A vertical column subjected to axial force P and a horizontal flexible beam are connected by rigid connection, as shown in Figure

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Q1 A vertical column subjected to axial force P and a horizontal flexible beam are connected by rigid connection, as shown in Figure Q1. Consider global buckling and local (Euler) buckling of column BC. At point B, beam AB and BD are rigidly connected, where beam BC has pin connection. 

(a) Derive the equilibrium equation for the deformed configuration. Assume small strains. Consider in-plane global buckling. [5] 

(b) Assuming small angles, calculate the critical global buckling force for global and local buckling of compressed column. [5] 

(c) Sketch post-buckling displacements. [5] 

(d) In which direction will vertical column buckle [2] 

(e) Give equation for local (Euler) buckling of beam BC. [8] 

(f) Explain what is bifurcation point. Sketch example of load-displacement path indicating bifurcation point.

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