Stress transformation screen
Plane-stress Mohr’s Circle
Inputs
Signed plane-stress component; tension positive under the stated convention.
Signed plane-stress component at the same point.
Signed shear stress at the same point and under one stated convention.
Results
Mohr circle center stress
60
Mohr circle radius / max in-plane shear
50
Maximum principal stressσ₁
110
Minimum principal stressσ₂
10
One principal-plane orientation
26.565
Mohr-circle double angle to principal plane
53.13
Mohr-circle double angle to max-shear plane
143.13
σavg = (σx + σy)/2; R = √[((σx−σy)/2)² + τxy²]; σ1,2 = σavg ± R; 2θp = atan2(2τxy, σx−σy); 2θs = 2θp + 90°
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
Resolve a plane stress state into circle center/radius, principal stresses, maximum in-plane shear, and one principal-plane orientation.
σavg = (σx + σy)/2; R = √[((σx−σy)/2)² + τxy²]; σ1,2 = σavg ± R; 2θp = atan2(2τxy, σx−σy); 2θs = 2θp + 90°
When
- Plane stress
- One point
- Signed stress components
- Elastic transformation only
Don’t
- This transforms one entered plane-stress state at one point. The reported angle follows the entered sign convention and is one of two orthogonal principal-plane orientations; the two Mohr-circle double-angle outputs are shown explicitly. It excludes 3D stress, stress gradients, principal strain, material failure criteria, buckling, fatigue, fracture, local concentration, and any design or compliance decision.