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X.—The Influence of the Ratio of Width to Thickness upon the Apparent 
Strength and Ductility of Flat Test-bars of Mild Steel. By W. Gordon, B.Sc., 
A.M.1.Mech.H., Lecturer in Mechanical Engineering in Leith Technical College, 
and G. H. Gulliver, B.Sc., A.M.I.Mech.E., Lecturer in Engineering in the University 
of Edinburgh. ) 
(MS. received October 24, 1911, Read November 20, 1911. Issued separately February 28, 1912.) 
1. INTRODUCTION. 
In a large class of engineering structures it is essential that the materials employed 
should be both strong and ductile, so that not only shall the structure be able to resist 
heavy loads, but that if by any chance it is overloaded it shall not collapse suddenly. 
In order to ascertain whether a metal is suitable for a particular structure, its strength 
and ductility are determined experimentally. The test most commonly in use con- 
sists in applying a gradually increasing pull to a bar of the metal until fracture takes 
place. The maximum load supported per unit of the original cross-sectional area of the 
bar is called the tensile strength or tenacity of the metal, and the elongation of an 
initial measured length, expressed as a proportion of that length, is called the extension, 
and is used as an index of the ductility of the metal. 
} Experience shows that both strength and ductility, as measured in the tensile test, 
‘depend not only upon the properties of the metal, but also upon the shape of the test- 
bar. If there are abrupt variations in the cross-sectional dimensions, the apparent 
‘strength of the metal is greater, and the apparent ductility is less, than when these 
dimensions are constant or vary gradually. Again, the apparent ductility diminishes 
as the original length of the test-bar is made greater, on account of the well-known 
phenomenon of constriction ; the bar suffers a considerable reduction of section in the 
region where fracture eventually takes place, and the extension in this part of the 
bar is correspondingly greater than elsewhere. It follows that the extensions of two 
bars of the same cross-sectional dimensions are not comparable unless the datum- 
lengths of the two bars are the same. 
= In measuring the extension of bars, similar in form but differing in dimensions, 
comparable results are obtained only by observing Barsa’s principle of similitude, 
which may be stated thus: ‘‘Similar bodies of the same material remain similar 
when distorted by similar systems of applied loads.” In other words, if the linear 
eross-sectional dimensions of one test-bar are double those of another, the datum- 
length of the former must be twice that of the latter. In practice, it is a great 
convenience to use test-bars of constant gauge-length, and this necessitates that the 
TRANS. ROY. SOC. EDIN., VOL. XLVIII. PART I. (NO. 10). 31 
