14 



PRACTICAL STRUCTURAL DESIGN 



tion of a cantilever beam is equal to the sum of the weight of the 

 beam and all loads it may carry. 



R = reaction. 



For beams carried on two or more supports a method will be 

 given later for computing the reactions on each support. 



Shear 



Shear is a downward cutting force exerted at the edge of each 

 support. It is called shear because if the material is soft the edge 

 of the support will cut it. A piece of butter resting on the edges of 

 two upturned knife blades is as good an example as any, perhaps, 

 of true shear. 



V = shear. It is always equal to the reaction at the support, 

 and at other points on the beam varies according to laws 

 to be hereafter explained. 



The use of the capital V to designate shear may be explained 



by its resemblance to a sharp cutting 

 edge. Mathematicians may give an- 

 other reason, but the writer is inter- 

 ested in fixing a fact in the mind of 

 the student. 



Graphical Methods for Moment, 

 Shear, etc. 



In Fig. 3 a concentrated load acts 

 at the point D on the beam, AD. 

 The beam is drawn to any scale and 

 the load shown on it, as in the figure. 

 Underneath is drawn the line A,D t 

 and the bending moment at the sup- 

 port is computed. Plot this to any 

 scale (say 1000 Ibs. = 1 in.) on the 



B, C, Shear 



Fig. 3 Concentrated Load at 

 End of Beam 



vertical line A, A,,. Connect A n to D, by a straight line A,, D, as 

 shown at (6). To find the bending moment at any intermediate 

 point on the beam drop a vertical line across the diagram and the 

 length of the line intercepted between the upper and lower lines 

 of the bending moment triangle gives the bending moment. For 

 example the bending moment at B is given by the line B,B,, and 

 the bending moment at C is given by the line C,C,,. The vertical 

 lines are forces and the horizontal lines are lengths, the closing 



