Question

A vertical, solid steel post 39 cm in diameter and 3.30 m long is required to support a load of 9900 kg. You can ignore the weight of the post. What are (a) the stress in the post; (b) the strain in the post; and (c) the change in the post’s length when the load is applied?

Answer 1

Answer:

(a) stress in the post is $\sigma =$ 816.4 M pa

(b). strain in the post is ∈ = 0.004082

(c). strain is dL = 0.01347 m

Explanation:

Given data

Force = mg = 9900 × 9.81 = 97119 N

Diameter (D) = 0.39 m

Radius = 0.195 m

Length = 3.3 m

(a) stress in the post is given by

$\sigma = \frac{F}{A}$

Area (A) = $\pi r^{2}$

A = 3.14 × $0.195^{2}$

A = 0.119 $m^{2}$

Now stress

$\sigma = \frac{97119}{0.119}$

$\sigma =$ 816.4 M pa

(b). strain in the post is given by

∈ = $\frac{\sigma }{E}$

E = 2 × $10^{5}$  M pa

Now strain

∈ = $\frac{816.4}{2(10^{5} )}$

∈ = 0.004082

(c). We know that strain is the ratio of change in length to original length.

∈ = $\frac{dL}{L}$

dL = ∈ × L

dL = 0.004082 ×  3.3

dL = 0.01347 m