3a e 14 if e 23a governs the moment under the exterior

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Unformatted text preview: as shown in Fig. 3A. E-1.4 If E-2.3(a) governs the moment under the exterior columns, contact pressures under the exterior columns and at end of the strip pe and pe can be determined as ( see Fig. 3C ): 6 Me 4 P e + ---------- – p m l 1 C p e = ----------------------------------------------C + l1 3 Me pe p c = – ------------ – ---2 C2 where Pe, pm, Me, l1, C as shown in Fig. 3C. E-1.5 If E-2.3 (b) governs the moment under the exterior columns, the contact pressures pe and pc are determined as ( see Fig. 3C ): pe = pc = 4 P e – p m l 1 ---------------------------4 C + l1 E-2. BENDING MOMENT DIAGRAM E-2.1 The bending moment under an interior column located at i ( see Fig. 3A ) can be determined as: Pi Mi = – ------ (0.24λl + 0.16) 4λ E-2.2 The bending moment at midspan is obtained as ( see Fig. 3B ): Mm = Mo + Mi where Mo = moment of simply supported beam l 2= ----- [ pi ( l ) + 4 pm + pi ( r ) ] 48 where l, pi( l ), pi( r ), pm are as shown in Fig. 3B. 19 IS : 2950 (Part I) - 1981 FIG. 3 MOMENT AND PRESSURE DISTRIBUTION AT COLUMNS 20 IS : 2950 (Part I) - 1981 E-2.3 The bending moment Me under exterior columns can be determined as the least of ( see Fig. 3C ): Pc a) ------ (0.13λl1 + 1.06 λC – 0.50) 4λ ( 4 Pe – pm l1 ) C 2 -b) – ------------------------------------ -----2 4 C + l1 APPENDIX F ( Clause 5.2.1.1 ) FLEXIBLE FOUNDATION — GENERAL CONDITION F-1. CLOSED FORM SOLUTION OF ELASTIC PLATE THEORY F-1.1 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 ( Mr ) tangential moment ( Mt ) and deflection ( w ) at any point by the following expressions: where P = column load; r = distance of the point under investigation from column load along radius; 21 IS : 2950 (Part I) - 1981 L = radius of effective stiffness; 4D --k k = modulus of subgrade reaction for footing of width B; D = flexural rigidity of the foundation; = t = raft thickness; E = modulus of elasticity of the foundation material; µ = poisson’s ratio of foundation material; and r r r Z3 --- , Z´3 --- , Z4 --- = functions of shear, moment and deflection L L L ( see Fig. 4 ). F-1.2 The radial and tangential moments can be converted to rectangular co-ordinates: Mx = Mr cos2 + Mt sin2 My = Mr sin2 + Mt cos2 where = is the angle with x axis to the line joining origin to the point under consideration. F-1.3 The shear Q per unit width of raft can be determined by: r PQ = – ------ Z´4 --- L 4L where Z´4 = function for shear ( see Fig. 4 ). F-1.4 When edge of the raft is located within the radius of influence, the following 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 : 2950 (Part I) - 1981 FIG. 4 FUNCTIONS FOR SHEAR MOMENT AND DEFLECTION 23 IS : 2950 (Part I) - 1981 ( Continued from page 2 ) Members Representing SHRI M. D. TAMBEKAR DR A. VARADARAJAN DR R. KANIRAJ ( Alternate ) SHRI G. RAMAN, Director (Civ Engg) Bombay Port Trust, Bombay Indian Institute of Technology, New Delhi Director General, BIS ( Ex-officio Member ) Secretary SHRI K. M. MATHUR Deputy Director (Civ Engg), BIS Bearing Capacity of Foundation Subcommittee, BDC 43 Convener SHRI S. GUHA Calcutta Port Trust, Calcutta Members DEPUTY DIRECTOR STANDARDS (B &...
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This note was uploaded on 03/14/2014 for the course CE 684 taught by Professor Prof.deepankarchoudhury during the Spring '13 term at IIT Bombay.

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