A rectangular block of steel supporting a very large component of a bridge has a height of 15 cm and a cross-section of 20 cm × 12 cm.

 Question 18

A rectangular block of steel supporting a very large component of a bridge has a height of 15 cm and a cross-section of 20 cm × 12 cm. It is designed to compress 1 mm when under maximum, evenly distributed, load.

 

The Young modulus of steel is 2.0 × 10¹¹ N m^-2.

 

What is the maximum load it can support?

A 32 MN                     B 56 GN                      C 720 GN                    D 32 TN

 

 

 

Reference: Past Exam Paper – November 2017 Paper 12 Q21

 

 

 

Solution:

Answer: A.

Length L = 15 cm = 0.15 m

Cross-sectional area A = (0.20 × 0.12) m²

Compression, e = 1 mm = 0.001 m

Young modulus E = 2.0×10¹¹ N m^-2

Maximum load F = ???

 

Young modulus E = stress / strain = FL / Ae

E = FL / Ae

F = EAe / L

F = (2.0×10¹¹ × 0.20×0.12 × 0.001) / 0.15

F = 32 000 000 N = 32×10⁶ N = 32 MN