36 PRACTICAL STRUCTURAL DESIGN 



due to the different load systems and making the sloped lines 

 parallel to those in the diagram of uniform load shear. 



General Method for Position of Maximum Bending Moment 



First. Find the reactions. 



Second. Starting from either end add the loads until a point 

 is reached where the sum of the loads equals or exceeds the reaction 

 at that end. This is the point of maximum bending moment. 



General Method for Locating Point of Zero Shear 



First. Call the left reaction positive (+) and the right reaction 

 negative (-). 



Second. Call each load negative (-) and successively subtract 

 from the left reaction each load, prefixing the proper sign until the 

 sign of the sum of the quantities changes from positive (+) to nega- 

 tive (-). This is the point of zero shear and maximum bending 

 moment. 



An inspection will show the two rules to be identical. 



For a uniform load the shear at any point distant x from either 



support is found as follows : 



wL 

 Shear at x = -^ wx. 



When a moving uniform load is passing over the beam, a train 

 of small trucks, for example, the maximum shear at any point 



(J ">2 



When the load covers the span x = and the maximum shear at 



wL 

 the ends = -~- 



A crane travels on a girder with two wheels equally loaded and 



separated by a constant dis- 

 tance. The maximum bending 

 moment is under one wheel 

 when this wheel is as far from 



~ 7 "% *f 



, L -__ 4 one SU pp 0r t as the center of 



Fig. 30 Two Equal Rolling Loads at gravity of the total load is 



from the opposite support. 

 Referring to Fig. 30, if a is less than 0.586 L, 



P(L - |) 2 

 M = 2L 



^ _k a 



