Plane stress superposition
Combined stress
Inputs
Signed normal stress from direct axial loading at the point of interest.
Signed normal stress from bending at the same point and along the same axis.
Signed in-plane shear stress at the same point.
Results
Combined normal stress σxσx
120
First principal stress σ₁σ₁
127.08
Second principal stress σ₂σ₂
-7.082
Maximum in-plane shearτmax
67.082
Plane-stress von Mises equivalentσvm
130.77
σx = σa + σb; σ₁,₂ = σx/2 ± √[(σx/2)² + τxy²]; σvm = √(σx² + 3τxy²)
A first-pass number, not a code check, certification, or approval. Read the method and its limits below. What this is and is not.
Nearby: Axial response · Beam deflection & reactions · Elastic stability · Solid-shaft torsion
Method
Formula, when it applies, and when it does not
Combine axial and bending normal stresses with one in-plane shear stress, then resolve principal and von Mises screening quantities.
σx = σa + σb; σ₁,₂ = σx/2 ± √[(σx/2)² + τxy²]; σvm = √(σx² + 3τxy²)
When
- Plane stress
- Linear superposition
- User-entered signed component stresses
- No local concentration
Don’t
- This screen adds user-entered axial and bending normal stresses and combines them with one in-plane shear stress under plane stress. It excludes local stress concentration, multiaxial/through-thickness stress, material allowables, fatigue, buckling, contact, and safety-factor decisions.