Rectangular Pier Spread Footing Analysis Calculator

Beam Deflection and Stress Formula and Calculators
Engineering Calculators

This calculator will analysis the rigid rectangular spread footings with up to 8 total piers, and for either uniaxial or biaxial resultant eccentricities. Overturning sliding, and uplift stability checks are made when applicable, and resulting gross soil bearing pressures at the four (4) corners of the footing are calculated. The maximum net soil bearing pressure is also determined.

Notes:
Calculations assumes that the spread footing is in fact "rigid", so that the bearing pressure is distributed linearly on a homogeneous soil. (Note: the actual footing is generally not "rigid", nor is the pressure beaneth it distributed linearly. However, it has been found that solutions using the assumed "rigid" concept are adequate and generally result in a conservative design.)

A specified permissible value for the factor of safety against overturning. However, a minimum value of 1.5 to 2.0 is suggested, based upon the particular conditions.

 

RECTANGULAR SPREAD FOOTING ANALYSIS
For Assumed Rigid Footing with from 1 To 8 Piers
Subjected to Uniaxial or Biaxial Eccentricity
Variables:
Footing Data:
Footing Length, L = ft.
Footing Width, B = ft.
Footing Thickness, T = ft.
Concrete Unit Wt., gc = kcf
Soil Depth, D = ft.
Soil Unit Wt., gs = kcf
Pass. Press. Coef., Kp =
Soil Parameters
f Ka Kp gs
20 0.49 2.04 0.900 - 0.120
25 0.41 2.46 0.900 - 0.130
30 0.33 3.00 0.900 - 0.130
35 0.27 3.69 0.900 - 0.130
40 0.22 4.60 0.900 - 0.140
where: f = angle of internal friction of soil (deg.)
Ka = active pressure coefficient = TAN(45-f/2)2
Kp = passive pressure coefficient = TAN(45+f/2)2
gs = unit weight of soil (kcf)
Coef. of Base Friction, m =
A suggested range of values for the coefficient of base friction (m) is as follows:
0.67*TANf <= m <= TANf
where: f = angle of internal friction for soil (deg.)
Uniform Surcharge, Q = ksf
Pier/Loading Data:
Number of Piers =
The 'Xp' coordinate is the x-distance from the origin Y-axis to centroid of a particular pier/loading.
Note: the origin axes are located at the centroid
of the footing base plan.
Xp (ft.) =
The 'Yp' coordinate is the y-distance from the origin X-axis to centroid of a particular pier/loading.
Note: the origin axes are located at the centroid
of the footing base plan.
Yp (ft.) =
The x-direction dimension, 'Lpx', of the particular pier.
Lpx (ft.) =
The y-direction dimension, 'Lpy', of the particular pier.
Lpy (ft.) =
The pier height, 'h', is also the distance from the point of application of any horizontal loads (Hx, Hy) to the top of the footing. The pier height, 'h', should always be a positive number, but it may be input = 0. The pier height, 'h', is used in conjunction with the horizontal loads to obtain any additional moments (Mx, My) that are to be eventually summed with the applied moments.
h (ft.) =
'Pz' is the vertical (Z-axis) load to be applied at the pier location.
Sign convention: + = upward (out of page in plan view) for uplift loads
- = downward (into page in plan view) for gravity loads
Pz (k) =
'Hx' is the horizontal (X-axis) load to be applied at the pier location.
Sign convention: + = to right
Hx (k) =
'Hy' is the horizontal (Y-axis) load to be applied at the pier location.
Sign convention: + = up the page
Hy (k) =
'Mx' is the X-axis moment to be applied at the pier location.
Sign convention: + = by "Right-Hand-Rule" about +X-axis
Mx (ft-k) =
'My' is the Y-axis moment to be applied at the pier location.
Sign convention: + = by "Right-Hand-Rule" about +Y-axis
My (ft-k) =
FOOTING PLAN
Results:
Nomenclature for Biaxial Eccentricity:
Total Resultant Load and Eccentricities:
SPz =
'S Pz' is the summation of all applied vertical loads at pier(s) plus footing weight, soil weight, and surcharge weight.
kips
ex =
The value, 'ex', is the eccenticity (location) of the resultant of all the weights and applied loads measured from the Y-axis of the footing.
ey =
The value, 'ey', is the eccenticity (location) of the resultant of all the weights and applied loads measured from the X-axis of the footing.
Overturning Check:
SMrx =
'S Mrx' is the summation of the (righting) moments resisting overturning about the X-axis of the footing.
Note: the applied live loads and the surcharge weight are not included.
ft-kips
SMox =
'S Mox' is the summation of the moments causing overturning about the X-axis of the footing.
This program considers applied moments and horizontal loads as forces causing overturning. However, an uplift load is considered as a force causing overturning only when there is an applicable resultant eccentricity in the direction of overturning. For an uplift pier load, the "excess" pier weight (pier weight less soil weight) is subtracted from the uplift load at the pier location.
ft-kips
FS(ot)x =
The Factor of Safety against
overturning about X-axis:
FS(ot)x = S Mrx/S Mox
SMry =
'S Mry' is the summation of the (righting) moments resisting overturning about the Y-axis of the footing.
Note: the applied live loads and the surcharge weight are not included.
ft-kips
SMoy =
'S Moy' is the summation of the moments causing overturning about the Y-axis of the footing.
This program considers applied moments and horizontal loads as forces causing overturning. However, an uplift load is considered as a force causing overturning only when there is an applicable resultant eccentricity in the direction of overturning. For an uplift pier load, the "excess" pier weight (pier weight less soil weight) is subtracted from the uplift load at the pier location.
ft-kips
FS(ot)y =
The Factor of Safety against
overturning about Y-axis:
FS(ot)y = S Mry/S Moy
Sliding Check:
Pass(x) =
'Pass(x)' is the passive soil pressure against the footing base of width, 'B', which is available to resist X-direction horizontal loads.
Note: passive pressure against piers is ignored.
kips
Frict(x) =
'Frict(x)' is the frictional resistance between the footing base (concrete) and the soil available to resist X-direction horizontal loads.
kips
FS(slid)x =
The Factor of Safety against sliding in X-direction:
FS(slid)x = (Pass(x)+Fric(x))/ABS(S Hx)
Passive(y) =
'Pass(y)' is the passive soil pressure against the footing base of length, 'L', which is availble to resist Y-direction horizontal loads.
Note: passive pressure against piers is ignored.
kips
Frict(y) =
'Frict(y)' is the frictional resistance between the footing base (concrete) and the soil available to resist Y-direction horizontal loads.
kips
FS(slid)y =
The Factor of Safety against sliding in Y-direction:
FS(slid)y = (Pass(y)+Fric(y))/ABS(S Hy)
Uplift Check:
SPz(down) =
'S Pz(down)' is the summation of all applied vertical dead loads acting downward at pier(s) plus footing weight and soil weight.
Note: the applied vertical live loads and the surcharge weight are not included.
kips
SPz(uplift) =
'S Pz(uplift)' is the summation of all applied vertical loads acting upward (uplift) at pier(s).
kips
FS(uplift) =
The Factor of Safety against uplift:
FS(uplift) = S P(down)/S P(uplift)
Bearing Length and % Bearing Area:
Dist. x =
For cases of biaxial resultant eccentricity with 1 to 3 corners without bearing (when ABS(6*ex/L)+ABS(6*ey/B) > 1.0), the Distance 'x', is the distance away from the corner of maximum soil bearing pressure to the "line of zero pressure", running in the X-axis direction along the edge of the footing. Distance 'x' has no sign convention associated to it.
ft.
Dist. y =
For cases of biaxial resultant eccentricity with 1 to 3 corners without bearing (when ABS(6*ex/L)+ABS(6*ey/B) > 1.0), the Distance 'y', is the distance away from the corner of maximum soil bearing pressure to the "line of zero pressure", running in the Y-axis direction along the edge of the footing. Distance 'y' has no sign convention associated to it.
ft.
ft.
ft.
%Brg. Area = %
Biaxial Case =
Gross Soil Bearing Corner Pressures:
P1 =
'P1' is the gross soil bearing at footing corner #1, which is located at the lower right-hand corner of footing plan.
ksf
P2 =
'P2' is the gross soil bearing at footing corner #2, which is located at the upper right-hand corner of footing plan.
ksf
P3 =
'P3' is the gross soil bearing at footing corner #3, which is located at the upper left-hand corner of footing plan.
ksf
P4 =
'P4' is the gross soil bearing at footing corner #4, which is located at the lower left-hand corner of footing plan.
ksf
 
Maximum Net Soil Pressure:
Pmax(net) = Pmax(gross)-(D+T)*gs
Pmax(net) = ksf
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