Question

A vertical, solid steel post 25 cm in diameter and 2.50m long is required to support a load of 8000kg. 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

(a) The stress in the post is 1,568,000 N/m²

(b) The strain in the post is  7.61 x 10⁻⁶  

(c) The change in the post’s length when the load is applied is 1.9 x 10⁻⁵ m.

Area of the steel post

A = πd²/4

where;

d is the diameter

A = π(0.25²)/4 = 0.05 m²

Stress on the steel post

σ = F/A

σ = mg/A

where;

• m is mass supported by the steel
• g is acceleration due to gravity
• A is the area of the steel post

σ = (8000 x 9.8)/(0.05)

σ = 1,568,000 N/m²

Strain of the post

E = stress / strain

where;

• E is Young's modulus of steel = 206 Gpa

strain = stress/E

strain = (1,568,000) / (206 x 10⁹)

strain = 7.61 x 10⁻⁶

Change in length of the steel post

strain = ΔL/L

where;

• ΔL is change in length
• L is original length

ΔL = 7.61 x 10⁻⁶ x 2.5

ΔL = 1.9 x 10⁻⁵ m

Learn more about Young's modulus of steel here: brainly.com/question/14772333

#SPJ1