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 J of this amount. Now f 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 1 *75 inches, and curve 
Fig. 4. 
