In designing roof trusses, two stress and two frame diagrams are generally drawn, one of each for the dead loads, which act vertically, and the others for wind loads, usually taken as normal to the slope.

That the frame and stress diagrams may be conveniently compared, the following system of lettering may be employed: In the frame diagram, write capital letters within every space that is cut off from the rest of the figure by lines, real or imaginary, along which forces act, as in Fig. 39. Then the member is named from the letters of the space it divides: thus, BK designates the lower quarter of the left-hand rafter; ML, the first vertical tension rod from the left The stresses in these members are designated by similar small letters in the stress diagram: thus, the stress in BK is b k in Fig. 40. and in M L is ml. It is to be understood that wherever capital letters are used, reference is made to the frame diagram; and where small letters are used, reference is made to the stress diagram.

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Analysis Of Howe Roof Truss

Vertical-Load Diagrams. - To explain the above principles in laying out stress diagrams for roof trusses, and the determination of the amount and kind of stress in any member, the vertical and wind-stress diagrams will be drawn for a Howe roof truss, Fig. 39; this shows the frame diagram with the vertical loads, which may be figured from Table I, page 62. Since the loads are equal and symmetrically placed, each reaction will be one-half the total load. Letter the frame diagram as shown, and proceed with the stress diagram, Fig. 40. The external forces, which include loads and reactions, having been determined (this should be done in every case), draw the load line aj vertically, as that is the direction in which the forces act. With any convenient scale, make a b, bc,cd, etc. equal, respectively, to the calculated forces AB,B C,CD, etc. The reactions J Zand ZA, being equal, z is located midway between j and a. Then the polygon of external forces, as it is called, is from a to b, b to c, c to d, d to e, and so on to j, where the reactions return on the load line from j to z, and from z to a, the starting point. It will be observed from this that, though a straight line has been drawn, in reality a many-sided polygon has been traced, each external force constituting a side.

The internal forces, or the stresses in the truss members, may now be determined, as follows: Beginning at the left-hand joint in the frame diagram, the forces are B K, KZ, ZA, and A B. Care must be taken, in reading these forces, to go around each joint in the same direction in which the external forces were designated. From b draw b k parallel to B K, and from z draw z k parallel to K Z; their intersection is at k, and the polygon of forces around the joint is from a to 6, b to k,k to z, and z to a, the starting point. After having designated all the forces at a joint in the stress diagram, always read around the polygon of forces as given above, and see that it closes, that is, that the last line joins the forming a closed figure. Also, note the direction in which the forces travel along each line in the stress diagram, and mark the same by arrowheads upon the members in the frame diagram. Arrowheads acting away from a joint, as in KZ, denote tension; those acting towards one, as in B K, denote compression.

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FIG. 40.

The next joint is B CLK, and the lines determining the stresses are obtained by drawing, from c,cl parallel to CL, and, from k, I k parallel to L K; their intersection is at I, and the polygon of forces around this joint is from c to I, I to k, k to b, and b to c, the starting point. In similar manner the stresses around any joint may be obtained.

When the apex joint is reached, the diagram begins to repeat; thus, fq is the same as ep. It is therefore unnecessary to proceed further, as the loads being symmetrically placed, the stresses in the right half of the truss will be identical with those on the left half.

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