22. It is necessary, in estimating the strength of framing, that we should be able to distinguish the struts from the ties; that is, to ascertain what beams are compressed, and what are stretched. By attending to the following considerations, this may be easily determined. From the point on which the straining force is exerted, draw a line in the direction it would move in, if the framing were taken away. When this line falls within the angle formed by the pieces strained, then both pieces are compressed. But when it falls within the angle formed by producing the directions of the sustaining pieces, then both the pieces are in a stato of tension.

The following method is a more general one, and includes the case just stated.

23. Let a parallelogram be constructed, on the direction of the straining force as a diagonal, the sides of the parallelogram being parallel to the sustaining forces; then, let the other diagonal of the parallelogram be drawn; and parallel to it, draw a line through the point where the directions of the forces meet. Consider towards which side of this line the straining force would move if left at liberty; and all supports on that side will be in a state of compression, and all those on the other side will be in a state of tension.

The same thing would be true of a plane passing through the point where three or more forces meet, which are not in the same plane; but such cases are of rare occurrence; therefore, if we show how the method applies to the examples in Figs. 3, 7, and 8, the reader will be able to apply it to all cases where the sustaining forces are in the same plane.

In Fig. 3, 7, 8, and 9, C c is the direction of the straining force, on which as a diagonal the parallelogram Cbca is drawn, the sides of it being parallel to the resisting or sustaining beams: join b a, and draw the dotted line e e parallel to ba in each figure; then, in Fig. 3, the straining force would move towards E, if left at liberty; therefore both the beams are compressed, being on that side of the line e e'.

In Figs. 7, 8, and 9, only the lower sustaining beams are compressed, the upper ones being extended; and if the line e e' were drawn to Fig. 2, it would show that both the supports are in a state of tension.