Procedure for the Design of Combined Footing

In a previous post: Conditions to Use Combined Pad Footing in Buildings, I showed when combined pad footings should be considered to be used in buildings. In this post, I would show simple procedures to be followed in order to carry out the geotechnical and structural design of combined pad footings.

Prior to the design of combined pad footings, the following assumptions should be made:

Assumptions

1. S_k2 ≥ S_k1
2. F₂ ≥ F₁ (distance from column to edge of footing)
3. B = 2F₂

Procedures/Steps

1. The footing should be proportioned in such a way that there should be zero eccentricity i.e. the resultant load ∑S_k should pass through the centroid of the footing.

Taking moment about S_k1:

x₁∑S_k + M_k2 = CS_k2 + M_k1 >> x₁ = (CS_k2 + M_k1 – M_k2)/ ∑S_k

If there are no moments, x₁ = CS_k2/ ∑S_k

In that case, L = F₁ + C + F₂ = 2 (F₁ + x₁)

If x₁ is at the centroid, F₁ + C + F₂ = 2 (F₁ + x₁) >> F₂ = 2F₁ + 2x₁ – F₁ – C = 2F₁ – F₁ + 2x₁ – C >> F₂ = F₁ + 2x₁ – C

N.B.: F₁ and F₂ is the only unknown

F₂ can be obtained once the value is assigned to F₁

2. Determine the area of the footing required, A_req = (∑S_k + w)/q_allowable

w is usually determined as a percentage of S_k using the table provided below

3. Determine the actual area of the footing provided by trial and error (sample table is provided below) using the already established equations. Assign values to F₁ until A_prov ˃ A_reqd.

4. Estimate the height of the footing, h; h = w/24A_prov

5. Check for punching shear stress at the column face. This is done at the column with higher load i.e. v = (S_k2 + w)/ (2(a₁ + a₂) d). If a square column, then (S_k2 + w)/4a₁d ≤ 0.8√f_cu or 5N/mm²

Note: a₁ and a₂ are the dimensions of the column of interest.

6. Determine the design moments and shear forces and draw the moment and shear force diagrams

7. Determine the reinforcement areas and detail properly.