Assigned: $02/12/2024$ Due: $02/22/2024$

A steel column made of A$572$ Grade $50$ steel with the length given in the table has two different boundary conditions:

Case $1$: fixed$-$pinned in $xz$ plane, fixed$-$pinned in yz plane;

Case $2$: fixed$-$pinned in xz plane, fixed$-$pinned from top and bottom & pinned from mid point in yz plane.

Please ensure to keep translation $3$ free at the top node to allow buckling.

Each student has different cross section as shown in the table below. For each boundary condition:

a$.$ Find the Euler buckling load with SAP$2000$;

b$.$ Find the Euler buckling load with hand calculation;

c$.$ Compare SAP$2000$ and hand calculation results, and discuss the reasons for differences;

d$.$ Calculate the design strength of the column using the column curve and compare with the Euler buckling load.