This may be done by the following rule. In Fig. 22-B, the timbers C and D are the sustaining forces, and the weight W is the straining force; and if the support be removed, the straining force would move from the point of support b towards d. Let it be required to ascertain whether the sustaining forces are stretched or pressed by the straining force. Rule: Upon the direction of the straining force b d, as a diagonal, construct a parallelogram ebfd whose sides shall be parallel with the direction of the sustaining forces C and D; through the point b draw a line parallel to the diagonal ef; this may then be called the dividing line between ties and struts. Because all those supports which are on that side of the dividing line which the straining force would occupy if unresisted are compressed, while those on the other side of the dividing line are stretched.
In Fig. 22-B, the supports are both compressed, being on that side of the dividing line which the straining force would occupy if unresisted. In Figs. 26 and 27, in which A B and A C are the sustaining forces, A C is compressed, whereas A B is in a state of tension; A C being on that side of the line h i which the straining force would occupy if unresisted, and A B on the opposite side. The place of the latter might be supplied by a chain or rope. In Fig. 25, the foot of the rafter at A is sustained by two forces, the wall and the tiebeam, one perpendicular and the other horizontal: the direction of the straining force is indicated by the line b a. The dividing line h i, ascertained by the rule, shows that the wall is pressed and the tie-beam stretched.
84. - Another Example - Let E A B F (Fig. 31) represent a gate, supported by hinges at A and E. In this case, the straining force is the weight of the materials, and the direction of course vertical. Ascertain the dividing line at the several points, G, B, I, f, H, and F. It will then appear that the force at G is sustained by A G and G E, and the dividing line shows that the former is stretched and the latter compressed. The force at H is supported by A H and HE - the former stretched and the latter compressed. The force at B is opposed by HB and A B, one pressed, the other stretched. The force at F is sustained by GF and FE, GF being stretched and FE pressed. By this it appears that A B is in a state of tension, and E F of compression; also, that A H and G F are stretched, while B H and G E are compressed: which shows the necessity of having A H and G F each in one whole length, while B H and G E may be, as they are shown, each in two pieces. The force at J is sustained by GJ and JH, the former stretched and the latter compressed. The piece CD is neither stretched nor pressed, and could be dispensed with if the joinings at J and I could be made as effectually without it. In case A B should fail, then C D would be in a state of tension.