SM 143 Beams in shear

Assumptions

• Sections remain plane and perpendicular to neutral axis

• Valid only for slender beams (small depth compared to length) as distortion remains small

• Note: it is not possible to have a shear force without a change in moment

Shear formula

shear at a spefic point instead of just average (V/A)

V - internal shear force, Q - 1st area of inertia, I - moment of inertia, t - section width

First area of inertia Q

Q = ΣyA, but only for side above/below NA depending on which option is easier to calculate. Axis can also be at point of interest, then choose side closer to outside.

Therefore A is area of segment above/below NA, y is distance from NA to segment centroid.

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