46 



PRACTICAL STRUCTURAL DESIGN 



reactions by the exact method and at the same time find the 

 maximum shear. The beam will be designed for maximum shear 

 and the supports will be properly taken care of. 



The accompanying table of strength and stiffness of beam is 

 valuable for daily reference in beam calculations. The subject 

 of deflection will be taken up later. This table, Fig. 38, takes 

 as a basis the uniformly distributed load on a beam resting freely 

 on two supports. In the first column is shown the loading con- 

 dition; in the second column the formulas for ascertaining the 

 bending moments; in the third column the relative loads, and in 

 the fourth column the relative deflection due to these loads. For 

 example, the cantilever beam carrying a concentrated load at one 

 end will support only one-eighth the load the same size beam with 

 the same span will carry when freely supported at the two ends. 

 The deflection under this load will be 3.2 times the deflection of 

 the freely supported beam carrying 8 times the load. The uni- 

 formly distributed load on a beam securely fastened over supports 

 is 1.5(3/2) times the load carried on the same beam on the 

 same span when freely supported and the deflection is greatly 

 lessened, being only 0.3 the deflection of the freely supported 

 beam carrying two-thirds the load of the restrained beam. 



Restrained Beams 



In Fig. 39 is shown a beam tied into the supports. This is known 

 as a restrained beam. A restrained beam carrying one centrally 

 concentrated load will be first considered. 





Fig. 39 Beam Resting on 

 Supports 



Fig. 40 Beam Deflected under 

 Loads 



When a beam is simply supported, that is rests on supports 

 without being fastened in place, it deflects under load as shown 

 in an exaggerated manner in Fig. 40, so the ends A B and CD 

 slope and are no longer vertical. At E there is compression and 

 at F there is tension, but no tensile or compressive stresses exist 

 at A, B, C and D. 



When a beam having a uniform moment of inertia (that is, a 



