Slide 1
A beam’s cross-section changes how it bends
A beam carries loads across a span by developing internal bending and shear. Its cross-sectional shape affects how strongly it resists bending.
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Two beams with the same material and cross-sectional area can deflect differently. Placing more material farther from the neutral axis increases the second moment of area for that bending direction.
Slide 2
One side stretches while the other compresses
In simple bending, fibres on one side lengthen and those on the other shorten. Between them lies a neutral region with little longitudinal strain.
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For a homogeneous elastic beam, bending stress increases with distance from the neutral axis. The outermost fibres therefore deserve attention even though the entire cross section participates in carrying the load.
Slide 3
Extra depth can resist bending more than extra width
Increasing section depth can greatly improve bending stiffness about the relevant axis. This is why a ruler bends differently when turned on edge.
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For a rectangular section, the second moment of area contains depth cubed. Doubling depth while keeping width fixed increases this geometric stiffness term eightfold, before considering weight and other limits.
Slide 4
An I-section places material away from the neutral axis
An I-shaped beam places flanges far from its neutral axis. The connecting web links them and carries substantial shear.
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The thin parts can suffer local buckling, and an unrestrained beam can twist sideways under bending. Efficient material placement therefore introduces stability checks rather than eliminating the need for them.
Slide 5
Staying unbroken is different from staying stiff enough
A beam can remain unbroken while bending too much for its task. Design considers both failure resistance and acceptable movement.
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Excessive deflection can damage attached finishes, misalign machinery or make a floor uncomfortable. Those service requirements may control the design before the material reaches its strength limit.
Sources
- Stresses in Beams
MIT / David Roylance
- Beam Displacements
MIT / David Roylance