196 Mr Wimperis, Some Experiments upon Beams 



The observed value of the deflection is greater than that 

 calculated, because the elastic limit had been exceeded and the 

 material had " flowed " under the stress. Taking this observed 

 value of the deflection, i.e. 2 inches, the tensile stress that would 

 have had to be withstood on the elastic hypothesis comes out as 

 62 tons per square inch, which is considerably greater than the 

 stress at which fracture in direct tension was found to occur in a 

 similar rod. With a deflection as large as 2 inches, however, the 

 plane section hypothesis breaks down and the real stress would be, 

 as previously suggested, more nearly f of this amount. Now § of 

 62 tons is 41 '3 tons, and this is in very close agreement with the 

 41 tons per square inch actually obtained as the breaking stress in 

 direct tension. It therefore seems that for a ductile material the 

 above hypothesis is very fairly approximate, and this is about as 

 much as can be expected in such complex phenomena. These 

 observations plotted with respect to P and W are shown in 

 Fig. 4, the curve A is the curve outside (i.e. on the right of) 

 which the stress in the strut-beam must have exceeded the elastic 

 limit; the other two curves are obtained as follows. Curve B shows 

 the result of assuming, on the elastic theory, that fracture occurs 

 whenever the maximum deflection exceeds 175 inches, and curve 



too 



