building design
TRANSCRIPT
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CHAPTER-1
INTRODUCTION
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1.1 BUILDING: Any structure for whatever purpose and of any material and every part of them whether for human or any other purpose, including all the structural elements like foundations, masonry, roofs, etc., with all the services like water closet, bathroom, staircase, etc., is termed as building. Building does not only refer to house but also implies the masonry the building is providing for sheltering the human beings.
Building can be classified based on the occupancy and the type of construction. On the basis of occupancy, the buildings are classified as:
1. Residential building 2. Educational building 3. Institutional building 4. Assembly building 5. Mercantile building 6. Business building 7. Industrial building 8. Storage building 9. Hazardous building
1.1.1. Residential building: Residential building includes all the building in which the food and lodging accommodation is provided for normal residential purposes with lodging room, water closet and bath are included for small family, private dwellers, dormitories, apartments houses(flats), hotel and hostels.
1.1.2. Educational building: This building includes any building used for schools and colleges.
1.1.3. Institutional building: These buildings include hospitals and sanatoria, custodial homes such as homes in firms and orphanages and penal institutions such as jails, prisons, mental hospitals and reformatories.
1.1.4. Assembly building: These are buildings where group of people congregate or gather for amusements, recreation, social, religious, patriotic, civil, travel and similar purposes, theatres, motion pictures houses, assembly halls, auditorium, exhibition halls, museums, places of worships, club rooms, etc., are such buildings.
1.1.5 Mercantile building:
These buildings are used for the transactions of business.
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1.1.6 Business building: These buildings are also used for the transactions of business.
1.1.7 Industrial building:
These are the buildings where products or materials of all kinds and properties are fabricated, assembled or processed. Assembly plans laboratories, power plants, dry cleaning plants, refineries, etc., are the example of such buildings.
1.1.8 Storage building: These buildings are used primarily for the storage or sheltering of goods, ware or merchandise. Cold storage, ware houses, freight depots, transit sheds, store houses, etc., are the example of such houses.
1.1.9 Hazardous building: These are buildings which are used for storage, handling and manufacturing of highly combustible or explosive materials.
Buildings can be classified, based on the construction as:
1. Heat Resistance Building 2. Fire Resistance Building 3. Sound Proof Building, etc.
Before constructing any type of building, each building needs a special type of planning as per their functions. Similarly it needs a special and different treatment.
1.2 PLANNING OF BUILDING:
Apart from the fact that building must be designed and planned according to the functional requirement. The basic principles have been enunciated or broad lined only and may be applied to the problem on its industrial merits. These natures are not as rigid as of nature. General plan is done with respect to some natural point around its location. It is done according to its natural surrounding condition such as geographical feature of the area such as hilly, rocky or plains, climate conditions such as warm or cold, direction of sun rays, wind, etc. Before planning any type of structure of the building the area should be favorable for that structure. More attention should be taken in soil test in order to find the bearing capacity of the soil as the foundation is heavy for structure of multistoried building. In addition, there are certain principles of planning which should be regarded while planning the building. These are:
1. Aspects 2. Prospect
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3. Furniture requirement 4. Roominess 5. Grouting 6. Circulation 7. Privacy 8. Sanitation 9. Elegance 10. Economy 11. Flexibility 12. Practical consideration
1.3 MULTISTORIED BUILDING
Reinforced concrete building consists of floor slabs, beams, girders and columns continuously placed to form a rigid monolithic system. A continuous system leads to greater redundancy, reduced moments and distributes the load more evenly. The floor slab may rest on a system of interconnected beams. Thus a building frame is a three dimensional structure or space structure. It is idealized as a system of interconnected two-dimensional vertical frames along the two mutually perpendicular horizontal axes for analysis.
The degree of sophistication to which a structural analysis is carried out depends on the importance of the structure. A wide range of approaches are available which can be carried out manually or with the aid of pocket calculators to more refined techniques involving computer solutions. In this project, manual analysis is done using methods such as moment distribution and portal method. We separate the structural system into two load transmission mechanisms, viz. gravity load resisting and lateral load resisting, although, in effect, these two systems are complimentary and interactive. As an integrated system, the structure must resist and transmit all the effects of gravity loads and lateral loads acting on it to the foundation and the ground below.
1.4 LOADS
The loads acting on the structure are due to dead loads (due to self weight), live loads (due to occupants, water in tank, and maintenance on the roof etc.), wind loads (acting on the exposed surface areas of the tank, staging etc.) and seismic loads (due to earthquake induced ground excitation). Our project work has not been designed for wind loads since earthquake loads exceed the wind loads.
DEAD LOADS
The dead loads on a frame is calculated floor wise and consists of weight of floors, girders, partition walls, false ceilings, parapets, balconies, fixed or permanent equipment and half the column above and below a floor. The load acting on a column is calculated from all the beams framing into it.
LIVE LOADS
The magnitude of live loads depends upon the type of occupancy of the building. IS: 875 (Part 2) -1987 has specified certain minimum values of live loads (or imposed loads) for specific purposes. The live load distribution varies with time. Hence, each member is designed for the worst combination of dead and live loads.
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SEISMIC LOADS
Earthquake or seismic load on a building depends upon its geographical location, lateral stiffness and mass and is reversible. Its effect should be considered along both axes of the building taken on at a time. A force is defined as the product of mass and acceleration. During an earthquake, the mass is imparted by the building whereas the acceleration is imparted by the ground disturbance. In order to have a minimum force, the mass of the building should be as low possible. There can be no control on the ground acceleration being an act of nature. The point of application of this inertial force is the centre of gravity of the mass on each floor of the building. Once there is a force, there has to be an equal and opposite reaction to balance this force. The inertial force is resisted by the building and the resisting force acts at the centre of rigidity at each floor of the building. The seismic forces are calculated in accordance to IS: 1893 (Part I) - 2002. The wind load and earthquake loads are assumed not to act simultaneously.
1.5 DESIGN METHODOLOGY ADOPTED
The design philosophy that has been adopted in this project is the limit state method. The philosophy of the limit state method of design represents a definite advancement over the traditional design philosophies. Unlike working stress method, which is based on calculation on service load conditions alone and unlike ultimate load method, which is based on calculation on ultimate load conditions alone, Limit state method aims for a comprehensive and rational solution to the design problem by considering safety at ultimate loads and serviceability at working loads.
Limit state design has originated from ultimate or plastic design. The object of design based on the limit state concept is to achieve an acceptable probability that a structure will not become unserviceable in its life time for use for which it is intended, that is it will not reach limit state. A structure with appropriate degrees of reliability should be able to withstand safely all loads that are liable to act on it throughout and it should also satisfy the serviceability requirements such as limitations on deflection and cracking. All relevant limit states must be considered in design to ensure an adequate degree of safety and serviceability.
IS: 456-2000 and Design Aid to IS: 456-1978 (also known as SP 16) is followed in this regard to ensure this design philosophy.
1.6 PHASES OF THE PROJECT
For the considered structural system, the design problem consisted of the following steps:
• Idealization of the structure for analysis
• Estimation of loads • Analysis of the idealized structural model to determine axial loads, shear and bending
moments. • Design of various structural elements. • Detailed structural drawing and schedule of reinforcing bars.
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CHAPTER-2
BUILDING PLAN
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LINE DIAGRAM OF BUILDING PLAN
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9
Frame of the Building
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ASSUMPTIONS
Dead Load As per IS 875 (Part 1) : 1987
Live load As per IS 875 (Part 2) : 1987
i. Terrace: 1.5 KN/m2
ii. Typical floors: 2.0 KN/m2
iii. Balcony and Corridors : 3 KN/m2
iv. Staircase : 4 KN/m2
Floor finish 1 KN/m2
Wind load As per IS: 875. Not designed for wind load since seismic loads exceed the wind loads.
Earthquake load As per IS: 1893(Part 1)-2002
Depth of foundation below GL 2.1 m
Type of soil Type II, medium as per IS: 1893 (Part 1)-2002
Allowable bearing capacity 150 KN/m2
Floor G.F. + 3 upper floors
Walls 150mm (both external and internal walls)
Concrete M20 conforming to IS: 456-2000
Steel Fe 415 conforming to IS: 1786-1979
Member Size Beam
i. 300 mm x 450 mm (Primary)
ii. 250 mm x 300 mm (Secondary)
Column : 300 mm x 450 mm
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CHAPTER-03
GRAVITY ANALYSIS
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FRAME ALONG PRIMARY DIRECTION OF THE BUILDING:
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GRAVITY ANALYSIS OF FRAME YY
I. Assumptions: � Imposed Load → Residential Building
1) For Roof : 1.5 KN/m2 2) On Balcony : 3 KN/m2 3) On Corridors : 3 KN/m2 4) On Rooms : 2 KN/m2
3.1 LOAD CALCULATION OF DIFFERENT FLOORS:
3.1.1 Load Calculation at Roof Level:
MEMBER RY1RY2
Area S4 = 0.5 x (0.6+3.3) x 1.35 = 2.632 m2
Total Self Weight of Slab = 2.632 x 4 = 10.528 KN
Imposed Load = 2.632 x 1.5 = 3.948 KN
Equivalent UDl for Self-wt. of Slab = = 5.399 KN/m
Equivalent UDl for Imposed Load = = 2.025 KN/m
Area S5 = 0.5 x 1.650 x 3.3 = 2.722 m2
Total Self Weight of Slab = 2.722 x 4 = 10.89 KN
Imposed Load = 2.722 x 1.5 = 4.084 KN
Equivalent UDl for Self-wt. of Slab = = 6.6 KN/m
Equivalent UDl for Imposed Load = = 2.475 KN/m
UDL due to Beam = 3.375 KN/m
Total Load on the member = (5.399+2.025+6.6+2.475+3.375) = 19.874 KN/m
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MEMBER RY2RY3
Area S3 = 0.5 x (0.4+3.1) x 1.35 = 2.362 m2
Total Self Weight of Slab = 2.362 x 4 = 9.448 KN
Imposed Load = 2.362 x 1.5 = 3.543 KN
Equivalent UDl for Self-wt. of Slab = = 5.399 KN/m
Equivalent UDl for Imposed Load = = 2.025 KN/m
UDL due to Beam = 3.375 KN/m
Total Load on the member = 5.399 + 2.025 + 3.375 = 10.799 KN/m
Point Load on the member due to Secondary beam = 18.72 KN
MEMBER RY3RY4
Area S1 = 0.5 x 1.650 x 3.3 = 2.722 m2
Total Self Weight of Slab = 2.722 x 4 = 10.89 KN
Imposed Load = 2.722 x 1.5 = 4.084 KN
Equivalent UDl for Self-wt. of Slab = = 6.6 KN/m
Equivalent UDl for Imposed Load = = 2.475 KN/m
Area S2 = 0.5 x (2.7+1.35) x 0.675 = 1.367m2
Total Self Weight of Slab = 2.722 x 4 = 5.468 KN
Imposed Load = 2.722 x 1.5 = 2.051 KN
Equivalent UDl for Self-wt. of Slab = = 2.7 KN/m
Equivalent UDl for Imposed Load = = 1.013 KN/m
UDL due to Beam = 3.375 KN/m
Point Load on the member due to Secondary beam = 18.72 KN
Total Load on the member = (6.6+2.475+2.7+1.013+3.375) = 16.163 KN/m
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3.1.2 Load Calculation at Typical Floor Level (1ST, 2ND & 3RD Floor):
MEMBER CY1CY2
Area S4 = 0.5 x (0.6+3.3) x 1.35 = 2.632 m2
Total Self Weight of Slab = 2.632 x 4 = 10.528 KN
Imposed Load = 2.632 x 2 = 5.264 KN
Equivalent UDl for Self-wt. of Slab = = 5.399 KN/m
Equivalent UDl for Imposed Load = = 2.699 KN/m
Area S5 = 0.5 x 1.650 x 3.3 = 2.722 m2
Total Self Weight of Slab = 2.722 x 4 = 10.89 KN
Imposed Load = 2.722 x 2 = 5.444 KN
Equivalent UDl for Self-wt. of Slab = = 6.6 KN/m
Equivalent UDl for Imposed Load = = 3.299 KN/m
UDL due to Beam = 3.375 KN/m
UDL due to Wall = 8.55 KN/m
Total Load on the member = (5.399+2.699+6.6+3.299+3.375+8.55) = 29.922 KN/m
MEMBER CY2CY3
Area S3 = 0.5 x (0.4+3.1) x 1.35 = 2.362 m2
Total Self Weight of Slab = 2.362 x 4 = 9.448 KN
Imposed Load = 2.362 x 2 = 4.724 KN
Equivalent UDl for Self-wt. of Slab = = 5.399 KN/m
Equivalent UDl for Imposed Load = = 2.699 KN/m
UDL due to Beam = 3.375 KN/m
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UDL due to Wall = 8.55 KN/m
Total Load on the member = 5.399 + 2.699 + 3.375 + 8.55 = 20.023 KN/m
Point Load on the member due to Secondary beam = 20.115 KN
MEMBER CY3CY4
Area S1 = 0.5 x 1.650 x 3.3 = 2.722 m2
Total Self Weight of Slab = 2.722 x 4 = 10.89 KN
Imposed Load = 2.722 x 2 = 5.444 KN
Equivalent UDl for Self-wt. of Slab = = 6.6 KN/m
Equivalent UDl for Imposed Load = = 3.299 KN/m
Area S2 = 0.5 x (2.7+1.35) x 0.675 = 1.367m2
Total Self Weight of Slab = 2.722 x 4 = 5.468 KN
Imposed Load = 2.722 x 2 = 2.734 KN
Equivalent UDl for Self-wt. of Slab = = 2.7 KN/m
Equivalent UDl for Imposed Load = = 1.35 KN/m
UDL due to Beam = 3.375 KN/m
UDL due to Wall = 8.55 KN/m
Point Load on the member due to Secondary beam = 10.328 KN
Total Load on the member = (6.6+3.299+2.7+1.35+3.375+8.55) = 25.874 KN/m
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Table: 1 CALCULATION OF LOAD FOR ROOF LEVEL:
Area(m2)
Dead load (KN)FROM
SLAB INCLUDING
FINISH (2KN/m2)@ 5
kn/m2
Equivalent dead load
from Slab(KN/m)
Live load on Slab@ 1.5kKN/m
2
Equivalent live load on Slab(KN/m
2)
Dead load of Beam (KN/m)
BEAM
Total load
(KN/m)
S1=0.5X(1.650X3.300)=2.722 10.888 6.6 4.084 2.475
3.375
R3-R4
12.450
S2=0.5X(1.35+2.7)X0.675=1.367 5.468 2.7 2.051 1.013 7.088
S3=0.5X(0.4+3.1)X1.35=2.362 9.448 5.399 3.543 2.025 R2-R3 10.799
S4=0.5X(0.6+3.3)X1.35=2.632 10.528 5.399 3.948 2.025 R1-R2
10.799
S5=0.5X(1.650X3.300)=2.722 10.888 6.6 4.084 2.475 12.450
Table: 2 CALCULATION OF POINT LOAD FOR ROOF:
BEAM POINT LOAD(KN) R2-R3 18.72 R3-R4 9.784
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Table: 2 CALCULATION OF DEAD LOAD FOR 3RD FLOOR:
Area(m2)
Dead load (KN)FROM
SLAB INCLUDING
FINISH (1KN/m2)@ 5
KN/m2
Equivalent dead load
from Slab(KN/m)
Live load on Slab@ 1.5kn/m2
Equivalent live load on slab(KN/m2
)
Dead load of Beam (KN/m)
Dead
load of Wall
(KN/m)
BEAM
Total Load
transferred on Beam (KN/m)
S1=0.5X(1.650X3.300)=2.722 10.89 6.6 5.444 3.299
3.375
8.55
C3-C4
21.824
S2=0.5X(1.35+2.7)X0.675=1.367 5.468 2.7 2.734 1.35 15.975
S3=0.5X(0.4+3.1)X1.35=2.362 9.448 5.399 4.724 2.699 C2-C3 20.023
S4=0.5X(0.6+3.3)X1.35=2.632 10.528 5.399 5.264 2.699 C1-C2
20.023
S5=0.5X(1.650X3.300)=2.722 10.89 6.6 5.444 3.299 21.824
Table: 2 CALCULATION OF POINT LOAD FOR 3RD FLOOR:
BEAM POINT LOAD(KN) C2-C3 20.115 C3-C4 10.328
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Table: 2 CALCULATION OF DEAD LOAD FOR 2ND FLOOR:
Area(m2)
Dead load (KN)FROM
SLAB INCLUDING
FINISH (1KN/m2)@
KN/m2
Equivalent dead load
from Slab(KN/m)
Live load on Slab@ 1.5kn/m2
Equivalent live load on slab(KN/m2
)
Dead load of Beam (KN/m)
Dead
load of Wall
(KN/m)
BEAM
Total Load
transferred on Beam (KN/m)
S1=0.5X(1.650X3.300)=2.722 10.89 6.6 5.444 3.299
3.375
8.55
B3-B4
21.824
S2=0.5X(1.35+2.7)X0.675=1.367 5.468 2.7 2.734 1.35 15.975
S3=0.5X(0.4+3.1)X1.35=2.362 9.448 5.399 4.724 2.699 B2-B3 20.023
S4=0.5X(0.6+3.3)X1.35=2.632 10.528 5.399 5.264 2.699 B1-B2
20.023
S5=0.5X(1.650X3.300)=2.722 10.89 6.6 5.444 3.299 21.824
Table: 2 CALCULATION OF POINT LOAD FOR 2ND FLOOR:
BEAM POINT LOAD(KN) B2-B3 20.115 B3-B4 10.328
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Table: 2 CALCULATION OF DEAD LOAD FOR 1ST FLOOR:
Area(m2)
Dead load (KN)FROM
SLAB INCLUDING
FINISH (1KN/m2)@ 5
KN/m2
Equivalent dead load
from Slab(KN/m)
Live load on Slab@ 1.5kn/m2
Equivalent live load on slab(KN/m2
)
Dead load of Beam (KN/m)
Dead
load of Wall
(KN/m)
BEAM
Total Load
transferred on Beam (KN/m)
S1=0.5X(1.650X3.300)=2.722 10.89 6.6 5.444 3.299
3.375
8.55
A3-A4
21.824
S2=0.5X(1.35+2.7)X0.675=1.367 5.468 2.7 2.734 1.35 15.975
S3=0.5X(0.4+3.1)X1.35=2.362 9.448 5.399 4.724 2.699 A2-A3 20.023
S4=0.5X(0.6+3.3)X1.35=2.632 10.528 5.399 5.264 2.699 A1-A2
20.023
S5=0.5X(1.650X3.300)=2.722 10.89 6.6 5.444 3.299 21.824
Table: 2 CALCULATION OF POINT LOAD FOR 1ST FLOOR:
BEAM POINT LOAD(KN) A2-A3 20.115 A3-A4 10.328
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TABLE: 9 CALCULATION OF DEAD LOAD OF GROUND FLOOR
On ground floor, the live load on slab will directly go to the ground and there will be no live load on the beam. Also only the self weight of the beam and walls act on the beams. The weight due to slab and finish do not come.
BEAM
Dead load of beam (KN/m) Load transferred on beam (KN/m)
G1-G2 3.375
3.375 G2-G3 3.375 G3-G4 3.375
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3.2 CALCULATIONS OF DISTRIBUTON FACTORS:
TABLES FOR DISTRIBUTION FACTORS:
3.2.1 DETERMINATION OF DISTRIBUTION FACTOR AT ROOF LEVEL:
JOINT MEMBE
R L(M) B(M) D(M)
I=BD3/12
K=I/L ∑K DF=K/∑
K
R1 R1-R2 3.3 0.3 0.45 0.002278 0.00069 0.001381 0.50 R1-C1 3.3 0.3 0.45 0.002278 0.00069 0.001381 0.50
R2 R2-R1 3.3 0.3 0.45 0.002278 0.00069 0.002116 0.33
R2-R3 3.1 0.3 0.45 0.002278 0.00073
5 0.002116 0.35 R2-C2 3.3 0.3 0.45 0.002278 0.00069 0.002116 0.33
R3 R3-R2 3.1 0.3 0.45 0.002278 0.00073
5 0.002116 0.35 R3-R4 3.3 0.3 0.45 0.002278 0.00069 0.002116 0.33 R3-C3 3.3 0.3 0.45 0.002278 0.00069 0.002116 0.33
R4 R4-R3 3.3 0.3 0.45 0.002278 0.00069 0.001381 0.50 R4-C4 3.3 0.3 0.45 0.002278 0.00069 0.001381 0.50
3.2.2 DETERMINATION OF DISTRIBUTION FACTOR AT 3RD FLOOR LEVEL:
JOINT MEMBE
R L(M) B(M) D(M)
I=BD3/12
K=I/L ∑K DF=K/∑
K
C1 C1-R1 3.3 0.3 0.45 0.002278 0.00069 0.002071 0.33 C1-C2 3.3 0.3 0.45 0.002278 0.00069 0.002071 0.33 C1-B1 3.3 0.3 0.45 0.002278 0.00069 0.002071 0.33
C2 C2-C1 3.3 0.3 0.45 0.002278 0.00069 0.002806 0.25 C2-B2 3.3 0.3 0.45 0.002278 0.00069 0.002806 0.25 C2-R2 3.3 0.3 0.45 0.002278 0.00069 0.002806 0.25
C2-C3 3.1 0.3 0.45 0.002278 0.00073
5 0.002806 0.26 C3 C3-R3 3.3 0.3 0.45 0.002278 0.00069 0.002806 0.25
C3-B3 3.3 0.3 0.45 0.002278 0.00069 0.002806 0.25
C3-C2 3.1 0.3 0.45 0.002278 0.00073
5 0.002806 0.26 C3-C4 3.3 0.3 0.45 0.002278 0.00069 0.002806 0.25
C4 C4-R4 3.3 0.3 0.45 0.002278 0.00069 0.002071 0.33 C4-B4 3.3 0.3 0.45 0.002278 0.00069 0.002071 0.33 C4-C3 3.3 0.3 0.45 0.002278 0.00069 0.002071 0.33
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3.2.3 DETERMINATION OF DISTRIBUTION FACTOR AT 2ND FLOOR LEVEL:
JOINT MEMBE
R L(M) B(M) D(M)
I=BD3/12
K=I/L ∑K DF=K/∑
K
B1 B1-C1 3.3 0.3 0.45 0.002278 0.00069 0.002071 0.33 B1-B2 3.3 0.3 0.45 0.002278 0.00069 0.002071 0.33 B1-A1 3.3 0.3 0.45 0.002278 0.00069 0.002071 0.33
B2 B2-B1 3.3 0.3 0.45 0.002278 0.00069 0.002806 0.25 B2-C2 3.3 0.3 0.45 0.002278 0.00069 0.002806 0.25 B2-A2 3.3 0.3 0.45 0.002278 0.00069 0.002806 0.25
B2-B3 3.1 0.3 0.45 0.002278 0.00073
5 0.002806 0.26
B3 B3-B2 3.1 0.3 0.45 0.002278 0.00073
5 0.002806 0.26 B3-B4 3.3 0.3 0.45 0.002278 0.00069 0.002806 0.25 B3-C3 3.3 0.3 0.45 0.002278 0.00069 0.002806 0.25 B3-A3 3.3 0.3 0.45 0.002278 0.00069 0.002806 0.25
B4 B4-B3 3.3 0.3 0.45 0.002278 0.00069 0.002071 0.33 B4-C4 3.3 0.3 0.45 0.002278 0.00069 0.002071 0.33 B4-A4 3.3 0.3 0.45 0.002278 0.00069 0.002071 0.33
3.2.4 DETERMINATION OF DISTRIBUTION FACTOR AT 1ST FLOOR LEVEL:
JOINT
MEMBER
L(M) B(M) D(M) I=BD3/1
2 K=I/L ∑K
DF=K/∑K
A1 A1-B1 3.3 0.3 0.45 0.002278 0.00069 0.002224 0.31 A1-G1 2.7 0.3 0.45 0.002278 0.000844 0.002224 0.38 A1-A2 3.3 0.3 0.45 0.002278 0.00069 0.002224 0.31
A2 A2-B2 3.3 0.3 0.45 0.002278 0.00069 0.002959 0.23 A2-A1 3.3 0.3 0.45 0.002278 0.00069 0.002959 0.23 A2-A3 3.1 0.3 0.45 0.002278 0.000735 0.002959 0.25 A2-G2 2.7 0.3 0.45 0.002278 0.000844 0.002959 0.29
A3 A3-B3 3.3 0.3 0.45 0.002278 0.00069 0.002959 0.23 A3-A2 3.1 0.3 0.45 0.002278 0.000735 0.002959 0.25 A3-A4 3.3 0.3 0.45 0.002278 0.00069 0.002959 0.23 A3-G3 2.7 0.3 0.45 0.002278 0.000844 0.002959 0.29
A4 A4-A3 3.3 0.3 0.45 0.002278 0.00069 0.002224 0.31 A4-G4 2.7 0.3 0.45 0.002278 0.000844 0.002224 0.38 A4-B4 3.3 0.3 0.45 0.002278 0.00069 0.002224 0.31
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3.2.5 DETERMINATION OF DISTRIBUTION FACTOR AT GROUND FLOOR
LEVEL:
JOINT
MEMBER
L(M) B(M) D(M) I=BD3/1
2 K=I/L ∑K
DF=K/∑K
G1 G1-A1 2.7 0.3 0.45 0.002278 0.000844 0.002619 0.32 G1-F1 2.1 0.3 0.45 0.002278 0.001085 0.002619 0.41 G1-G2 3.3 0.3 0.45 0.002278 0.00069 0.002619 0.26
G2 G2-G1 3.3 0.3 0.45 0.002278 0.00069 0.003354 0.21 G2-A2 2.7 0.3 0.45 0.002278 0.000844 0.003354 0.25 G2-F2 2.1 0.3 0.45 0.002278 0.001085 0.003354 0.32 G2-G3 3.1 0.3 0.45 0.002278 0.000735 0.003354 0.22
G3 G3-G2 3.1 0.3 0.45 0.002278 0.000735 0.003354 0.22 G3-G4 3.3 0.3 0.45 0.002278 0.00069 0.003354 0.21 G3-A3 2.7 0.3 0.45 0.002278 0.000844 0.003354 0.25 G3-F3 2.1 0.3 0.45 0.002278 0.001085 0.003354 0.32
G4 G4-A4 2.7 0.3 0.45 0.002278 0.000844 0.002619 0.32 G4-F4 2.1 0.3 0.45 0.002278 0.001085 0.002619 0.41 G4-G3 3.3 0.3 0.45 0.002278 0.00069 0.002619 0.26
25
3.3 CALCULATIONS OF FIXED END MOMENTS:
3.3.1 Calculation of FIXED END MOMENT at ROOF Level:
3.3.1 Calculation of FIXED END MOMENT at 3RD FLOOR Level:
3.3.2 Calculation of FIXED END MOMENT at 2ND FLOOR Level:
MEMBER
LENGTH(M)
UDL(KN/m)
POINT LOAD(KN)
FIXED END MOMENTS (KNM)
1.4 m from C2
2.7 m from C4
FEML FEMR
R1-R2 3.3 19.874 +18.036 -18.036
R2-R3 3.1 10.799 18.72 +16.529 -15.139
R3-R4 3.3 16.163 9.784 +18.598 -15.541
MEMBER
LENGTH(M)
UDL(KN/m)
POINT LOAD(KN)
FIXED END MOMENTS (KNM)
1.4 m from C2
2.7 m from C4
FEML FEMR
C1-C2 3.3 29.922 +27.154 -27.154
C2-C3 3.1 20.023 20.115 +24.504 -23.009
C3-C4 3.3 25.874 10.328 +27.628 -24.402
MEMBER
LENGTH(M)
UDL(KN/m)
POINT LOAD(KN)
FIXED END MOMENTS (KNM)
1.4 m from B2
2.7 m from B4
FEML FEMR
B1-B2 3.3 29.922 +27.154 -27.154
B2-B3 3.1 20.023 20.115 +24.504 -23.009
B3-B4 3.3 25.874 10.328 +27.628 -24.402
26
3.3.3 Calculation of FIXED END MOMENT at 1ST FLOOR Level:
3.3.4 Calculation of FIXED END MOMENT at GROUND Level:
MEMBER
LENGTH(M)
UDL(KN/m)
POINT LOAD(KN)
FIXED END MOMENTS (KNM)
1.4 m from A2
2.7 m from A4
FEML FEMR
A1-A2 3.3 29.922 +27.154 -27.154
A2-A3 3.1 20.023 20.115 +24.504 -23.009
A3-A4 3.3 25.874 10.328 +27.628 -24.402
MEMBER
LENGTH(M)
UDL(KN/m)
Fixed end moments (KNm)
FEML FEMR G1-G2 3.3 3.375 +3.063 -3.063
G2-G3 3.1 3.375 +2.703 -2.703
G3-G4 3.3 3.375 +3.063 -3.063
27
3.4MOMENT DISTRIBUTION TABLES:
3.4.1 Moment Distribution table for ROOF LEVEL:
R1-R2 R2-R3 R3-R4 DF 0.5 0.33 0.35 0.35 0.33 0.5 FEM 18.036 -18.036 16.529 -15.139 18.598 -15.541 DISTRB -9.018 0.497 0.527 -1.211 -1.141 7.771 C.O. 0.249 -4.509 -0.605 0.264 3.885 -0.571 DISTRB -0.124 1.688 1.790 -1.452 -1.094 -1.657 C.O. 0.844 -0.062 -0.726 0.895 -0.829 -0.547 DISTRB -0.422 0.260 0.276 -0.023 -0.022 0.273 C.O. 0.130 -0.211 -0.012 0.138 0.137 -0.011 DISTRB -0.065 0.073 0.078 -0.096 -0.091 0.005 C.O. 0.037 -0.033 -0.048 0.039 0.003 -0.045 DISTRB -0.018 0.027 0.028 -0.015 -0.014 0.023 SUM 9.648 -20.305 17.837 -16.600 19.433 -10.300
3.4.2 Moment Distribution table for 3RD FLOOR LEVEL:
C1-C2 C2-C3 C3-C4 DF 0.33 0.25 0.26 0.26 0.25 0.33
FEM 27.154 -27.154 24.504 -23.009 27.628 -24.402
DISTRB -8.961 0.663 0.689 -1.201 -1.155 8.053 C.O. 0.331 -4.480 -0.600 0.345 4.026 -0.577 DISTRB -0.109 1.270 1.321 -1.136 -0.862 -1.138 C.O. 0.635 -0.055 -0.568 0.661 -0.569 -0.431 DISTRB -0.210 0.156 0.162 -0.024 -0.023 0.142 C.O. 0.078 -0.105 -0.012 0.081 0.071 -0.011 DISTRB -0.026 0.029 0.030 -0.040 -0.038 0.004 C.O. 0.015 -0.013 -0.020 0.015 0.002 -0.019 DISTRB -0.005 0.008 0.008 -0.004 -0.004 0.006 SUM 18.903 -29.681 25.514 -24.313 29.076 -18.374
28
3.4.3 Moment Distribution table for 2ND FLOOR LEVEL:
B1-B2 B2-B3 B3-B4 DF 0.33 0.25 0.26 0.26 0.25 0.33
FEM 27.154 -27.154 24.504 -23.009 27.628 -24.402
DISTRB -8.961 0.663 0.689 -1.201 -1.155 8.053 C.O. 0.331 -4.480 -0.600 0.345 4.026 -0.577 DISTRB -0.109 1.270 1.321 -1.136 -0.862 -1.138 C.O. 0.635 -0.055 -0.568 0.661 -0.569 -0.431 DISTRB -0.210 0.156 0.162 -0.024 -0.023 0.142 C.O. 0.078 -0.105 -0.012 0.081 0.071 -0.011 DISTRB -0.026 0.029 0.030 -0.040 -0.038 0.004 C.O. 0.015 -0.013 -0.020 0.015 0.002 -0.019 DISTRB -0.005 0.008 0.008 -0.004 -0.004 0.006 SUM 18.903 -29.681 25.514 -24.313 29.076 -18.374
3.4.4 Moment Distribution table for 1ST FLOOR LEVEL:
A1-A2 A2-A3 A3-A4 DF 0.31 0.23 0.25 0.25 0.23 0.31
FEM 27.154 -27.154 24.504 -23.009 27.628 -24.402
DISTRB -8.418 0.610 0.663 -1.155 -1.062 7.565 C.O. 0.305 -4.209 -0.577 0.331 3.782 -0.531 DISTRB -0.094 1.101 1.197 -1.028 -0.748 -1.008 C.O. 0.550 -0.047 -0.514 0.598 -0.504 -0.374 DISTRB -0.171 0.129 0.140 -0.024 -0.022 0.116 C.O. 0.065 -0.085 -0.012 0.070 0.058 -0.011 DISTRB -0.020 0.022 0.024 -0.032 -0.029 0.003 C.O. 0.011 -0.010 -0.016 0.012 0.002 -0.015 DISTRB -0.003 0.006 0.007 -0.003 -0.003 0.005 SUM 19.379 -29.638 25.415 -24.239 29.102 -18.652
29
3.4.5 Moment Distribution table for GROUND FLOOR LEVEL:
G1-G2 G2-G3 G3-G4 DF 0.26 0.21 0.22 0.22 0.21 0.26 FEM 3.063 -3.063 2.703 -2.703 3.063 -3.063 DISTRB -0.796 0.076 0.079 -0.079 -0.076 0.796 C.O. 0.038 -0.398 -0.040 0.040 0.398 -0.038 DISTRB -0.010 0.092 0.096 -0.096 -0.076 -0.094 C.O. 0.046 -0.005 -0.048 0.048 -0.047 -0.038 DISTRB -0.012 0.011 0.012 0.000 0.000 0.010 C.O. 0.006 -0.006 0.000 0.006 0.005 0.000 DISTRB -0.001 0.001 0.001 -0.002 -0.002 0.000 C.O. 0.001 -0.001 -0.001 0.001 0.000 -0.001 DISTRB 0.000 0.000 0.000 0.000 0.000 0.000 SUM 2.333 -3.292 2.803 -2.787 3.265 -2.427
30
3.5 FINAL END MOMENTS BY GRAVITY ANALYSIS:
3.5.1 Calculation of FINAL MOMENTS at ROOF Level:
SPAN
LENGTH(m) L
UDL(KN/m) W
MIDSPAN SAGGING MOMENT
CONSIDERING SIMPLY
SUPPORTED, KNm
End hogging moments as per moment distribution,
FINAL MOMENTS, KNm
KNm MID MOMENT
=(WL2/8)+((ML+MR)/2))
LEFT RIGHT LEFT MID RIGHT R1-R2 3.3 19.874 -27.053 9.648 20.305 9.648 -12.077 20.305 R2-R3 3.1 10.799 -26.076 17.837 16.600 17.837 -8.858 16.600 R3-R4 3.3 16.163 -24.937 19.433 10.300 19.433 -10.070 10.300
3.5.2 Calculation of FINAL MOMENTS at 3RD FLOOR Level:
SPAN LENGTH(m)
L UDL(KN/m)
W
MIDSPAN SAGGING MOMENT CONSIDERING SIMPLY
SUPPORTED, KNm( = WL2/8)
End hogging moments as per
moment distribution,
FINAL MOMENTS, KNm
KNm MID MOMENT
=(WL2/8)+((ML+MR)/2))
LEFT RIGHT LEFT MID RIGHT
C1-C2 3.3 29.922 -40.731 18.903 29.681 18.903 -16.439 29.681 C2-C3 3.1 20.023 -38.134 25.514 24.313 25.514 -13.220 24.313 C3-C4 3.3 25.874 -38.319 29.076 18.374 29.076 -14.594 18.374
31
3.5.3 Calculation of FINAL MOMENTS at 2ND FLOOR Level:
SPAN LENGTH(m)
L UDL(KN/m)
W
MIDSPAN SAGGING MOMENT CONSIDERING SIMPLY
SUPPORTED, KNm( = WL2/8)
End hogging moments as per
moment distribution,
FINAL MOMENTS, KNm
KNm MID MOMENT
=(WL2/8)+((ML+MR)/2)) LEFT RIGHT LEFT MID RIGHT
B1-B2 3.3 29.922 -40.731 18.903 29.681 18.903 -16.439 29.681 B2-B3 3.1 20.023 -38.134 25.514 24.313 25.514 -13.220 24.313 B3-B4 3.3 25.874 -38.319 29.076 18.374 29.076 -14.594 18.374
3.5.4 Calculation of FINAL MOMENTS at 1ST FLOOR Level:
SPAN LENGTH(m)
L UDL(KN/m)
W
MIDSPAN SAGGING MOMENT CONSIDERING SIMPLY
SUPPORTED, KNm( = WL2/8)
End hogging moments as per
moment distribution,
FINAL MOMENTS, KNm
KNm MID MOMENT
=(WL2/8)+((ML+MR)/2))
LEFT RIGHT LEFT MID RIGHT
A1-A2 3.3 29.922 -40.731 19.379 29.638 19.379 -16.223 29.638 A2-A3 3.1 20.023 -38.134 25.415 24.239 25.415 -13.307 24.239 A3-A4 3.3 25.874 -38.319 29.102 18.652 29.102 -14.442 18.652
32
3.5.5 Calculation of FINAL MOMENTS at GROUND FLOOR Level:
SPAN LENGTH(m)
L UDL(KN/m)
W
MIDSPAN SAGGING MOMENT CONSIDERING SIMPLY
SUPPORTED, KNm( = WL2/8)
End hogging moments as per
moment distribution,
FINAL MOMENTS, KNm
KNm MID MOMENT
=(WL2/8)+((ML+MR)/2)) LEFT RIGHT LEFT MID RIGHT
G1-G2 3.3 3.375 -4.594 2.333 3.292 2.333 -1.782 3.292 G2-G3 3.1 3.375 -4.054 2.803 2.787 2.803 -1.259 2.787 G3-G4 3.3 3.375 -4.594 3.265 2.427 3.265 -1.748 2.427
33
3.6 BEAM SHEAR FORCES:
BEAM LENGTH
L (m)
UDL
(KN/m)
POINT LOAD(KN)
S.F(KN) M1(KNm) M2(KNm)
V=(M1-M2)/L
CORRECTED SHEAR FORCE(KN)
LEFT RIGHT LEFT MID RIGHT R1-R2 3.3 19.874
32.79 32.79 9.648 20.305 3.230 36.020 3.17 29.560
R2-R3 3.1 10.799 18.72 27.00 25.16 17.837 16.600 0.400 26.600 0.85 25.560 R3-R4 3.3 16.163 9.784 34.67 28.45 19.433 10.300 2.760 31.910 -7.64 38.750 C1-C2 3.3 29.922
49.30 49.30 18.903 29.681 3.260 52.560 3.29 46.040
C2-C3 3.1 20.023 20.115 42.00 40.20 25.514 24.313 0.390 41.610 -9.29 40.590 C3-C4 3.3 25.874 10.328 51.14 44.56 29.076 18.374 3.240 47.900 -5.17 47.800 B1-B2 3.3 29.922
49.30 49.30 18.903 29.681 3.260 52.560 3.29 46.040
B2-B3 3.1 20.023 20.115 42.00 40.20 25.514 24.313 0.390 41.610 -9.29 40.590 B3-B4 3.3 25.874 10.328 51.14 44.56 29.076 18.374 3.240 47.900 -5.17 47.800 A1-A2 3.3 29.922
49.30 49.30 19.379 29.638 3.100 52.400 2.98 46.200
A2-A3 3.1 20.023 20.115 42.00 40.20 25.415 24.239 0.380 41.620 -9.53 40.580 A3-A4 3.3 25.874 10.328 51.14 44.56 29.102 18.652 3.160 47.980 -5.15 47.720 G1-G2 3.3 3.375
5.57 5.57 2.245 3.516 0.380 5.900 0.34 5.200
G2-G3 3.1 3.375
5.23 5.23 3.677 3.662 0.004 5.234 0 5.226 G3-G4 3.3 3.375
5.57 5.57 3.447 2.355 0.330 5.900 0.34 5.200
34
CHAPTER-4
SEISMIC ANALYSIS
35
4.1 Seismic Load diagram
36
4.1 INTRODUCTION
During an earthquake, ground motions occur in a random fashion, both horizontally and vertically, in all directions radiating from the epicenter. The ground accelerations cause the structure to vibrate and induce inertial forces on them. Hence, structures in such locations need to be suitably designed and detailed to ensure stability, strength and serviceability with acceptable levels of safety under seismic effects. Earthquake can cause damage not only on account of shaking which results from them but also due to other chain effects like landslides, floods, fire etc. it is therefore important to take necessary precautions in the design of structures so that they are safe against such secondary effects also.
The project work being the design of a residential building in Guwahati, which lies in Zone V, necessitates rigorous seismic analysis for proper subsequent designing and detailing. In this regard, the various clauses of IS: 1893(Part 1) – 2002 and IS: 13920 – 1993 are followed.
4.2 SEISMIC WEIGHT OF THE BUILDING:
4.2.1 Load calculation by lump mass model (W):
At roof level (W5):
1. Self weight of slab = (2.7/2+3.6/2)*(3.3+3.1+3.3)*5 = 152.775 KN 2. Self weight of primary beam = (1.375*4+1.8*4+9.7)*3.375 = 75.6 KN 3. Self weight of secondary beam = (2.7+1.35+1.8)*1.875 = 10.97 KN 4. Self weight of wall
= ((3.3-0.3)/2*(2.7/2*3+3.6/2*2) + (3.3-0.25)/2*2.7/2*1+3.6/2*1+ (3.3-0.45)/2*9.7)*3 = 87.58 KN
5. Self wt. of parapet wall = (2.7/2+3.6/2)*2*3 = 18.9 KN 6. Self weight of column = (3.3*0.5*4)*3.375 =22.275 KN 7. Imposed load = 0.00 KN
W5 = 367.9875 KN
At 3rd floor level (W4): 1. Self weight of slab = (2.7/2+3.6/2)*(3.3+3.1+3.3)*5 = 152.775 KN 2. Self weight of primary beam = (1.375*4+1.8*4+9.7)*3.375 = 75.6 KN 3. Self weight of secondary beam = (2.7+1.35+1.8)*1.875 = 10.97 KN 4. Self weight of wall
= ((3.3-0.3)*0.5*(2.7*0.5*3+3.6*0.5*2)+(3.3-0.25)*0.5*(2.7*0.5*1+3.6*0.5*1)+(3.3-0.45)*0.5*9.7+((2.7-0.3)*0.5*(2.7*0.5*3+3.6*0.5*2)+(2.7-0.25)*0.5*(2.7*0.5*1+3.6*0.5*1)+(2.7-0.45)*0.5*9.7))*3 = 162.16 KN
5. Self weight of column = (3.3*0.5*4)*3.375*2 =44.55 KN 6. Imposed load = (2.7/2+3.6/2)*(3.3+3.1+3.3)*(0.25*2) =15.28 KN
W4= 474.11KN
37
At 2nd floor level (W3): 1. Self weight of slab = (2.7/2+3.6/2)*(3.3+3.1+3.3)*5 = 152.775 KN 2. Self weight of primary beam = ((1.375*4+1.8*4+9.7)*3.375 = 75.6 KN 3. Self weight of secondary beam = (2.7+1.35+1.8)*1.875 = 10.97 KN 4. Self weight of wall
= ((3.3-0.3)*0.5*(2.7*0.5*3+3.6*0.5*2)+(3.3-0.25)*0.5*(2.7*0.5*1+3.6*0.5*1)+(3.3-0.45)*0.5*9.7+((2.7-0.3)*0.5*(2.7*0.5*3+3.6*0.5*2)+(2.7-0.25)*0.5*(2.7*0.5*1+3.6*0.5*1)+(2.7-0.45)*0.5*9.7))*3 = 162.16 KN
5. Self weight of column = (3.3*0.5*4)*3.375*2 =44.55 KN 6. Imposed load = (2.7/2+3.6/2)*(3.3+3.1+3.3)*(0.25*2) =15.28 KN
W4= 474.11KN
At 1st floor level (W2): 1. Self weight of slab = (2.7/2+3.6/2)*(3.3+3.1+3.3)*5 = 152.775 KN 2. Self weight of primary beam = (1.375*4+1.8*4+9.7)*3.375 = 75.6 KN 3. Self weight of secondary beam = (2.7+1.35+1.8)*1.875 = 10.97 KN 4. Self weight of wall
= ((3.3-0.3)*0.5*(2.7*0.5*3+3.6*0.5*2)+(3.3-0.25)*0.5*(2.7*0.5*1+3.6*0.5*1)+(3.3-0.45)*0.5*9.7+((2.7-0.3)*0.5*(2.7*0.5*3+3.6*0.5*2)+(2.7-0.25)*0.5*(2.7*0.5*1+3.6*0.5*1)+(2.7-0.45)*0.5*9.7))*3 = 162.16 KN
5. Self weight of column = ((3.3*0.5*4)+(2.7*0.5*4))*3.375 =40.50 KN 6. Imposed load = (2.7/2+3.6/2)*(3.3+3.1+3.3)*(0.25*2) =15.28 KN
W4= 457.28KN
At plinth level (W1): 1) Self weight of primary beam = (1.375*4+1.8*4+9.7)*3.375 = 75.60KN 2) Self weight of columns = (2.1*0.5*4)*3.375 = 14.18 KN
W5 = 89.78 KN
Hence, Total weight W= W5+W4+W3+W2 + W1 = 1389.15 KN
38
4.3 Calculation of Base Shear (VB): VB = Ah.W (as per cl.7.5.3- IS: 1893-2002) Ah = Z.I.Sa/ 2Rg (as per cl.6.4.2- IS: 1893-2002) Z = 0.36 (as per Table 2- IS: 1893-2002) I = 1.0 (as per Table 6- IS: 1893-2002) R = 5.0 (as per Table 7- IS: 1893-2002, for SMRF with ductile detailing) Now, Height h = 3.3 + 3.3 + 3.3 + 2.7+2.1 = 14.2 m Ta = 0.075 × 14.20.75 = 0.56 (as per cl. 7.6.1 IS 1893 (Part 1): 2002) Hence, for medium soil, Sa/g = 2.5 (as per cl.6.4.5 IS 1893 (Part 1): 2002) Ah = 0.36 × 1 × 2.5 / (2 × 5) = 0.09
VB = 0.09 × 1389.15 = 125.02 KN 4.3.1 Distribution of base shear at each floor (Qi): Qi = (Wihi
2/Σ Wihi2) × VB
Wi hi hi2 Wihi2 Wihi2/ΣWihi
2 Q=(Wihi2/ΣWihi2)V
B
roof 367.98
8 14.7 216.09 79518.53 0.434120816 54.28 3rd floor
474.108 11.4 129.96 61615.08 0.336379306 42.06
2nd floor
474.108 8.1 65.61 31106.23 0.169820301 21.23
1st floor
457.278 4.8 23.04 10535.69 0.057518171 7.19
PL 89.775 2.1 4.41 395.9077 0.002161406 0.27
Σ Wihi
2=183171.4 Σ =125.02 = VB
39
SEISMIC ANALYSIS
4.4 ANALYSIS BY CANTILEVER METHOD:
4.4.1 Calculation of distance of centroidal axis:
3.3 3.1 3.3
A A A A
X̅ =
=
= 4.85 m
Fig. 4.1
Fig. 4.2
40
Now, P1 =K x 4.85
P2 = Kx1.55
P3 = Kx1.55
P4 = Kx4.85
P1 = P4
P3 = P2
P2 = 0.319 P1
P3 = 0.319 P1
Plinth level:
Taking moment of all the forces @ the point
-50.69x13.65-39.28x10.35-19.83x7.05-6.72x3.75-0.25x1.05+P1x9.7+P2x6.4-P3x3.3 = 0
Using eqn. 1,
P1 = 118.21KN, P2 = 37.71 KN, P3 = 37.71 KN, P4 = 118.21 KN
For ground floor:
-50.69x11.25-39.28x7.95-19.83x4.65-6.72x1.35+P1x9.7+P2x6.4-P3x3.3 = 0
Using eqn. 1,
P1 = 92.03KN, P2 = 29.36 KN, P3 = 29.36 KN, P4 = 92.03 KN
For 1st floor:
-50.69x8.25-39.28x4.95-19.83x1.65+ P1x9.7+P2x6.4-P3x3.3 = 0
Using eqn. 1
P1 = 60.37 KN, P2 = 19.25 KN, P3 = 19.25 KN, P4 = 60.37 KN
Equation 1
41
For 2nd floor:
-50.69x4.95-39.28x1.65+ P1x9.7+P2x6.4-P3x3.3 = 0
Using eqn 1
P1 = 29.54 KN, P2 = 9.42 KN, P3 = 9.42 KN, P4 = 29.54 KN
For 3rd floor:
-50.69x1.65+ P1x9.7+P2x6.4-P3x3.3 = 0
Using eqn 1
P1 = 7.82 KN, P2 = 2.49 KN, P3 = 2.49KN, P4 = 7.82 KN
4.4.2 CALCULATION OF BEAM SHEAR, BEAM MOMENT, COLUMN SHEAR
AND COLUMN MOMENT
4.4.2.1 Considering the joints J21 – J22 – J23 – J24
Calculation of shear forces in beams
J21- J22 = 7.82
J22 – J23 = 10.31
J23 – J24 = 7.82
Calculation of beam moments
M (J21-J22) = 7.82x3.3/2 = 12.903 KNm
M (J22- J23) = 10.31x3.1/2 = 15.98 KNm
M (J23-J24) = 7.82x3.3/2 = 12.903 KNm
Fig. 4.3
42
Calculation of column moments and column shear:
Joint J21:
M (J21- J17) + M(J21- J22) = 0
⇒ M (J21- J17) = - 12.903 KNm
∴ Column shear = 12.903/(3.3/2) = 7.82 KN
Joint J22:
M (J22- J21) + M (J22- J23) + M (J22- J18) = 0
⇒-2.903+15.98 = M (J22- J18)
⇒ M (J22- J18) = 28.883 KNm
∴ Column shear = 28.883/ (3.3/2) = 17.50 KN
Joint J23:
M (J23- J19) = 28.883 KNm
Column shear = 28.883/ (3.3/2) = 17.50 KN
Joint J24:
M (J24- J20) = 12.903 KNm
∴ Column shear = 12.903/ (3.3/2) = 7.82 KN
Fig. 4.4
43
4.4.2.2 Considering the joints J17 – J18 – J19 – J20
Calculation of shear forces in beams:
J17 – J18 = 21.72 KN
J18 – J19 = 28.65 KN
J19 – J20 = 21.72 KN
Calculation of beam moments:
M (J17-J18) = 21.72x3.3/2 = 35.838 KNm
M (J18- J19) = 28.65x3.1/2 = 44.41 KNm
M (J19-J20) = 21.72x3.3/2 = 35.838 KNm
Fig. 4.5
Fig. 4.6
44
Calculation of column moments and column shear:
Joint J17:
M (J17- J21) + M (J17- J18) + M (J17- J13) = 0
⇒ M (J17- J13) + (35.838- 12.903) = 0 KNm
⇒ M (J17- J13) = 22.935 KNm
∴ Column shear = 22.935/(3.3/2) = 13.9 KN
Joint J18:
M (J18- J22) + M (J18- J19) + M (J18- J17) + M (J18-J14) = 0
⇒ M (J18-J14) = 51.36 KNm
∴ Column shear = 51.36/ (3.3/2) = 31.12 KN
Joint J19:
M (J19- J23) + M (J19- J18) + M (J19- J20) + M (J19- J15) = 0
⇒ M (J19- J15) = 51.36 KN
∴ Column shear = 51.36/ (3.3/2) = 31.12 KN
Joint J20:
M (J20- J24) + M (J20- J19) + M (J20- J16) = 0
⇒ M (J20- J16) = 22.935 KNm
∴ Column shear = 22.935/(3.3/2) = 13.9 KN
Fig. 4.7
45
4.4.2.3 Considering the joints J13 – J14 – J15 – J16
Calculation of shear forces in beams:
J13 – J14 = 30.83 KN
J14 – J15 = 40.66 KN
J15 – J16 = 30.83 KN
Fig. 4.8
Fig. 4.9
46
Calculation of beam moments:
M (J13 – J14) = 30.83x3.3/2 = 50.86 KNm
M (J14 – J15) = 40.66x3.1/2 = 63.023 KNm
M (J15 – J16) = 30.83x3.3/2 = 50.86 KNm
Calculation of column moments and column shear:
Joint J13:
M (J13- J17) + M (J13- J14) + M (J13- J9) = 0
⇒ M (J13- J9) = 27.925 KNm
∴ Column shear = 27.925/(3.3/2) = 16.93 KN
Joint J14:
M (J14- J18) + M (J14- J15) + M (J14- J13) + M (J14 - J10) = 0
⇒ M (J14 - J10) = 62.523 KNm
∴ Column shear = 62.523/(3.3/2) = 37.89 KN
Joint J15:
M (J15- J19) + M (J15- J16) + M (J15- J14) + M (J15 - J11) = 0
⇒ M (J15 - J11) = 62.523 KNm
∴ Column shear = 62.523/(3.3/2) = 37.89 KN
Fig. 4.10
47
Joint J16:
M (J16- J20) + M (J16- J15) + M (J16- J12) = 0
⇒ M (J16- J12) = 27.925 KNm
∴ Column shear = 27.925/(3.3/2) = 16.93 KN
4.4.2.4 Considering the joints J9 – J10 – J11 – J12
Calculation of shear forces in beams:
J9 – J10 = 31.66 KN
J10 – J11 = 41.77 KN
J11 – J12 = 31.66 KN
Calculation of beam moments:
M (J9 – J10) = 31.66 x3.3/2 = 52.239 KNm
M (J10 – J11) = 41.77 x3.1/2 = 64.744 KNm
M (J11 – J12) = 31.66 x3.3/2 = 52.239 KNm
Fig. 4.11
Fig. 4.12
48
Calculation of column moments and column shear:
Joint J9:
M (J9- J13) + M (J9- J10) + M (J9- J5) = 0
⇒ M (J9- J5) = 24.314 KNm
∴ Column shear = 24.314/ (2.7/2) = 18.01 KN
Joint J10:
M (J10- J14) + M (J10- J11) + M (J10- J9) + M (J10 – J6) = 0
⇒ M (J10 – J6) = 54.46 KNm
∴ Column shear = 54.46/ (2.7/2) = 40.34 KN
Joint J11:
M (J11- J15) + M (J11- J10) + M (J11- J12) + M (J11 – J7) = 0
⇒ M (J11 – J7) = 54.46 KNm
∴ Column shear = 54.46/ (2.7/2) = 40.34 KN
Joint J12:
M (J12- J16) + M (J12- J11) + M (J12- J8) = 0
⇒ M (J12- J8) = 24.314 KNm
∴ Column shear = 24.314/ (2.7/2) = 18.01 KN
Fig. 4.13
49
4.4.2.5 Considering the joints J5 – J6 – J7 – J8
Calculation of shear forces in beams:
J5 – J6 = 26.18 KN
J6 – J7 = 34.53 KN
J7 – J8 = 26.18 KN
Calculation of beam moments:
M (J5 – J6) = 26.18 x3.3/2 = 43.197 KNm
M (J6 – J7) = 34.53 x3.1/2 = 53.52 KNm
M (J7 – J8) = 26.18 x3.3/2 = 43.197 KNm
Fig. 4.14
Fig. 4.15
50
Calculation of column moments and column shear:
Joint J5:
M (J5- J9) + M (J5- J6) + M (J5- J1) = 0
⇒ M (J5- J1) = 18.883 KNm
∴ Column shear = 18.883/ (2.1/2) = 17.98 KN
Joint J6:
M (J6- J10) + M (J6- J5) + M (J6- J7) + M (J6 – J2) = 0
⇒ M (J6 – J2) = 42.257 KNm
∴ Column shear = 42.257/ (2.1/2) = 40.24 KN
Joint J7:
M (J7- J12) + M (J7- J6) + M (J7- J8) + M (J7 – J3) = 0
⇒ M (J7 – J3) = 42.257 KNm
∴ Column shear = 42.257/ (2.1/2) = 40.24 KN
Joint J8:
M (J8 – J12) + M (J8- J7) + M (J8- J4) = 0
⇒ M (J8- J4) = 18.883 KNm
∴ Column shear = 18.883/ (2.1/2) = 17.98 KN
Fig. 4.16
51
Fig. 4.17
52
CHAPTER – 5
DESIGN OF SLAB
53
5.1 Desig
n consideration:
Let, Span / effective depth
= 26x1.51
Where 1.51 is the modification factor as per cl. 23.2.1(c), IS 456:2000 (obtained for 25% tension reinforcement)
⇒ 3600/d = 26x1.51
⇒ d = 91.69 m
Nominal cover = 20 mm (mild exposure)
Diameter of the bar = 8 mm
∴ Total depth = 91.69+20+8/2
= 115.69 < 120
Thus it is satisfactory.
∴ Effective depth provided
d = 120- 20- 8/2 = 96 mm
lx = 3300 mm
ly = 3600 mm
Therefore, ly/lx = 3600/3300 = 1.09 < 2
So the slab is a two way slab
Determination of moments of slabs(Laterally restrained slabs):
According to IS 456: 2000, clause D-1.1 , the maximum B.M. per width in the slab are given by,
Mx = αxwlx2
My = αywly2
Where, lx and ly = length of shorter and longer span respectively
αx and αy = co-efficient
Mx and My = moments on strips of unit width spanning lx and ly respectively
W = total design load per unit area
54
5.2 Load diagram for Slab
55
5.3 Design Loads for Slab:
For roof slab:
W1 = 1.5x (0.120x25+1.5+1)
= 8.25KN/m2
For floor slab,
W2 = 1.5x (0.120x25+2+1)
= 9KN/m2
For ly/lx = 1.09 and two adjacent edges discontinuous
Short span co-efficient (αx)
Negative moment at continuous edges = - 0.0524
Positive moment at the midspan = + 0.0395
Long span co-efficient (αy)
Negative moment at the support = - 0.047
Positive moment at the midspan = + 0.035
5.4 Design moments for Slab:
Short span
Long span
Near support midspan Near support midspan Mroof = - 0.0524x8.25x3.32 = -4.71KNm
Mroof = 0.0395x8.25x3.32 =+3.55KNm
Mroof = --0.047x8.25 x3.32
= -4.22KNm
Mroof = +0.035x8.25 x3.32
= +3.14KNm
Mfloor= -0.0524x9x3.32 =-5.136KNm
Mfloor= 0.0395x9x3.32 = +3.87KNm
Mfloor= -0.047x9x3.32 = -4.61KNm
Mfloor= 0.035x9x3.32 = 3.43KNm
56
Now,
R = Mu/bd2 = (Mx106)/(1000x962)
Ast = bd x fck / 2fy [1 - √1-4.598xR/fck]
Spacing = 1000 x Ab / Ast
For 8mm dia,
Ab = π/4 x 82 = 50 mm2
5.5 Design of Slab:
Short span
Long span
ROOF
Support
Midspan Support Midspan
R 0.511
0.39 0.46 0.341
Ast 140.12
106.14 125.73 92.53
Spacing 356.83
451.08 397.66 540.39
Reinforcement provided
Provide 8ɸ @ 280c/c
Provide 8ɸ @ 280c/c
Provide 8ɸ @ 280c/c
Provide 8ɸ @ 280c/c
FLOOR
R
0.56 0.42 0.50 0.37
Ast
154.04 114.52 137.01 100.57
Spacing
324.59 436.62 364.93 497.15
Reinforcement provided
Provide 8ɸ @ 280c/c
Provide 8ɸ @ 280c/c
Provide 8ɸ @ 280c/c
Provide 8ɸ @ 280c/c
5.6 Check for spacing:
cl. 26.3.3 (b)
Spacing should be less than
a. 3xd = 3x96 = 288 mm
57
b. 300 mm
Therefore, spacing < 288 mm i.e. 280mm < 288mm
5.7 Check for thickness of slab:
Maximum B.M. = 5.136KNm
∴ dreqd = √(5.136x106)/(0.138x20x1000) = 43.14mm
∴ Dreqd = 43.14+20+4 = 67.14 mm < 120 mm
Hence safe…..
5.8 Cross section of the Slab
58
CHAPTER- 6
DESIGN MOMENTS AND
SHEAR FORCES
(For Beam)
59
6.1 DESIGN TABLES FOR BENDING MOMENTS
60
A. Load combination for B.M. of beams at ROOF level
MEMBER R1-R2 R2-R3 R3-R4
Load combination END MID END END MID END END MID END
DL+LL 9.648 -12.077 20.305 17.837 -8.858 16.600 19.433 -10.070 10.300
EL -12.903 0.000 12.903 -15.980 0.000 15.980 -12.903 0.000 12.903
1.5(DL+LL) 14.472 -18.116 30.458 26.756 -13.287 24.900 29.150 -15.105 15.450
1.2(DL+LL+EL) -3.906 -14.492 39.850 2.228 -10.630 39.096 7.836 -12.084 27.844
1.2(DL+LL-EL) 27.061 -14.492 8.882 40.580 -10.630 0.744 38.803 -12.084 -3.124
Design moment
27.943 36.744 34.038 31.134 33.108 27.409
-12.903 -19.505 -15.98 -2.696 -7.218 -12.903 -14.534 -3.558
B. Load combination for B.M. of beams at 3RD FLOOR level
MEMBER C1-C2 C2-C3 C3-C4
Load combination END MID END END MID END END MID END
DL+LL 18.903 -16.439 29.681 25.514 -13.220 24.313 29.076 -14.594 18.374
EL -35.838 0.000 35.838 -44.400 0.000 44.400 -35.838 0.000 35.838
1.5(DL+LL) 28.355 -24.659 44.522 38.271 -19.830 36.470 43.614 -21.891 27.561
1.2(DL+LL+EL) -20.322 -19.727 78.623 -22.663 -15.864 82.456 -8.114 -17.513 65.054
1.2(DL+LL-EL) 65.689 -19.727 -7.388 83.897 -15.864 -24.104 77.897 -17.513 -20.957
Design moment
65.689 78.623 83.897 82.456 77.897 65.054
-35.838 -24.659 -7.388 -44.4 -19.83 -24.104 -35.838 -21.891 -20.957
61
C. Load combination for B.M. of beams at 2ND FLOOR level
MEMBER B1-B2 B2-B3 B3-B4
Load combination END MID END END MID END END MID END
DL+LL 18.903 -16.439 29.681 25.514 -13.220 24.313 29.076 -14.594 18.374
EL -50.869 0.000 50.869 -63.023 0.000 63.023 -50.869 0.000 50.869
1.5(DL+LL) 28.355 -24.659 44.522 38.271 -19.830 36.470 43.614 -21.891 27.561
1.2(DL+LL+EL) -38.359 -19.727 96.660 -45.011 -15.864 104.803 -26.152 -17.513 83.092
1.2(DL+LL-EL) 83.726 -19.727 -25.426 106.244 -15.864 -46.452 95.934 -17.513 -38.994
Design moment 83.726
96.66 106.244
104.803 95.934
83.092
-50.869 -24.659 -25.426 -63.023 -19.83 -46.452 -50.869 -21.891 -38.994
D. Load combination for B.M. of beams at 1ST FLOOR level
MEMBER A1-A2 A2-A3 A3-A4
Load combination END MID END END MID END END MID END
DL+LL 19.379 -16.223 29.638 25.415 -13.307 24.239 29.102 -14.442 18.652
EL -52.239 0.000 52.239 -64.743 0.000 64.743 -52.239 0.000 52.239
1.5(DL+LL) 29.069 -24.335 44.457 38.123 -19.961 36.359 43.653 -21.663 27.978
1.2(DL+LL+EL) -39.432 -19.468 98.252 -47.194 -15.968 106.778 -27.764 -17.330 85.069
1.2(DL+LL-EL) 85.942 -19.468 -27.121 108.190 -15.968 -48.605 97.609 -17.330 -40.304
Design moment 85.942 98.252 108.19 106.778 97.609 85.069
-52.239 -24.335 -27.121 -64.743 -19.961 -48.605 -52.239 -21.663 -40.304
62
E. Load combination for B.M. of beams at GROUND FLOOR level
MEMBER G1-G2 G2-G3 G3-G4
Load combination END MID END END MID END END MID END
DL+LL 2.245 -1.714 3.516 3.677 -0.385 3.662 3.447 -1.693 2.355
EL -43.197 0.000 43.197 -53.522 0.000 53.522 -43.197 0.000 43.197
1.5(DL+LL) 3.368 -2.571 5.274 5.516 -0.578 5.493 5.171 -2.540 3.533
1.2(DL+LL+EL) -49.142 -2.057 56.056 -59.814 -0.462 68.621 -47.700 -2.032 54.662
1.2(DL+LL-EL) 54.530 -2.057 -47.617 68.639 -0.462 -59.832 55.973 -2.032 -49.010
Design moment 54.53 56.056 68.639 68.621 55.973 54.662
-49.142 -2.571 -47.617 -59.814 -0.578 -59.832 -47.7 -2.54 -49.01
63
6.2 DESIGN TABLES FOR SHEAR FORCES
64
A. Load Combination for Shear Forces of beams at ROOF level:
R1-R2 R2-R3 R3-R4
Load
combination END MID END END MID END END MID END
DL+LL 36.02 3.17 29.56 26.6 0.85 25.56 31.91 7.64 38.75
EL 7.82 7.82 7.82 10.31 10.31 10.31 7.82 7.82 7.82
1.5(DL+LL) 54.03 4.755 44.34 39.9 1.275 38.34 47.865 11.46 58.125
1.2(DL+LL+EL) 52.608 13.188 44.856 44.292 13.392 43.044 47.676 18.552 55.884
Design shear 52.608 13.188 44.856 44.292 13.392 43.044 47.676 18.552 55.884
B. Load Combination for Shear Forces of beams at 3RD FLOOR level:
R1-R2 R2-R3 R3-R4
Load
combination END MID END END MID END END MID END
DL+LL 52.56 3.29 46.04 41.61 -9.29 40.59 47.9 5.17 47.8
EL 21.27 21.27 21.27 28.65 28.65 28.65 21.27 21.27 21.27
1.5(DL+LL) 78.84 4.935 69.06 62.415 -13.935 60.885 71.85 7.755 71.7
1.2(DL+LL+EL) 88.596 29.472 80.772 84.312 23.232 83.088 83.004 31.728 82.884
Design shear 88.596 29.472 80.772 84.312 23.232 83.088 83.004 31.728 82.884
C. Load Combination for Shear Forces of beams at 2ND FLOOR level:
R1-R2 R2-R3 R3-R4
Load
combination END MID END END MID END END MID END
DL+LL 52.56 3.29 46.04 41.61 -9.29 40.59 47.9 5.17 47.8
EL 30.83 30.83 30.83 40.66 40.66 40.66 30.83 30.83 30.83
1.5(DL+LL) 78.84 4.935 69.06 62.415 -13.935 60.885 71.85 7.755 71.7
1.2(DL+LL+EL) 100.068 40.944 92.244 98.724 37.644 97.5 94.476 43.2 94.356
Design shear 100.068 40.944 92.244 98.724 37.644 97.5 94.476 43.2 94.356
65
D. Load Combination for Shear Forces of beams at 1ST FLOOR level:
R1-R2 R2-R3 R3-R4
Load
combination END MID END END MID END END MID END
DL+LL 52.4 2.98 46.2 41.62 -9.53 40.58 47.98 5.15 47.72
EL 31.66 31.66 31.66 41.77 41.77 41.77 31.66 31.66 31.66
1.5(DL+LL) 78.6 4.47 69.3 62.43 -14.295 60.87 71.97 7.725 71.58
1.2(DL+LL+EL) 100.872 41.568 93.432 100.068 38.688 98.82 95.568 44.172 95.256
Design shear 100.872 41.568 93.432 100.068 38.688 98.82 95.568 44.172 95.256
E. Load Combination for Shear Forces of beams at GROUND FLOOR level:
R1-R2 R2-R3 R3-R4
Load
combination END MID END END MID END END MID END
DL+LL 5.9 0.34 5.2 5.234 0 5.226 5.9 0.34 5.2
EL 26.18 26.18 26.18 34.53 34.53 34.53 26.18 26.18 26.18
1.5(DL+LL) 8.85 0.51 7.8 7.851 0 7.839 8.85 0.51 7.8
1.2(DL+LL+EL) 38.496 31.824 37.656 47.7168 41.436 47.7072 38.496 31.824 37.656
Design shear 38.496 31.824 37.656 47.7168 41.436 47.7072 38.496 31.824 37.656
66
CHAPTER- 7
DESIGN MOMENTS AND
AXIAL LOADS
(FOR COLUMNS AND FOOTINGS)
67
7.1 CONSIDERATIONS
For getting worst condition of bending moment in columns, let us consider that, in each floor of frame F, slab F1-F2 is assumed to be fully loaded and slab F2-F3 (each floor) is loaded only by the dead load. Similarly, in frame 2, slab G2-F2 (each floor) is assumed to be fully loaded and slab F2-E2 (each floor) is considered to be loaded only by the dead load.
7.2 FIXED END MOMENTS FOR COLUMN 1 (FRAME YY)
FEM (R1R2) = +18.063 KNm
FEM (C1C2) = +27.154KNm
Fig. 7.1
68
FEM (B1B2) = +27.154KNm
FEM (A1A2) = +27.154KNm
FEM (G1G2) = +3.063KNm
7.2 DESIGN MOMENTS FOR COLUMN 1
MEMBER R1-C1 C1-B1 B1-A1 A1-G1 G1-F1
Load combination
DL+LL -9.030 -8.960 -8.960 -10.32 -1.250
EL 12.903 22.935 27.934 24.305 18.892
1.5(DL+LL) -13.545 -13.440 -13.440 -15.480 -1.875
1.2(DL+LL+EL) 4.648 16.770 22.769 16.782 21.170
1.2(DL+LL-EL) -26.320 -38.274 -44.273 -41.550 -24.170
Design moment -26.320 -38.274 -44.273 -41.550 -24.170
7.3 CALCULATION OF COLUMN AXIAL
AT ROOF LEVEL
Load on Column R1C1
= Half of Load carried by Beam (RY1RY2+ RY1Rz1+ Rx1RY1) + Self weight of Column R1C1
= 0.5 x (19.874x3.3+13.801x2.7+15.451x3.6) + 3.375 x 3.3
= 90.372 KN
AT 3RD FLOOR LEVEL
Load on Column C1B1
= Half of Load carried by Beam (CY1CY2+ CY1CZ1+CX1CY1) + Self weight of Column C1B1+
= 0.5x (20.027x2.7+21.827x3.6+29.922x3.3) + 3.375x3.3+90.372
= 217.206 KN
69
AT 2ND FLOOR LEVEL
Load on Column B1A1
= Half of Load carried by Beam (BY1BY2+ BY1BZ1+BX1BY1) + Self weight of Column B1A1+217.206
= 0.5x (20.027x2.7+21.827x3.6+29.922x3.3) + 3.375x3.3+217.206
= 348.258 KN
AT 1ST FLOOR LEVEL
Load on Column A1G1
= Half of Load carried by Beam (AY1AY2+ AY1AZ1+AX1AY1) + Self weight of Column A1G1+348.258
= 0.5x (20.027x2.7+21.827x3.6+29.922x3.3) + 3.375x2.7+348.258
= 468.848 KN
AT GROUND FLOOR LEVEL
Load on Column G1F1
= Half of Load carried by Beam (GY1GY2+ GY1GZ1+GX1GY1) + Self weight of Column G1F1
= 0.5x (3.375x3.3+3.375x2.7+3.375x3.6) +3.375x2.1+468.848
= 492.136 KN
7.4 DESIGN AXIAL FORCES FOR COLUMN 1
MEMBER R1-C1 C1-B1 B1-A1 A1-G1 G1-F1
Load combination
DL+LL 90.372 217.206 348.258 468.848 492.136
EL 7.820 29.540 60.370 92.030 118.21
1.5(DL+LL) 135.558 325.809 522.387 703.272 738.204
1.2(DL+LL+EL) 117.830 296.095 490.354 673.054 732.415
1.2(DL+LL-EL) 99.062 225.199 345.466 452.182 448.711
DESIGN AXIAL FORCE 135.558 325.809 522.387 703.272 738.204
70
Fig. 7.2
71
7.5 FIXED END MOMENTS FOR COLUMN 2 (FRAME YY)
FEM (R1R2) = -18.063 KNm
FEM (R2R3) = +16.529 KNm
FEM (C1C2) = -27.154KNm
FEM (C2C3) = +24.504KNm
FEM (B1B2) = -27.154 KNm
FEM (B2B3) = +24.504 KNm
Fig. 7.3
72
FEM (A1A2) = -27.154 KNm
FEM (A2A3) = +24.504 KNm
FEM (G1G2) = -3.063KNm
FEM (G2G3) = +2.703 KNm
7.6 DESIGN MOMENTS FOR COLUMN 2
MEMBER R2-C2 C2-B2 B2-A2 A2-G2 G2-F2
Load combination
DL+LL 0.660 0.660 0.660 0.768 0.115
EL 28.883 51.355 62.537 54.445 42.274
1.5(DL+LL) 0.990 0.990 0.990 1.152 0.173
1.2(DL+LL+EL) 35.452 62.418 75.836 66.256 50.867
1.2(DL+LL-EL) -33.868 -60.834 -74.252 -64.412 -50.591
Design moment 35.452 62.418 75.836 66.256 50.867
7.7 CALCULATION OF COLUMN AXIAL
AT ROOF LEVEL
Load on Column R2C2
= Half of Load carried by Beam (RY1RY2+ RY2Rz2+ Rx2Ry2 +RY2RY3) + Self weight of Column R2C2+ Load due to Secondary Beam (PR1)
= 0.5 x (19.874 x 3.3+10.799 x 3.1 + 18.227 x 2.7+ 16.301 x 3.6) + 10.225+3.375 x3.3
= 124.872 KN
AT 3RD FLOOR LEVEL
Load on Column C2B2
= Half of Load carried by Beam (CY1CY2+ CY2CZ2+CX2CY2+CY2CY3) + Self weight of Column C2B2+ Load due to Secondary Beam (PC1)+124.872
= 0.5x (20.023x3.1+29.922x3.3+28.129x2.7+17.477x3.6)+11.031+3.375x3.3+124.872
= 296.88 KN
73
AT 2ND FLOOR LEVEL
Load on Column B2A2
= Half of Load carried by Beam (BY1BY2+ BY2BZ2+BX2BY2+BY2BY3) + Self weight of Column B2A2+ Load due to Secondary Beam (PB1)+296.88
= 0.5x (20.023x3.1+29.922x3.3+28.129x2.7+17.477x3.6) +11.031+3.375x3.3+296.88
= 473.101 KN
AT 1ST FLOOR LEVEL
Load on Column A2G2
= Half of Load carried by Beam (AY1AY2+ AY2AZ2+AX2AY2+AY2AY3) + Self weight of Column A2G2+ Load due to Secondary Beam (PA1)+473.101
= 0.5x (20.023x3.1+29.922x3.3+28.129x2.7+17.477x3.6) +11.031+3.375x2.7+473.101
= 638.872 KN
AT GROUND FLOOR LEVEL
Load on Column G2F2
= Half of Load carried by Beam (GY1GY2+ GY2GZ2+GX2GY2+GY2GY3) + Self weight of Column G2F2 +638.872
= 0.5x (3.375x3.1+3.375x3.3+3.375x2.7+3.375x3.6) + 3.375x2.1+638.872
= 667.513 KN
7.8 DESIGN AXIAL FORCES FOR COLUMN 2
MEMBER R2-C2 C2-B2 B2-A2 A2-G2 G2-F2
Load combination
DL+LL 124.872 296.88 473.101 638.872 667.513
EL 2.490 9.420 19.250 29.360 37.710
1.5(DL+LL) 187.308 445.320 709.652 958.308 1001.270
1.2(DL+LL+EL) 152.834 367.560 590.821 801.878 846.268
1.2(DL+LL-EL) 146.858 344.952 544.621 731.414 755.764
DESIGN AXIAL FORCE 187.308 445.320 709.652 958.308 1001.270
74
Fig. 7.4
75
7.9 FIXED END MOMENTS FOR COLUMN 3 (FRAME YY)
FEM (R2R3) = -15.139 KNm
FEM (R3R4) = +18.598 KNm
FEM (C3C4) = +27.628 KNm
Fig. 7.5
76
FEM (C2C3) = -23.009 KNm
FEM (B3B4) = +27.628 KNm
FEM (B2B3) = -23.009 KNm
FEM (A3A4) = +27.628 KNm
FEM (A2A3) = -23.009 KNm
FEM (G3G4) = +3.063KNm
FEM (G2G3) = -2.703 KNm
7.10 DESIGN MOMENTS FOR COLUMN 3
MEMBER R3-C3 C3-B3 B3-A3 A3-G3 G3-F3
Load combination
DL+LL -1.150 -1.150 -1.150 -1.34 -0.115
EL 28.883 51.355 62.537 54.445 42.274
1.5(DL+LL) -1.725 -1.725 -1.725 -2.010 -0.173
1.2(DL+LL+EL) 33.280 60.246 73.664 63.726 50.591
1.2(DL+LL-EL) -36.040 -63.006 -76.424 -66.942 -50.867
Design moment -36.040 -63.006 -76.424 -66.942 -50.867
7.11 CALCULATION OF COLUMN AXIAL
AT ROOF LEVEL
Load on Column R3C3
= Half of Load carried by Beam (RY2RY3+ RY3Rz3+ Rx3Ry3 +RY3RY4) + Self weight of Column R3C3+ Load due to Secondary Beam(PR1)+ Load due to Secondary Beam(PR2)
= 0.5 x (16.163 x 3.3 + 10.799 x3.1 + 16.301 x 3.6 +12.451 x 2.7) + 8.465 + 8.005 + 3.375 x 3.3
= 117.166 KN
77
AT 3RD FLOOR LEVEL
Load on Column C3B3
= Half of Load carried by Beam (CY2CY3+ CY3CZ3+CX3CY3+CY3CY4) + Self weight of Column C3B3+ Load due to Secondary Beam(PC1)+ Load due to Secondary Beam(PC2)+117.166
= 0.5(25.874x3.3+20.023x3.1+13.277x2.7+17.477x3.6)+9.084+8.45+3.375x3.3+117.166
= 268.938 KN
AT 2ND FLOOR LEVEL
Load on Column B3A3
= Half of Load carried by Beam (BY2BY3+ BY3BZ3+BX3BY3+BY3BY4) + Self weight of Column B3A3+ Load due to Secondary Beam(PB1)+ Load due to Secondary Beam(PB2)+268.938
= 0.5(25.874x3.3+20.023x3.1+13.277x2.7+17.477x3.6)+9.084+8.45+3.375x3.3+268.938
= 420.711 KN
AT 1ST FLOOR LEVEL
Load on Column A3G3
= Half of Load carried by Beam (AY2AY3+ AY3AZ3+AX3AY3+AY3AY4) + Self weight of Column A3G3+ Load due to Secondary Beam(PA1)+ Load due to Secondary Beam(PA2)+420.711
= 0.5(25.874x3.3+20.023x3.1+13.277x2.7+17.477x3.6)+9.084+8.45+3.375x2.7+420.711
= 570.458 KN
AT GROUND FLOOR LEVEL
Load on Column G3F3
= Half of Load carried by Beam (GY2GY3+ GY3GZ3+GX3GY3+GY3GY4) + Self weight of Column G3F3+570.458
= 0.5(3.375x3.3+3.375x3.1+3.375x2.7+3.375x3.6) +2.1x3.375+570.458
= 598.976 KN
78
7.12 DESIGN AXIAL FORCES FOR COLUMN 3
MEMBER R3-C3 C3-B3 B3-A3 A3-G3 G3-F3
Load combination
DL+LL 117.166 268.938 420.711 570.458 598.976
EL -2.490 -9.420 -19.250 -29.360 -37.71
1.5(DL+LL) 175.749 403.407 631.067 855.687 898.464
1.2(DL+LL+EL) 137.611 311.422 481.753 649.318 673.519
1.2(DL+LL-EL) 143.587 334.030 527.953 719.782 764.023
DESIGN AXIAL FORCE 175.749 403.407 631.067 855.687 898.464
Fig. 7.6
79
7.13 FIXED END MOMENTS FOR COLUMN 4 (FRAME YY)
FEM (R3R4) = -15.541 KNm
FEM (C3C4) = -24.402 KNm
FEM (B3B4) = -24.402 KNm
FEM (A3A4) = -24.402 KNm
FEM (G3G4) = -3.063 KNm
Fig. 7.7
80
7.14 DESIGN MOMENTS FOR COLUMN 4
MEMBER R4-C4 C4-B4 B4-A4 A4-G4 G4-F4
Load combination
DL+LL 8.050 8.050 8.050 8.78 1.250
EL 12.903 22.935 27.934 24.305 18.892
1.5(DL+LL) 12.075 12.075 12.075 13.170 1.875
1.2(DL+LL+EL) 25.144 37.182 43.181 39.702 24.170
1.2(DL+LL-EL) -5.824 -17.862 -23.861 -18.630 -21.170
Design moment 25.144 37.182 43.181 39.702 24.170
7.14 CALCULATION OF COLUMN AXIAL
AT ROOF LEVEL
Load on Column R4C4
= Half of Load carried by Beam (RY1RY2+ RY1Rz1+ Rx1Ry1) + Self weight of Column R1C1+ Load due to Secondary Beam (PR2)
= 0.5 x (16.163 x 3.3 +15.451 x3.6 + 10.09 x 2.7) +3.375 x 3.3 + 5.249 + 1.779
= 86.268 KN
AT 3RD FLOOR LEVEL
Load on Column C4B4
= Half of Load carried by Beam (CY1CY2+ CY1CZ1+CX1CY1) + Self weight of Column C4B4+ Load due to Secondary Beam (PC2)+86.268
= 0.5 x (15.978x2.7+21.827x3.6+25.874x3.3) +5.366+1.878+3.375x3.3+86.268
= 208.2 KN
AT 2ND FLOOR LEVEL
Load on Column B4A4
= Half of Load carried by Beam (BY1BY2+ BY1BZ1+BX1BY1) + Self weight of Column B4A4+ Load due to Secondary Beam (PB2)+208.2
81
= 0.5 x (15.978x2.7+21.827x3.6+25.874x3.3) +5.366+1.878+3.375x3.3+208.2
= 334.345 KN
AT 1ST FLOOR LEVEL
Load on Column A4G4
= Half of Load carried by Beam (AY1AY2+ AY1AZ1+AX1AY1) + Self weight of Column A4G4+ Load due to Secondary Beam (PA2)+334.345
= 0.5 x (15.978x2.7+21.827x3.6+25.874x3.3) +5.366+1.878+3.375x2.7+334.345
= 450.04 KN
AT GROUND FLOOR LEVEL
Load on Column G4F4
= Half of Load carried by Beam (GY1GY2+ GY1GZ1+GX1GY1) + Self weight of Column G4F4++450.04
= 0.5 x (3.375x3.6+3.375x2.7+3.375x3.3) +2.1x3.375+450.04
= 473.328 KN
7.15 DESIGN AXIAL FORCES FOR COLUMN 4
MEMBER R4-C4 C4-B4 B4-A4 A4-G4 G4-F4
Load combination
DL+LL 86.268 208.2 334.345 450.04 473.328
EL -7.820 -29.540 -60.370 -92.030 -118.21
1.5(DL+LL) 129.402 312.300 501.518 675.060 709.992
1.2(DL+LL+EL) 94.138 214.392 328.770 429.612 426.142
1.2(DL+LL-EL) 112.906 285.288 473.658 650.484 709.846
DESIGN AXIAL FORCE 129.402 312.300 501.518 675.060 709.992
82
Fig. 7.8
83
CHAPTER- 8
DESIGN OF BEAM
84
8.1 DESIGN FOR BENDING MOMENT
85
8.1.1 Design of Beam at Roof level
R1-R2 R2-R3 R3-R4 END MID END END MID END END MID END
DESIGN MOMENT 27.061 39.85 40.58 39.096 38.803 27.844
-12.903 -18.116 -15.98 -13.287 -12.903 -15.105 -3.124
Mu/bd2 0.531 0 0.783 0.797 0 0.768 0.762 0 0.547
-0.253 -0.356 0 -0.314 -0.261 0 -0.253 -0.297 -0.061 Pt 0.158 0.233 0.233 0.233 0.233 0.158 Ast 195.288 0 287.988 287.988 0 287.988 287.988 0 195.288 Pt 0.085 0.114 0.099 0.085 0.085 0.085 0.085 Ast 105.06 140.904 0 122.364 105.06 0 105.06 105.06 105.06 NO OF BARS AT TOP 2 nos 16 Ф bars (402 )throughout the length NO OF BARS AT BOTTOM 2 nos 16 Ф bars (402) throughout the length
8.1.2 Design of Beam at 3rd FLOOR level
C1-C2 C2-C3 C3-C4 END MID END END MID END END MID END
DESIGN MOMENT 65.689 78.623 83.897 82.456 77.897 65.054
-35.838 -24.659 -7.388 -44.4 -19.83 -24.104 -35.838 -21.891 -20.957
Mu/bd2 1.303 0.000 1.559 1.664 0.000 1.635 1.545 0.000 1.290
-0.711 -0.489 -0.147 -0.880 -0.393 -0.478 -0.711 -0.434 -0.416 Pt 0.392 0.494 0.53 0.512 0.477 0.392 Ast 482.16 0 607.62 651.9 0 629.76 586.71 0 482.16 Pt 0.218 0.143 0.085 0.264 0.114 0.143 0.218 0.128 0.128 Ast 268.14 175.89 104.55 324.72 140.22 175.89 268.14 157.44 157.44 no of bars at top 2 nos 20 Ф bars (628 mm2) throughout the length no of bars at top 1 nos 20 Ф bar (314) no of bars at bottom 2 nos 16 Ф bars (402) throughout the length
86
8.1.2 Design of Beam at 2ND FLOOR level
B1-B2 B2-B3 B3-B4 END MID END END MID END END MID END
DESIGN MOMENT 83.726 96.66 106.244 104.803 95.934 83.092
-50.869 -24.659 -25.426 -63.023 -19.83 -46.452 -50.869 -21.891 -38.994
Mu/bd2 1.660 0.000 1.917 2.107 0.000 2.078 1.902 0.000 1.648
-1.009 -0.489 -0.504 -1.250 -0.393 -0.921 -1.009 -0.434 -0.773 Pt 0.53 0.621 0.685 0.67 0.602 0.53 Ast 651.9 0 763.83 842.55 0 824.1 740.46 0 651.9 Pt 0.327 0.143 0.143 0.376 0.114 0.28 0.295 0.128 0.233 Ast 402.21 175.89 175.89 462.48 140.22 344.4 362.85 157.44 286.59 no of bars at top 2 nos 20 Ф bars (628 mm2) throughout the length no of bars at top 1 nos 20 Ф bar (314) curtailing no of bars at bottom 2 nos 20 Ф bars (628) throughout the length
8.1.2 Design of Beam at 1ST FLOOR level
A1-A2 A2-A3 A3-A4 END MID END END MID END END MID END
DESIGN MOMENT 85.942 98.252 108.19 106.778 97.609 85.069
-52.239 -24.335 -27.121 -64.743 -19.961 -48.605 -52.239 -21.663 -40.304
Mu/bd2 1.704 0.000 1.948 2.145 0.000 2.117 1.936 0.000 1.687
-1.036 -0.483 -0.538 -1.284 -0.396 -0.964 -1.036 -0.430 -0.799 Pt 0.53 0.621 0.701 0.685 0.621 0.53 Ast 651.9 0 763.83 862.23 0 842.55 763.83 0 651.9 Pt 0.311 0.143 0.158 0.392 0.114 0.295 0.311 0.128 0.233 Ast 382.53 175.89 194.34 482.16 140.22 362.85 382.53 157.44 286.59 no of bars at top 2 nos 20 Ф bars (628 mm2) throughout the length no of bars at top 1 nos 20 Ф bar (314) curtailing no of bars at bottom 2 nos 20 Ф bars (628) throughout the length
87
8.1.3 Design of Beam at Ground FLOOR level
G1-G2 G2-G3 G3-G4 END MID END END MID END END MID END
DESIGN MOMENT 54.53 56.056 68.639 68.621 55.973 54.662
-49.142 -2.571 -47.617 -59.814 -0.578 -59.832 -47.7 -2.54 -49.01
Mu/bd2 1.081 0.000 1.112 1.361 0.000 1.361 1.110 0.000 1.084
-0.974 -0.051 -0.944 -1.186 -0.011 -1.186 -0.946 -0.050 -0.972 Pt 0.327 0.343 0.426 0.426 0.343 0.327 Ast 404.172 0 423.948 526.536 0 526.536 423.948 0 404.172 Pt 0.295 0.085 0.28 0.359 0.085 0.359 0.28 0.085 0.295 Ast 362.85 104.55 344.4 441.57 104.55 441.57 344.4 104.55 362.85 no of bars at top 2 nos 20 Ф bars (628) throughout the length no of bars at bottom 2 nos 20 Ф bars (628) throughout the length
88
.
8.2 DESIGN FOR SHEAR FORCE
89
8.2.1
Minimum shear reinforcement, Asv/bSv = 0.4/.87fy (as per cl.26.5.1.6 of IS 456:2000)
Maximum spacing smaller of, (i) 300mm (as per cl.26.5.1.5 of IS 456:2000)
(ii) 0.75d = 346.5 mm (as per cl.26.5.1.5 of IS 456:2000)
(iii) Sv = 0.87x250x56/(250x0.4) = 121.8 (6φ)
Or, Sv = 0.87x250x100/(250x0.4) = 217.5 (8φ)
8.2.2 Design of Beam at Roof level
R1-R2 R2-R3 R3-R4 END MID END END MID END END MID END
Design shear 52.608 13.188 44.856 44.292 13.392 43.044 47.676 18.552 55.884
τv=Vu/bd 0.390 0.098 0.332 0.328 0.099 0.319 0.353 0.137 0.414
Ast 804 804 804 804 804 804 804 804 804
pt 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 τc 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55
τc>τv , minimum shear reinforcement is required
Spacing 2 legged 6 φ bars @ 120 mm c/c
90
8.2.3 Design of Beam at 3rd Floor level
C1-C2 C2-C3 C3-C4
END MID END END MID END END MID END
Design shear 88.596 29.472 80.772 84.312 23.232 83.088 83.004 31.728 82.884
τv=Vu/bd 0.656 0.218 0.598 0.625 0.172 0.615 0.615 0.235 0.614 Ast 1030 1030 1030 1344 1344 1344 1030 1030 1030
pt 0.763 0.763 0.763 0.996 0.996 0.996 0.763 0.763 0.763
τc 0.676 0.676 0.676 0.62 0.62 0.62 0.676 0.676 0.676
τc>τv , minimum shear reinforcement is required
Sv provided 2 legged 6 φ bars @ 120 mm c/c
8.2.4 Design of Beam at 2nd Floor level
B1-B2 B2-B3 B3-B4
END MID END END MID END END MID END
Design shear 100.068 40.944 92.244 98.724 37.644 97.5 94.476 43.2 94.356
τv=Vu/bd 0.741 0.303 0.683 0.731 0.279 0.722 0.700 0.320 0.699
Ast 1570 1570 1570 1570 1570 1570 1570 1570 1570 pt 1.163 1.163 1.163 1.163 1.163 1.163 1.163 1.163 1.163
τc 0.653 0.653 0.653 0.653 0.653 0.653 0.653 0.653 0.653
Vus/d=(τv-τc)b 0.265 0.091 0.235 0.208 0.140 0.138 Sv 80 200 90 100 150 150
maximum Sv 80
Sv provided 2 legged 8 φ bars at 80mm c/c
91
8.2.5 Design of Beam at 1st Floor level
A1-A2 A2-A3 A3-A4
END MID END END MID END END MID END
Design shear 100.872 41.568 93.432 100.068 38.688 98.82 95.568 44.172 95.256
τv=Vu/bd 0.747 0.308 0.692 0.741 0.287 0.732 0.708 0.327 0.706 Ast 1570 1570 1570 1570 1570 1570 1570 1570 1570
pt 1.163 1.163 1.163 1.163 1.163 1.163 1.163 1.163 1.163
τc 0.653 0.653 0.653 0.653 0.653 0.653 0.653 0.653 0.653 Vus/d=(τv-τc)b 0.283 0.117 0.265 0.237 0.165 0.158
Sv 70 180 80 90 130 130
maximum Sv 70 Sv provided 2 legged 8 φ bars at 70 mm c/c
8.2.6 Design of Beam at Ground Floor level
G1-G2 G2-G3 G3-G4 END MID END END MID END END MID END
Design shear 38.496 31.824 37.656 47.7168 41.436 47.7072 38.496 31.824 37.656
τv=Vu/bd 0.285 0.236 0.279 0.353 0.307 0.353 0.285 0.236 0.279
Ast 1256 1256 1256 1256 1256 1256 1256 1256 1256 pt 0.930 0.930 0.930 0.930 0.930 0.930 0.930 0.930 0.930
τc 0.606 0.606 0.606 0.606 0.606 0.606 0.606 0.606 0.606
τc>τv , minimum shear reinforcement is required spacing 2 legged 6 φ bars @ 120 mm c/c
92
8.3 DETAILING OF BEAM
93
Beam development length
Shear Reinforcement in Beams
Fig 8.1
Fig 8.2
94
Curtailment of Main reinforcement
Fig 8.3
Fig 8.4
95
Detailing of Beam in second floor
Fig 8.5
96
CHAPTER-9
DESIGN OF COLUMN
97
9.1 COLUMN 1
9.1.1 Considerations:
Here, b = 300 mm
D = 450 mm
d’ = 40+20/2 = 50 mm
... d’//D= 50/450 = 0.111
Column Design moment(Mu)
Design axial
force (Pu) Mu/(fckbD2)
Pu/(fckbD) P/fck P P provided
Ast
R1-C1 26.320 135.558 0.022 0.050 0.01 0.2 0.8 1080
C1-B1 38.274 325.809 0.032 0.120 0.01 0.2 0.8 1080
B1-A1 44.273 522.387 0.036 0.193 0.01 0.2 0.8 1080
A1-G1 41.550 703.272 0.034 0.260 0.01 0.2 0.8 1080
R1-C1 4 nos 20 ɸ bars (1256) at each corner
C1-B1 4 nos 20 ɸ bars (1256) at each corner
B1-A1 4 nos 20 ɸ bars (1256) at each corner
A1-G1 4 nos 20 ɸ bars (1256) at each corner
9.1.2 Lateral ties (As per Cl.26.5.3.2(c) of IS: 456-2000)
Column
Diameter (mm)
should not be less than
Pitch (mm)
should not be more than Lateral ties provided
(i) (ii) (i) (ii) (iii)
R1-C1 5 6 300 320 300 6 ɸ bar 2L 300mm
C1-B1 5 6 300 320 300 6 ɸ bar 2L 300mm
B1-A1 5 6 300 320 300 6 ɸ bar 2L 300mm
A1-G1 5 6 300 320 300 6 ɸ bar 2L 300mm
98
9.2 COLUMN 2:
9.2.1 Considerations:
Here, b = 300 mm
D = 450 mm
d’ = 40+20/2 = 50 mm
... d’//D= 50/450 = 0.111
Column Design
moment(Mu)
Design axial
force (Pu) Mu/(fckbD2)
Pu/(fckbD) P/fck P P provided
Ast
R2-C2 35.452 187.308 0.03 0.07 0.01 0.2 0.8 1080
C2-B2 62.418 445.320 0.05 0.16 0.01 0.2 0.8 1080
B2-A2 75.836 709.652 0.06 0.26 0.01 0.2 0.8 1080
A2-G2 66.256 958.308 0.05 0.35 0.01 0.2 0.8 1080
R2-C2 4 nos 20 ɸ bars (1256) at each corner
C2-B2 4 nos 20 ɸ bars (1256) at each corner
B2-A2 4 nos 20 ɸ bars (1256) at each corner
A2-G2 4 nos 20 ɸ bars (1256) at each corner
9.2.2 Lateral ties (As per Cl.26.5.3.2(c) of IS: 456-2000)
Column
Diameter (mm)
should not be less than
Pitch (mm)
should not be more than Lateral ties provided
(i) (ii) (i) (ii) (iii)
R2-C2 5 6 300 320 300 6 ɸ bar 2L 300mm
C2-B2 5 6 300 320 300 6 ɸ bar 2L 300mm
B2-A2 5 6 300 320 300 6 ɸ bar 2L 300mm
A2-G2 5 6 300 320 300 6 ɸ bar 2L 300mm
99
9.3 COLUMN 3:
9.3.1 Considerations:
Here, b = 300 mm
D = 450 mm
d’ = 40+20/2 = 50 mm
... d’//D= 50/450 = 0.111
Column Design
moment(Mu)
Design axial
force (Pu) Mu/(fckbD2)
Pu/(fckbD) P/fck P P provided
Ast
R3-C3 36.040 175.749 0.03 0.06 0.01 0.2 0.8 1080
C3-B3 63.006 403.407 0.05 0.15 0.01 0.2 0.8 1080
B3-A3 76.424 631.067 0.06 0.23 0.01 0.2 0.8 1080
A3-G3 50.867 855.687 0.04 0.32 0.01 0.2 0.8 1080
R3-C3 4 nos. 20 ɸ bars (1256) at each corner
C3-B3 4 nos. 20 ɸ bars (1256) at each corner
B3-A3 4 nos. 20 ɸ bars (1256) at each corner
A3-G3 4 nos. 20 ɸ bars (1256) at each corner
9.3.2 Lateral ties (As per Cl.26.5.3.2(c) of IS: 456-2000)
Column
Diameter (mm)
should not be less than
Pitch (mm)
should not be more than Lateral ties provided
(i) (ii) (i) (ii) (iii)
R2-C2 5 6 300 320 300 6 ɸ bar 2L 300mm
C2-B2 5 6 300 320 300 6 ɸ bar 2L 300mm
B2-A2 5 6 300 320 300 6 ɸ bar 2L 300mm
A2-G2 5 6 300 320 300 6 ɸ bar 2L 300mm
100
9.4 COLUMN 4:
9.4.1 Considerations:
Here, b = 300 mm
D = 450 mm
d’ = 40+20/2 = 50 mm
... d’//D= 50/450 = 0.111
Column design
moment(Mu)
design axial
force (Pu) Mu/(fckbD2)
Pu/(fckbD) P/fck P P provided
Ast
R4-C4 25.144 129.402 0.02 0.05 0.01 0.2 0.8 1080
C4-B4 37.182 312.300 0.03 0.11 0.01 0.2 0.8 1080
B4-A4 43.181 501.518 0.04 0.18 0.01 0.2 0.8 1080
A4-G4 39.702 675.060 0.03 0.25 0.01 0.2 0.8 1080
R4-C4 4 nos. 20 ɸ bars (1256) at each corner
C4-B4 4 nos. 20 ɸ bars (1256) at each corner
B4-A4 4 nos.20 ɸ bars (1256) at each corner
A4-G4 4 nos. 20 ɸ bars (1256) at each corner
9.4.2 Lateral ties (As per Cl.26.5.3.2(c) of IS: 456-2000)
Column
Diameter (mm)
should not be less than
Pitch (mm)
should not be more than Lateral ties provided
(i) (ii) (i) (ii) (iii)
R2-C2 5 6 300 320 300 6 ɸ bar 2L 300mm
C2-B2 5 6 300 320 300 6 ɸ bar 2L 300mm
B2-A2 5 6 300 320 300 6 ɸ bar 2L 300mm
A2-G2 5 6 300 320 300 6 ɸ bar 2L 300mm
101
DETAILING OF COLUMN
102
Fig. 9.1
103
CHAPTER 10
FOOTING DESIGN
104
10.1 FOOTING DESIGN FOR THE COLUMN R1-F1
Axial load on the column to the footing = 738.204 KN
Moment at the base of the column = 24.17 KNm
SBC of the soil = 150 KN/m2
10.1.1 GEOTECHNICAL CONSIDERATION
Now,
P = 492 KN
M = 16.11 KNm
Axial Load on the column = 492
Add 10% for self weight = 49.2
Total load on footing = 541.2 KN
Area required = = 3.608 m2
Add 10% for moment= .3608m2
Total area required = 3.9 m2
L/B = 450/300 = 1.5
L = 1.5 B
1.5 B2 = 3.9 m2
B = 1.59 m
L = 2.4 m
Provide footing size 2.9 m x 1.9 m
Pmax = P/A + M/Z
= 541.2/(2.9x 1.9)+ (16.11 x 6)/(1.9 x 2.92)
= 98.3 KN/m2 <150 KN/m2 (hence safe)
P min = P/A - M/Z
= 541.66/(2.9x 1.9) - (16.11 x 6)/(1.9 x 2.92) = 80.21KN/m2
105
10.1.2 STRUCTURAL CONSIDERATION
1. CHECK FOR BENDING
a) Longer direction
x = 7.64 KN/m2
y = 90.66 KN/m2
BM at the face of the column, M
= 90.66x1.225 x1.9x1.225 x .5 + .5 x7.64 x1.225 x1.9 x 2/3 x 1.225
M = 133.24 KNm
Mu = 1.5×133.24=200 KNm
Now, effective width of the footing = b +1/8(B-b)
Fig. 10.1
106
= 450 + 1/8(2900-450)
= 756. 25 mm
dreqd = √(200x 106)/(.138 x 20 x 756.25)
= 309.5 mm
Using 50 mm clear cover and 16ᵠ bars
Overall depth = 309.5 + 50 +16/2
= 367.5 mm
We provide overall depth = 700 mm
davailable = 700 – 50- 16/2
= 642 mm
Now
Mu/be = 310/.756=410 and d= 64.2 cm
From chart 15 of SP 16
Pt = 0.3
As = (.3 x 756 x 642)/ 100
= 1457 mm2
From table 96 of SP 16
Provide 16φ bars at 100 mm c/c (2011 mm2)
So actual steel provided = (2011 x 100)/ (756 x 642)
= 0.414
107
b) For shorter direction
X=7.61 Y=90.61
BM at the face of the column = 90.69x 0.8 x 0.8 x 2.9 x .5 + 0.5x 7.61 x 0.8 x 2.9 x 2/3 x 0.8
=88.89 KNm
Mu = 133.33 KNm
Now, effective width of the footing = b +1/8(B-b)
= 300 + 1/8(1900-300)
= 500 mm
dreqd = √(133.83 x 106)/(.138 x 20 x 500) = 310.83
Fig. 10.2
108
Overall depth = 310.83 + 50 +16+16/2
= 384.83 mm
Provided depth = 700 mm
davailable = 700 -50 -16 -16/2 = 626 mm
Now,
Mu/be = 133.3/.500 = 266 and d= 62.6 cm
Pt = 0.18
As = (.18 x 500 x 626)/ 100
= 563.4 mm2
From table 96 of SP 16
We provide 16φ bars at 300 mm c/c (670 mm2)
So actual steel provided = (670 x 100)/ (500 x 626)
= 0.21
109
2. CHECK FOR ONE WAY SHEAR
Critical section for one way shear occurs at a distance of “d” from the face of the column
d= 642 mm
de = (550 x 583)/ 1225
= 261.75 mm
Fig. 10.3
110
Overall depth = 261.75 +150
= 411.75 mm
Available depth = 411.75 – 50 – 16/2 = 353.75 mm
Actual amount of steel = 2011x 2.9 = 5831.9 mm2
Area of trapezoid = 923704mm2
Percentage of steel at critical section
=
=
= .63 %
For Pt= 0.63 %,
τc = .522 N/mm2
X = 2.02
Y = 88.28
V = [.5 x (88.07+90.3)] x .583 x 1.9
= 98.90 KN
Vu = 148.36 KN
τv = (Vu/bd)
= (148.36 x 103)/ [.5 x (1584+2714) x 353.75]
0.19 < τc
Hence safe
Fig. 10.4
111
3. CHECK FOR TWO WAY SHEAR
Critical section for punching shear occurs at a distance of “d/2” from the face of the column
d/2 = 642/2 = 321 mm
b= 2 x 321 + 300
= 942 mm
Now
de = (550 x 904)/ 1225= 405.44 mm
Fig. 10.5
112
Overall depth = 405.44 + 150
= 555.8 mm
Available depth = 555.8 – 50 -16/2
= 497.87 mm
Punching shear stress = (541.2 x 103)/(4x 942 x 497.87)
= 0.28 N/mm2
Permissible punching shear stress = 0.25 √ (fck)
= 0.25 x √20
= 1.12 N/mm2
Hence safe
4. CHECK FOR BEARING
As per clause 34.4 of IS 456
Safe bearing capacity = 0.45 fck √ (A1 / A2)
A1 = (b +4D) 2
A2 = (450 x 300)
Now A1/ A2 = 8.44 and √ (A1 / A2) = 2.97>2
So take √ (A1 / A2) = 2
Actual bearing stress = (column load/column area)
= (492 x 103)/ (450 x 300)
= 3.64 N/mm2
Safe bearing stress = 0.45 fck √ (A1 / A2)
= 0.45 x 20 x √2
= 18 N/mm2
Hence safe
113
5. CHECK FOR DEVELOPMENT LENGTH
For 16 φ bars and M20 concrete from table 66 of SP 16
Development length = 752 mm
a) Available length in longer direction = 1225 mm. b) Available length in shorter direction = 800 mm.
Fig. 10.6
114
10.2 FOOTING DESIGN FOR THE COLUMN R2-F2
Axial load on the column to the footing = 1001.27 KN
Moment at the base of the column = 51 KNm
SBC of the soil = 150 KN/m2
10.2.1 GEOTECHNICAL CONSIDERATION
Now,
Pu = 667.5 KN
Mu = 42.5 KNm
Axial Load on the column = 667.5
Add 10% for self weight = 66.75
Total load on footing = 734.25 KN
Area required = = 4.89 m2
Add 10% for moment= .489 m2
Total area required = 5.4 m2
L/B = 450/300 = 1.5
L = 1.5 B
1.5 B2 = 5.4 m2
B = 1.9 m
L = 2.89 m
Provide footing size 2.9 m x 1.9 m
Pmax = P/A + M/Z
= 734.25/(2.9x 1.9)+ (42.5 x 6)/(1.9 x 2.92)
= 149.2 KN/m2
P min = P/A - M/Z
= 734.25/(2.9x 1.9) - (42.5 x 6)/(1.9 x 2.92) = 117.3 KN/m2
115
10.2.2 STRUCTURAL CONSIDERATION
1. CHECK FOR BENDING
a) Longer direction
x = 13.5 KN/m2
y = 135.7 KN/m2
BM at the face of the column, M
= 135.7x1.225 x1.9x1.225 x .5 + .5 x13.5 x1.225 x1.9 x 2/3 x 1.225
M = 206.34 KNm
Mu = 310 KNm
Now, effective width of the footing = b +1/8(B-b)
= 450 + 1/8(2900-450)
= 756. 25 mm
Fig. 10.7
116
dreqd = √(310 x 106)/(.138 x 20 x 756.25) = 385.4 mm
Using 50 mm clear cover and 16ᵠ bars
Overall depth = 385.4 + 50 +16/2
= 441.4 mm
We provide overall depth = 700 mm
davailable = 700 – 50- 16/2
= 642 mm
Now
Mu/be = 310/.756 and d= 64.2 cm
From table 15 of SP 16
Pt = 0.3
As = (.3 x 756.25 x 642)/ 100
= 1457 mm2
From table 96 of SP 16
Provide 16φ bars at 100 mm c/c (2011 mm2)
So actual steel provided = (2011 x 100)/ (756.5 x 642)
= 0.41
117
b) For shorter direction
X = 13.43
Y = 135.76
BM at the face of the column = .5x (149.2 + 117.3) x 0.8 x 2.9 x 2.9 x .5
= 280.05 KNm
Mu = 420 KNm
Now, effective width of the footing = b +1/8(B-b)
= 300 + 1/8(1900-300)
= 500 mm
dreqd = √(420 x 106)/(.138 x 20 x 500)
= 551.67
Overall depth = 551.67 + 50 +16+16/2
= 625.67 mm
Fig. 10.8
118
Provided depth = 700 mm
davailable = 700 -50 -16 -16/2 = 626 mm
Now
Mu/be = 420/.500 = 840 and d= 62.6 cm
Pt = 0.3
As = (.3 x 500 x 626)/ 100
= 939 mm2
From table 96 of SP 16
We provide 16φ bars at 180 mm c/c (1117 mm2)
So actual steel provided = (1117 x 100)/ (500 x 626)
= 0.35
119
2. CHECK FOR ONE WAY SHEAR
Critical section for one way shear occurs at a distance of “d” from the face of the column
d= 642 mm
de = (550 x 583)/ 1225
= 261.75 mm
Overall depth = 261.75 +150= 411.75 mm
Fig. 10.9
120
Available depth = 411.75 – 50 – 16/2 = 353.75 mm
Actual amount of steel = 2011 x 2.9 = 5831.9 mm2
Area of trapezoid = .5 x (1584+2900) x412
= 923704 mm2
Percentage of steel at critical section
=
=
= .63 %
For Pt 0.63 %,
τc = .552 N/mm2
X = 6.413
Y = 142.8
V= [.5 x(142.8+149.2)] x .583 x 1.9
= 161.72 KN
Vu = 242.58 KN
τv = (Vu/bd)
= (242.58 x 103)/ [.5x (1584+2714) x 353.75]
0.32 < τc
Hence safe
121
3. CHECK FOR TWO WAY SHEAR
Critical section for punching shear occurs at a distance of “d/2” from the face of the column
d/2 = 642/2 = 321 mm
b= 2 x 321 + 300
= 942 mm
Now
de = (550 x 904)/ 1225
= 405.44 mm
Fig. 10.10
122
Overall depth = 405.44 + 150
= 555.8 mm
Available depth = 555.8 – 50 -16/2
= 497.87 mm
Punching shear stress = (734.25 x 103)/(4x 942 x 497)
= 0.39 N/mm2
Permissible punching shear stress = 0.25 √(fck)
= 0.25 x √20
= 1.12 N/mm2
Hence safe
4. CHECK FOR BEARING
As per clause 34.4 of IS 456
Safe bearing capacity = 0.45 fck √ (A1 / A2)
A1 = (b +4D)2
A2 = (450 x 300)
Now A1/ A2 = 8.44 and √(A1 / A2 ) = 2.97>2
So take √ (A1 / A2 ) = 2
Actual bearing stress = (column load/column area)
= (667.5 x 103)/(450 x 300)
= 4.94 N/mm2
Safe bearing stress = 0.45 fck √(A1 / A2)
= 0.45 x 20 x √2
= 18 N/mm2
Hence safe
123
5. CHECK FOR DEVELOPMENT LENGTH
For 16 φ bars and M20 concrete from table 66 of SP 16
Development length = 752 mm
c) Available length in longer direction = 1225 mm. d) Available length in shorter direction = 800 mm.
DETAILING OF FOOTING:
Fig. 10.11
124
10.3 FOOTING DESIGN FOR THE COLUMN R3-F3
Axial load on the column to the footing = 898.46 KN
Moment at the base of the column = 50.867 KNm
SBC of the soil = 150 KN/m2
10.3.1 GEOTECHNICAL CONSIDERATION
Now,
P = 599 KN
M = 34 KNm
Axial Load on the column = 599
Add 10% for self weight = 59.1
Total load on footing = 658.9 KN
Area required = = 4.4 m2
Add 10% for moment= 0.44m2
Total area required = 4.84 m2
L/B = 450/300 = 1.5
L = 1.5 B
1.5 B2 = 4.84 m2
B = 1.79 m
L = 2.69 m
Provide footing size 2.9 m x 1.9 m
Pmax = P/A + M/Z
= 658.9/(2.9x 1.9)+ (34 x 6)/(1.9 x 2.92)
= 132.34 KN/m2 <150 KN/m2 (hence safe)
P min = P/A - M/Z
= 658.9/(2.9x 1.9) - (34 x 6)/(1.9 x 2.92) = 107 KN/m2
125
10.3.2 STRUCTURAL CONSIDERATION
1. CHECK FOR BENDING
a) Longer direction
x = 14.63 KN/m2
BM at the face of the column, M
= (107+14.63) x1.225 x1.9x1.225 x .5 + .5 x(132.34-107-14.63) x1.225 x1.9 x 2/3 x 1.225
M = 184 KNm
Mu = 1.5×184=276 KNm
Fig. 10.12
126
Now, effective width of the footing = b +1/8(B-b)
= 450 + 1/8(2900-450)
= 756 mm
dreqd = √(276x 106)/(.138 x 20 x 756)
= 363.69 mm
Using 50 mm clear cover and 16ᵠ bars
Overall depth = 363.69 + 50 +16/2
= 421.7 mm
We provide overall depth = 800 mm
davailable = 800 – 50- 16/2
= 742 mm
Now
Mu/be = 276/.756=365 and d= 74.2 cm
From chart 15 of SP 16
Pt = 0.28
As = (.28 x 756 x 742)/ 100
= 1570.68 mm2
From table 96 of SP 16
Provide 16φ bars at 120 mm c/c (1675 mm2)
127
b) For shorter direction
BM at the face of the column =0.5(107+132.34) x 0.8x2.9x2.9x0.5
= 402.6 KNm
Mu = 603.8 KNm
Now, effective width of the footing = b +1/8(B-b)
= 300 + 1/8(1900-300)
= 500 mm
dreqd = √(603.8 x 106)/(.138 x 20 x 500)
= 661.46 mm
Overall depth = 661.46 + 50 +16+16/2
= 735.46 mm
Provided depth = 800 mm
Fig. 10.13
128
davailable = 800 -50 -16 -16/2 = 726 mm
Now
Mu/be = 603.8/.500 = 1207 and d= 72.6 cm
Pt = 0.78
As = (0.78 x 500 x 726)/ 100
= 2831.4 mm2
From table 96 of SP 16
We provide 16φ bars at 60 mm c/c (3351 mm2)
2. CHECK FOR ONE WAY SHEAR
Critical section for one way shear occurs at a distance of “d” from the face of the column
d= 742 mm
129
Fig. 10.14
130
de = (650 x 483)/ 1225
= 256.3 mm
Overall depth = 256.3 +150
= 406.3 mm
Available depth = 406.3 – 50 – 16/2 = 348.3 mm
Actual amount of steel = 1675x 2.9 = 4857.9 mm2
Percentage of steel at critical section
=
=
= .97 %
For Pt= 0.97 %,
τc = .62 N/mm2
V= [.5 x (107+21.2+132.34)] x .483 x 1.9
= 119.50 KN
Vu = 179.3 KN
τv = (Vu/bd)
= (179.3 x 103)/ [.5x (1934+2762) x 348.3]
0.21 < τc
Hence safe
Fig. 10.15
131
3. CHECK FOR TWO WAY SHEAR
Critical section for punching shear occurs at a distance of “d/2” from the face of the column
d/2 = 742/2 = 371 mm
b= 2 x 0.371+0.300
= 1.042 m
Now
de = (650 x 0.854)/ 1.225= 453.1 mm
Fig. 10.16
132
Overall depth = 453.1 + 150
= 603.1 mm
Available depth = 603.1 – 50 -16/2
= 545.1 mm
Punching shear stress = (658 x 103)/(4x 1042 x 545.1)
= 0.29 N/mm2
Permissible punching shear stress = 0.25 √(fck)
= 0.25 x √20
= 1.12 N/mm2
Hence safe
4. CHECK FOR BEARING
As per clause 34.4 of IS 456
Safe bearing capacity = 0.45 fck √ (A1 / A2)
A1 = (b +4D)2
A2 = (450 x 300)
Now A1/ A2 = 8.44 and √ (A1 / A2 ) = 2.97>2
So take √ (A1 / A2 ) = 2
Actual bearing stress = (column load/column area)
= (599 x 103)/ (450 x 300)
= 4.4 N/mm2
Safe bearing stress = 0.45 fck √ (A1 / A2)
= 0.45 x 20 x √2
= 18 N/mm2
Hence safe
133
5. CHECK FOR DEVELOPMENT LENGTH
For 16 φ bars and M20 concrete from table 66 of SP 16
Development length = 752 mm
e) Available length in longer direction = 1225 mm. f) Available length in shorter direction = 800 mm.
DETAILING OF FOOTING:
Fig. 10.17
134
10.4 FOOTING DESIGN FOR THE COLUMN R4-F4
Axial load on the column to the footing = 709.9 KN
Moment at the base of the column = 24.17 KNm
SBC of the soil = 150 KN/m2
10.4.1 GEOTECHNICAL CONSIDERATION
Now,
P = 473.328 KN
M = 16.11 KNm
Axial Load on the column = 473.328
Add 10% for self weight = 47.33
Total load on footing = 520.66 KN
Area required = = 3.47 m2
Add 10% for moment= .347m2
Total area required = 3.8 m2
L/B = 450/300 = 1.5
L = 1.5 B
1.5 B2 = 3.8 m2
B = 1.59 m
L = 2.4 m
Provide footing size 2.9 m x 1.9 m
Pmax = P/A + M/Z
= 520.66/(2.9x 1.9)+ (16.11 x 6)/(1.9 x 2.92)
= 100.5 KN/m2 <150 KN/m2 (hence safe)
P min = P/A - M/Z
= 520.66/ (2.9x 1.9) - (16.11 x 6)/(1.9 x 2.92) = 88.4 KN/m2
135
10.4.2 STRUCTURAL CONSIDERATION
1. CHECK FOR BENDING
a) Longer direction
x = 7 KN/m2
y = 107 KN/m2
BM at the face of the column, M
= (88.4+7) x1.225 x1.9x1.225 x .5 + .5 x(100.5-88.4-7) x1.225 x1.9 x 2/3 x 1.225
M = 140.84 KNm
Mu = 1.5×140.84=211.3 KNm
Now, effective width of the footing = b +1/8(B-b)
= 450 + 1/8(2900-450)
= 756. 25 mm
Fig. 10.18
136
dreqd = √(211.3 x 106)/(.138 x 20 x 756.25)
= 318.2 mm
Using 50 mm clear cover and 16ᵠ bars
Overall depth = 318.2 + 50 +16/2
= 376.2 mm
We provide overall depth = 700 mm
davailable = 700 – 50- 16/2
= 642 mm
Now
Mu/be = 211.3/.756=280 and d= 64.2 cm
From chart 15 of SP 16
Pt = 0.2
As = (.2 x 756 x 642)/ 100
= 970.704 mm2
From table 96 of SP 16
Provide 16φ bars at 180 mm c/c (1117 mm2)
So actual steel provided = (1117 x 100)/ (756 x 642)
= 0.23
137
b) For shorter direction
BM at the face of the column = .5x (88.4+100.5) x 0.8 x 2.9 x 2.9 x .5
= 317.7 KNm
Mu = 476.6 KNm
Now, effective width of the footing = b +1/8(B-b)
= 300 + 1/8(1900-300)
= 500 mm
dreqd = √(476.6 x 106)/(.138 x 20 x 500)
= 587.6
Overall depth = 587.6 + 50 +16+16/2
= 661.6 mm
Provided depth = 700 mm
Fig. 10.19
138
davailable = 700 -50 -16 -16/2 = 626 mm
Now
Mu/be = 626/.500 = 1252 and d= 62.6 cm
Pt = 0.95
As = (.95 x 500 x 626)/ 100
= 2973.5 mm2
From table 96 of SP 16
We provide 16φ bars at 60 mm c/c (3351 mm2)
So actual steel provided = (3351 x 100)/ (500 x 626)
= 1.07
2. CHECK FOR ONE WAY SHEAR
Critical section for one way shear occurs at a distance of “d” from the face of the column
d= 642 mm
139
de = (550 x 583)/ 1225
= 261.75 mm
Overall depth = 261.75 +150
= 411.75 mm
Fig. 10.20
140
Available depth = 411.75 – 50 – 16/2 = 353.75 mm
Actual amount of steel = 1117x 2.9 = 3239.3 mm2
Area of trapezoid = .5 x(1584+2900)x412
= 923704 mm2
Percentage of steel at critical section
=
=
= .35 %
For Pt= 0.35 %,
τc = .415 N/mm2
X = 2.43
Y = 98.07
V= [.5 x(98.07+100.5)] x .583 x 1.9
= 109.97 KN
Vu = 165 KN
τv = (Vu/bd)
= (165 x 103)/ [.5x (1584+2714) x 353.75]
0.21 < τc
Hence safe
141
3. CHECK FOR TWO WAY SHEAR
Critical section for punching shear occurs at a distance of “d/2” from the face of the column
d/2 = 642/2 = 321 mm
b= 2 x 321 + 300
= 942 mm
Now
de = (550 x 904)/ 1225
= 405.44 mm
Fig. 10.21
142
Overall depth = 405.44 + 150
= 555.8 mm
Available depth = 555.8 – 50 -16/2
= 497.87 mm
Punching shear stress = (520.66 x 103)/(4x 942 x 497)
= 0.27 N/mm2
Permissible punching shear stress = 0.25 √ (fck)
= 0.25 x √20
= 1.12 N/mm2
Hence safe
4. CHECK FOR BEARING
As per clause 34.4 of IS 456
Safe bearing capacity = 0.45 fck √(A1 / A2 )
A1 = (b +4D)2
A2 = (450 x 300)
Now A1/ A2 = 8.44 and √(A1 / A2 ) = 2.97>2
So take √(A1 / A2 ) = 2
Actual bearing stress = (column load/column area)
= (473.328 x 103)/ (450 x 300)
= 3.50 N/mm2
Safe bearing stress = 0.45 fck √ (A1 / A2)
= 0.45 x 20 x √2
= 18 N/mm2
Hence safe
143
5. CHECK FOR DEVELOPMENT LENGTH
For 16 φ bars and M20 concrete from table 66 of SP 16
Development length = 752 mm
g) Available length in longer direction = 1225 mm. h) Available length in shorter direction = 800 mm.
DETAILING OF FOOTING:
Fig. 10.22
144
CHAPTER- 11
DESIGN OF STAIRCASE
145
DESIGN OF STAIRCASE
Fig. 11.2
Fig. 11.1
146
11.1 AVAILABLE DATA:
Storey height = 3.3m
Height of each flight = 3.3/2 = 1.65m = 1650 mm
Let us provide a riser, R= 160mm
And tread, T = 250mm
Therefore number of risers in each flight = 1650/160 = 10.33 ≈ 11
Number of tread in each flight = 11-1 = 10
Space provided for going = 10×250 = 2500mm = 2.5m
Space provided for landing slab = 1500mm = 1.50m
Horizontal space available = 3300mm
CHECK FOR THUMB RULE:
i) 2R + T = 2×160 + 250 = 570mm< 600mm ii) R + T = 160 + 250 = 420 mm, which is in between 400mm and 450mm iii) RT = 160×250 = 40000 mm2, which is in between 40000mm and 50000mm
Thus riser and tread satisfies all the thumb rules.
Corrected rise = 1650/11 = 150mm
Hence for design purpose rise and tread are taken as 150mm and 250mm respectively.
11.2 DESIGN OF WAIST SLAB:
α = = = 1.17
Let us provide thickness of waist slab = 200 mm
Let us use M20 grade of concrete and Fe – 415 steel.
Therefore, fy = 415 N/mm2 and fck = 20 N/mm2
11.3 DESIGN OF EACH FLIGHT:
Let us design the landing slab, flight and passage as a single slab which would be supported at each end by means of landing beam.
147
So, effective span of slab = 5.50m
Using 10ϕ bars and 15mm effective cover
Effective depth = (220-15-10/2) = 200mm
LOADING ON EACH FLIGHT:
Considering 1m width of the waist slab,
i) Steps 0.5×0.15×1×25 = 1.875 KN/m2 ii) Waist slab 0.2×1.17×25 = 5.850 KN/m2 iii) Floor finish (assumed) = 1.000 KN/m2 iv) SIL (as per IS 875 1987, Part 2) = 3.000 KN/m2
Total load, w = 11.725 KN/m2
Considering partial fixity,
Maximum bending moment, Mmax = 0.1wl2 = 0.1×11.725×5.52
= 35.468 KNm
Factored bending moment, Mu = 1.5 × Mmax = 53.202 KNm
Effective depth required, deff,req =
=
= 138.838 mm
Therefore, overall depth required, D= 138.838+25+5 = 168.838 mm < 200mm
Hence,safe.
Let us provide overall depth, D= 190mm
So, effective depth provided, deff = 190 – 25- 5= 160mm
REINFORCEMENT REQUIRED:
Mu/bd2= (53.202 x 106/ 1000 x 1602) = 2.078
Pt = 100Ast / bd
Ast = (.670 x 1000 x 160) / (100) = 1072 mm2.
Spacing for 10 mm dia bars, S = 70 mm (from table 96 of SP16)
148
Let us provide 10ϕ bars @ 70 mm c/c (1122 mm2)
Distribution steel = 0.0012×200×1000 = 240 mm2
Spacing required for 8ϕ bar = 50×1000/240 = 208.33 mm
Let us use 8ϕ bars @ 300 mm c/c (240 mm2 )
11.4 DESIGN OF LANDING BEAM:
Load calculation:
i) Load from stairs: 0.5wL = 0.5×11.725×5.5 = 32.244 KN/m ii) Load from wall: 0.15×20×3.3/2 = 4.95 KN/m iii) Self weight(200 x 350): =25×0.20×(0.35-0.20) = 0.75 KN/m
Total load w = 37.944 KN/m
Maxm BM, Mmax = 37.944×2.552/10 = 24.67 KNm
Mu = 1.5×24.67 = 37.005 KNm
Effective depth required, deff = √ (37.005x106/(0.138×20×200))
= 258.917 mm
Davailable = 350 – 25 – 16/2 = 317 mm
Let us adopt landing beam = 200×300
Effective depth = 300 – 25 – 16/2 = 267 mm
Hence, Area of steel required, Ast = 37.005×106/0.696×415×267
= 479.835mm2
Provide 4 nos. 16 ϕ bars (800 mm2).
11.5 CHECK FOR SHEAR
Maximum SF, Vmax = 0.5×37.944×2.55= 48.378
Vu = 1.5×48.378 = 72.56 KN
Nominal shear stress, τv = 72.56×1000/200×267 = 1.35 N/mm2
149
Pt = 603.2×100/200×267 = 1.12
τc = 0.644 N/mm2
τc max = 2.8 N/mm2
τc < τc max, the section need not redesign
τv > τc, hence additional shear reinforcement is required.
Vus = (1.35 – 0.644)×200×267 = 37700.4 N
Assuming 2 legged 6ϕ stirrup, spacing reqd.
S = 0.87×250×2× (π/4×62) ×267/37700.4 = 87.06 mm < 0.75 d (= 200.25)
Hence, spacing 80 mm c/c
Fig. 11.3
150
CHAPTER – 12
DESIGN OF CHAJJA
151
12.1 ASSUMPTIONS
Let us provide a Chajja projection beyond external wall = 600 m and
use 6 mm dia. bars as reinforcement.
12.2 Effective depth calculations
As per Cl 23.2.1 of IS 456:2000, for cantilever slab
71 =
deff
=> deff =
7
1
effd⇒ = 7
600
=> deff = 85.714 mm
Let us provide overall thickness of chajja = 100
... Effective depth provided, deff = 100 -15 -6/2 = 82 mm
12.3 Load calculations for chajja at roof
Self Weight of Chajja = 0.1 x 25 = 2.5 KN/m2 Finish =0.2 x 2.5 = 0.5 KN/m2 Live load = 1.5 KN /m2 Total Load, W = 4.5 KN/m2
12.4 Bending moment and shear force calculations:
Considering 1 m width of strip of cantilever slab, we have
Maximum BM = 2
2Wl
= 2
60.05.4 2×
= 0.81 KNm
... Factored moment, Mu = 1.5 x 0.81 = 1.215 KNm
152
Also, Max. S.F. = wl
= 4.5 x 0.60
= 2.7 KN
... Factored shear force, Vu = 1.5 x 2.7 = 4.05 KN
12.5 Check for effective depth:
We know,
Effective depth required, d = bf
M
ck
u
138.0
= 100020138.0
10215.1 6
xx
x
= 20.98 mm < 82 mm (d provided), hence safe
Now, Mu = )1(87.0ck
yststy bdf
fAdAf −
=> )20821000
4151(8241587.010215.1 6
xx
AxxAxx st
st −=
=> Ast = 41.50 mm2 or 3911.09 mm2
Neglecting the very high value obtained from the above equation, let us accept
Ast = 41.50 mm2
As per Cl. 26.5.2.1 of IS 456: 2000,
Minimum reinforcement required 21201000100100
12.0mmxx ==
From Table 96 of Design Aid SP-16,
Let us provide 6 mm dia. bars @ 200 mm C/C. (A st, provided = 141mm2)
153
12.6 Check for shear:
Induced shear stress, τv
bd
Vu=
821000
100005.4
x
x= = 0.049N/mm2
Now Pt, provided bd
xAst100=
= 0.17%
From Table 61 of Design Aid SP-16, the value of τc corresponding to Pt = 0.20 (minimum) is,
τc = 0.33 N/mm2
Since τv < τc hence the design is safe in shear.
12.7 Distribution reinforcement:
Minimum distribution steel = 100
12.0 xDxb
100
100010012.0 xx=
= 120 mm2
From Table 96 of Design Aid SP-16;
Let us provide 6 mm dia. Bars @ 200 mm C/C. (Ast, provided = 141mm2)
12.8 Load calculations for chajja at floor
Self Weight of Chajja = 0.1 x 25 = 2.5 KN/m2 Finish =0.2 x 2.5 = 0.5 KN/m2 Live load = 2.0KN /m2 Total Load, W = 5.0 KN/m2
154
12.9 Bending moment and shear force calculations:
Considering 1 m width of strip of cantilever slab, we have
Maximum BM = 2
2Wl
= 2
60.05 2×
= 0.9 KNm
... Factored moment, Mu = 1.5 x 0.9 = 1.35 KNm
Also, Max. S.F. = wl
= 5 x 0.60
= 3KN
... Factored shear force, Vu = 1.5 x 3= 4.5 KN
12.10 Check for effective depth:
We know,
Effective depth required, d = bf
M
ck
u
138.0
= 100020138.0
1035.1 6
xx
x
= 22.12 mm < 82 mm (d provided), hence safe
Now, Mu = )1(87.0ck
yststy bdf
fAdAf −
=> )20821000
4151(8241587.01035.1 6
xx
AxxAxx st
st −=
=> Ast = 46.14mm2 or 3906.61 mm2
Neglecting the very high value obtained from the above equation, let us accept
Ast = 46.14mm2
155
As per Cl. 26.5.2.1 of IS 456: 2000,
Minimum reinforcement required 21201000100100
12.0mmxx ==
From Table 96 of Design Aid SP-16,
Let us provide 6 mm dia. bars @ 200 mm C/C. (A st, provided = 141mm2)
12.11 Check for shear:
Induced shear stress, τv
bd
Vu=
821000
10005.4
x
x= = 0.055N/mm2
Now Pt, provided bd
xAst100=
= 0.17%
From Table 61 of Design Aid SP-16, the value of τc corresponding to Pt = 0.20 (minimum) is,
τc = 0.33 N/mm2
Since τv < τc hence the design is safe in shear.
12.12 Distribution reinforcement:
Minimum distribution steel = 100
12.0 xDxb
100
100010012.0 xx=
= 120 mm2
From Table 96 of Design Aid SP-16;
Let us provide 6 mm dia. Bars @ 200 mm C/C. (Ast, provided= 141mm2)
156
CHAPTER-11
DESIGN OF LINTEL
157
13.1 Introduction:
It becomes necessary to provide openings in walls for doors, windows, cupboards, etc. Such opening must be bridged over so as to support the load of the wall above them. This is accompanied by providing a lintel.
13.2 Design of Lintel:
Assumptions:
Let lintel beam size = 125 mm x 250 mm
Main beam size = 300mm x 450 mm
Wall thickness = 150 mm
Projection of Chajja = 600 mm
A. Load calculations for external lintel (for roof)
1. Wall load = (3.2 – 2.1 – 0.45 – 0.25) x 0.15 x 20 = 1.2KN/m 2. Load from Chajja = 4.5 x 0.6 = 2.70 KN/m 3. Self weight of lintel 0.125 x 0.25x 25 = 0.781KN/m
Total, w = 4.681KN/ m
Bending moment and shear force calculations:
8..
2wlMBMax =
8
6.3681.4 2x=
= 7.58KNm
... Factored moment, Mu = 1.5 x 7.58= 11.37KNm
Also, Max. S.F. 2
wl=
2
6.3*681.4=
= 8.43KN
... Factored shear force, Vu = 1.5 x 8.43= 12.64KN
158
Check for effective depth:
Here effective depth provided, d available mm2
1225250 −−=
= 219 mm
(Providing 25 mm clear cover and using 12 mm dia. bars)
We know,
Effective depth required, d required bf
M
ck
u
138.0=
12520138.0
1037.11 6
xx
x=
= 181.54 mm
... d available > dreqd ... Safe
Calculation of required reinforcement:
22
6
2/90.1
219125
1037.11mmN
x
x
bd
M u ==
Therefore, from Table 2 of Design Aid SP-16, we provide
pt= 0.602%
... 602.0100 =
bd
xAst
=> 602.0219125
100 =x
xAst
=> Ast = 164.79 mm2
... No. of bars required = 2 (as per table 95 of SP 16)
Let us provide 2-12 mm dia. (226 mm2) bars as tensile reinforcement and 2-12 mm dia. Bars as nominal reinforcement at top layers.
Check for shear:
Induced shear stress, bd
Vuv =τ
159
219125
100064.12
x
x=
= 0.46N/mm2
Now, Pt, provided 219125
226100
x
x= = 0.82
From Table 61 of Design Aid SP-16, the value of cτ corresponding to Pt = 0.82 is
cτ = 0.57 N/mm2
Since cτ > vτ , hence shear reinforcement is not reqd. but nominal shear reinforcement has to be provided
in accordance with Cl. 26.5.1.6 of IS: 456-2000
Using 6 mm dia. bars we have
22
55.564
62mm
xxAsv == π
We have,
yv
sv
fbS
A
87.0
4.0=
� Sv = 408.35 mm As per Cl. 26.5.1.5 of 456-2000 spacing should in no case exceed 300 mm
Let us provide 6 mm 2 – legged vertical stirrups @ 300 mm c/c.
B. Load calculations for external lintel (for floor)
1. Wall load = (3.2 – 2.1 – 0.45 – 0.25) x 0.15 x 20 = 1.2KN/m 2. Load from chajja = 5.0 x 0.6 = 3 KN/m 3. Self weight of lintel 0.125 x 0.25x 25 = 0.781KN/m
Total, w = 4.981KN/ m
Bending moment and shear force calculations:
8..
2wlMBMax =
160
8
6.3981.4 2x=
=8.07KNm
... Factored moment, Mu = 1.5 x8.07= 12.1KNm
Also, Max. S.F. 2
wl=
2
6.3*981.4=
=8.97KN
... Factored shear force, Vu = 1.5 x8.97= 13.45KN
Check for effective depth:
Here effective depth provided, d available mm2
1225250 −−=
= 219 mm
(Providing 25 mm clear cover and using 12 mm dia. bars)
We know,
Effective depth required, d required bf
M
ck
u
138.0=
12520138.0
101.12 6
xx
x=
= 187.27mm
... d available > dreqd ... Safe
Calculation of required reinforcement:
22
6
2/02.2
219125
101.12mmN
x
x
bd
M u ==
Therefore, from Table 2 of Design Aid SP-16, we provide
pt= 0.647%
... 647.0100 =
bd
xAst
161
=> 647.0219125
100 =x
xAst
=> Ast = 177.12 mm2
... No. of bars required = 2 (as per table 95 of SP 16)
Let us provide 2-12 mm dia. (226 mm2) bars as tensile reinforcement and 2-12 mm dia. Bars as nominal reinforcement at top layers.
Check for shear:
Induced shear stress, bd
Vuv =τ
219125
100045.13
x
x=
= 0.49 N/mm2
Now, Pt, provided 219125
226100
x
x= = 0.82
From Table 61 of Design Aid SP-16, the value of cτ corresponding to Pt = 0.82 is
cτ = 0.57 N/mm2
Since cτ > vτ , hence shear reinforcement is not reqd. but nominal shear reinforcement has to be provided
in accordance with Cl. 26.5.1.6 of IS: 456-2000
Using 6 mm dia. bars we have
22
55.564
62mm
xxAsv == π
We have,
yv
sv
fbS
A
87.0
4.0=
� Sv = 408.35 mm As per Cl. 26.5.1.5 of 456-2000 spacing should in no case exceed 300 mm
Let us provide 6 mm 2 – legged vertical stirrups @ 300 mm c/c.
162
C. Load calculations for internal lintel:
1. Wall load = (3.2 – 2.1 – 0.45 – 0.25) x 0.15 x 20 = 1.2 KN/m 2. Self weight of lintel 0.125 x 0.25x 25 = 0.781KN/m
Total, w = 1.981KN/ m
Bending moment and shear force calculations:
8..
2wlMBMax =
8
6.3981.1 2x=
= 3.21KNm
... Factored moment, Mu = 1.5 x 3.21= 4.81 KNm
Also, Max. S.F. 2
wl=
2
6.3981.1 x=
= 3.56KN
... Factored shear force, Vu = 1.5 x 3.56= 5.35 KN
Check for effective depth:
Here effective depth provided, d available mm2
1225250 −−=
= 219 mm
(Providing 25 mm clear cover and using 12 mm dia. bars)
We know,
Effective depth required, d required bf
M
ck
u
138.0=
12520138.0
1081.4 6
xx
x= = 118.07 mm
... d available > dreqd ... Safe
163
Calculation of required reinforcement:
22
6
2/80.0
219125
1081.4mmN
x
x
bd
M u ==
Therefore, from Table 2 of Design Aid SP-16, we provide
pt= 0.233%
... 233.0100 =
bd
xAst
=> 242.0219125
100=
x
xAst
=> Ast = 63.78 mm2
... No. of bars required = 2 (as per table 95 of SP 16)
Let us provide 2-12 mm dia. (226 mm2) bars as tensile reinforcement and 2-12 mm dia. Bars as nominal reinforcement at top layers.
Check for shear:
Induced shear stress, bd
Vuv =τ
219125
100035.5
x
x=
= 0.19N/mm2
Now, Pt, provided 219125
226100
x
x= = 0.82
From Table 61 of Design Aid SP-16, the value of cτ corresponding to Pt = 0.82 is
cτ = 0.57 N/mm2
Since cτ > vτ , hence shear reinforcement is not reqd. but nominal shear reinforcement has to be provided
in accordance with Cl. 26.5.1.6 of IS: 456-2000
Using 6 mm dia. bars we have
22
55.564
62mm
xxAsv == π
164
Again we have,
yv
sv
fbS
A
87.0
4.0=
� Sv = 408.35 mm As per Cl. 26.5.1.5 of 456-2000 spacing should in no case exceed 300 mm
Let us provide 6 mm 2 – legged vertical stirrups @ 300 mm c/c.
165
CHAPTER-14
CONCLUSION
166
This project aims at the structural design of a multi-storied residential building in Guwahati City. The first phase of the project was to plan a building according to the existing Guwahati Metropolitan Development Authority (GMDA) bye laws. The planning of the building has been done to arrange the location of various rooms and their sizes so that it fulfills the functional requirements of the intended purpose.
After the planning stage, estimation of the various loads, viz. gravity and seismic loads are carried out. During this stage, analysis has been done by approximate methods such has moment distribution and portal methods to yields the various bending moments, shear forces and axial loads acting at the various section at different levels. The results of the computations are then subjected to load combination that can be accepted as the design values, i.e. that values for which the various components of the structure has to be designed.
The design phase consisted of designing of the various components that constitutes the structure such as beams, columns, slabs, staircase, Chajja/sunshade, lintels and footing. The final output is in the form of reinforcement detailing of the various constituents parts as they are essential for the execution of the actual construction work. Ductile detailing has been incorporated as per IS 13920: 1993.
167
ANNEX A
LIST OF REFERRED INDIAN STANDARDS AND CLAUSES
IS: 875 (Part II)– 1987:Code of practice for Design loads (other than earthquake) for Building and Structures
• Clause.3.1.2
IS: 1983 (Part II) – 2002: Criteria for Earthquake Resistant Design of Structures Part I General provision and buildings
• Clause.6.4.2
• Clause.7.3.1
• Clause.7.3.2
• Clause.7.4.2
• Clause.7.5.3
• Clause.7.6.1
• Table 2
• Table 6
• Table 7
• Fig. 2
IS 456- 2000 – Plain and Reinforced Concrete Code of Practice
• Clause 23.2.1
• Clause 26.2.1
• Clause 26.3.2
• Clause 26.4.1
• Clause 26.5.1.1
• Clause 26.5.1.5
• Clause 26.5.1.6
• Clause 26.5.2.1
• Clause 26.5.2.1
• Clause 26.5.3.1(a)
168
• Clause 26.5.3.2 (C)
• Clause D.1.1
• Clause D.1.8
• Clause D.1.9
• Clause D.2.1
• Table 26
DESIGN AID TO IS: 456-1978 (SP-16)
• Chart 11
• Chart 12
• Chart 13
• Chart 14
• Chart 15
• Chart 44
• Table 2
• Table 37
• Table 61
• Table 62
• Table 96
IS: 13920-1993- Ductile Detailing of Reinforced Concrete Structures Subjected to Seismic Forces.
• Clause 3.4
• Clause 5.1
• Clause 5.2
• Clause 5.3
• Clause 6.2.1
• Clause 6.2.2
• Clause 6
• Clause 6.2.12.3
• Clause 6.2.4
169
ANNEX B
LIST OF REFERRED BOOKS AND REPORTS
1. Jain , Ashok K. (2006) Reinforced Concrete- Limit State Design, 6th Edition ,
NemChand & Bros, Roorkee.
2. Ramamrutham, S (2006), Design of Reinforced Concrete Structures, Sixteenth Edition,
Dhanpat Rai Publishing Company (P) Ltd, New Delhi.
3. Saran, Swami (2006), Analysis and Design of Substructures – Limit state Design, Second
Edition Oxford & IBH published Co.Pvt. Ltd., New Delhi.
4. Shah, Dr. H.J. and Jain DrSudhir K, Design example of a Six Storey Building, Document
No. IITK –GSDMA –EQ26 –V3.0 IITK-GSDMA Project on Building Codes.
5. Ramamrutham, S and Narayana, R (2003), Theory of Structures, Seventh Edition,
DhanphatRai Publishing Company (p) Ltd, New Delhi.
6. Guide Lines for Guwahati Metropolitan Development Authority (GMDA),
Guwahati.(Building Permission.)