218 



PRACTICAL STRUCTURAL DESIGN 



diagram, from w to v and then from s to r. With unequal load- 

 ing this method must not be attempted. It cannot be used for 

 wind loads. 



A third method is known as the "Moment solution." A truss 

 is merely a framed beam. Find the maximum bending moment 

 and divide by the depth of the truss at the point of maximum 

 moment. In the figure the maximum moment is at the middle 

 of the span, where the rise is a maximum. Dividing the moment 

 by the depth gives the force in the tie rod QX. Set this off to 

 scale from x on the reciprocal diagram, to q. Transfer the line 

 QR from the truss diagram to the reciprocal diagram, from q 



Fig. 133. Three Solutions of the Fink Truss Problem. 



to r. This fixes the point r and from here the reciprocal dia- 

 gram may be completed. This method is applicable for cases of 

 unequal loading and for wind. 



Unequal Loading 



In Fig. 134 is shown a beam loaded at several points with loads 

 varying in amount. The problem is to find the reactions. Draw 

 the beam to scale and place the loads on it at the proper points. 

 To the right draw a vertical line and set off the loads to scale. 



Set off a point, 0, at any distance, but the best position is one 

 which will make the two lines drawn from it to the end of the 

 load line about equal in length. This would make the pole dis- 

 tance, horizontally, about half the length of the load line. The 

 scale will be chosen so the diagram will not be too large, provided 

 the scale used will give all the necessary information. From the 

 points on the load line indicating the loads, draw lines to the pole. 



Through the load points on the beam drop vertical lines and 

 transfer the rays from the polar diagram to form the equilibrium 

 polygon at (6). The broken line forming the bottom of the 



