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Mechanics of Materials 1 & 2
Interactive, step-by-step calculators for normal stress, torsion, bending, shear, Mohr's circle and pressure vessels. Every formula is annotated with its source textbook equation number.
📚 References: Beer F.P. & Johnston E.R. Mechanics of Materials 8th ed. · Hibbeler R.C. Mechanics of Materials 10th ed. · Gere J.M. & Goodno Mechanics of Materials 9th ed.
Mechanics of Materials 1 Basic stress and strain
Stress
Normal Stress and Axial Elongation
σ=P/A · δ=PL/(EA) · ε=δ/L · Stepped section · Thermal stress α·ΔT
Beer Eq.(1.5)(2.7)(2.21)
Torsion
Torsion — τ = Tc/J, θ = TL/(GJ)
J=πd⁴/32 solid, J=π(d_o⁴−d_i⁴)/32 tube · Angle of twist · P=Tω power
Beer Eq.(3.9)(3.16)
Bending & Shear
Bending and Shear Stress
σ=My/I · τ=VQ/(Ib) · Rectangular τ_max=1.5V/A · Neutral axis
Beer Eq.(4.15)(5.3)
Section Properties
Cross-Section Geometric Properties
A, Ix, Iy, Sx, Zx, rx · Rectangle, circle, tube · Parallel-axis (Steiner) theorem
Beer App.A · Steiner I'=I+Ad²
Mechanics of Materials 2 Advanced stress analysis
Mohr's Circle
Mohr's Circle — Plane Stress
σ₁,σ₂ principal stresses · τ_max · 2θ_p angle · Canvas plot · Beer §7.3
Beer Eq.(7.10)(7.12)
Pressure Vessel
Pressure Vessel — Thin / Thick Wall
σ₁=pr/t (hoop) · σ₂=pr/2t (axial) · Sphere · Lamé thick-wall formulas
Beer §7.9 · Lamé
Yield Criteria + Plastic
von Mises, Tresca and Plastic Moment
σ_vm=√(σ²+3τ²) · Tresca τ_max · Mp=Fy·Zp · Shape factor f=Zp/S
Beer Eq.(7.26) · Beer §4.9