Plan the Solution  
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The problem statement says:

Determine the maximum load P that may be supported by the structure without exceeding either allowable normal stress.

In general, only one axial member will reach its allowable stress upon application of load P.

While the other member cannot exceed its allowable stress, it is acceptable for the second member's normal stress to be less than its allowable stress.

Also, keep in mind that equilibrium must always be satisfied.

The figure shows a diagonal member labeled 1 and a horizontal member labeled fixed to a column on the right at the points A on top and C below. The diagonal member runs between points A and B and the horizontal member runs between the points B and C. Joint B is at a distance of 4.3 meters to the left of A and 5 meters below A. Joint C is at a distance of 7 meters directly below A. The load at joint B is labeled P and it is directed downwards.