Question
A uniform light slender beam AB of section modulus EI is pinned by a frictionless joint A to the ground and supported by a light inextensible cable CB to hang a weight W as shown. If the maximum value of W to avoid buckling of the beam AB is obtained as βπ2EI,where π is the ratio of circumference to diameter of a circle, then the value of β is
Options :
0.0924 m-2
0.0713 m-2
0.1261 m-2
0.1417 m-2
Answer :
0.0924 m-2
Solution :
W = βπ2EI, L = 2.5
T sin 30∘ = W
T = 2W
load on beam F = T cos 30°
F = √3 W
To stop buckling of the beam, load on the beam must be equal to Euler's buckling load
= √3 βπ2EI
β =
β = 0.0924
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