Question: A column of 6m effective length is to be made from 3 plates as shown in fig.
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A column of 6 m effective length is to be made from 3 plates as shown in fig. Using E=210GPa find the factor of safety with respect to buckling for an axial load of 17 kN. Use Euler’s Theory.

Subject Strength of Materials Topic Columns and Struts Difficulty Medium

(6 marks) May-15

 modified 12 days ago by RB ♦♦ 110 written 12 months ago by
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 written 12 months ago by
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 written 12 months ago by
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 written 12 months ago by
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Data:

E = 210 Gpa

$E = 210 \times 10^3 \ Mpa$

$L_e = 6m = 6000 \ mm$

1] Moment of Inertia:

$I_{xx} = \frac{80 \times (120 + 10 + 10)^3}{12} - \frac{(80 – 20) \times 120^3}{12} = 9.65 \times 10^6 \ mm^4$

$I_{yy} = \frac{ 2 \times 10 \times 80^3}{12} + \frac{120 \times 20^3}{12} = 9.33 \times 10^5 \ mm^4$

$Lesser \ moment \ of \ Inertia = I = I_{yy} = 9.33 \times 10^5 \ mm^4$

2] (P) Crippling load by Euler’s formula:

$P = \frac{\pi^2 \ E \ I}{L^2e} = \frac{\pi^2 \times 210 \times 10^3 \times 9.33 \times 10^5} {6000^2} = 53.71 \ KN$

3] $Safe \ load = \frac{Crippling \ Load}{F.O.S}$

$\therefore \ F.O.S = \frac{53.71}{17} = 3.15$ (Ans).