208 



PRACTICAL STRUCTURAL DESIGN 



BC and BD. That is, if the horizontal force had been given, the 

 line CB could have been drawn. The vertical force having been 

 given, the line BD could have been drawn, it being assumed that 

 the two forces meet at one point, B. From D draw a horizontal 

 line and from C draw a vertical line to intersect it, at A. The 

 diagonal line AB is the resultant of 

 the two forces. 



The resultant is the line required 

 to close a figure and the other forces 



are components of the resultant, 



T TV in* 'j. u AU A M. Fl 8- 124. Triangle of Forces. 



In Fig. 124 it is shown that it is 



not necessary to complete the parallelogram. Let AB and AB' 

 be two forces acting at the point A. Draw them to scale and 

 from B' draw a line parallel to AB. From B draw a line parallel 

 to AB'. The two lines will meet at C. The line AC is the result- 

 ant. The force AB' is the force BC. The resultant would have 

 been obtained if we had merely drawn A B and then from B 

 drawn BC to represent the force AB'. The figure ABC is known 

 as the Triangle of Forces. It is formed by drawing the forces 

 end to end and obtaining the resultant by drawing a closing line. 

 In order to obtain equilibrium it is necessary that all the forces 

 acting on any body meet at a common point or be parallel. If 

 all non-parallel forces do not meet at a point then there will be a 



moment arm which will cause 

 rotation. When all the forces 

 are parallel equilibrium is ob- 

 tained by supplying a result- 

 ant large enough to balance 

 the forces acting in opposite 

 directions. 



In Fig. 125 are four forces 

 acting at the point 0, of a 

 body. The polygon of forces 

 is shown at the right and all 



Fig. 125. Polygon of Forces. 



the lines are drawn to scale. The line 04 drawn to close the 

 polygon represents the weight which the body must have to resist 

 being moved by the forces. It represents also the direction in 

 which the body will move if not heavy enough to resist the push. 

 This polygon could have been drawn as follows, and the student 

 is advised so to draw it in order to get a clear idea of the matter; 



