652 PROCEEDINGS OF SECTION H. 
ON A GRAPHIC METHOD OF DETERMINING. 
THE CHANGE OF FORM OF FRAMED STRUC- 
TURES UNDER STRESS. 
By Professor W. C. Kernot, M.A., M.C.E. 
[ Plates. ] 
WHEN a framed structure, such as, for example, the girder 
or truss of a roof or bridge, or a trestle-tower for carrying a 
railway viaduct or elevated water-tank, is loaded, its form 
is altered by the elastic deprivation of its various elements. 
In well-designed structures these elements are usually 
exposed to longitudinal thrusts and pulls, all bending 
actions being eliminated as far as possible. From these 
calculable thrusts and pulls, the cross-sectional areas, 
lengths, and direct modulus of elasticity of the material, 
the change in length of each element is easily determined. 
The problem that next presents itself is this-—‘‘ Having 
given the change in length of the various elements, to deter- 
mine the alteration in form of the whole structure.” As 
such structures almost always consist of a series of triangles, 
this may be done by plane trigonometry. Taking the 
altered lengths of the sides of the triangles, the alteration 
in the angles may be computed, and then by a further 
calculation based on the alteration.of both sides and angles, 
the movement of any point in the structure from its 
original position may be determined. The whole calcula- 
tion involves but simple mathematics, but is very laborious, 
and consequently rarely attempted. To find a rapid and 
convenient mode of arriving at the same result within such 
limits of approximation as are needed for practical pur- 
poses appeared therefore desirable, and after some con- 
sideration the writer was led to adopt a graphic method 
suited for rapid and convenient use in the drawing office. 
Of this,‘as of other graphic operations now popular with 
engineers, it may be remarked that, while subject to small 
errors due to imperfections of draughtsmanship, such errors 
are of no practical moment, being under ordinary office 
conditions less in magnitude than the inevitable uncertainty 
in the computed stresses and modulus of elasticity of the 
‘material. The system is best illustrated by a series of 
examples, commencing with a very simple case, and pro- 
ceeding thence to more complex ones. 
Let ABC in Fig. 1 represent a bracket attached to arigid 
wall; and loaded at B. It is required to find the magni- 
tide: and direction of the movement of B when the load 
