The critical load for a long column with both ends fixed is 160 kN. If the same section is to be used for
another column of double the length, the critical load is:
-
A.
80 kN
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B.
320 kN
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C.
160 kN
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D.
40 kN
Correct Answer:
D. 40 kN
Explanation:
The critical load for a column is calculated using Euler's buckling formula: Pcr = (π² * E * I) / (Leff²). In this equation, the critical load (Pcr) is inversely proportional to the square of the effective length (Leff).
For a column with both ends fixed, the effective length is 0.5L. When the actual length (L) is doubled for the same section and end conditions, the effective length also doubles. Since the load is inversely proportional to the square of the length, increasing the length by a factor of 2 reduces the critical load by a factor of 2² (or 4).
Calculation:
Initial Load = 160 kN
New Load = 160 kN / 4 = 40 kN
Therefore, the critical load for the column with double the length is 40 kN.
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