A block of 250-mm length and 54 * 40-mm cross section is to support a centric compressive load P. The material to be used is a bronze for which E = 95 GPa. Determine the largest load that can be applied, knowing that the normal stress must not exceed 80 MPa and that the decrease in length of the block should be at most 0.12% of its original length.

P = 17.28*10⁶ N

Explanation:

Given

L = 250 mm = 0.25 m

a = 0.54 m

b = 0.40 m

E = 95 GPa = 95*10⁹ Pa

σmax = 80 MPa = 80*10⁶ Pa

ΔL = 0.12%*L = 0.0012*0.25 m = 3*10⁻⁴ m

We get A as follows:

A = a*b = (0.54 m) * (0.40 m) = 0.216 m²

then, we apply the formula

ΔL = P*L / (A*E) ⇒ P = ΔL*A*E/L

⇒ P = (3*10⁻⁴ m) * (0.216 m²) * (95*10⁹ Pa) / (0.25 m)

⇒ P = 24624000 N = 24.624*10⁶ N

Now we can use the equation

σ = P/A

⇒ σ = (24624000 N) / (0.216 m²) = 114000000 Pa = 114 MPa > 80 MPa

So σ > σmax we use σmax

⇒ P = σmax*A = (80*10⁶ Pa) * (0.216 m²) = 17280000 N = 17.28*10⁶ N