List of top Structural Engineering Questions on Concept of plastic analysis

A rigid-jointed portal frame, shown in the figure, consists of beam and columns of equal length \(L\). The frame has a fixed support at one end and a roller support at the other end. The frame is subjected to a uniformly distributed load \(w\) and a lateral load \(P\) as shown in the figure. The plastic moment capacity of the beam and column sections is \(M_p\). Consider a combined beam-column mechanism for plastic collapse. By applying the virtual work equation corresponding to the combined plastic collapse mechanism, \(M_p\) is expressed as
\[ M_p = C_1 P L + C_2 w L^2 \]
where \(C_1\) and \(C_2\) are constants.

The value of \((C_1/C_2)\) is ______ (in integer).

For the square steel beam cross-section shown in the figure, the shape factor about \(z - z\) axis is \(S\) and the plastic moment capacity is \(M_P\). Consider yield stress \(f_y = 250 \, \text{MPa}\) and \(a = 100 \, \text{mm}\). The values of \(S\) and \(M_P\) (rounded-off to one decimal place) are: