A simply supported beam with a span of 6 meters is subjected to a central point load. If the beam has a section modulus Z = 8000 mm³ and a yield strength f y = 250 MPa, what is the maximum moment that can cause the formation of a plastic hinge in the beam?
- A2.0 kN-mCorrect
- B5.3 kN-m
- C12.0 kN-m
- D32.0 kN-m
Solution
Concept
Plastic moment capacity of steel beams
Formula
M = fy × Z
Step-by-step solution
1. The plastic moment capacity is given by the product of section modulus Z and yield strength fy. Answer: A
Explanation
The bending moment capacity in this calculation is determined by multiplying the section modulus by the yield strength of the steel. Multiplying 8000 cubic millimeters by 250 megapascals yields 2,000,000 Newton-millimeters, which equals 2.0 kilonewton-meters. Therefore, option A correctly determines the resulting maximum moment.
Why the other options are wrong
B) 5.3 kN-m does not match the product of section modulus and yield strength. D) 32.0 kN-m exceeds the calculated moment required to form a plastic hinge.
Shortcut
Plastic moment Mp = Z × fy = 8000 mm³ × 250 MPa = 2,000,000 N-mm = 2.0 kN-m.
Common mistake
Miscalculating the plastic moment capacity using span length or elastic modulus and selecting option B or C.
Correct answer: A) 2.0 kN-m