16 



PRACTICAL STRUCTURAL DESIGN 



w 



Beam 



to be constant and equal to the load at the end until it reaches 

 the next load. It immediately changes to the sum of the two 

 loads and continues as a constant amount to the next load, when 

 it immediately becomes the sum of the three loads, continuing 

 thus to the point of support. 



In Fig. 5 are shown the diagrams for a uniformly distributed 

 load. 



The shear at the end = and the moment at the end = 0. 

 | The shear diagram is a triangle and 



the shear at intermediate sections 

 varies as the vertical depth of the 

 triangle at the respective sections. 



The bending moment diagram is 

 formed by a closing line which is a 

 semi-parabola. This may be proven 



. by dividing the uniform load into any 



j f number of loads equal in amount and 



finding the moment, as in Fig. 4, for 

 each load and connecting the ends of 

 the moments drawn to scale. The 

 closing line is a broken line, which 

 approaches a curve, depending upon 

 the number of unit loads into which 

 the uniform load is divided. By using 



Moment 

 Diagram 



Shear Diagram 



Fig. 5 Diagrams for a Uni- 

 formly Distributed Load 



a sufficient number the closing line becomes a parabolic curve. 



If we assume the unit load to be one foot long and call it w, and 

 the length from any point to the free end is I feet, the moment 

 at any point is 



-. r Wi 



M b = -- 



By using this formula points may be plotted one foot apart and 

 the ends connected by using a French curve. 



In Fig. 6 is illustrated the effect of concentrated loads combined 

 with a uniformly distributed load. When a beam carries concen- 

 trated loads the shear and moment diagrams are drawn as de- 

 scribed for the uniform load. Then the moments and shears due 

 to the concentrated loads are drawn upward from the top hori- 

 zontal line of the diagrams. The total moment at any point is 

 the distance, BB, or CC, from the top closing line to the bot- 

 tom closing line, the intermediate horizontal line being disregarded. 



