The resultant stresses should be used in designing the truss. The method of obtaining the stresses in a framed structure, such as a crane, is illustrated in Figs. 130 and 131. The force polygon in this case consists simply of the line RZ, representing the load W suspended from the end of the cantilever. The magnitude of the RY and RZ, acting as shown in Fig. 130, are found by means of the polar and funicular polygons shown in dotted lines, the point Y being determined by drawing OY parallel to the closing line as before. The magnitude and sense of the stresses in the various members of the cantilever may be determined by measuring the lines of the Κ reciprocal diagram, Fig. 131, to the proper scale, or by applying the method of moments. Fig. 132 represents a diagram of a roof-truss, for which the reciprocal diagrams have been drawn for the dead load and wind pressure shown in Figs. 133 to 136. The following data have been employed in drawing these diagrams: U T S R Distance between joints measured along principal rafters Inclination of principal rafters to the horizon Rise of tie-rod in the centre ... ... ... ... ... ... 46.20 11.55 22 30 degrees. 2500 lbs. Normal pressure at the three intermediate joints on one side 4000 ... Fig. 133 represents the stresses due to the dead load; Fig. 134, DEAD LOAD. FIG. 133. the stresses due to the wind acting on the left when both ends are fixed; Fig. 135 represents the stresses due to the wind acting on the left when the left end is free to move; and Fig. 136 represents the stresses with the wind on the right when the left end is free to move. The stresses may be tabulated in a similar manner to that illustrated in connection with the roof-truss shown in Fig. 125. Fig. 137 represents another example of a roof-truss, for which reciprocal diagrams have been drawn from the following data— Distance between the joints measured along the principal rafters 8.1 Inclination of the principal rafter to the horizon ... ... ... ... 221 degrees. 2 feet. 1053 lbs. at supports 526-5 ... ... ... S ... ... ... 33 8100 ... Total normal pressure on one side Normal pressure at the three intermediate joints on one side Normal pressure at apex and support Fig. 138 represents the stresses due to the dead load; Fig. 139, the stresses due to the wind acting on the left when both ends are fixed; Fig. 140, the stresses due to wind acting on the left when the left end is free to move; and Fig. 141, the ZICHIJKL WIND ON LEFT. LEFT END MOVEABLE. FIG. 135. stresses with the wind acting on the right when the left end The stresses in this and the foregoing example may be tabulated in the manner fully explained in the first example, Figs. 125 to 129. Fig. 142 represents a diagram of a polygonal roof-truss, for which reciprocal diagrams have been drawn for the dead load and wind pressures, Fig. 143 to 146. The following data have been employed : ... ... 7 ... 6 The figure is redundant, but one set of diagonals is supposed to be omitted, otherwise the reciprocal stress diagrams could not be drawn. Fig. 143 represents the stresses due to the dead load. Fig. 144 represents the stresses due to wind acting on the left side when both ends of the principal are fixed in position. The point Z is determined by means of the polar and funicular polygons shown in dotted lines. The force polygon for the loads P2, P3, and P, which produce reactions at both supports, is shown in Fig. 144, viz. PQRSZP, in which SR, RQ, and PQ are drawn parallel to P2, P3, and P1 (Fig. 142). PS is the resultant, and equals the sum of the reactions at the supports due to the three loads under consideration. 'The force polygon for the four forces P1, P2, P3, and P. is PQRSTZP, in which ST is drawn parallel to P, and ZT joined. |