A column of height {h} with a rectangular cross-section of size a \times 2 a has a buckling load of {P}. If the cross-section is changed to 0.5 {a} \times 3 {a} and its height changed to 1.5 {h}, the buckling load of the redesigned column will be

GATE Civil Engineering (CE) 2018 Shift 1 Solved Paper

Question : 18 of 65

Marks: +1, -0

A column of height

{h}

with a rectangular cross-section of size

a × 2 a

has a buckling load of

{P}

. If the cross-section is changed to

0.5 {a} × 3 {a}

and its height changed to

1.5 {h}

, the buckling load of the redesigned column will be

Solution:

For column,

P=\;{π^{2} E I_{\min }}/{L^{2}}

=\;{π^{2} E({2 a × a^{3}}/{12})}/{h^{2}}=\;{π^{2} E a^{4}}/{6 h^{2}}

For new column,

P^{'}=\;{π^{2} E[{3 a ×(0.5 a)^{3}}/{12}]}/{(1.5 h)^{2}}

=\;{1}/{2} × \;{π^{2} E a^{4}}/{6 h^{2}}=\;{P}/{12}

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