Project ForgeA rod of length L having uniform cross-sectional area A is subjected to a tensile force P. If the Young's modulus of the material varies linearly from E1 to E2 along the length of the rod, the normal stress developed at the mid-length section-SS is
- P/A
- BP(E1−E2)/(A(E1+E2))
- CPE2/(AE1)
- DPE1/(AE2)
Explanation
For a prismatic bar (uniform cross-sectional area A) under pure axial tension P, static equilibrium requires the internal normal stress to be P/A at EVERY section along the length — this is independent of how the Young's modulus varies with position, since stress depends only on force and area, not stiffness. E only affects how much each section stretches, not the stress it carries.
Source: GATE ME 2013 (Booklet Code A) (2013)
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