Basic mechanics of materials shear stress: direct shear, shaft torsion, and beam bending shear.
τ = V / A · Puntir: τ = T · r / J · Geser lentur: τ = V · Q / (I · b)Need twist angle φ = T·L/(G·J) or a 5-variable torsion solver? Use the angle of twist calculator.
For a rectangular beam, maximum τ at the neutral axis = 1.5 × V/A. See the beam shear diagram.
Shear stress (τ, tau) is the internal force per unit area acting parallel (tangential) to the material cross-section, with units of Pascal (Pa) or psi. It arises when two parts of a material are sheared in opposite directions, unlike normal stress which acts perpendicular to the cross-section.
The most basic formula is τ = V / A, with V = shear force (newtons) and A = cross-sectional area (m²). Example: a 10 kN force on a 100 mm² section gives τ = 100 MPa.
Use the torsion formula τ = T · r / J, with T = torque, r = radius of the point of interest, and J = polar moment of inertia of the section. For a solid shaft J = π·d⁴/32; for a hollow shaft J = π·(D⁴−d⁴)/32. Maximum shear stress occurs at the outermost radius.
The transverse shear formula is τ = V · Q / (I · b), with V = shear force, Q = first moment of the area above/below the point of interest, I = section moment of inertia, and b = section width at that point. For a rectangular beam, maximum shear stress at the neutral axis = 1.5 × V/A.
Normal stress (σ) acts perpendicular to the cross-section — e.g. tension and compression — while shear stress (τ) acts parallel to the cross-section, tending to slide one material layer against its neighbor. Both can occur together at one point, as in torsion and bending.
This calculator computes shear stress directly from loading (V/A, torsion, beam bending). The principal stress calculator analyzes the complete 2D/3D stress state: finding σ₁, σ₂, principal plane angles, and maximum τ via Mohr's circle — a more advanced level of analysis.
SI units are Pascals: Pa, kPa, MPa (most common in engineering), and GPa. Imperial units: psi and ksi (1 ksi = 1000 psi). Key conversions: 1 MPa = 145.0377 psi and 1 ksi = 6.8948 MPa. This calculator shows results in all of these units.
As a rule of thumb, allowable shear stress is often taken around 40% of tensile yield strength for static loads (e.g. A36 steel with 250 MPa yield → allowable shear ≈ 100 MPa per the Tresca criterion τ_allow = σ_yield/2 with a safety factor). Always follow the applicable design code for real applications.
Use the automatic formula for solid circular shafts (d) or hollow ones (outer D, inner d). Choose manual J & r input for non-standard sections or when J is already known from a profile table. The τ = T·r/J formula is only exact for circular sections; rectangular sections need non-circular torsion theory.
Because the shear stress distribution over a rectangular section is parabolic with zero at the top/bottom fibers and a peak at the neutral axis. Integrating that distribution gives τ_max = 3V/(2A) = 1.5 × the average shear stress V/A.
Q is the first moment (static moment) of the cross-sectional area on one side of the point of interest about the neutral axis: Q = A' · ȳ', with A' = area above (or below) that point and ȳ' = distance from A' centroid to the neutral axis. Q is maximum at the neutral axis and zero at the outer fibers.
Not for final design. This calculator is for education and early estimation using linear elastic theory. Structural, pressure vessel, and safety-critical component design must follow standard codes (e.g. SNI, AISC, ASME) and be verified by a licensed engineer.
⚠️ Disclaimer: This calculator is for education and early estimation. Not a substitute for certified engineering calculations for structural, pressure vessel, or safety-critical component design.
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