Analyze yielding using Tresca maximum shear theory fast. Enter stresses choose units compute instantly now. Compare against yield strength and plan safer designs confidently.
The Tresca criterion is based on the maximum shear stress theory.
For principal stresses σ1, σ2, and σ3, compute:
σTresca = max(|σ1−σ2|, |σ2−σ3|, |σ3−σ1|)τmax = σTresca / 2
If yield strength σy is provided, the factor of safety is
FoS = σy / σTresca.
| Case | Mode | Inputs | Units | σTresca | τmax | FoS (σy=250) |
|---|---|---|---|---|---|---|
| 1 | Principal | σ1=120, σ2=40, σ3=-10 | MPa | 130 | 65 | 1.923 |
| 2 | Plane | σx=80, σy=20, τxy=30 | MPa | ~102.426 | ~51.213 | ~2.441 |
| 3 | Principal | σ1=60, σ2=10, σ3=0 | MPa | 60 | 30 | 4.167 |
Tresca theory predicts yielding when the maximum shear stress in a material reaches the shear stress at yield in a uniaxial test. In practice, this is implemented by comparing the largest difference between principal stresses to an allowable limit. The calculator reports an equivalent value, σTresca, along with τmax, making it easy to connect stress states to yield strength data.
Many ductile metals begin plastic flow when shear-driven slip systems activate. Tresca focuses directly on that mechanism, so it is widely used in mechanical design checks, pressure vessel screening, and quick safety evaluations. Because it uses the largest principal stress gap, it often provides a conservative boundary compared with energy-based criteria.
If you already know principal stresses (σ1, σ2, σ3) from a solver or Mohr’s circle, choose the principal mode. If your data is in-plane (σx, σy, τxy), use plane stress mode. The calculator converts plane stress to principal stresses internally and then applies the Tresca check.
Select one unit set and keep every stress in that same unit. Tension is treated as positive and compression as negative, so mixed loading is handled correctly. For example, a tensile σ1 combined with a compressive σ3 can increase the stress difference and raise σTresca noticeably.
σTresca is the maximum of |σ1−σ2|, |σ2−σ3|, and |σ3−σ1|. τmax is half of that value. The table of stress differences helps you identify which principal pair controls the design, which is useful when adjusting geometry or load paths.
Tresca and von Mises are both used for ductile yielding, but they measure different things. Tresca tracks maximum shear, while von Mises tracks distortion energy. For many stress states, Tresca predicts yielding at a slightly lower load, which is why it is considered conservative in routine design.
If you enter yield strength, the calculator returns a factor of safety defined as FoS = σy / σTresca. This is a direct ratio using the same unit system. A FoS above 1 indicates the stress state is below yield by this criterion, while lower values suggest yielding risk.
Verify that the input stresses describe the same point and load case. For plane stress, remember σ3 is assumed to be zero, which is valid for thin plates where out-of-plane stress is negligible. When in doubt, compare results for several unit choices and re-check sign entries before exporting.
Tresca stress is an equivalent value based on the largest difference between principal stresses. It represents the shear-driven yielding limit used in maximum shear stress theory for ductile materials.
Use plane stress mode when your known inputs are σx, σy, and τxy from a thin plate or surface stress state. The calculator converts them into principal stresses before applying the criterion.
Yes. Enter compression as negative and tension as positive. The calculator uses absolute principal stress differences, so mixed tension-compression cases are handled correctly.
Choose any one unit system (Pa, kPa, MPa, GPa, psi, or ksi) and keep all stresses and yield strength in that same unit. Results and exports follow the selected unit.
Plane stress assumes negligible out-of-plane normal stress, typical for thin components. Setting σ3 = 0 matches that assumption. If out-of-plane stress is significant, use principal stresses from a full 3D analysis.
The factor of safety is FoS = σy / σTresca when a yield strength is provided. It is a simple ratio, so it is unit-consistent and easy to interpret for screening decisions.
Often, yes. Tresca typically predicts yielding at a slightly lower load for the same stress state. However, the difference depends on the stress combination, so engineering standards and material behavior should guide which criterion you use.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.