186 



RESISTANCE OF MATERIALS 



FIG. 124 



latter method requires the accurate use of instruments, and is 

 therefore confined chiefly to office work. Both methods are illus- 

 trated in what follows. 



1. Analytical method. Consider first the analytical determination 

 of the external forces acting on a simple structure, such as the 

 loaded jib crane, shown in Fig. 124. This consists of a vertical 



mast ED, supported by a collar 

 B and footstep (7, and carrying 

 a jib AD, supported by the guy 

 AEF. The external forces acting 

 on the crane are the load W, 

 the counterweight W l (including 

 hoisting engine and machinery), 

 and the reactions at B and C. 

 The reaction of the collar B can 

 have no vertical component, as 

 the collar is made a loose fit so 

 that the crane may be free to 

 swivel. For convenience, the reaction of the footstep C may be 

 replaced by its horizontal and vertical components H and V. 



Applying the conditions of equilibrium to the structure as a 

 whole, we have, therefore, 



^ vertical forces = 0, W + W^ + weight of crane V = 0, 



2 horizontal forces = 0, Jf 1 + Jf z = 0, 



2) moments = (taken about B), W1 2 - W^ + Hj = 0. 



From the first condition the vertical reaction of the footstep is 

 found to be equal to the entire weight of the structure and its 

 loads. In applying the last condition, moments are taken about 

 B, since one unknown H 2 is thus eliminated, leaving the resulting 

 moment equation with only one unknown H^ The other unknown 

 H z is then found from the second condition, H 2 H^ 



The moment of the counterweight W^ should, when possible, 



Wl 

 be made equal to 2 , where W is the maximum load the crane is 



2 



designed to lift. The mast will then never be subjected to a bending 

 moment of more than one half that due to the lifted load ; that is to 



