176 HOMOGENEOUS BEAMS 



inches, of a beam 1 ft. long having a load of 1,000 Ib. Mul- 

 tiplying the proper coefficient by the cube of the span, in 

 feet, and by the number of 1,000-lb. units in the given load, 

 will give the deflection of a beam for any load and span. 



EXAMPLE. What is the deflection of a 20-in. 65-lb. 

 I beam that carries a center load of 28,000 Ib. and has a span 

 of 20 ft. ? 



SOLUTION. The amount of deflection is obtained by mul- 

 tiplying the coefficient of deflection for beams with center 

 loads (column 13 in the table of properties of I beams) 

 by the cube of the span, in feet, and the number of 

 1,000-lb. by units in the load. Hence, the deflection equals 

 .00000106 X 203 X -nn3f = -237 in. 



SUDDENLY APPLIED LOADS 



In the formulas and investigations so far discussed, it 

 has been assumed that the loads on the beams were laid 

 gently in place. This, however, is not always the case, for 

 the load may be suddenly or almost instantaneously applied, 

 or it may even be dropped on the beam. Of course, in design- 

 ing such beams, a large factor of safety may be employed, 

 but if the load is dropped or very suddenly applied, this 

 method is at best a matter of guesswork and experience. 



The investigation of sudden loads divides itself naturally 

 into two classes. The first includes loads that are not 

 raised above a beam and whose weight is suddenly applied 

 to the beam. The second class of loads includes those that 

 fall vertically on a beam, as when heavy boxes or crates are 

 dropped on the beams of a floor. 



As the problems of the first class are the simplest to solve, 

 they will be taken up first. When a load is placed suddenly 

 on a beam, the stress produced is twice as great as if the 

 same load had been at rest; that is, a beam to sustain a sud- 

 denly applied load should have twice the transverse strength 

 required to sustain the same load at rest. 



Often, a problem occurs concerning suddenly applied loads 

 in which the beam has a quiet load, which is the dead load, 

 and a suddenly applied load, which is the live load. Such a 

 problem should be solved as follows: 



