General Bearing Capacity Theory, Strip Foundation, SI Units

Geotechnical and Structural Design
Strip Shallow Foundation
SI Units

Bearing Capacity Factors

Enter the value of the angle of shearing resistance (f) degrees
Enter the value of soil cohesion (c) kPa

SHAPE, DEPTH, AND INCLINATION FACTORS

Enter depth of foundation (D_f) m
Enter width of strip foundation (B) m. Length of foundation (L) is considered infinite.
Enter angle of load inclination from the vertical (y) degrees

Ratio D_f / B

If D_f / B > 1, the equations for the depth factor are given in the following [notice that the factor tan^-1 (D_f / B) is in radians]:

Fcs Fqs Fgs
Fcd Fqd Fgd
Fci Fqi Fgi

CALCULATION OF SURCHARGE AT FOUNDATION LEVEL

Enter depth of Ground Water Table from Ground Surface (D_GWT) m
Enter dry unit weight of soil g kN/m³
Enter saturated unit weight of soil g_sat kN/m³

Width of strip foundation (B) m, and depth of foundation (D_f) m
(D_f + B) m

If D_GWT < D_f, check here
If D_f < D_GWT < (D_f + B), check here
If D_GWT > (D_f + B), check here

q kPa
g' kN/m³

CALCULATION OF BEARING CAPACITY OF SOIL

Enter Factor of Safety against bearing capacity FS

Ultimate Bearing Capacity q_u kPa
Allowable Bearing Capacity q_all kPa
Net Allowable Bearing Capacity q_all(net) kPa

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) kN
Enter Live Load (LL) kN
If Wind Load (WL) exists, check here and Enter Wind Load (WL) kN
If Wind Load (WL) exists with no Live Load, check here

Ultimate load carrying capacity of the structural member (U) kN
q_all(net) kPa
Required width of foundation (B) m

If width of foundation should be altered, Enter (B) m

Soil Contact Pressure and Ultimate Moment

Width of foundation (B) m
Soil Contact Pressuer (q_s) kPa

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

Size	#10	#15	#20	#25	#30	#35	#45	#55
d_b (mm)	11.3	16	19.5	25.2	29.9	35.7	43.7	56.4

From Table above, select size of reinforcement bars. Enter bar diamter d_b mm and size #
Propose a thickness for concrete cover (t) mm

Effective Depth of foundation (d) m
Ultimate Moment acting on the foundation (M_u) kN.m

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 j_f
From Table above, Enter the value of j for shear j_s

Design of a Rectangular Section in Bending

Flexure Strength

b	fc' (MPa)
0.65	56
0.70	49
0.75	42
0.80	35
0.85	28
0.85	21
0.85	14
0.85	7

Enter the value of compressive strength of concrete at 28 days (f_c^') MPa
Enter the value of yield stress of reinforcement in tension (f_y) MPa
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) m

Calculation of Area Steel

A_s1 mm², and A_s2 mm²

Steel percentage s₁ and s₂

Maximum steel percentage (s_max)

fy (MPa)	fc' = 21 MPa	fc' = 28 MPa	fc' = 35 MPa	fc' = 42 MPa
276	0.0284	0.0378	0.0445	0.0501
345	0.0209	0.0279	0.0329	0.0370
414	0.0163	0.0217	0.0255	0.0287

(fc') MPa and (f_y) MPa
From Table above, Enter s_max

Minimum steel percentage (s_min) is 0.0018

If s₁>s_max and s₂< s_min , check here
If s₁>s_max and s₂> s_min , check here
If s₁<s_max and s₂> s_min , check here
If s₁<s_max and s₂< s_min , check here

Steel percentage to be used in the design (s) Area steel to be used in foundation (A_s) mm²
Bar diameter (d_b) mm, and size # Number of bars based on d_b proposed above (n)

Standard Metric Bars (Areas in mm²)

Size	d_b (mm)	A	2A	3A	4A	5A	6A	7A	8A	9A	10A
# 10	11.3	100	200	300	400	500	600	700	800	900	1000
# 15	16.0	200	400	600	800	1000	1200	1400	1600	1800	2000
# 20	19.5	300	600	900	1200	1500	1800	2100	2400	2700	3000
# 25	25.2	500	1000	1500	2000	2500	3000	3500	4000	4500	5000
# 30	29.9	700	1400	2100	2800	3500	4200	4900	5600	6300	7000
# 35	35.7	1000	2000	3000	4000	5000	6000	7000	8000	9000	10000
# 45	43.7	1500	3000	4500	6000	7500	9000	10500	12000	13500	15000
# 55	56.4	2500	5000	7500	10000	12500	15000	17500	20000	22500	25000

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 (d_b) mm

Shear Strength

Ultimate shear force acting on the foundation (V_u) kN

For members subjected to shear and flexure		(fc' in MPa)
For members subjected to diagonal tension		(fc' in MPa)

Allowable shear force of concrete (V_c) kN

If design is safe (V_c and V_u 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 (d_b) mm
Compressive strength of concrete at 28 days (fc') MPa
Area of one reinforcement bar (A_b) mm²

For 35 mm bar and smaller	minimum L_d = 0.058 d_b f_y	(fc' in MPa, A_b in mm², d_b in mm)
For 43 mm bar		(fc' in MPa, A_b in mm², d_b in mm)
For 57 mm bar		(fc' in MPa, A_b in mm², d_b in mm)

For 35 mm bar and smaller, check here
For 43 mm bar, check here
For 57 mm bar, check here

Development Length (L_d) mm
Minimum Development Length for 35 mm bar and smaller (L_dmin) mm
Available length for bond development (L_av) mm

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 f_y > 414 MPa	2 - 414 / f_y
For light weight concrete	1.33
Reinforcement spaced at least 152 mm on center and at least 76 mm in from all sides	0.8
Reinforcement in excess of that required	Enter A_srequired / A_sprovided

Modified Development Length (L_d(mod)) mm

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

SUMMARY OF DESIGN

Angle of shearing resistance (f) degrees
Soil cohesion (c) kPa
Width of strip foundation (B) m
Depth of Ground Water Table (D_GWT) m
Ultimate Bearing Capacity of soil (q_u) kPa
Height (thickness) for foundation (h) m
Compressive strength of concrete at 28 days (f_c') MPa
Yield stress of reinforcement in tension (f_y) MPa
Number of bars (n) and size (#)

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.