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Focused engineering tools for fast, well-defined problems.
20 calculators · Structural Mechanics
Structural Mechanics
20 calculatorsDomain overview →
Axial Loading
- Normal Stress CalculatorAverage normal stress σ = N/A on a cross-section from an internal axial force and an area, with the tension or compression sense preserved.
- Normal Strain CalculatorEngineering normal strain ε = ΔL/L from a change in length and an original length, in both plain and microstrain form.
- Hooke's Law CalculatorSolve σ = Eε for stress, strain or Young's modulus in the uniaxial linear-elastic range.
- Axial Deformation CalculatorElongation δ = NL/(AE) of a prismatic axially loaded member, signed so that tension lengthens and compression shortens.
Stress & Strain
- Factor of Safety CalculatorFactor of safety n = S/|σ| against a declared yield, ultimate or custom reference strength, with the matching utilisation.
- Plane Stress Transformation CalculatorTransform a plane-stress state σx, σy, τxy through a counter-clockwise rotation θ and read the rotated components.
- Principal Stresses CalculatorPrincipal stresses σ1 ≥ σ2, their orientations, and the maximum in-plane shear of a plane-stress state.
- Mohr's Circle CalculatorCentre, radius, principal stresses and maximum in-plane shear of a plane-stress state, drawn as a true Mohr circle with τ positive upward.
- Von Mises Stress CalculatorVon Mises equivalent stress for a plane-stress state, with an optional yield strength giving utilisation and a yield-based factor of safety.
Beams & Bending
- Beam Reactions CalculatorSupport reactions of a statically determinate beam — cantilever, simply supported or overhanging — from point loads, couples and uniform distributed loads, with equilibrium residuals and a determinacy verdict.
- Shear Force CalculatorInternal shear force at any station of a determinate beam, with both one-sided limits and the exact jump wherever a concentrated force or a support reaction acts.
- Bending Moment CalculatorInternal bending moment at any station of a determinate beam, sagging positive, with the exact −Mz jump at an applied couple and the analytically located extremes.
- Bending Stress CalculatorExtreme-fibre flexural stress σ = −My/I taken from the bending moment of the beam itself, with tension and compression named.
- Transverse Shear Stress CalculatorTransverse shear stress τ = VQ/(It) in a beam section, using the shear force the beam engine computes for the chosen station.
- Beam Deflection CalculatorSlope and deflection of a determinate beam by direct integration of EI v'' = M, with continuity at every load event and exact support conditions.
Torsion
- Torsional Shear Stress CalculatorShear stress in a solid or hollow circular shaft under torsion, τ = Tρ/J, at the outer surface and at any radius, with the polar second moment reported alongside.
- Angle of Twist CalculatorRelative rotation of one end of a circular shaft with respect to the other, φ = TL/(GJ), in radians and degrees, with the torsional stiffness GJ/L.
Columns & Buckling
- Slenderness Ratio CalculatorEffective length KL and slenderness ratio λ = KL/r of a column, from a radius of gyration entered directly or derived from I and A, with the theoretical end-condition factors.
- Euler Buckling Load CalculatorElastic critical load Pcr = π²EI/(KL)² of an ideal slender column, with critical stress and slenderness, reported explicitly as a bifurcation load and not a design capacity.