COMPLEX STRESS DISTRIBUTIONS IN ENGINEERING MATERIALS. 369 
and the Board of Trade, had adhered to the principle that every bridge composed of 
wrought iron, whether designed upon the plate, lattice, or tubular principle, should 
have a resistance, tending to break the bridge, (sic) of six times the rolling load, 
exclusive of its own weight.+ 
* Owing to the success of these undertakings (the Britannia and Conway tubular 
bridges) there was a general demand for wrought-iron bridges in every direction, 
and numbers were made without any regard to first principles . . . so clearly and 
satisfactorily shown in the early experiments. The result of this was a number of 
weak bridges, many of them so disproportioned in the distribution of material as 
to be almost at the point of rupture with little more than double the permanent 
load. 
‘The defects and breakdowns which followed the first successful application of 
wrought iron to bridge-building led to doubts and fears on the part of engineers ; 
and many of them contended for eight and even ten times the heaviest load as the 
safe margin of strength. Others, and amongst them the late Mr. Brunel, fixed a 
lower standard; and, I believe, that gentleman was prepared in practice to work up 
to one-third or two-fifths of the ultimate strength of the weight that would break 
the bridge. Ultimately it was decided by the authorities of the Board of Trade, but 
from what data I am not informed, that no wrought-iron bridge should with the 
heaviest load exceed a strain of 5 tons per sq. in.’? 
The coefficient to give the breaking strength was used in the simple formula : 
adc 
W= dia 
W = breaking load in tons applied at centre of girder; 
a sectional area of flange in tension ; 
overall depth in inches; 
length in inches between supports ; 
coefficient. 
R 
Holl i A 
Applied to cast-iron girders, for instance, in which the tension flange had an area 
six times as great as the compression flange, the coefficient was 26. For wrought-iron 
tubular or box girders it was 80, for plate-web girders 74, and lattice girders 67. 
These coefficients were based on experiments made on large-scale models, in which 
the most satisfactory distribution of sectional area for tension and compression was 
determined, and coefficients were applied to full-size girders with the metal in the 
flanges similarly distributed. This system, not being based on stress, did not assume 
a straight-line distribution of stress ; but with a coefficient based on a breaking strength, 
when parts would be stressed beyond the yield-point, it must of necessity indirectly 
assume other than a straight-line distribution. Among the many famous iron bridges 
built on this coefficient principle are the Britannia and Conway tubular bridges 
(c = 80), and the Tay bridge (Highland Railway) (c = 74). 
The introduction of the stress method revolutionised the system of design, and 
the distribution of stress had to be considered. The fixing of a stress of 5 tons per 
sq. in. as the maximum, without any details as to its application to different parts, led 
to great uncertainty, but also to further most important investigations. In applying 
the coefficient method the reduction of area by rivets in the tension flange had been 
disregarded, as it was also disregarded when determining the coefficients experi- 
mentally. The unexpected necessity of measuring the strength of a girder in a 
new unit with which engineers were not familiar naturally led to inquiries as to how 
the new standard compared with what had been proved by actual practice to be 
satisfactory. Fairbairn having at that date (1859) just completed the Spey bridge, 
and the Board of Trade taking exception to it on account of the stress being above. 
5 tons per sq. in., it was decided to make a test on a riveted girder roughly of the 
proportions of the Spey bridge. To quote Fairbairn: ‘. .. the Board of Trade 
threatened to stop the traffic which had been at work some months over the bridge. 
To make everything smooth, it was ultimately arranged that the bridge should be 
1 Researches on the Application of Iron to Buildings. W. Fairbairn. 
2 Philosophical Transactions, 1864, p.316. ‘ Experiments to Determine the Effect 
of Impact, Vibratory Action and long-continued Changes of Load on Wrought-iron 
_ Girders,’ by W. Fairbairn, LL.D., F.R.S. 
cc2 
