In this post, I will go over the second example in our structural reinforced concrete design course covering the design of footing foundations. The goal of this reinforced concrete design example is to design a reinforced concrete, square, spread footing foundation to support a single square column using ACI Code 318-11.

 

The problem statement states,

 

Design a single square footing to support an interior square tied column given the following design parameters:

 

Width of Column: 18 inches

Column Reinforcement: (8) #9 bars

Column dead load: 250 k

Column live load: 200 k

Distance from final grade to bottom of footing: 4 ft

Normal weight concrete

Compressive strength of concrete: 4 ksi

Yield strength of reinforcement: 60 ksi

Allowable soil pressure: 5 ksf

Unit weight of concrete: 150 lb/ft^3

Unit weight of soil: 100 lb/ft^3

 

 

 

 

The first step is to assume a depth for the square footing foundation, h, based on previous experience and engineering judgment.

 

The second step is to find the weight of the square footing, W_f, which is equal to the depth of the square footing multiplied by the unit weight of concrete.

 

 

The third step is to find the weight of the soil on top of the square footing, W_s, which is equal to the distance from the final grade minus the depth of the square footing foundation multiplied by the unit weight of soil.

 

 

The fourth step is to calculate the effective soil pressure at the bottom of the square footing, p_e. It is equal to the allowable soil pressure minus the weight of the square footing foundation minus the weight of the soil on top of the footing.

 

 

The fifth step is to compute the required width of the footing per unit length of the wall. Before the required width can be found, the required area must be known. The required area is equal to the sum of the unfactored dead and live load divided by the effective soil pressure. By taking the square root of the required area, the required width for the square footing can be determined. After finding the required width, a design width is selected by rounding up the required width to the nearest foot.

 

 

The sixth step is to determine the factored load, P_u, per ASCE 7 load combination. It is equal to 1.2 times the dead load plus 1.6 times the live load.

 

 

The seventh step is to calculate the net upward pressure, q_u, and this is equal to the factored load divided by the design width of the square footing foundation.

 

 

The eighth step is to determine the required effective depth for the square footing foundation based on one-way shear. The critical section for one-way shear is located at a distance equal to the effective depth away from the face of the column or wall. By setting the allowable shear force equal to the maximum factored shearing force at the critical section, the minimum required effective depth for one-way shear can be found. The allowable shear force is equal to two times the strength reduction factor times lambda times the square root of the the compressive strength of the concrete times the unit wall length times the effective depth per ACI Code 318-11 Section 11.2.1.1. The maximum factored shearing force for one-way shear is equal to the net upward pressure times the design footing width times the distance from the critical section to the edge of the footing. 

 

 

The ninth step is to determine the required effective depth for the square footing foundation based on two-way punching shear. The critical section for two-way shear is located at a distance equal to one-half the effective depth away from the face of the column or wall. By setting the allowable shear force equal to the maximum factored shearing force at the critical section, the minimum required effective depth for two-way shear can be found. The allowable shear force is given in ACI Code 318-11 Section 11.11.2.1. The maximum factored shearing force for two-way shear in a square footing is equal to the factored load minus the net upward pressure times the square of the sum of the column width and effective depth. Once the required effective depth for two-way is found, it is compared to the required effective depth for one-way shear, and the larger value will serve as the governing effective depth.  After finding the governing effective depth, the design effective can be found, and it is equal to the total depth minus the concrete cover minus the primary reinforcement bar diameter divided by two. It is critical to make sure that the design effective depth is greater than or equal to the required effective depth.

 

 

The tenth step is to calculate the maximum bending moment, M_u, which occurs at the face of the wall. Since the footing behaves similar to a cantilever beam, the maximum bending moment is equal to the net upward pressure times the footing design width times one-half times the distance from the face of the wall to the edge of the footing squared.

 

 

The eleventh step is to solve for the required steel area. The governing steel area can be found by choosing the larger of the required flexural steel area, the minimum required flexural steel area, and the minimum required shrinkage steel area. 

 

 

The twelfth step is to compute the bearing strength at the base of the column, N₁, using ACI Code 318-11 Section 10.14. It is equal to the strength reduction factor for bearing times 0.85 times the compressive strength of concrete times the bearing area of the column. If the

 

 

The thirteenth step is to compute the bearing strength of the footing, N₂, using ACI Code 318-11 Section 10.14. It is equal to the bearing strength at the base of the column times the square root of the area of the part of the supporting footing that is geometrically similar and concetric to the loaded area divided by the bearing area of the column. The upper limit for the bearing strength of the footing is equal to two times the bearing strength at the base of the column. If both the bearing strength at the base of the column and the bearing strength of the footing are greater than the factored load, the overall bearing strength is adequate.

 

 

The fourteenth step is to determine the minimum required dowel area based on ACI Code 318-11 Section 15.8.2.1. The code requires a minimum of four dowel bars with a total area equaling 0.005 times the gross cross-sectional area of the column. The dowel reinforcement is chosen and the design dowel area is equal to four times the cross-sectional area of a single dowel reinforcement bar. To ensure code compliance, the design dowel area must be greater than the minimum required dowel area.

 

 

The last step is to check the development length for the primary reinforcement. The required development length is equal to reinforcement yield stress times bar location factor times the coating factor times the diameter of the reinforcement bar divided by the product of 20 times lambda times the square root of the compressive strength of the concrete.The actual development length is equal to the distance from the face of the column to the bar cutoff point. If the actual development length is greater than or equal to the required development length, then the development length is satisfactory. If the actual development length is less than the required development length, then the development length is unsatisfactory.