Mechanical & Civil Engineering
Tresca Maximum Shear Yield Calculator
Evaluate the Tresca (maximum shear stress) yield criterion from principal stresses.
Your inputs
Change any value to update the result instantly.
Max shear stress
100 MPa
Tresca yield limit (Sy/2)
125 MPa
Factor of safety
1.25
Yield strength
250 MPa
What this calculator does
Tresca Maximum Shear Yield Calculator: Applies the standard mechanics-of-materials relationship for this load case so a student can see how the stress, strain or deflection follows from the geometry and the load.
What your result means
The headline figure tells you how hard the material is being worked, or how much it moves, under the load you entered. Compare it with the allowable value for your material and required factor of safety.
Formula and working
τmax = (σmax - σmin) / 2; yields when τmax = Sy/2
- 1
Collect the inputs
Principal stress σ1 = 180 MPa; Principal stress σ2 = -20 MPa; Yield strength Sy = 250 MPa
- 2
Apply the formula
τmax = (σmax - σmin) / 2; yields when τmax = Sy/2
- 3
Result
Max shear stress = 100 MPa
Frequently asked questions
Symbols and assumptions
- s1
- Principal stress σ1 (MPa)
- s2
- Principal stress σ2 (MPa)
- sy
- Yield strength Sy (MPa)
- • The material is homogeneous, isotropic and loaded within its linear-elastic range.
- • Inputs are entered in a consistent unit system, as labelled on each field.
Sources and review
Reviewed 2026-09-22 · Next review 2027-09-22
- • This is an educational estimate for learning and checking, not a design deliverable.
- • Real design must follow the governing code or standard for your jurisdiction and be reviewed and signed off by a qualified engineer.
- • Safety factors, load combinations and material certification are the responsibility of the designer, not of this page.
Important limitation
This is an educational estimate based only on the values and formula shown. Verify current rates, rules, units, and professional standards before relying on the result. It is not personalized financial or investment advice.
Report a mistake or request an improvement
Tell us if a formula, unit, explanation, or result needs attention. Your message will include this calculator’s name and page.
Related calculators
Von Mises Equivalent Stress Calculator
Calculate von Mises equivalent stress from principal stresses for ductile yield prediction.
Area Moment of Inertia (Parallel Axis) Calculator
Calculate the moment of inertia about a shifted axis using the parallel axis theorem.
Beam Section Modulus Calculator
Compute the elastic section modulus Z = I/y for a beam cross-section.
Curved Beam Circumferential Fibre Stress Calculator
Calculate circumferential fibre stress in a curved beam using the Winkler-Bach theory.
Fatigue Endurance Limit (S-N Marin Factors) Calculator
Estimate the corrected endurance limit of a material using Marin surface, size, and load factors.
Fixed-End Continuous Beam Deflection Calculator
Estimate maximum deflection and fixed-end moment for a fixed-end beam under uniform load.