The column shown in Figure Q1 has length L and is subject to an axial compression force P. The column has fixed supports

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The Column Shown In Figure Q1 Has Length L And Is Subject To An Axial Compression Force P The Column Has Fixed Supports 1 (40.69 KiB) Viewed 61 times

The column shown in Figure Q1 has length L and is subject to an axial compression force P. The column has fixed supports at A and B. The differential equation of the deflection curve is given by, dy EI dx? MA-Pv where v is the lateral deflection of the column, MA is the reaction bending moment at the base of the column and x is the coordinate along the length of the column. B 1 Figure Q1 (a) Derive an expression for the critical buckling load for nth mode of buckling. You may assume that the general solution to the governing differential equation is given by. v = C; sin(kx) + C2 cos(kx) + Awhere k = P/EI. (15 marks) (b) Confirm through derivation that the expression for the buckled shape of mode one is given by 2πχ) cos (5 marks) (c) Explain briefly the influence of rotational fixity on the buckling capacity of an axially loaded column (5 marks)