F-01 — shear resistance

stress peaks where you least expect it.

shear stress probe

drag the probe. see where shear stress peaks.

Drag the yellow probe up and down — shear stress peaks at the neutral axis and drops to zero at the edges.

V20 k
b (in)4.0
h (in)12.0
τ_max (ksi)
live equation
Q = (b/2)(h²/4 − y²) = 2.0 × (36.0 − 0.0) = 72.0 in³ τ = VQ/Ib = 20 × 72.0 / (576.0 × 4.0) = 0.625 ksi
τ_max = 3V/2A = 0.625 ksi — at the neutral axis, shear stress is 1.5× the average.
τ = Internal shear force per unit area
V = Internal vertical force at the section
Q = Statical moment of area above the cut point
I = Cross-section bending resistance
b = Width of the section at the cut point
explained
Shear stress varies parabolically across a rectangular section — zero at the top and bottom edges, maximum at the neutral axis. The formula VQ/Ib captures this: Q is largest at mid-depth where the most area lies on one side of the cut.
key concepts
overview Shear stress follows τ = VQ/Ib and peaks at the neutral axis

Shear stress in a cross-section follows τ = VQ/Ib — V is the applied shear, Q is the first moment of area above the point of interest, I is the moment of inertia, and b is the section width at that depth. The result: stress peaks at the neutral axis and drops to zero at the top and bottom fibers. For a rectangle, τ_max = 3V/2A — 50% higher than the average.

what shear actually does Internal forces slide horizontal layers like a deck of cards

When a transverse load pushes down on a beam, internal shear forces try to slide one horizontal layer of the cross-section past the next — like a deck of cards. This sliding action produces shear stress (τ) on every horizontal plane through the section. Unlike bending stress (which is zero at the center and maximum at the edges), shear stress is maximum at the center and zero at the top and bottom.

why stress isn't uniform Q peaks at the neutral axis, making τ_max = 1.5× average

The formula τ = VQ / Ib explains why. Q is the first moment of area above the point you're checking — it's largest at the neutral axis (lots of area above, with a large lever arm) and zero at the extreme fibers (no area above the top). For a rectangle, the peak shear stress at the neutral axis is exactly 1.5× the average: τ_max = 3V / 2A. The probe in the tool below lets you see this variation directly.