Mechanical and structural analysis miscellaneous
- A "H" shaped frame of uniform flexural rigidity EI is loaded as shown in the figure. The relative outward displacement between points K and O is
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Deflection diagram:
Moment in member JN = R.h.Slope at N or J = Rh.L 2EI Deflection at O or k = RhL × h 2EI = Rh2L 2EI
Relative outward displacement of K and O is= 2 × Rh2L 2EI = Rh2L EI Correct Option: A
Deflection diagram:
Moment in member JN = R.h.Slope at N or J = Rh.L 2EI Deflection at O or k = RhL × h 2EI = Rh2L 2EI
Relative outward displacement of K and O is= 2 × Rh2L 2EI = Rh2L EI
- Consider the following statements for a compression member:
I. The elastic critical stress in compression increases with decrease in slenderness ratio.
II. The effective length depends on the boundary conditions at its ends.
III. The elastic critical stress in compression is independent of the slenderness ratio.
IV. The ratio of the effective length to its radius of gyration is called as slenderness ratio.
The TRUE statements are
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II, III and IV
Correct Option: C
II, III and IV
- U1 and U2 are the strain energies stored in a prismatic bar due to axial tensile forces P1 and P2, respectively. The strain energy U stored in the same bar due to combined action of P1 and P2 will be
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u1 = 1 .P1 × δl 2 = 1 × P1 × P1 × l 2 AE = 1 × P12L 2 AE u2 = 1 P22L 2 AE = 1 (P12 + P22)L 2 AE u = 1 (P12 + P22 + 2P1P2)L 2 AE = u1 + u2 + 1 2P1P2L 2 AE
∴ u > u1 + u2Correct Option: D
u1 = 1 .P1 × δl 2 = 1 × P1 × P1 × l 2 AE = 1 × P12L 2 AE u2 = 1 P22L 2 AE = 1 (P12 + P22)L 2 AE u = 1 (P12 + P22 + 2P1P2)L 2 AE = u1 + u2 + 1 2P1P2L 2 AE
∴ u > u1 + u2
- The influence line diagram (ILD) shown is for the member
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PS
Correct Option: A
PS
- The shape of the cross-section, which has the largest shape factor, is
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diamond
Correct Option: C
diamond
