HOMOGENEOUS BEAMS 177 



EXAMPLE. Design an I beam to carry a uniformly dis- 

 tributed load of 140 Ib. per ft. on a span of 12 ft., and also 

 a centrally concentrated, suddenly applied load of 3,700 Ib. 



SOLUTION. The bending moment due to the uniformly 



distributed load is = = 2,520 ft.-lb., or 



2,520X12 = 30,240 in.-lb. The concentrated load, if gently 



3,700X12 

 applied, would cause a bending moment of 



= 11,100 ft.-lb., or 11, 100X 12= 133,200 in.-lb. Since, how- 

 ever, the load is suddenly applied, it will produce stresses 

 equivalent to twice this bending moment, or 133,200X2 

 = 266,400 in.-lb. The total moment that the beam must 

 be designed to withstand is therefore 266,400+30,240 

 = 296,640 = 55. Since 5 = 16,000, then, 5 = 296,640 + 16,000 

 = 18.54. Referring to the table on page 148, it will be found 

 that a 9-in., 21.5-lb. I beam is required. 



The other class of loads referred to are those which drop 

 on a beam from a distance above it. It is customary in 

 considering the effect of a falling concentrated load to deter- 

 mine the statical or quiet load concentrated at the center 

 that would produce the same stress, and then to design the 

 beam for this statical load. The formula used to accom- 

 plish this is 



in which W\ is the static load, in pounds, concentrated at the 

 center, that would produce the same stress in the beam as 

 the falling load; W, the falling load, in pounds, that strikes 

 the beam in the center of the span; h, the distance, in inches, 

 that the load falls; d, the deflection of beam, in inches, pro- 

 duced by load W statically applied; and a, the constant. 



The value of d is found as previously explained, while a is 

 found by the formula 



in which Wz is the combined weight, in pounds, of beam and 

 dead load that it supports; and W is the falling load. 



