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Unformatted text preview: as shown in Fig. 3A.
E1.4 If E2.3(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.
E1.5 If E2.3 (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
E2. BENDING MOMENT DIAGRAM
E2.1 The bending moment under an interior column located at i ( see
Fig. 3A ) can be determined as:
Pi
Mi = –  (0.24λl + 0.16)
4λ
E2.2 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
E2.3 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
F1. CLOSED FORM SOLUTION OF ELASTIC PLATE THEORY
F1.1 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 ).
F1.2 The radial and tangential moments can be converted to
rectangular coordinates:
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.
F1.3 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 ).
F1.4 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.
F1.5 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 ( Exofficio 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.
 Spring '13
 PROF.DEEPANKARCHOUDHURY

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