Why is an I-beam stronger than a solid rectangle of the same weight and material?
AThe I-shape is aesthetically better
BThe I-beam places material far from the neutral axis where it resists bending most effectively
CThe I-beam has more total material
DThe I-beam shape eliminates all stress
Material near the neutral axis contributes little to bending resistance. The I-beam removes material from the middle (where it does little work) and keeps it at the top and bottom flanges (where it resists compression and tension most effectively).
Question 2 True / False
If you double the length of a simply supported beam while keeping the load and cross-section the same, the deflection increases by a factor of 8.
TTrue
FFalse
Answer: True
Beam deflection is proportional to the cube of the span length (L³). Doubling L means deflection increases by 2³ = 8. This is why long-span structures need much deeper beams or alternative structural forms like trusses or arches.
Question 3 Short Answer
Hold a ruler flat and try to bend it, then turn it on edge and try again. Why is it so much stiffer on edge?
Think about your answer, then reveal below.
Model answer: When the ruler is on edge, the material is distributed farther from the neutral axis. The top and bottom edges are farther apart, giving them more leverage to resist bending. This increases the moment of inertia, which is the geometric property that determines bending stiffness.
The ruler has the same material and cross-sectional area in both orientations, but the on-edge orientation has a much larger depth in the direction of loading. The moment of inertia (a measure of how well the cross-section resists bending) depends on depth cubed, so even a small increase in depth dramatically increases stiffness.