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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.
C2.1.1 For K > 0.5, the foundation may be considered as rigid
( see 5.1.1 ).
C3. DETERMINATION OF CRITICAL COLUMN SPACING
C3.1 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
D1. DETERMINATION OF PRESSURE DISTRIBUTION
D1.1 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 = coordinates 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
E1. CONTACT PRESSURE DISTRIBUTION
E1.1 The distribution of contact pressure is assumed to be linear with
maximum value attained under the columns and minimum at mid
span.
E1.2 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
E1.3 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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 Spring '13
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