Note for DESIGN OF REINFORCED CONCRETE STRUCTURES - DRCS By Noor Mohd

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Design of Square Footing: Footing or foundation is defined as the part of substructure, which transmits the loads from the super-structure to surrounding soil stratum safely. Foundation are classified as two types, 1. Shallow foundation 2. Deep foundation The depth of the foundation is less than or equal to the width of the foundation then the foundation is said to be shallow foundation. If the depth of the foundation is greater than width of the foundation then the foundation is said to be Deep foundation. Design of footing mainly depends on the safe bearing capacity of the soil on which the footing rests and the load coming from the superstructure. Footings may be isolated, combined. Isolated or independent footings are the footings that support the individual columns. They distribute and spread the load over a sufficiently large of the soil stratum to minimize the bearing pressure. Isolated footings may be square, rectangular or circular. In general, it is assumed that the soil behaves elastically that is the strain in the soil is proportional to applied stress and strain distribution in the soil immediately under the base of the footing is linear. Stress distribution is different soils. For analysis purpose, a footing can be compared with a rigid body in equilibrium subjected to loads. Like other structural members, a footing is designed to resist shear forces and bending moments. In design, for any soil the pressure distribution is assumed to uniform. In design, the critical section for one way shear (beam shear) is at a distance equal to the effective depth, d from the face of column footing. The critical section for two way shear or slab type shear shall be at a distance d/2 from the periphery of column, perpendicular to the plane of the slab. The critical section for bending moment is at the face of the column. Generally the footing is sensitive to punching shear. IS-CODE PROVISIONS FOR DESIGN OF FOOTINGS: 1. Footings shall be designed to sustain the applied loads, moment and forces. And safe bearing capacity is not exceeded. 2. In R.C.C. footing, the thickness at the edge shall not be less than 15cm for footing on soil. 3. The greatest bending moment to be used in the design of an isolated concrete at the face of the column.

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The critical section for diagonal cracking is taken at a distance equal to the effective depth from the face of the column in hard soils and shall not exceed nominal shear stress. No-26 1) Type of footing = Square footing 2) Size of the column = 230 X 450 mm 3) Load on footings: Axial Load on footing (ETABS) (P) = 850 KN = 250kN/m2 (Assume) S.B.C of soil STEP – 1: Self-weight of footing = 10 % of axial load. = 850 X 0.10 = 85 KN Total load transmitted to the soil = axial load + self-weight = 850 + 85 = 935 KN = 250kN/m2 S.B.C of soil STEP – 2: Area of footing (A) = Total load/SBC of soil = 935 / 250 =3.74 ≅ 4.0 m2 Size of the square footing = √𝐵 = √4 = adopt = 2m x 2m ULTIMATE BEARING CAPACITY; qu = 𝑃𝑢 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑓𝑜𝑜𝑡𝑖𝑛𝑔 = 850 2𝑥2 = 220 N-M ≅ 0.22 𝐾𝑁 − 𝑀 BENDING MOMENT: M U = qu x B x ( B−b )2 = 0.22 x 2000 x 8 ( 2000−230)2 8 = 172.3 x 106 N-mm

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Calculating depth (d) ∴ MU = 0.138 fck bd2 172.3 x 106 = 0.138 x 25 x 2000 x d2 d = 158 mm ∴ So provide twice the depth (Take 350mm) Assume Cover as 50mm Overall depth = 350 + 50 = 400 mm d = depth – half dia of bar – effective cover d = 400 – 12/2 – 50 = 344mm (Provide 12mm bar) Area of Steel:- Ast = 0.5 x fck x fy 4.6MU [1 − √1 − fckbd2 ] x bd 4.6 x 172.3 x 106 25 = 0.5 x 415 x [1 − √1 − 25 x 2000 x3442 ] x 2000x344 = 1437.84 mm2 SPACING: S = ast x B 𝑎𝑠𝑡 = 113.09 x 2000 1437.84 = 157 mm ≅ 160 c/c

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Provide 12mm @ 160 c/c in both direction Check for one way shear: Critical section for one way shear is‘d’ from face of the column.  ( B  b)   d  2  Shear Force Vu  Pu xB  (2000  230)   350 2   Shear Force Vu  0.22 x 2000 Shear Force Vu = 235400 N. Nominal Shear stress  v= 235400 = 0.33 2000𝑥350 N/mm2 Percentage of steel:Pt = 𝜋 𝑥122 𝑥100 100 Ast =4 = 2.01 spacingxdepth 160𝑋350 From IS 456-2000 Table No-19 Shear stress in concrete = τc= 0.82 N/mm2 τv<τc Hence it is safe 1) Check for two-way shear: 2000 b+d 230 2000 2000 450 450 b+d b+d 230 2000 b+d