Question

A vertical solid steel post of diameter d = 21 cm and length L = 2.70 m is required to support a load of mass m = 8300 kg . You can ignore the weight of the post. Take free fall acceleration to be g=9.8m/s2. a. What is the stress in the post?

b. What is the strain in the post?

c.What is the change in the post's length when the load is applied?

Answer 1

Step-by-step explanation:

Cross sectional area of post = 3.14 x(10.5)² x 10⁻⁴ = 346.18 x 10⁻⁴ m²

Weight = mg = 8300 x 9.8 = 8.134 x 10⁴ N

Stress = weight / area

= 8.134 x 10⁴ / (346.18 x 10⁻⁴)

23.49 x 10⁵ N / m²

Strain = stress / modulus of elasticity of steel

modulus of elasticity = 190 x 10⁹ Pa

strain = Stress \ young modulus

=
`(23.49*10^5)/(190*10^9)`

= 12.36 x 10⁻⁶

strain = change in length / original length

change in length = original length x strain

= 2.7 x 12.36 x 10⁻⁶

= 33.372 x 10⁻³ mm

.033 mm.