Figure $4$: Three story building

Two$-$dimensional analysis project

For this problem, write a two$-$dimensional frame analysis matlab program code to solve the problem.

The building in Figure $4$ is a simple model for a light industrial building. The second and third stories are loaded uniformly, the roof is unloaded. Since this is a steel frame, we will ignore self$-$weight. Along the side at the roof and each floor level are applied point loads representing an environmental load, say wind loading. The horizontal beams are W$12$x$26$ members, orineted so the strong axis is in bending under the applied gravity loads.

Your job is to perform an analysis to determine the wind load that will first yield any of the sections. This would be the beginning of a push$-$over analysis, as described in class.

$1.$ Assume the columns are W$12$x$14,$ oriented so the strong axis is in bending. Apply a scale factor to the wind loads proportionately to determine first yield.

$2.$ Repeat the analysis with the columns being W$12$x$26.$

Your deliverables are:

$1.$ The matlap program source code used for the analysis.

$2.$ For each case above,

$($a$)$ Provide the input files describing your structure.

$($b$)$ A sketch of the deformed structure, highlighting the location of the first plastic hinge.

$($c$)$ The load to develop the plastic hinge.

$($d$)$ Sample calculation of the section analysis to determine the plastic hinge.