3 the bending moment m under exterior columns can be

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Unformatted text preview: FOUNDATION - GENERAL CONDITION F-l. CLOSED FORM SOLUTION OF ELASTIC PLATE THEORY F-l.1 For a flexible raft foundation with nonuniform column spacing and load intensity, solution of the differential equation governing the behaviour of plates on elastic foundation ( Winkler Type ) gives radial moment ( M, ) tangential moment ( Mt ) and deflection ( w ) at any point by the following expressions: PL= w=40za (+ 1 where P = column load; r = distance of the point under investigation load along radius; 21 from column lib--.__------_..._ _ - IS : 2950 ( Part I ) - 1981 L = radius of effective stiffness; 4D k J k = modulus of subgrade reaction for footing of width B; D = flexural rigidity of the foundation; = Et2 12 ( 1 - Pa ) t = raft thickness; E = modulus of elasticity of the foundation p = poisson’s ratio of foundation material; material; and Z,, Z;, Z, = functions of shear, moment and deflection ( see Fig. 4 ). F-l.2 The radial and tangential moments can be converted to rectangular co-ordinates: M, _= M, co.9 4 -I- Mt sina 4 Mv = M, sin8 4 + Mt cos2 4 where 4 = is the angle with x axis to the line joining origin to the point under consideration. F-l.3 The shear Q per unit width of raft can be determined by: Q=- &z;(+) where 2; = function for shear ( see Fig. 4 ). F-l.4 when edge of the raft is located within the radius of influence, the followmg corrections are to be applied. Calculate moments and shears perpendicular to the edge of the raft within the radius of influence, assuming the raft to be infinitely large. Then apply opposite and equal moments and shears on the edge of the mat. The method for beams on elastic foundation may be used. : F-1.5 Finally all moments and shears calculated for each individual column and walls are superimposed to obtain the total moment and shear values. 22 IS : 29Jo ( Part I ) - 1981 : I I 0 I I I I I 1 2 3 L 5 r/L FIG. 4 FUNCTIONS FORSHEARMOMENTAND 23 DEFLECTION 6 ( Continued from page 2 ) Representing Members Bombay Port Trust, Bombay SHRI M. D. TAMBEKAR DR A. VARADARAJAN DR R. KANLRAJ Alternate ) ( SHRI G. RAMAN, Indian Institute of Technology, New Delhi Director General, BfS ( Ex-officio Member ) Director ( Civ Engg ) Secretary SHRIK. M. MATHUR Deputy Director ( Civ Engg ). BIS Bearing Capacity of Foundation Subcommittee, BDC 43 Convener SHRI S. GUHA Calcutta Port Trust, Calcutta Members DEPUTY DIRE~OR ( B & S ), CB-II STANDARDS Researc~rcsigns EXECWWE ENGINEER DESIGN) V ( SHRIT. N. MUKHERJEE & Standards Organization, SHRI B. G. RAO Central Public Works Department, New Delhi Martin & Bums Co Ltd, Calcutta Central Building Research Institute, Roorkee DR SWAMISARAN University of Roorkee, Roorkee SHRI AMAR S~NGH ( Alfernate ) Engineering Research Laboratories, Hyderabad SHRI K. R. SAXENA Cement Corporation of India, New Delhi SHRI 0. S. SRIVASTAVA SHRIS. K. CHAPERJEE( Alternate ) 24 BUREAU OF. Headquarters INDIAN STANDARDS : Manak Bhavan, 9 Bahadur Shah Zafar Marg. NEW DELHI 110002 Telephones Regional Central l t : 331 01 31 Telegram...
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