Mechanics of Materials Expert

Before Starting

1. Which loading type? (axial, torsional, bending, combined)
2. Which material behavior? (elastic, plastic, viscoelastic)
3. Static or fatigue loading?

Core Expertise Areas

Stress and Strain

Normal stress: sigma = F over A, force per unit area perpendicular to surface. Shear stress: tau = V times Q over I times t, parallel to surface. Normal strain: epsilon = delta over L, deformation per unit length. Hooke law: sigma = E times epsilon for linear elastic material. Poisson ratio: lateral strain is negative nu times axial strain.

Axial Loading

Deformation: delta = PL over AE. Statically indeterminate: compatibility equation provides additional equation. Thermal stress: sigma = E times alpha times delta T for constrained member. Stress concentration: geometric discontinuities increase local stress by Kt factor.

Torsion

Shear stress: tau = T times rho over J, varies linearly with radius. Angle of twist: phi = TL over JG. Polar moment of inertia: J = pi r4 over 2 for solid circle. Thin-walled sections: tau = T over 2 times A_enclosed times t.

Bending

Flexure formula: sigma = M times y over I, linear stress distribution. Neutral axis: zero normal stress, centroidal axis for symmetric sections. Shear formula: tau = VQ over It, parabolic distribution in rectangular section. Deflection: integrate moment-curvature relation, M = EI times d2y over dx2.

Failure

Von Mises criterion: equivalent stress for ductile materials under combined loading. Tresca criterion: maximum shear stress theory, conservative for ductile materials. Buckling: Euler formula Pcr = pi squared EI over L_effective squared. Fatigue: S-N curve, endurance limit, stress concentration in fatigue.

Best Practices

• Always identify cross section properties before stress calculation
• Draw shear and moment diagrams for beam problems
• Apply appropriate failure theory for material ductility
• Include stress concentrations in fatigue analysis

Common Pitfalls

Pitfall	Fix
Wrong sign for bending stress	Define positive M direction and y direction consistently
Using gross section in buckling	Use minimum moment of inertia for column buckling
Ignoring shear in beam deflection	Include shear deflection for short deep beams
Applying Euler buckling to short columns	Check slenderness ratio before applying Euler formula

Related Skills

• statics-expert
• dynamics-expert
• cad-design-expert