204: 



Mr. 0. H. Lander an Struts and Tie-Rods 



uniform intensity such as that caused by the inertia of an 

 engine connecting-rod, the following graphical methods 

 present many advantages over analytical determinations. 

 The}- are simple in application and, moreover, the error 

 caused by any approximations can be readily estimated. In 

 cases where beams are continuous over several supports, and 

 have endlong loads applied, as for example the spars of 

 aeroplanes, analytical expressions although obtainable are 

 very difficult in application. 



Let A, B, C (fig. 1 a) represent the centre line of a 

 strut which is subjected simultaneously to an end load and 

 to any system of lateral loading. Let the curve ADEFCA 

 (fig. 1 6) be the bending moment diagram for the lateral 



Fi<r. 1 a 



Fig. 1 b. 



loads acting alone. The bending moment diagram due to 

 the load P is given by the shape of the distorted column, 

 that is by the curve ABCA. The total bending moment on 

 each section is then given by the sum of the ordinates, that is 

 yi-\-y P , yv being taken to the proper scale, yi is already 

 known, and it remains therefore to determine y P the deflexion 

 of the column at any point due to both loadings acting 

 together. 



The deflexion curve of a beam can be drawn if the bending' 

 moment diagram is known since the deflexion curve is the 

 funicular polygon of the bending moment curve. Taking a 

 beam under any loading, the method consists in first drawing 

 the bending moment diagram for the lateral system acting* 

 alone. Now treat this diagram as if it were a curve showing- 

 load intensity at any point of the beam, and draw the 

 bending moment diagram for this load intensity curve. We 

 shall now have obtained a figure which will be such that its 

 ordinates when divided by E X I will give the deflexions due 



