Complete Engineering Analysis & Design Tool Suite
Calculate tensile and compressive stress in materials.
Calculate material strain from deformation.
Calculate elastic modulus of materials.
Determine shear modulus from elastic properties.
Understanding basic material properties is fundamental to engineering design. The stress-strain relationship defines how materials deform under applied loads. Our stress calculator and strain calculator help determine these critical material characteristics.
Normal Stress (σ) is calculated by dividing the applied force by the cross-sectional area. This is one of the most fundamental calculations in strength of materials. Tensile stress occurs when materials are pulled apart, while compressive stress occurs under crushing loads.
Strain (ε) represents the deformation relative to original dimensions. It's a dimensionless quantity showing how much a material stretches or compresses. Young's Modulus (E) relates stress to strain and indicates material stiffness.
Shear Modulus (G) measures resistance to shear deformation. Use Poisson's ratio to convert between different elastic constants for complete material characterization.
Calculate maximum bending moment in beams.
Calculate shear force in beam sections.
Compute beam deflection under loads.
Calculate bending stress in beams.
Beam analysis is critical for structural design. The bending moment calculator determines the internal moments that cause beam bending. Maximum bending moment typically occurs at the center of simply supported beams under point loads.
Shear force represents internal forces perpendicular to the beam axis. The shear force calculator helps identify where shear stress is maximum. Shear force diagrams (SFD) and bending moment diagrams (BMD) are essential tools for understanding beam behavior.
Beam deflection is the vertical displacement under load. The beam deflection calculator uses the formula δ = PL³/(48EI) for simply supported beams. Excessive deflection can cause serviceability issues even if strength is adequate.
Our calculators handle multiple loading conditions: point loads, uniform distributed loads (UDL), triangular loads, and various support configurations including cantilever and simply supported beams.
Calculate I for rectangular cross-sections.
Calculate I for circular cross-sections.
Calculate section modulus for beam design.
Calculate J for circular shafts.
Moment of inertia (I), also called second moment of area, is crucial for beam and column design. It measures how area is distributed about an axis. The moment of inertia calculator handles standard shapes: rectangles, circles, tubes, I-beams, and U-channels.
For rectangular sections: I = (b×h³)/12. For circular sections: I = πr⁴/4. Larger moments of inertia mean less deflection and greater bending strength.
Section modulus (W) is the ratio of moment of inertia to distance from neutral axis: W = I/c. The section modulus calculator is essential for beam design, as bending stress directly relates to section modulus.
Polar moment of inertia (J) is used for torsional analysis of shafts. For solid circular shafts: J = πd⁴/32. The calculator handles both solid and hollow circular cross-sections.
Analyze torsional stress in shafts.
Calculate shear stress distribution.
Calculate equivalent stress.
Calculate angular deflection in shafts.
Torsion occurs when torque (twisting moment) is applied to shafts. The torsion calculator computes maximum torsional stress: τ = T·r/J. Shafts experience maximum shear stress at the outer fiber.
Twist angle (θ) represents angular deflection along the shaft length. The formula θ = TL/(GJ) shows that longer shafts and smaller polar moments result in greater twist. Use the twist angle calculator to ensure shaft stiffness is adequate.
Shear stress (τ) develops across beam cross-sections perpendicular to bending. The formula τ = V·Q/(I·b) shows how shear varies across the section. Maximum shear often occurs at the neutral axis.
Von Mises equivalent stress (σ_vm = √(σ² + 3τ²)) combines normal and shear stresses to predict failure for ductile materials. Our Von Mises stress calculator is essential for complex loading states.
Determine critical buckling load.
Calculate contact stresses.
Calculate bolt shear capacity.
Convert torque to preload force.
Calculate stress in welds.
Predict component fatigue life.
Fatigue failure occurs after many load cycles at stresses below yield strength. The fatigue life calculator uses S-N (Wöhler) curves to predict component lifespan.
The relationship between stress (S) and cycles to failure (N) is logarithmic: log(N) = [log(S_f) - log(S)]/m. Higher stresses reduce life; lower stresses extend life. The slope (m) depends on material and environment.
Mean stress effects are critical—components under tensile mean stress fail faster than those under zero mean stress. The Goodman diagram accounts for mean stress when predicting fatigue strength.
Common applications include rotating shafts, engine components, suspension systems, and aircraft structures. Use our calculator to verify adequate fatigue safety for cyclic loading.
Stress concentration factors and surface finish effects further reduce fatigue strength in real components. Conservative design practice includes safety margins of 2-4 on fatigue life.