Shear Stress Calculator
The vertical half of the beam's workload: peak and average shear on a rectangular section, with the parabola explained.
Shear Stress Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- Rectangular sections; elastic peak at the neutral axis
- No shear buckling or Hoop/ torsion paths
In short: A 30 kN peak shear on a 100 × 200 mm rectangular section averages 1.500000 MPa over the section and peaks at 2.250000 MPa on the neutral axis — three-halves of the average, the rectangle's built-in constant. Shear stress is the quiet twin: bending takes the flanges, shear takes the web, and short deep beams are the ones where the quiet twin wins the argument.
Formula
τₘₐₓ = 3V/2A ··· τₐᵥᵍ = V/A ··· (A = b × h)
Shear stress on a rectangle distributes as a parabola: zero at the surfaces, maximum on the neutral axis, and the parabola's average works out to exactly two-thirds of the peak — which is why the 3/2 constant exists. The general formula is τ = VQ/(Ib); for the rectangle the first-moment algebra collapses to 3V/2A, and the page shows both roads.
Worked Example
- Take the peak shear from the beam load page.
- Enter the section's width and depth.
- Read the peak and average shear stress.
- Compare against the shear yield — roughly 0.58 of tensile yield by the von Mises convention.
Defaults: 30 kN on 100 × 200 → average 1.500000 MPa, peak 2.250000 MPa — the 3/2 constant visible. Double the width and both halve; the parabola keeps its shape whatever the numbers.
Strengths & Limits Of This Model
Where this engine is strong
- Both the peak and the average printed
- The parabola explained, not just computed
Where it stops
- No I-section web approximation
- No connector shear-flow table
Practical Use Cases
Short deep beams
where shear governs bending
Web and timber checks
the neutral-axis peak
Teaching
VQ/(Ib) made concrete
Methodology & Editorial Standards
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Shear Stress Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
When does shear govern instead of bending?
On short deep members — corbels, deep transfer beams, timber joists at supports. Bending scales with span's leverage; shear scales with the load alone, so shortening the span starves bending while shear stays put. When the span-to-depth ratio drops below about two or three, the shear check stops being a formality and starts being the design.
Why is the peak on the neutral axis?
Because shear flow accumulates from the outer surface inward — the parabola's apex sits where the bending stress is zero. The two diagrams cross: bending peaks where shear vanishes and vice versa. It is the section's workload splitting by levels, flanges to bending and web-core to shear.
What is this Q in the general formula?
The first moment of the area beyond the level you are checking — the slice's area times its centroid's distance from the neutral axis. At the outer surface the slice is empty and Q is zero; at the neutral axis the slice is half the section and Q peaks. For the rectangle the substitution collapses to 3V/2A, which is why the page can carry one constant.
What shear capacity should I compare against?
By the von Mises convention shear yield sits near 58% of tensile yield — about 145 MPa for S235 — far above anything this arithmetic prints for stock sections. Real shear failures live in thin webs (shear buckling), timber (rolling shear) and concrete (diagonal tension), each with its own code model. The page's number is the section's honest peak; the material's story is code territory.
Does the parabola matter, or just the peak?
The peak matters for the material check and the shape matters for everything bolted or glued there — shear flow is what connectors carry, and it follows the same parabola. A flitch plate's bolts, a timber composite's glue line, a welded stud: all are sized off the flow at their level, which the 3/2 arithmetic brackets from above.
My section is an I-beam — does 3V/2A apply?
Not as written — the 3/2 constant is the rectangle's alone. For I-sections the web carries nearly all the shear and the honest approximation is V over the web's area, which lands within a few percent of the true peak because the web is tall and thin. The page is the rectangle's arithmetic and says so; the web approximation is the I-beam's version of the same honesty.
Why kN and mm together?
They are the structural trade's working units: loads in kN, sections in mm, and the division lands in N/mm² — megapascals — after the thousand cancels. The page does the thousands shuffle in plain sight: 30 kN over 20,000 mm² is 30,000 N over 20,000 mm², which is where 1.5 MPa comes from.
Is the average value ever the useful one?
Yes — for bolts, welds and plates loaded in pure shear, where the stress is taken as uniform by convention and the average IS the design number. The parabola is a beam phenomenon; a lap joint's shear plane knows nothing of it. The page prints both so the beam check and the connection check can share one visit.