Notation. The calculation of strains in trusses and arches is based on the law Known as the "Parallelogram of Forces." Before going into same it will be necessary to explain the notation used. If Fig. 15 represents a truss, and the arrows the loads, and the two reactions (or supporting forces), we should call the left reaction O A and the right reaction F O. The loads would be, taking them in their order, A B, B C, C D, D E and E F. The foot, or lower half, of left rafter would be called B K, the upper half C I, while the respective parts of right rafter would be G E and H D. The King-post (tie) is I II, and the struts K I and H G, while the lower ties are K O and O G.

In the strain diagram, Fig. 16 (which will be explained presently), the notation is as usual; that is, loads A B, B C, C D, etc., are represented in the strain diagram by the lines ab, bc, cd, etc. Rafter pieces B K, C I, D II and E G are in the strain diagram b k, c i, dh and eg (g and k falling on the same point). I II in Fig. 15 becomes i h in strain diagram. K I becomes k i, H G becomes h g, O K becomes o k, G O becomes g o, O A becomes o a and F O becomes f o.

Or, in the drawing of the truss itself the lines are called, not by letters placed at the ends of the lines, but by letters place 1 each side of the lines, the lines being between; it is also usual to put these letters in capitals to distinguish them from the letters representing the strain diagram, which are, as usual, at each end of the line they represent.

Fig. 15.

Fig. 16.

One thing is very important, however, and that is, always to read the pieces off in the correct direction and in their proper order. For instance, if we were examining the joint at middle of left rafter we must read off the pieces in their proper order, as B C, C I, I K, K B, and not jump, as B C, I K, C I, etc., as this would lead to error. Still more important is it to read around the joint in one direction, as from left to right (Fig. 17), that is, in the direction of the arrow. If we were to reverse the reading of the pieces, we should find the direction of the strain or stress reversed in the strain diagram. For instance, if we read K I and then find its corresponding line k i in the strain diagram, we find its direction downward, that is, pulling away from the joint, which would make K I a tie-rod, which, of course, is wrong, as we know it is a strut. If, however, we had read correctly i k it would be pushing upwards, which, of course, is correct and is the action of a strut.

When we come to examine the joint at O, however, we reverse the above and here have to read k i, which is in the same relative direction for the point O, as was i k for the point at centre of left rafter.

Fig. 17.

Fig. 18.

The arrows in the accompanying figure (18) show how each joint must be read, and remember always to read the pieces in their proper succession.

It makes no difference with which joint or with which piece of the joint we begin, so long as we read in correct succession and direction, thus: for joint No 1 we can read A B, B K, K O and O A or K O, O A, A B and B K, or B K, K O, O A and A B, etc. In the strain sheet of course we read in the same succession, and it will be found that the lines, as read, point always in the correct direction of the strain or stress.