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Q9) A 2 m long solid, square section steel column has a 2500 mm² cross-sectional area and is fixed at both ends to support a compressive axial load. A 100 mm long test specimen of the column extends 0.16 mm when axially loaded to its yield stress.

Using Euler’s relationship for a column with both ends fixed:

P_C = (4π² EI)/L²

where:

P_C = Euler' scritical load

E = Young' smodulus

I = the 2nd moment of area

L = the effective length

Calculate EACH of the following:

(a) The maximum load the column can support for a safety coefficient of 4; (12)

(b) The slenderness ratio of the column. (4)

Note:

Yield stress for the column material= 320 MN/m².