Which is the CORRECT reason for the 5%-10% of error in Euler’s cr

Which is the CORRECT reason for the 5%-10% of error in Euler’s cr
| Which is the CORRECT reason for the 5%-10% of error in Euler’s crippling load, when estimated theoretically?

A. Effect of direct stress is neglected

B. Presence of friction in pin joints

C. The assumptions made are not met in real life conditions

D. Material does not behave as an ideal elastically

Please scroll down to see the correct answer and solution guide.

Right Answer is: C

SOLUTION

The following assumptions are made in Euler's column theory:

  • The column is initially straight and load is applied axially
  • The cross-section of the column is uniform throughout its length
  • The column material is perfectly elastic, homogeneous and isotropic
  • The length of the column is very large as compared to its lateral dimensions
  • The direct stress is very small as compared to the bending stress
  • The column will fail by buckling alone
  • The self-weight of the column is negligible

 

As the assumptions made are not met in real-life conditions, so there is 5%-10% of error in Euler’s crippling load.

\(P_{cr} = \frac{{{n^2}{\pi ^2}EI}}{{{L^2}}}\)

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