COMPLEX STRESS DISTRIBUTION IN ENGINEERING MATERIALS. 339 
cial sections, if the load is applied at the ends in the manner adopted by most experi- 
menters, the stress will not be uniformly distributed owing to slight curvature of the 
specimen and eccentricity of loading. By assuming that a portion of the heavily 
stressed side only sustains a strain less than the yield, it is possible to calculate the new 
position of the resultant of the stresses. If the new position is such that the bending 
moment is increased, then complete collapse is inevitable. It is found that with mild 
steel this will occur for all struts having & (ratio of length to radius of gyration) less 
than about 85. That is to say, taking Tetmayer’s test results of mild steel, and deter- 
mining the eccentricity of the load at the point of failure for a sturt having e less 
than 85, complete collapse would occur if the stress on the concave side ‘reached the 
yield. In cases where the eccentricity is greater, complete collapse would not neces- 
sarily occur immediately, though the specimen would be overstrained and permanently 
bent. Thusin all tests on struts which are deliberately loaded eccentrically it is found 
that in the region where the eccentric effects are most marked, i.e. Z less than 80, 
the struts do sustain more load than would be calculated on the basis of the maximum 
stress being equal to the yield. In these cases, however, the direct stress is small and 
the bending stress high, so that the conditions approximate more closely to a beam 
test. These considerations fix the yield point as the maximum stress that a strut 
reasonably accurately loaded will sustain. 
On this basis the author has examined all the important series of strut tests, and 
has found that they can all be represented extremely well by the equivalent curvature 
formula first proposed by Professor Perry, but using the yield as the maximum stress 
term. For a full discussion of these results, and for some tests on eccentrically loaded 
struts, reference should be made to the author’s paper on the ‘Strength of Struts ’ 
published by the Institution of Civil Engineers. 
For materials that have no yield (as defined by a drop of stress) but only a more or 
less well-marked point at which a rapid change of slope of the stress strain diagram 
occurs, the collapse is not so sudden, and struts will sustain greater stresses than the 
yield. 
In the particular case of cast iron the author has found very good agreement with 
Southwell’s* formula, and in one case of bright rolled steel and in another of a 
sample of duralumin a fair approach to this formula. 
Ultimate Strength of I Beams of Ductile Materials. 
The strength of I beams is another case in which the attaining of the yield stress 
at any point corresponds to the ultimate strength of the specimen. The stress distri- 
bution just before yield is reached may be assumed to be linear, but after yield there 
will be portions on both flanges which sustain only the reduced stress. This will 
obtain for very great deflection, for it is not till the plastic strain is many times the 
elastic strain that the specimen again sustains the yield stress. In these yielded 
regions the stress is practically uniform. The inner portion which has not yielded will 
be elastic. Suppose we assume that the tension and compression flanges behave in 
the same way, and calculate the reduced stress, which applied over the whole flanges 
will just give, together with the moment of the web (which is assumed still elastic 
with a maximum stressequal to the yield), the same moment as that required to initiate 
the yield. To simplify the analysis we will take a 10in. x 5 in. section, having webs 
0-4 in. thick and flanges 0-6 in., and assume a yield of 18 tons per sq.in. For thissection 
it is found that if the drop of stress is about 8 per cent., the moment is only just equal 
to the moment required to produce the yield on the outer layers. This is much less 
than the magnitude of the drop found in several steels, so we should not expect that 
this I beam would stand more than the moment that will produce a stress at its surface 
equal to the yield. A number of tests on I beams have been carried out by Professor 
H. F. Moore,‘ and in all the cases where the failure was by primary flexure it was found 
that the computed fibre stress at the maximum applied load was generally slightly 
greater than the yield. In the seventeen tests recorded, the average ratio of maximum 
stress to yield stress was 1-07, varying from 1-01 to 1-18. In these tests it is probable 
that the yield is somewhat higher than that given, as the method adopted for loading 
the compression specimens would not ensure a uniform distribution of stress. It is 
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