34 



PRACTICAL STRUCTURAL DESIGN 



the boundary is a parabola. Knowing this to be true a parabola 

 with a height represented by 



wl? _ WL 

 8 "T" 



M 



is drawn to represent the bending moment for uniformly loaded 



beams. The bending 

 moment at any point 

 is obtained by measur- 

 ing vertically from the 

 center line of the beam 

 to the parabola. The 

 bending moment at any 

 point of a uniformly 

 loaded beam is com- 

 puted as follows, call- 

 ing the distance from 

 the end of the beam to 

 the point hi question x : 



-., wlx wx z 

 ~2 2~* 



A moving load, for 

 example a single wheel, 

 occupies each point on 

 the beam as it travels. 

 If a triangle is drawn 

 for each position of the 

 load and the triangles 

 are connected by a 

 bounding line a para- 

 bola will be formed 

 with a middle ordinate 

 equal to 



Fig. 28 Graphical Method for Uniformly 

 Distributed Load on a Beam 



M = 



PL 



for the continuous line across the span, of units each equal to the 

 load on the wheel, compares with a uniform load. Consequently, 

 to ascertain the bending moment at any point on a beam due to 

 a single traveling load, construct a parabola with a middle ordinate 



