MecMovies 4.0 : M1.13: Force Based on Inclined Plane Stresses

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. The load P on the inclined surface is directed vertically downwards and it is resolved into a vector v parallel to the inclined surface and a vector N perpendicular to the inclined surface.

The area of the inclined plane must be determined before the forces acting on section $a - a$ can be computed. The bar width is $50 mm$ . Use the angle $θ$ to compute the length of the inclined surface:

$length of plane a - a = \frac{50 mm}{\cos 54^{\circ}} = 85.065 mm$

The bar is $10 mm$ thick; therefore, the inclined plane area is:

$A_{a - a} = (85.065 mm) (10 mm) = 850.65 {mm}^{2}$