This section is from the book "The Building Trades Pocketbook", by International Correspondence Schools. Also available from Amazon: Building Trades Pocketbook: a Handy Manual of reference on Building Construction.
A body resting upon supports and liable to transverse strew is called a beam. Beams are designated by the number and location of the supports, and may be either simple, cantilever, fixed, or continuous. A simple beam is one that is supported at each end, the distance between its supports being the span. A cantilever is a beam that has one or both ends overhanging the support; a beam having one end firmly fixed and the other end free is a cantilever. A fixed beam is one that has both ends firmly secured. A continuous beam is one which rests upon more than two supports.
The moment of a force around a fixed point is equal to the force multiplied by its lever arm, which is the perpendicular distance from the line of action of the force to the point; this product is called foot-pounds or inch-pounds, according to the unit used. Thus in (a), Fig. 12, the moment about c = 10 lb.
x 10 ft.= 100 ft.-lb. In (6) the moment about c is 10 lb. X 8 ft. = 80 ft.-lb. Likewise in (c) the moment around c is 20 lb. X 24 in. = 480 in.-lb. In (d), the beam is supported at c; the force a has a moment about c of 30 lb. X 8 ft. = 240 ft.-lb., acting in a direction contrary to the motion of clock hands. The force b has a moment about c of 20 lb. X 10 ft. = 200 ft.-lb., acting in the direction of motion of clock hands. It is evident that the beam will turn around c in the direction of the greater moment, with a moment of 240 ft.-lb.-200ft.-lb.= 40ft.-lb.; the beam is, therefore, not in equilibrium. If a force of 4 lb. be added to b, creating a moment of 4 lb. X 10 ft.= 40 ft.-lb., to counterbalance the moment of 40 ft.-lb. tending to rotate the beam, the latter will then be in equilibrium. Hence, moments tending to produce rotation in the same direction are alike, and should be added; those acting in opposite directions are unlike, and the smaller should be deducted from the greater. The total moment of a system of forces about a point is the algebraic sum of the moments of all the forces around that point. If a body is in equilibrium, the algebraic sum of the moments of the forces acting upon that body is zero about any point in that body.