For Soil Supported Beam, Combined Footing, Slab Strip or Mat Strip of Assumed Finite Length with Both Ends Free
Input Data
Result :
'E' is the modulus of elasticity for the beam material.  
for Concrete:  
f'c  E 
3000 psi  3120 ksi 
4000 psi  3600 ksi 
5000 psi  4030 ksi 
Note: values of 'E' listed above are determined by: E = 57*SQRT(f'c) in units of ksi 
Modulus of Subgrade Reaction, K  
Sandy Soils:  
Loose Sand  30100 kcf 
Medium Sand  60500 kcf 
Dense Sand  400800 kcf 
Sand w/Clay (mix)  200500 kcf 
Sand w/Silt (mix)  150300 kcf 
Clayey Soils: 

qu < 4 ksf  75150 kcf 
4 ksf < qu < 8 ksf  150300 kcf 
qu > 8 ksf  > 300 kcf 
where: qu = unconfined compression strength  
Note: if 'K' is known/given in units of kcf, E = multiply by 1000/1728 = 0.5787 to convert kcf to pci for input.  
This program takes 'K' input in pci and
multiplies it by 1728/1000 = 1.728 to E = convert to kcf for use throughout. 
Moment of inertia of beam crosssection:
I = B*T^3/12
I = B*T^3/12
Note: in formula for 'b',
'E' is multiplied by 144 to convert from units of
ksi to units of ksf for consistency.
'E' is multiplied by 144 to convert from units of
ksi to units of ksf for consistency.
'+V(max)' is the maximum positive shear in beam.
This value represents total shear, +V(max),
on assumed beam/strip width = B.
This value represents total shear, +V(max),
on assumed beam/strip width = B.
'V(max)' is the maximum negative shear in beam.
This value represents total shear, V(max),
on assumed beam/strip width = B.
This value represents total shear, V(max),
on assumed beam/strip width = B.
'x' is the location of the maximum positive
shear from left end of beam.
shear from left end of beam.
'x' is the location of the maximum negative
shear from left end of beam.
shear from left end of beam.
'+M(max)' is the maximum positive moment in beam.
Positive (+) moment = tension in bottom of beam.
This value represents total moment, +M(max) on
assumed beam/strip width = B
Positive (+) moment = tension in bottom of beam.
This value represents total moment, +M(max) on
assumed beam/strip width = B
'M(max)' is the maximum negative moment in beam.
Negative () moment = tension in top of beam.
This value represents total moment, M(max) on
assumed beam/strip width = B
Negative () moment = tension in top of beam.
This value represents total moment, M(max) on
assumed beam/strip width = B
'x' is the location of the maximum positive
moment from left end of beam.
moment from left end of beam.
'x' is the location of the maximum negative
moment from left end of beam.
moment from left end of beam.
'D(max)' is the maximum deflection in beam.
Negative deflection is in downward direction.
Negative deflection is in downward direction.
'x' is the location of the maximum
deflection from left end of beam.
deflection from left end of beam.
'Q(max)' is the maximum bearing pressure.
'x' is the location of the maximum
soil pressure from left end of beam.
soil pressure from left end of beam.
'Lr' is the radius relative of stiffness for the
slab/mat and subgrade, from H.M.
Westergaard's theory for slabs on grade
subjected to concentrated loads (1926).
Lr = ((E*T^3/(12*(1m^2)*K))^(1/4)
where: m = Poisson's Ratio
(assumed =0.15 for concrete)
slab/mat and subgrade, from H.M.
Westergaard's theory for slabs on grade
subjected to concentrated loads (1926).
Lr = ((E*T^3/(12*(1m^2)*K))^(1/4)
where: m = Poisson's Ratio
(assumed =0.15 for concrete)
The user assumed percentage, '%B', may vary between
50% up to a limiting value of 88.62% for determining the
estimated effective strip width for slab or mat.
The maximum value may be determined by equating the
area of a circle of diameter = 2*Lr to an equivalent square:
%B(max) = SQRT(p*(2*Lr)^2/4)/(2*Lr)*100
= SQRT (p)/2*100 = 88.62%
A square inscribed inside a circle of diameter = 2*Lr
would have a side dimension = SQRT(2)*Lr, thus:
%B = SQRT(2)*Lr/(2*Lr)*100
= SQRT(2)/2*100 = 70.71%
50% up to a limiting value of 88.62% for determining the
estimated effective strip width for slab or mat.
The maximum value may be determined by equating the
area of a circle of diameter = 2*Lr to an equivalent square:
%B(max) = SQRT(p*(2*Lr)^2/4)/(2*Lr)*100
= SQRT (p)/2*100 = 88.62%
A square inscribed inside a circle of diameter = 2*Lr
would have a side dimension = SQRT(2)*Lr, thus:
%B = SQRT(2)*Lr/(2*Lr)*100
= SQRT(2)/2*100 = 70.71%
Estimated effective width of strip of slab/mat,
'B(est)', is assumed
to be an assumed percentage of 2 times the radius of slab/mat
relative stiffness, 'Lr'.
'B(est)', is assumed
to be an assumed percentage of 2 times the radius of slab/mat
relative stiffness, 'Lr'.
Shear at distance = x1
from left end of beam.
Sign convention:
positive (+) = upward.
from left end of beam.
Sign convention:
positive (+) = upward.
Moment at distance = x1
from left end of beam.
Sign convention: positive
(+) = tension in bottom of beam.
from left end of beam.
Sign convention: positive
(+) = tension in bottom of beam.
Deflection at distance = x1
from left end of beam.
Sign convention: positive
(+) = upward.
from left end of beam.
Sign convention: positive
(+) = upward.
Bearing pressure at distance = x1
from left end of beam.
Sign convention: positive
(+) = compression.
from left end of beam.
Sign convention: positive
(+) = compression.
Shear at distance = x2
from left end of beam.
Sign convention:
positive (+) = upward.
from left end of beam.
Sign convention:
positive (+) = upward.
Moment at distance = x2
from left end of beam.
Sign convention: positive (+)
= tension in bottom of beam.
from left end of beam.
Sign convention: positive (+)
= tension in bottom of beam.
Deflection at distance = x2
from left end of beam.
Sign convention: positive (+)
= upward.
from left end of beam.
Sign convention: positive (+)
= upward.
Bearing pressure at distance = x2
from left end of beam.
Sign convention: positive (+)
= compression.
from left end of beam.
Sign convention: positive (+)
= compression.
Shear at distance = x3
from left end of beam.
Sign convention:
positive (+) = upward.
from left end of beam.
Sign convention:
positive (+) = upward.
Moment at distance = x3
from left end of beam.
Sign convention: positive (+)
= tension in bottom of beam.
from left end of beam.
Sign convention: positive (+)
= tension in bottom of beam.
Deflection at distance = x3
from left end of beam.
Sign convention:
positive (+) = upward.
from left end of beam.
Sign convention:
positive (+) = upward.
Bearing pressure at distance = x3
from left end of beam.
Sign convention:)
positive (+ = compression.
from left end of beam.
Sign convention:)
positive (+ = compression.
Shear at distance = x4
from left end of beam.
Sign convention:
positive (+) = upward.
from left end of beam.
Sign convention:
positive (+) = upward.
Moment at distance = x4
from left end of beam.
Sign convention: positive (+)
= tension in bottom of beam.
from left end of beam.
Sign convention: positive (+)
= tension in bottom of beam.
Deflection at distance = x4
from left end of beam. Sign convention:
positive (+) = upward.
from left end of beam. Sign convention:
positive (+) = upward.
Bearing pressure at distance = x4
from left end of beam.
Sign convention: positive (+)
= compression.
from left end of beam.
Sign convention: positive (+)
= compression.
Beam Flexiblity Criteria:  
for b*L <= p/4  beam is rigid 
for p/4 < b*L < p  beam is semirigid 
for b*L >= p  beam is flexible 
for b*L >= 6  beam is semiinfinite long 
Disclaimer: This calculator is not intended to be used for the design of actual structures, but only for schematic (preliminary) understanding of structural design principals. For the design of an actual structure, a competent professional should be consulted.
‘Calculations courtesy of Alex Tomanovich, PE ’