At a Point in a stressed body the principal stresses are 80 MN/m² (Tensile) and 40 MN/m² (Compressive). Calculate the maximum shear stress at the point.
- A40 MN/m²
- B60 MN/m²Correct
- C80 MN/m²
- D120 MN/m²
Solution
Concept
Calculation of maximum shear stress
Formula
τmax = (σ1 - σ2) / 2
Step-by-step solution
1. Let tensile principal stress σ1 = +80 MN/m² and compressive principal stress σ2 = -40 MN/m². 2. Maximum shear stress formula is τmax = (σ1 - σ2) / 2. 3. τmax = (80 MN/m² - (-40 MN/m²)) / 2 = 120 MN/m² / 2 = 60 MN/m². Answer: B
Explanation
Maximum shear stress at a point subjected to principal stresses is calculated using the formula where maximum shear stress equals half the difference between the principal stresses. Substituting the tensile stress of +80 MN/m² and compressive stress of -40 MN/m² yields (80 - (-40)) divided by 2. This calculates to 120 divided by 2, which equals 60 MN/m².
Why the other options are wrong
A) 40 MN/m² results from taking only the magnitude of one principal stress. C) 80 MN/m² represents the maximum principal tensile stress. D) 120 MN/m² represents the total difference between principal stresses, not half of it.
Shortcut
Maximum Shear Stress with opposite signs = (σ1 + |σ2|) / 2 = (80 + 40) / 2 = 60 MN/m².
Common mistake
Failing to account for the negative sign of compressive stress when calculating maximum shear stress.
Correct answer: B) 60 MN/m²