STRENGTH OF MATERIALS 295 



2,000X120 250X10X120 

 M = -- 1 -- = 97,500 in.-lb. 



4 8 



M 97,500 



For a steel beam, = -- - = 6.5. From a manufacturer's 

 / 15,000 



handbook, a 6-in. I beam at 12.25 Ib. has a section modulus 

 of 7.3 and can therefore be used. For a wooden beam, 



97,500 



2 , - 



97.5=- . Assuming that b = Q in., d= \'J7.5 



1,000 



= 10 in. nearly. 



Stiffness. In designing a beam, it sometimes becomes 

 necessary to ascertain the amount that it will deflect under 

 given loads. This, for instance, is the case when designing 

 supports for machinery parts or joists for plastered ceilings, 

 in which latter case the deflection should not exceed 3^5 of the 

 span. The accompanying table gives deflection formulas for 

 the most usual cases. In these formulas I is the span, in 

 inches; W, the total load acting on the beam; /, the moment of 

 inertia of the cross-section of the beam; and E, the modulus 

 of elasticity of the material. 



EXAMPLE 1. A timber simple beam 10 ft. long, and having 

 a width of 4 in. and a depth of 12 in., carries a uniform load of 

 400 Ib. per ft. What is the deflection? 



SOLUTION. According to the table, the deflection for a 



5WP 

 uniformly distributed load is - . In this case, 1= 10X12 



= 120; W= 400X10 = 4,000; = 1,500,000; and / = 



576. Substituting in the formula, 



5X4,000X1203 



Deflection = = . 1 in. 



384X1,500,000X576 



