kN/m Mu/bd2 = = 0.36From sp16 we get area of steel requiredAst = 0.0846%Therefore, steel required = 116mm2So, we shall Provide 2 rods of 12 mm diameter.So, Ast provided = 226.25mm2 According to IS:456, as there is no shear acting on the beam, minimum shear reinforcement is provided .Shear reinforcement of 10 mm dia @300mm C/C spacing is provided.

Development length 1500mm 12 mm dia compressive reinforcement

600 mm 3600mm 600 mm 3600 mm 230mm 10 mm stirrups @ 500 C/C spacing

230mm main steel 4 bars @12mm dia600 mm

Fig 3.6 Reinforcement detailing of beam B7, B16

Fig 3.7

3.2 l

3.3 ColumnsA Column is a vertical compression member which transfers the loads of super structure to the foundation. The transfer of load may be directly from the roof or floor slabs through the columns to the foundation or indirectly through a beam to the columns and then to the foundation.All vertical members may not be termed as columns. Only those members whose effective length is more than 3 times the lateral dimension are called as COLUMNS and those members whose effective length is less than 3 times the least lateral dimension are called PEDSTALS or short columns.

Axially loaded columns are those in which the line of action of external load supported by a column coincides with the centroidal axis of the column. As per IS: 456-2000, all columns shall be designed for a minimum eccentricity equal to the unsupported length of columns/500 plus least lateral dimension/30 subject to a minimum of 20.The failure modes depend primarily on the slenderness ratio of the member which is in turn depends on the cross sectional dimensions, effective length, and support conditions of the member.

3.3.1 Classification of columns

Depending on slenderness ratio, columns are classified asi. Short columnsii. long columns or slender columns

3.3.1.1 Short columns: A column is considered as short when the slenderness ratio in both the directions (lex / D and ley /b) is less than 12.

3.3.1.2 Slender columns: If the above slenderness ratio in both the directions is greater than 12, then the column is called as long column where, lex ,ley effective length in respect of the major axis and minor axis respectively.D = depth in respect of the major axisb = width of the member

3.3.2 Grouping of columns

Since designing every column in a building is difficult and time consuming, columns are grouped according to their loads and the column is designed for maximum load in each group. The same design is adopted for all the columns in that group.

Table 3.4 Grouping of columns available the plan of the buildingGroup no.LOADS (kN)COLUMN NUMBERS

1300 -500C7,C25

2500 -1000C1,C3,C6,C10,C12,C22,C27,C34,C36

31000-1500C2,C4,C8,C11,C13,C15,C24,C26,C31,C33,C35

41500 -2000-Nil-

52000-2500C5,C14,C23,C32

3.3.3 Design of Columns in group-2 (C1,C3,C6,C10,C12,C22,C27,C34,C36)

Factored load =1000 KNSelf weight = 10.35 KNTotal load, PU =1000+10.35 =1010.35 KNMUX =51.8KN-mMUy =11.41KN-mEffective lengths, lex =3m = leylex/D = =3.25 20Ey min = + > 20 3.9+7.6 < 20 So, consider min eccentricity 20mmMoments:Mux min =1010.350.0239 =24.14 kN-mMuy min =0.0201010.35 =20.207 kN-mMU = 36.20 kN-mPu/fckbD = = 0.28MU /fckb = = 0.17d/D =50/600 =0.08take p =1%AS/bd 100 =1AS =Ast = 780mmNo of bars = 8 bars of 12mm diaP/fck =1/25 =0.04 Pu/fckbD = =0.29d/D =0.08MU / fckbd =0.15MX1 =0.15252306002 =310.5 KN-md/b =0.20P/fck =0.04Pu /fckbd =0.29Mu/ fckbD2 =0.095Mu = 0.095252302600 =75.38 Pu /Puz = 1010.35 /1800 =0.56 0.2 0.56 0.8 1 1.6 210.016+0.12 10.136 1 (safe)

230mm8 bars of 12 mm dia 600 mm 8 mm dia bars@200mm c-c spacing

Fig 3.8 reinforcement detailing of column

3.3.4 DETAILS OF OTHER COLUMNS

LOADCOLUMN NUMBERSMOMENTSClassification based on slenderness ratio

300-500C7,C25SHORT COLUMN

1000-1500C2,C4,C8,C11,C13,C15C24,C26,C31,C33,C35SHORT COLUMN

2000-2500C5,C14,C23,C32SHORT COLUMN

lelllllllly3.4 Footings

Reinforced concrete columns are supported by the footings which are located below the ground level and is referred to as the foundation structure. The main purpose of the footing is to effectively support the super structure by transmitting the applied loads, moments and other forces to the soil without exceeding the safe bearing capacity of the soil.The footings are designed according to IS: 456-2000 to resist the bending moments and shear forces developed due to the soil pressure.

3.4.1 Footing design

Lets consider SBC =450kN/m2Area of footing = = 2.46m2Net upward pressure = = 412.38 < 450MOMENTS:Mxx = 412.381.750.582 /2 = 121.38 kN-mMyy =412.381.400.572/2 = 93.7 kN-mMU limit =0.133fckbd2121.38106 =0.133251400d2d =158.52mmLets provide 250mmCheck for 2 way shear:Punching shear (VUD ) =P0[(lb)-2(0.23+d)(0.60+d)] = 412.38[(1.401.75)-2(0.48)(0.85)] =673.8 kNtVD = = = 1.01 kN/m2

Check:tVD < kst cks =(0.5 +0.23/0.60) 1so take ks = 0.88tc = 1.25kst c =1.15 Hence satisfiedArea of steel along shorter dimension: Cu=Tu0.36 fckbu =0.87fy Ast0.36251750Xu =0.87500AstXu = Xu =0.027 AstMu limit = 0.87fyAst[250-0.42Xu]121.38 =0.87500Ast[250-0.011Ast]121.38 =108750Ast -4.785Ast2Ast =1177.10mm6 bars of 16 mm diaArea of steel along longer dimension0.36251400Xu =0.87500AstXu =0.034Ast93.7 = 0.87500Ast[250-0.420.034Ast]Ast =897.06mm28 bars of 12mm dia

Check for one way shear:Pt = 8113.09100 /1400250 = 0.18%Shear force at the critical section:tv = 412.08(0.58 -0.359) = 189.69 = 189.691000 /3501400 = 0.270 kN/m2By intrapolation, 0.29 < tv tv (hence satisfied )Check for development: Ld = = 451.31 mm

6 bars of 16mm dia

8 bars of 12mm dia

Column of 230mmx600mm

Fig 3.9 reinforcement detailing of footing

3.5 Stair case

A stair case consists of a number of steps arranged in a series, with landings at appropriate locations, for the purpose of giving access to different floors of a building.

The width of a stair case depends on the purpose for which it is provided generally it will be around 1m for residential buildings and 2m for public buildings.

3.5.2 CalculationsFloor-floor height = 3m = 1.5m (for each flight) No. of steps = stepsNo. of threads= 9 9250=2250mm

d = mmProviding overall depth of waist slab = 200mmdeff = 200-25-6=169mm

Load calculations:Dead load from steps =kN/m2Dead load from waist slab = 5.55kN/m2Live load = 3kN/m2Floor finishers = 1.5kN/m2 Total = 11.8751.5 = 17.81kN/m2 Design BM = = 64.2kN-m64.2106=0.133251000d2 d=138.95mmBut deff = 169mm (hence ok) Cu = Tu 0.36251000Xu = 0.87500Ast Xu = 0.048AstM u =?64.2106 = 0.87500Ast64.2106 =73515Ast8.77Ast28.77Ast273515Ast+64.2106 =0 Ast = 990.27 991mm2 Spacing: S = S = 114.14mmSo providing spacing of 100mmDistribution steel =Spacing =As spacing should not exceed =300 mm S = 300mm

Chapter-4CONCLUSION

A five storied residential building has been analyzed and designed satisfying all the design requirements as per Indian standard specifications. The Dead and Imposed load are considered as per IS: 875-1987 (part 1& part 2). All Slabs, Beams, Columns, Footings, Staircase are designed according to the Indian standard code IS: 456-2000. The structure is analyzed using Substitute frame method and subsequently the moments and shear forces are calculated. The slabs are designed based on these loads. Both One-way slabs and two way slabs were designed as per the aspect ratio. Then beams were designed based on the loads from slabs. As the beams were not subjected to greater shear forces, only minimum amount of shear reinforcement specified in code was provided. The columns were grouped based on the load transferred onto them in intervals of 500KN. Then columns were designed for maximum load in each group. This design is applicable for all the columns in that group. Then footings were designed. All the footings were designed as isolated footings as there was no space problem for considering other types of footings.

Chapter-5REFERENCES

1. PLAIN AND REINFORCED CONCRETE -CODE OF PRACTICE IS 456:2000 (Bureau of Indian Standards, New Delhi)

2. CODE OF PRACTICE FOR DESIGN LOADS for Buildings and structures, part-1 dead loads: IS 875(part I):1987

3. CODE OF PRACTICE FOR DESIGN LOADS for Buildings and structures (part-II) live loads: IS 875(part 2):1987

4. SP 16-1980 DESIGN AIDS FOR REINFORCED CONCRETE TO IS 456:1978 (Bureau of Indian Standards, New Delhi)

5. SP 34-1980 DESIGN AIDS FOR REINFORCED CONCRETE TO IS 456:1978 (Bureau of Indian Standards, New Delhi).

6. Limit State Design of Reinforced Concrete by P.C.Varghese, PHI, New Delhi.

5