Stress Calculator — anjanspatel.com

Mohr's Circle — Principal Stresses

σx (normal stress)

σy (normal stress)

τxy (shear stress)

Material Yield Strength σy_mat

σ₁ (max principal)

—

MPa / ksi

σ₂ (min principal)

—

MPa / ksi

τmax

—

MPa / ksi

θp (°)

—

to σ₁ plane

Von Mises σ′

—

MPa / ksi

Safety Factor (VM)

—

vs. yield

Yield Status

—

Von Mises

σ₁,₂ = (σx+σy)/2 ± R | R = √[((σx−σy)/2)² + τxy²] | Von Mises = √(σ₁²−σ₁σ₂+σ₂²)

Fatigue & Safety Factor

Yield Strength Sy

Ultimate Tensile Strength Su

Max Stress σmax

Min Stress σmin

Endurance Limit Se (≈ 0.5Su)

Stress Concentration Kt

Mean Stress σm

—

MPa / ksi

Alternating σa

—

MPa / ksi

R ratio

—

σmin/σmax

Stress Amplitude

—

MPa / ksi

Goodman NF

—

safety factor

Gerber NF

—

safety factor

Soderberg NF

—

safety factor

Yield Safety

—

σmax vs. Sy

Goodman: σa/Se + σm/Su = 1/N | Gerber: σa/Se + (σm/Su)² = 1/N | Soderberg: σa/Se + σm/Sy = 1/N

Thin / Thick Wall Pressure Vessel

Internal Pressure P

Inner Radius ri

Wall Thickness t

Allowable Stress S

ri/t Ratio

—

classification

Theory

—

Thin/Thick

Hoop Stress σθ

—

MPa / ksi

Axial Stress σa

—

MPa / ksi

Lamé Hoop σθ (at inner)

—

thick wall

Required t (thin)

—

ASME/thin wall

Thin wall (ri/t > 10): σθ = P·ri/t, σa = P·ri/2t | Thick wall (Lamé): σθ = P(ri²+ro²)/(ro²−ri²) at inner radius