140 POINTS OF CONTRARY FLEXURE. Art. 89. 



tion of the load is not only instantaneous, but an initial energy 

 equal to Ph must be accounted for. The work done is equal to 

 P(/t+2/0 but it is not all spent in deforming the beam; a large 

 percentage of the energy may be spent in deforming the falling 

 body and the beam's supports, and if the elastic limit is exceeded 

 some of the energy is transformed into heat. To determine the 

 effect upon the beam from the load, and height of fall, is a 

 problem of great difficulty, but if the maximum deflection is 

 measured, the stress may be calculated from the static load, 

 which will produce the same deflection. 



It is apparent now that the proper way to determine the 

 resilience of a beam is by means of a static load. The usual 

 impact tests which are made upon railway rails serve, at best, 

 only as a comparison of the shock-resisting qualities of the rails 

 tested under the same conditions 1 . 



It is of practical importance to note that while a defect 

 (a flaw, a crack, or a hole) reduces the static strength of a beam, 

 it reduces its resilience in a much greater degree, so that the 

 factor of safety is much less for moving load than for static load. 

 An abrupt change of section has the effect of concentrating the 

 work done upon the beam, at the weak section. 



89. Points of Contrary Flexure. A beam simply sup- 

 ported at the ends, and carrying loads, will be concave on its 

 upper side. If by some means opposite moments are applied at 

 the ends, the slope of the beam, near the supports, will be 

 decreased, and the curvature reversed; near the supports, the 

 beam will be convex on its upper side. The points in the axis of 

 the beam where the curvature reverses (where the curvature is 

 zero, and the radius of curvature infinite) are points of inflection, 

 and are called points of contrary flexure or points of contra- 

 flexure. 



Points of contra-flexure occur in beams with fixed ends, and 

 in beams continuous over supports as shown in Figs. 98, 99, 

 102, 103, 107, 108, 109, 111, and 112. 



The curvature at these points being zero, it follows that the 

 moment is zero, and their location is found by finding the value 

 of x. for which the moment is zero. 



! See Johnson's Materials of Construction for a full explanation of 

 resilience. 



