τ=VQ/Ib varies across the section, peaking near the neutral axis.
τ=VQ/(Ib) where Q is the first moment of the area above the point. For a rectangle τmax=1.5V/A at the neutral axis; for an I-beam most shear is carried by the web. Matters in short deep beams and glued or bolted joints.
A rectangular beam with V=30 kN, 100×200 mm has τmax=2.25 MPa.
Shear stress in beams is largest near the neutral axis, which matters for timber and welded sections where shear failure can happen first.
τ=VQ/Ib varies across the section, peaking near the neutral axis.
Shear stress in beams is largest near the neutral axis, which matters for timber and welded sections where shear failure can happen first.
The free surfaces carry no shear, so the shear stress must vanish there, and the formula gives a parabolic distribution peaking at the neutral axis.
It is the shear force per unit length along a connection, found by the Q value, and it sizes welds or fasteners.
Typical applications include checking shear capacity of a timber joist near a support, finding the shear stress in the web of a steel I-beam and designing glue lines in a laminated beam.
Study "Statically indeterminate beams" first (topic 58 of 106 in Engineering Mechanics). It covers the groundwork this topic builds on.
Zero at outer fibres. Shear flow q=VQ/I for fasteners. Complementary shear stresses.
A rectangular beam with V=30 kN, 100×200 mm has τmax=2.25 MPa.
The next topic is "Combined loading", which builds directly on this one.
It is classed as Intermediate in Engineering Mechanics (topic 59 of 106). It is an intermediate topic. Work through the beginner topics in Engineering Mechanics first.
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