Home
Back
Formula Used:
| From: | To: |
This formula calculates the shear stress (τ) on an oblique plane when the normal stress (σθ) acting on that plane and the angle (θ) are known. It's derived from stress transformation equations in solid mechanics.
The calculator uses the formula:
Where:
Explanation: This formula relates the normal stress acting on an oblique plane to the resulting shear stress, considering the angle of the plane relative to the applied stress direction.
Details: Calculating shear stress on oblique planes is crucial in material science and structural engineering for analyzing stress distributions, predicting failure points, and designing safe structures under complex loading conditions.
Tips: Enter normal stress in Pascals (Pa) and angle in radians. Both values must be positive numbers. The angle should be between 0 and π/2 radians for meaningful results.
Q1: What are the units for shear stress and normal stress?
A: Both are typically measured in Pascals (Pa) in the SI system. 1 Pa = 1 N/m².
Q2: Why is the angle measured in radians?
A: Radians are the standard angular measure in mathematical calculations involving trigonometric functions, though degrees can be converted to radians (1° = π/180 radians).
Q3: What is the physical significance of this calculation?
A: It helps determine how stresses transform when considering different planes within a material, which is essential for failure analysis and material strength evaluation.
Q4: Are there limitations to this formula?
A: This formula assumes homogeneous, isotropic materials and applies to elastic deformation under plane stress conditions. It may not accurately represent behavior in anisotropic materials or under complex loading.
Q5: How does this relate to complementary shear stresses?
A: The formula incorporates the principle that shear stresses on perpendicular planes are equal in magnitude but opposite in direction, which is fundamental to stress transformation analysis.