How this instrument works
Shear stress τ measures how hard a force is trying to slide one layer of material past the layer beneath it, rather than stretch or crush it outright. Take a force F acting parallel to a cut through the material — along the surface, not through it — and divide by the area A of that cut: τ = F ⁄ A. The unit is the pascal, the same unit normal stress uses, because both answer the identical question, force intensity per unit area; only the direction of the force relative to the surface tells them apart. A rivet clamping two steel plates together does not feel them pulling it apart the way a bolt in tension does — it feels the plates trying to slide sideways past each other, and the rivet shank is what stands in the way.
The formula treats that load as spread perfectly evenly across the whole section, a simplification called direct or punching shear. In a bolt, rivet or pin loaded across a single cross-section, this average is close enough to reality that structural and mechanical design codes size fasteners against it directly, with a safety factor already covering the small unevenness near the edge of a real hole. That averaging fails once the geometry stops being a compact plug and becomes a slender beam instead: shear inside a beam runs to zero at the outer fibres and peaks at the neutral axis, a distribution that needs the separate transverse formula τ = VQ ⁄ (Ib) rather than one flat division of force by area.
Shear strength, the value τ gets checked against, usually sits below a material's tensile strength, because a crystal lattice slides along certain planes more readily than it pulls apart cleanly; for ductile metals under the common von Mises estimate, yielding in pure shear begins near 0.577 of tensile yield, and fastener tables often round that to one half as a safe shortcut. That gap is exploited on purpose in a shear pin: a sacrificial pin sized to fail in direct shear at a known load, protecting an auger, an outboard propeller or a gearbox by breaking cleanly before anything costlier does.
- Enter the load into Applied shear force — the force acting parallel to the plane you are checking, in newtons, with kilonewtons on the unit menu.
- Enter Cross-sectional area resisting shear — the area of that shear plane itself, such as a pin or rivet shank, in mm² or cm².
- Read Shear stress in pascals, or switch its unit menu to kPa or MPa once the numbers run past hardware scale.
- For a bolt in double shear, enter the combined area of both shear planes rather than one shank, since the load splits between them.
- Compare the result against your material's shear yield or allowable shear stress, never its tensile strength, before calling a joint safe.
Worked example — a 5 kN load through a 10 cm² pin
Picture a clevis pin carrying a lifting shackle, its shank presenting a 10 cm² cross-section to the load — a round pin roughly 3.6 cm across. The rigging pulls with 5,000 N, about the weight of a grand piano set down on one point. Enter 5000 into Applied shear force and 0.001 into Cross-sectional area resisting shear, which is that 10 cm² written in square metres. Shear stress returns 5000 ⁄ 0.001 = 5,000,000 Pa — a clean 5 MPa once the unit menu is switched to megapascals.
Five megapascals is a gentle load for a steel pin: mild steel yields in shear near 150 MPa, so this shackle pin works at roughly one thirtieth of its capacity, ordinary margin for rigging hardware that must never let go without warning. Double the force to 10,000 N across the same 10 cm² and the reading simply doubles to 10 MPa, because the relationship is linear — stress rises exactly as fast as force does, no bolt loosens gracefully or braces for an exponent here.
Questions
How is shear stress different from normal stress?
Normal stress pulls or pushes straight through a section — tension or compression, perpendicular to the cut. Shear stress instead acts parallel to the cut, the force trying to slide one face past the other rather than lengthen or crush it. A bolt loaded straight down its axis feels tension; the same bolt clamped across a lap joint and loaded sideways feels shear instead, and the two failure modes look nothing alike — tension necks and pulls apart, shear slides cleanly along a flat plane.
Why does the formula assume shear stress is uniform across the area?
It is a deliberate simplification called direct or punching shear, and it holds up well for a compact section like a pin or rivet shank, where the real stress varies only mildly near the edge of the hole. It breaks down for a slender beam, where shear is genuinely zero at the outer fibres and peaks at the neutral axis — that case needs the transverse formula τ = VQ ⁄ (Ib), not a flat force-over-area division. Fastener design accepts the average because its safety factors already allow for the unevenness.
What is the difference between single shear and double shear?
In single shear, a bolt or pin crosses one interface — a bracket lapped onto a plate — and carries the whole load across one cross-section. In double shear, the same pin passes through a clevis with two supporting plates, so the load cuts across two cross-sections at once, each carrying roughly half of it. Enter the combined area of both shear planes here, not just one, and the resulting stress comes out at about half of what a single-shear connection would see under the same total load.
How do I use this formula to size a punch press?
Treat the sheared area as the perimeter of the hole times the sheet thickness, not a bolt's cross-section: a 20 mm diameter hole punched through 3 mm steel shears along a cylindrical surface of roughly π × 20 × 3 ≈ 188 mm². Multiply that area by the sheet's shear strength, often taken as about 80 percent of its tensile strength, to get the punching force the press must supply. The same τ = F ⁄ A relation runs both directions — given a press's rated force, it also tells you the maximum thickness that press can punch.
What shear stress is safe for a bolt or pin?
Whatever stays below the material's shear yield strength divided by your design's safety factor, not its tensile strength. For ductile metals under the usual von Mises estimate, shear yield runs near 0.577 of tensile yield — around 150 MPa for common structural steel — and codes typically allow only a fraction of that as a working stress. Compare the reading here against the allowable shear stress in your fastener standard or material datasheet, never against an ultimate tensile figure borrowed from a different test.
Can shear stress be negative?
In sign-convention terms yes, though this instrument reports magnitude. A shear stress marked positive or negative simply records which of two opposite directions the sliding force acts along the cut, relative to a chosen coordinate system — Mohr's circle for stress relies on that sign to track how shear and normal stress trade off as the cutting plane rotates. For checking whether a pin or plate is safe, only magnitude matters: the shank does not care which way the load points, only how large it is next to what the material can take.