FLEXURE OF BEAMS 85 



When a load is suddenly applied to a beam, as when a body falls 

 on the beam, or in the case of a railway train passing quickly over a 

 girder, the deflection of the beam is much greater than it would be if 

 the load was applied gradually, for in this case the full amount of 

 the load is applied at the start instead of gradually increasing from 

 zero up to tins amount. Since the load is not sufficiently great to 

 cause the beam to retain this deflection, the resilience of the beam 

 causes it to vibrate back and forth until the effect of the shock dies 

 away. The sudden application of a load is called impact, and the 

 study of its effect is of especial importance in designing machines, 

 railway bridges, or any construction liable to shocks. 



If a simple beam deflects an amount D under a load P suddenly 

 applied, the work of deformation is PD. If the beam deflects the 

 same amount under a load P 1 gradually applied, the work of defor- 



mation is \ P'D. Hence 



P' = 2 P. 



In other words, the strain produced in a beam by a load applied sud- 

 denly is equivalent to the strain produced by a load twice as great 

 applied gradually. In practical work P' is assumed to be about |P 

 instead of 2P, for it is inipussil.!.- t< apply a la<l instantaneously at 

 the most dangerous section. 



If a body of weight P falls on a beam from a height h and pro- 

 duces a deflection /), the work done by P is P(h + D). Therefore, 

 if P' is the amount of a static load which would produce the same 

 deflection, 



In order to find P' from tliis equation D must be expressed in terms 

 and its value substituted in the above expression before solving 

 for /". 



Problem 93. A Cambria steel I-beam, No. B 33, is 12 ft. long and 10 in. deep, 

 and has a moment of inertia about an axis perpendicular to the web of 122.1 in. 4 . 

 What is tin- maximum load that can fall on the center of the beam from a height 

 of > in. without producing a stress greater than 25,000 Ib. /in. 2 , if 75 per cent of the 

 kinetic energy of the falling body is transformed into work of deformation? 



Solution. Let P denote the weight of the falling body and P' the amount of a 

 I<>;td which would produce the same work of deformation. Then, since the 



moment at the center of the beam is M = , p = = - , whence P" = 



