Basic Engineering Mechanics by J. H. Hughes, K. F. Martin (auth.)

By J. H. Hughes, K. F. Martin (auth.)

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If the force tends to produce anticlockwise rotation then the turning effect will be considered to have a positive sense and the associated moment will also be positive. Although the moment is defined in relation to an axis at A, for coplanar forces it is usual to refer to moments about the point A, in which case the point A can be termed the moment-centre. The moment of a force has a magnitude and in the general three-dimensional case a direction would be, by definition, associated with it. In the case we have considered, the direction of an anticlockwise moment would be defmed as that of the axis at A, pointing upwards from the diagram.

Any two forces are combined into a single force passing through the intersection of their lines of action. The number of forces is therefore reduced by one. The process is repeated until there remains either a single force with a defmed line of action, or a couple. For particular cases the method becomes essentially graphical and will not be pursued in detail. By the use of force -couple sets more general results can be derived. z. 10a. Each force in turn can be replaced by an equal force at some particle A, together with a couple.

The force at B is supplied by a stay wire. By transferring these forces to the foot of the column deduce the reaction of the ground on the column. 11 b in which the force at B is resolved into two vector components where Fax = 2 sin 30° = 1 kN +Fay = 2 cos 30° = y3 kN -1The couple at C is equivalent to a couple at A having the same moment. The 1 kN force at E is equivalent to a vertical 1 kN force at A together with a clockwise couple having moment 1 x 1 = 1 kN m. The 2 kN force at D can be moved to A in its line of action.

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