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Bending of beams
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Deflection depends on Young's modulus and the second moment of area.
A beam bends under load; the deflection depends on Young's modulus and the second moment of area I. Deep beams (I-beams) resist bending as they put material far from the neutral axis.
A ruler is stiffer on edge than flat.
Deflection scales with L³.
In more detail
When a beam bends, its top is compressed and its bottom is stretched, with a neutral axis between them that does not change length. The bending stress grows with distance from the neutral axis.
Real-world uses
- Floor beams and bridge girders are designed to resist bending.
- Diving boards bend to store and release elastic energy.
- A diving board or a building floor sags under load, and engineers calculate the deflection using Young's modulus and the beam's cross-section.
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Frequently asked questions
Where is the stress greatest?
At the top and bottom surfaces, farthest from the neutral axis.
Why are I-beams used?
Their material is concentrated far from the neutral axis, which gives high bending strength for little weight.
Why are I-beams shaped that way?
Their cross-section places material far from the neutral axis, which gives a large second moment of area for little weight.
Related topics in Fluids & Elasticity
Stress–strain curve · Poisson's ratio · Elastic potential energy density · Torsion of a cylinder