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**Q.1 A column of height h with a rectangular cross-section of size a x 2a has a buckling load of P. If the cross-section is changed to 0.5 a x 3a and its height changed to 1.5h, the buckling load of the redesigned column will be [2018 : 1 Mark, Set-I](a) P/12(b) P/4(c) P/2(d) 3P/4Ans. **(a)

For column,

For new column,

∴ Required ratio =

(a) PL/4k

(b) PL/2k

(c) P/4k

(d) Pk/4L

Ans.

Deflection under load P= θL

Work done by force

Strain energy stored in spring

⇒ θ = PL/4k

If a is amplitude constant for y, then [2014 : 2 Marks, Set-I]

Ans.

∴ Solution of above differential equation is,

y = a sin mx + b cos mx

at = x = 0, y = 0

⇒ b = 0

at x = L, y = 0

⇒ 0 = sin mL

⇒ mL = nπ

⇒

∴

(a) P

(b) Q

(c) P

(d) S

Ans.

For no twisting

V x e = H x h

⇒

Hence possible location of shear centre is P.

(a) 0.5

(b) 1.0

(c) 2.0

(d) 4.0

Ans.

Buckling load,

∴

∴

(a) 0.5

(b) 1.0

(c) 2.0

(d) 4.0

Ans.

Eulars critical load,

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