Consider the following statements :
1. In a member subjected to uniaxial tensile force the maximum normal stress is the external
load divided by the maximum cross-sectional area
2. When the structural member is subjected to uniaxial loading, the shear stress is zero on a
plane where the normal stress is maximum
3. In a member subjected to uniaxial loading, the normal stress on the planes of maximum
shear stress is less than the maximum
Statement 1: "Maximum normal stress = external load / maximum cross-sectional area" (Incorrect)
· Normal stress = Load/Area is a general formula, but maximum normal stress actually occurs at the minimum cross-sectional area (weakest section), not the maximum area. A larger area gives lower stress, not higher. So this statement is wrong.
Statement 2: "Shear stress is zero on the plane where normal stress is maximum" (Correct)
· In uniaxial loading, the maximum normal stress occurs on the plane perpendicular to the load axis (θ= 0°). On this plane:
So shear stress is indeed zero where normal stress is maximum - this is a principal plane.
Statement 3: "Normal stress on planes of maximum shear stress is less than the maximum normal stress (Correct)
· Maximum shear stress occurs at θ = 45°, where:
Since σ /2 < σ (maximum normal stress), the normal stress on the max-shear plane is indeed less than the maximum normal stress. Correct.
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