A 40-kN axial load is applied to a short wooden post that is supported by a concrete footing resting on undisturbed soil. Determine (a) the maximum bearing stress on the concrete footing, (b) the size of the footing for which the average bearing stress in the soil is 145 kPa.

A) The maximum bearing stress on the concrete footing is; σ_max = 3.33 MPa

B) The size of the footing for which the average bearing stress in the soil is 145 kPa is; 525 mm by 525 mm

A) The image of the footing is missing and so i have attached it.

From the given image, dimensions of the short wooden post are;

width = 120 mm = 0.12 m

length = 100 mm = 0.1 m

Area of wooden post is;

A = 0.12 × 0.1

A = 0.012 m²

Formula for maximum bearing stress is;

σ_max = F/A

We are given; Force; F = 40 kN = 40000 N

Thus;

σ_max = 40000/0.012

σ_max = 3.33 × 10⁶ Pa

σ_max = 3.33 MPa

B) We are told that the average bearing stress is now 145 kPa = 145000 Pa

Thus;

σ = F/A

145000 = 40000/A

where A = b² (since the footing is square)

Thus;

b² = 40000/145000

b² = 0.2758620689655

b = √0.2758620689655

b = 0.525 m

b = 525 mm

Read more about average stress at; link

a. 3.33 MPa

b. 0.276 m^2

Explanation:

The image is attached below.

The load = 40 kN = 40000 N

side length of wooden post L = 120 mm = 0.12 m

side width of the wooden post B  = 100 mm = 0.1 m

Area of the beam = L x B = 0.12 x 0.1 = 0.012 m^2

a. Maximum bearing stress of the concrete footing = load/area

max. bearing stress = 40000/0.012 = 3.33 x Pa = 3.33 MPa

b. If the average bearing stress in the soil is 145 kPa = 145000 Pa

size of the footing will be =  load ÷ average bearing stress

size of footing = 40000/145000 ≅ 0.276 m^2

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