Shear Stress Calculator
Compute shear stress τ = F/A. Output in Pa, kPa and MPa.
Shear stress: τ = F/A
Shear stress τ = F/A measures the tangential force F (parallel to the surface) divided by the area A on which it acts. The unit is N/m² (Pa) or, more commonly in engineering, MPa. It differs from normal stress, where the force acts perpendicular to the surface. The shear strength of structural steel is roughly τ_max ≈ 0.6·σ_yield ≈ 150 MPa. Shear governs the design of bolts, rivets, and welds (NBR 8800 — steel; NBR 6118 — concrete). A pair of scissors cuts by shear. In a flowing fluid, shear follows Newton's law of viscosity: τ = μ·(dv/dy), with μ the dynamic viscosity. Example: a 1,000 N tangential force on a 0.01 m² area gives τ = 100,000 Pa = 0.1 MPa — far below steel's limit but already meaningful for plastics.
Applications
Bolt, rivet and weld sizing, beams under transverse loads (shear diagram), geotechnics (slope and embankment stability), tribology (lubrication and friction films), safety pin or shear pin design (calibrated to break first), and fluid-flow pressure-drop calculations.
FAQ
What's the difference between τ and σ? τ is tangential (parallel to surface); σ is normal (perpendicular). Both have the same units (Pa), but they describe different failure modes.
Why is τ_max ≈ 0.6·σ_yield? It comes from the von Mises criterion: in pure shear, an isotropic material yields when τ reaches about 0.577·σ_yield. Engineering codes round it to 0.6 for safety.
Does shear stress matter in fluids? Yes — it's the basis of viscosity. Internal shear creates the pressure drop in pipe flow and is what your stirring spoon overcomes.
Related Tools
Peak Shear Stress in a Bonded Lap Joint (Volkersen)
Computes the peak shear stress in the adhesive layer of a single lap joint using the Volkersen model, which treats the adherends as elastic membranes in tension and the adhesive in pure shear: τ_max = τ_avg·(λ/2)·coth(λ/2), with τ_avg = F/(b·L) and λ = L·√(2·G_a/(E·t·t_a)). Because the adherends stretch unevenly along the overlap, the adhesive does not work uniformly: load piles up at both ends while the middle stays almost unloaded, so the peak stress can be several times the average — 3.35 times in the default example. Hence the model most useful and counter-intuitive conclusion: lengthening the overlap pays less and less, because the extra length carries no load; doubling L from 25 to 50 mm halves the AVERAGE stress but cuts the PEAK stress by only 0.25 %, and it is the peak that breaks the joint. The model assumes a balanced joint, with both adherends of the same material and thickness — that is where the 2 inside the root comes from — and since adherend and adhesive thickness enter only as a product, thickening the adherend buys exactly what thickening the glue line does. Far more is gained by thickening the adhesive or choosing a less rigid one, which is what lowers λ. Enter the load, the overlap width and length, the adherend thickness and modulus, and the adhesive thickness and shear modulus.
Vessel Allowable Stress (ASME)
Calculate the design allowable stress of a pressure-vessel material by the ASME criterion, S = σ_uts ÷ n, from the material minimum tensile strength σ_uts (MPa) and the safety factor n (3.5 in the current ASME VIII Div. 1 edition for tensile strength). The allowable stress S is the MAXIMUM stress permitted in the vessel material in service, and is the basis of all thickness and MAWP calculations — it embeds the safety margin against failure. The ASME code sets the allowable stress as the SMALLEST among several criteria: a fraction of the TENSILE strength (σ_uts/3.5 in the current edition — formerly /4.0, reduced as materials and inspection advanced), a fraction of the YIELD strength (2/3 of σ_yield), and, at high temperatures, criteria based on CREEP and creep rupture (since at high temperature the material deforms slowly under constant load). For each material and temperature, the code TABULATES the S value — this formula shows the tensile-strength criterion, often governing at moderate temperatures. Using the correct allowable stress (from the code, for the right material and temperature) is absolutely essential: it is the safety margin protecting against vessel explosion. Enter the tensile strength and the safety factor.
Bolt Shear Stress
Calculate the shear stress in transversely loaded bolts, τ = F ÷ (n·A), from the total shear force F (N), the number of bolts (or shear planes) n and each bolt's area A (mm²). Unlike tensioned joints (where the bolt is tightened and the load is axial), in SHEAR joints the bolts resist a transverse force tending to slide one part over another (as in steel structural connections, splice plates, flanges under lateral load). The force is distributed among the bolts and each works in shear — hence the stress is force divided by the number of bolts times the area. There can be SINGLE shear (one shear plane) or DOUBLE shear (two planes, when the bolt passes through three plates), doubling capacity. The area used depends on whether the shear plane passes through the threaded part (use the tensile area) or the smooth shank (nominal-diameter area). Shear stress is compared with the bolt material's shear strength (typically ~0.6 of tensile strength). In structures, bearing-type (bolt in shear/bearing) and slip-critical (preload friction transmits load without bolt shear) connections are distinguished — this formula covers shear resistance. Enter the shear force, the number of bolts and the area.
Beam Shear Stress
Computes max shear stress for a rectangular beam under a shear force.
Sling Leg Tension
Calculate the tension in each leg of a multi-leg inclined sling, T = W ÷ (n·cos α), from the load weight W (N), the number of legs n and the angle of each leg from vertical α (degrees). When a load is lifted by a multi-leg sling (ropes or chains from the hook spreading to the attachment points on the load), the tension in each leg is NOT simply the weight divided by the number of legs — because the legs are INCLINED. The more OPEN the angle (more horizontal legs), the HIGHER the tension in each leg, possibly MULTIPLYING the load several times! This happens because, with inclined legs, part of each leg's force is 'spent' on the horizontal component (which cancels between opposite legs, compressing the load), and only the vertical component supports the weight — so the total tension must be higher for the vertical components to sum to the weight. This is one of the most dangerous and common rigging errors: using slings with very open angles overloads the legs, possibly breaking them even with a load 'apparently' within capacity. So codes LIMIT the leg angle (typically 60° max from vertical, ideally less) and sling WLL tables give the REDUCED capacity per angle. Enter the load weight, the number of legs and the angle.
Cable Tension in Accelerated Lift
Calculate the dynamic tension in a cable while lifting a load with acceleration, T = W·(1 + a/g), from the load weight W (N), the vertical lift acceleration a (m/s²) and gravity g. When a load is lifted with ACCELERATION (at lift start, when accelerating the rise), the cable must provide not only the force to support the weight (W) but ALSO the force to accelerate the mass upward — by Newton's second law, the total tension is the weight times the factor (1 + a/g). This means the DYNAMIC tension is GREATER than the static weight: an acceleration of g/2 (5 m/s²) raises the tension by 50%! That is why ABRUPT lifts (fast start, or worse, lifting an already-moving load or stopping abruptly) generate dangerous dynamic OVERLOADS in the cable, which can break it even with the static load within capacity. The effect is worse in abrupt STOPS and in loads 'snatching off the ground' (cable slack suddenly removed, generating an impact). So experienced operators lift SMOOTHLY (low acceleration), and the cable safety factors (5 or more) exist precisely to cover these inevitable dynamic overloads. This calculation quantifies the tension increase due to acceleration, essential in the safety analysis of dynamic lifts. Enter the load weight and the lift acceleration.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.