Project ForgeStrength of Materials
Bending of Beams
GATE 2016
Hard
Two hollow bars of the same material have concentric circular cross-sections, with r3 > r1 and r4 > r2, and the two cross-sections have the same area. J1 and J2 are the torsional rigidities of the bars with inner/outer radii (r1,r2) and (r3,r4) respectively. The ratio J2/J1 is
- > 1
- B< 0.5
- C= 1
- Dbetween 0.5 and 1
Explanation
For a hollow circular section, J = (π/32)(do⁴-di⁴). For the same cross-sectional area, spreading the material to a larger mean radius with a thinner wall (as in the r3,r4 bar) increases J substantially relative to a smaller, thicker-walled section of equal area, so J2/J1 > 1.
Source: GATE ME 2016 Set-1 (2016)
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