Geotechnical and Structural Design
Strip Shallow Foundation
US Units

TERZAGHI BEARING CAPACITY THEORY

Bearing Capacity Factors (General Shear Failure)

f Nc Nq Ng
0 5.70 1.00 0.00
1 6.00 1.1 0.01
2 6.30 1.22 0.04
3 6.62 1.35 0.06
4 6.97 1.49 0.10
5 7.34 1.64 0.14
6 7.73 1.81 0.20
7 8.15 2.00 0.27
8 8.60 2.21 0.35
9 9.09 2.44 0.44
10 9.61 2.69 0.56
11 10.16 2.98 0.69
12 10.76 3.29 0.85
13 11.41 3.63 1.04
14 12.11 4.02 1.26
15 12.86 4.45 1.52
16 13.68 4.92 1.82
f Nc Nq Ng
17 14.60 5.45 2.18
18 15.12 6.04 2.59
19 16.56 6.70 3.07
20 17.69 7.44 3.64
21 18.92 8.26 4.31
22 20.27 9.19 5.09
23 21.75 10.23 6.00
24 23.36 11.40 7.08
25 25.13 12.72 8.34
26 27.09 14.21 9.84
27 29.24 15.90 11.60
28 31.61 17.81 13.70
29 34.24 19.98 16.18
30 37.16 22.46 19.13
31 40.41 25.28 22.65
32 44.04 28.52 26.87
33 48.09 32.23 31.94
f Nc Nq Ng
34 52.64 36.50 38.04
35 57.75 41.44 45.41
36 63.53 47.16 54.36
37 70.01 53.80 65.27
38 77.50 61.55 78.61
39 85.97 70.61 95.03
40 95.66 81.27 115.31
41 106.81 93.85 140.51
42 119.67 108.75 171.99
43 134.58 126.50 211.56
44 151.95 147.74 261.60
45 172.28 173.28 325.34
46 196.22 204.19 407.11
47 224.55 241.80 512.84
48 258.28 287.85 650.67
49 298.71 344.63 831.99
50 347.50 415.14 1072.80
Enter the value of the angle of shearing resistance (f) degrees

Enter the value of soil cohesion (c) psf

From the table above, Enter Nc Nq Ng

 

CALCULATION OF SURCHARGE AT FOUNDATION LEVEL

Enter depth of foundation (Df) ft
Enter width of strip foundation (B) ft
Enter depth of Ground Water Table from Ground Surface (DGWT) ft
Enter dry unit weight of soil g pcf
Enter saturated unit weight of soil gsat pcf
Width of strip foundation (B) ft, and depth of foundation (Df) ft
(Df + B) ft

If DGWT < Df, check here
If Df < DGWT < (Df + B), check here
If DGWT > (Df + B), check here

q psf
 g' pcf

CALCULATION OF BEARING CAPACITY OF SOIL

Enter Factor of Safety against bearing capacity FS


Ultimate Bearing Capacity qu psf
Allowable Bearing Capacity qall psf
Net Allowable Bearing Capacity qall(net) psf

STRUCTURAL DESIGN OF FOUNDATIONS

Reinforced Concrete Design using the Strength Design Method

U = 1.4 DL + 1.7 LL
U = 0.75 (1.4 DL + 1.7 LL + 1.7 WL)
U = 0.9 DL + 1.3 WL
Enter Dead Load (DL) kip
Enter Live Load (LL) kip
If Wind Load (WL) exists, check here and Enter Wind Load (WL) kip
If Wind Load (WL) exists with no Live Load, check here
Ultimate load carrying capacity of the structural member (U) kip
 qall(net) psf
Required width of foundation (B) ft
If width of foundation should be altered, Enter (B) ft

Soil Contact Pressure and Ultimate Moment

Width of foundation (B) ft
Soil Contact Pressuer (qs) psf

Enter width of wall resting on foundation (w) ft
Propose a height (thickness) for foundation (h) ft

Size #3 #4 #5 #6 #7 #8 #9 #10 #11 #14 #18
db (in) 0.375 0.5 0.625 0.75 0.875 1 1.128 1.27 1.41 1.693 2.257
From Table above, select size of reinforcement bars. Enter bar diamter db in, and size #
Propose a thickness for concrete cover (t) in
Effective Depth of foundation (d) ft
Ultimate Moment acting on the foundation (Mu) kip.ft

Strength Reduction Factor

This factor is intoduced to account for inaccuracies in the design assumptions, changes in property or strength of the construction materials.

Condition

j
Axial tension, flexure with or without axial tension 0.90
Shear of tension 0.85
Axial compression with or without flexure, spiral reinforcement 0.75
Axial compression with or without flexure, tied reinforcement 0.70
Bearing on concrete 0.70
Flexure in plain concrete 0.65
From Table above, Enter the value of j for flexure jf
From Table above, Enter the value of j for shear js

Design of a Rectangular Section in Bending

Flexure Strength

b fc' (psi)
0.65 8000
0.70 7000
0.75 6000
0.80 5000
0.85 4000
0.85 3000
0.85 2000
0.85 1000
Enter the value of compressive strength of concrete at 28 days (fc') psi
Enter the value of yield stress of reinforcement in tension (fy) psi
From Table above, Enter the value of b
For a strip foundation, the design will be conducted for the entire width of the foundation (B) ft

Calculation of Area Steel

As1 in2, and As2 in2

Steel percentage s1 and s2

Maximum steel percentage (smax)

fy (psi) fc' = 3000 psi fc' = 4000 psi fc' = 5000 psi fc' = 6000 psi
40,000 0.0284 0.0378 0.0445 0.0501
50,000 0.0209 0.0279 0.0329 0.0370
60,000 0.0163 0.0217 0.0255 0.0287

(fc') psi and (fy) psi
From Table above, Enter smax

Minimum steel percentage (smin) is 0.0018

If s1>smax and s2< smin , check here
If s1>smax and s2> smin , check here
If s1<smax and s2> smin , check here
If s1<smax and s2< smin , check here

Steel percentage to be used in the design (s)
Area steel to be used in foundation (As) in2
 Bar diameter (db) in, and size #
Number of bars based on db proposed above (n)

Nominal Sizes of Reinforcing Bars Used in the US (Areas in in2)

Size db (in) A 2A 3A 4A 5A 6A 7A 8A 9A 10A
# 3 0.375 0.11 0.22 0.33 0.44 0.55 0.66 0.77 0.88 0.99 1.10
# 4 0.500 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00
# 5 0.625 0.31 0.62 0.93 1.24 1.55 1.86 2.17 2.48 2.79 3.10
# 6 0.750 0.44 0.88 1.32 1.76 2.20 2.64 3.08 3.52 3.96 4.40
# 7 0.875 0.60 1.20 1.80 2.40 3.00 3.60 4.20 4.80 5.40 6.00
# 8 1.000 0.79 1.58 2.37 3.16 3.95 4.74 5.53 6.32 7.11 7.90
# 9 1.128 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00
# 10 1.270 1.27 2.54 3.81 5.08 6.35 7.62 8.89 10.16 11.43 12.70
# 11 1.410 1.56 3.12 4.68 6.24 7.80 9.36 10.92 12.48 14.04 15.60
# 14 1.693 2.25 4.50 6.75 9.00 11.25 13.50 15.75 18.00 20.25 22.50
# 18 2.257 4.00 8.00 12.00 16.00 20.00 24.00 28.00 32.00 36.00 40.00

If desired number of bars and size should be different from those calculated above,
From Table above, Enter the desired number of bars (n) and the size (#) and the bar diameter (db) in

Shear Strength

Ultimate shear force acting on the foundation (Vu) kip
 
For members subjected to shear and flexure (fc' in psi)
For members subjected to diagonal tension (fc' in psi)

Allowable one way shear force of concrete (Vc) kip

If design is safe (Vcow and Vuow, and Vctw and Vutw are close), proceed to the next step.
If design is unsafe or too safe, click here to go back and alter the thickness of foundation.

Development Length

Diameter of a reinforcement bar (db) in
 Compressive strength of concrete at 28 days (fc') psi
 Area of one reinforcement bar (Ab) in2

For #11 US bar and smaller
minimum Ld = 0.0004 db fy
(fc' in psi, Ab in in2, dbin inch)
For #14 US bar (fc' in psi, Ab in in2, db in inch)
For #18 US bar (fc' in psi, Ab in in2, db in inch)

For #11 US bar and smaller, check here
For #14 US bar, check here
For #18 US bar, check here

Development Length (Ld) in
 Minimum Development Length for 35 mm bar and smaller (Ldmin) in
 Available length for bond development (Lav) in

The basic development length must be multiplied by appropriate factors given by ACI Code as follows. In any case, the basic development length should not be less than 12" (305 mm). Check the condition that applies.

Condition Factor
No special conditions 1
Top reinforcement 1.4
Reinforcement with fy > 60,000 psi 2 - 60,000 / fy
For light weight concrete 1.33
Reinforcement spaced at least 6" on center and at least 3" in from all sides 0.8
Reinforcement in excess of that required Enter Asrequired / Asprovided

Modified Development Length (Ld(mod)) in

If Lav > Ld(mod), foundation is safe.
If Lav <Ld(mod), click here to go back and alter the width of foundation.

SUMMARY OF DESIGN


Angle of shearing resistance (f) degrees
Soil cohesion (c) psf
Width of strip foundation (B) ft
Depth of Ground Water Table (DGWT) ft
Ultimate Bearing Capacity of soil (qu) psf
Height (thickness) for foundation (h) ft
Compressive strength of concrete at 28 days (fc') psi
Yield stress of reinforcement in tension (fy) psi
Number of bars (n) and size (#)

Copyright 1998-2024 A. Ghaly. All rights reserved.

Contact A. Ghaly at ghalya@union.edu

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Disclaimer: The author disclaims any and all responsibility for the application of stated principles, and shall not be liable for any loss or damage arising therefrom.