The figure shows a vertical bar of width 50 millimeters fixed to the ceiling. An inclined plane labeled a a is shown and it is at an angle of 36 degrees with respect to the vertical and 54 degrees with respect to the horizontal. The load on the inclined surface has a magnitude of 26.286 kilo newton and is directed vertically downwards. This load is resolved into a vector of magnitude 21.266 kilo newton parallel to the inclined surface and a vector of magnitude 15.451 kilo newton perpendicular to the inclined surface and making an angle theta which equals 54 degrees with the vertical.

Based on the 40 MPa allowable normal stress, a maximum load of P=57.888 kN could be supported by the bar.

Based on the 25 MPa allowable shear stress, the maximum load is P=26.286 kN.

The smaller of these two values controls; therefore, the maximum load that can be applied to the bar while satisfying both the normal stress and shear stress limits is P=26.286 kN.


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