QUESTION $1$

The figure shows a continuous triangular frame with the length of the members as assigned. The flexural

rigidity of the horizontal member is $(EI{)}_{13}=EI$ while those of the inclined members are $(EI{)}_{12}=(EI{)}_{23}=EI.$

Using slope deflection methods, determine the equation that satisfies all the boundary conditions for $(1)$

symmetric buckling; and $(2)$ antisymmetric buckling of the frame.

Assume the applied forces are resisted by the axial forces in the members and negligible shear forces.

For both symmetric and antisymmetric buckling, solve for the critical load factor given by $=\frac{P_{cr}}{{}^{2}E\frac{\text{I}}{l^2}}$

and the effective buckling length of member $12$ when $($i$)=0\mathrm{.}25$; $($ii$)=1$; and $($iii$)=9$

Which buckling mode should you use for design?

Symmetric or antisymmetric?