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4(a) if the mass of the plank is neglected. The forces exerted by the supports on the plank, RA and RB , act vertically upwards, and are called reactions. When the forces acting are all in one plane, the algebraic sum of the moments can be taken about any point. 4(b), at equilibrium (i) RA C RB D F1 C F2 , and (ii) taking moments about B, RA a C b C F2 c D F1 b Typical practical applications of simply supported beams with point loadings include bridges, beams in buildings, and beds of machine tools.

44° to the horizontal. The above example demonstrates the use of resolution of forces for calculating the resultant of two coplanar forces acting at a point. However, the method may also be used for more than two forces acting at a point. For example, three coplanar forces acting at a point are: 200 N acting at 20° to the horizontal, 400 N acting at 165° to the horizontal, and 500 N acting at 250° to the horizontal. To determine by resolution of forces the resultant of the forces: A tabular approach using a calculator may be made as shown below.

When acting by itself, the resultant force, given by oc, has the same effect on the point as forces F1 , F2 and F3 have when acting together. 8 is called the polygon of forces. For example, three coplanar forces acting at a point are: force A, 12 N acting horizontally to the right, force B, 7 N inclined at 60° to force A, and force C, 15 N inclined at 150° to force A. 9. e. 11 Coplanar Forces in Equilibrium When three or more coplanar forces are acting at a point and the vector diagram closes, there is no resultant.

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