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A hollow cylindrical column, with both ends hinged is 6 m long and has an outer diameter of 120 mm and an inner diameter of 80 mm

A hollow cylindrical column, with both ends hinged, is 6m long and has an outer diameter of 120mm and an inner diameter of 80mm. Compare the crippling loads obtained by Euler’s and Rankine’s approach E=80,000 MPa and crushing strength =550 MPa. The Rankine’s constant =1/1600. What is the length of the column if both crippling loads are equal?

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Data: Both ends hinged.

L = 6m = 600mm. i.e. Le = L

Do = 120 mm, di = 80 mm.

E = 80,000 Mpa.

Crushing strength Fe = 550 Mpa.

Rankine’s constant = $\frac{1}{1600}$

a] P by Euler's formula.

b] P by Rankine's formula.

c] {L} Length of column …

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