This relation 15 is 2950 part i 1981 is expressed by

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Unformatted text preview: on 15 IS : 2950 (Part I) - 1981 is expressed by the relative stiffness factor K given below: EI a) For the whole structure K = -----------------3 Es b a E- d3 b) For rectangular rafts or beams K = ------------ -- 12 E s b E - d- 3 c) For circular rafts K = -------------- --------- 12 E s 2 R where EI = flexural rigidity of the structure over the length ( a ) in kg/cm2, Es = modulus of compressibility of the foundation soil in kg/cm2, b = length of the section in the bending axis in cm, a = length perpendicular to the section under investigation in cm, d = thickness of the raft or beam in cm, and R = radius of the raft in cm. C-2.1.1 For K > 0.5, the foundation may be considered as rigid ( see 5.1.1 ). C-3. DETERMINATION OF CRITICAL COLUMN SPACING C-3.1 Evaluation of the characteristics λ is made as follows: λ= 4 kB -----------4 Ec I where k = modulus of subgrade reaction in kg/cm3 for footing of width B in cm ( see Appendix B ). B = width of raft in cm Ec = modulus of elasticity of concrete in kgf/cm2 I = moment of inertia of the raft in cm4 16 IS : 2950 (Part I) - 1981 APPENDIX D ( Clause 5.1.2 ) CALCULATION OF PRESSURE DISTRIBUTION BY CONVENTIONAL METHOD D-1. DETERMINATION OF PRESSURE DISTRIBUTION D-1.1 The pressure distribution ( q ) under the raft shall be determined by the following formula: Q e' x Q Q e' y q = ---- ± ---------- y ± ---------- x I' x I' y A' where Q = total vertical load on the raft, A´ = total area of the raft, e´x, e´y, I´x, I´y = eccentricities and moments of inertia about the principal axes through the centroid of the section, and x, y = co-ordinates of any given point on the raft with respect to the x and y axes passing through the centroid of the area of the raft. I´x, I´y, e´x, e´y may be calculated from the following equations: 2 I xy I' x = I x – --------- , Iy 2 I xy I' y = I y – --------- , Ix I xy e' x = e x – ------- e y , and Ix I xy e' y = e y – ------- e x Iy where Ix, Iy = moment of inertia of the area of the raft respectively about the x and y axes through the centroid, 17 IS : 2950 (Part I) - 1981 Ixy = ∫ xydA for the whole area about x and y axes through the centroid, and ex, ey = eccentricities in the x and y directions of the load from the centroid. For a rectangular raft the equation simplifies to: 12 e y y 12 e x x Q q = --- 1 ± -------------- ± -------------- 2 2 A b a where a and b = the dimensions of the raft in the x and y directions respectively. NOTE — If one or more of the values of ( q ) are negative, as calculated by the above formula, it indicates that the whole area of foundation is not subject to pressure and only a part of the area is in contact with the soil, and the above formula will still hold good, provided appropriate values of Ix, Iy, Ixy, ex and ey are used with respect to the area in contact with the soil instead of the whole area. APPENDIX E ( Clause 5.2.1 ) CONTACT PRESSURE DISTRIBUTION AND MOMENTS BELOW FLEXIBLE FOUNDATION E-1. CONTACT PRESSURE DISTRIBUTION E-1.1 The distribution of contact pressure is assumed to be linear with maximum value attained under the columns and minimum at mid span. E-1.2 The contact pressure for the full width of the strip under an interior column load located at point i ( pi ) can be determined as ( see Fig. 3B ): 5 P 48 M p i = --------i + -------------i l2 l where l = average length of adjacent span ( m ), Pi = column load at point i ( t ), and Mi = moment under an interior columns located at i. 18 IS : 2950 (Part I) - 1981 E-1.3 The minimum contact pressure for the full width of the strip at the middle of the adjacent spans pml and pmr can be determined as ( see Fig. 3A ): lr lpml = 2Pi -------- – p i ---ll ll l ll lpmr = 2Pi -------- – p i ---lr lr l p mr + p ml pm = -------------------------2 where lr, ll...
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