Unformatted text preview: FOUNDATION  GENERAL CONDITION Fl. CLOSED FORM SOLUTION OF ELASTIC PLATE THEORY
Fl.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 ).
Fl.2 The radial and tangential moments can be converted to rectangular
coordinates:
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. Fl.3 The shear Q per unit width of raft can be determined by:
Q= &z;(+) where
2; = function for shear ( see Fig. 4 ).
Fl.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.
: 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 : 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 ( Exofficio 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 ), CBII 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
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 Spring '13
 PROF.DEEPANKARCHOUDHURY
 Geotechnical Engineering, New Delhi, Raft, Contact pressure

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