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XX. On the Application of Graphical Methods to the Solution 

 of Problems on Struts and Tie-Rods ivith Lateral and Non- 

 Axial Loads. By Cecil H. Lander, M.Sc, A.M.Inst. C.E., 

 Lecturer in Civil Engineering in the University of 

 Manchester *. 



Ij^XCEPT in the most simple cases considerable difficulties 

 J present themselves in the determination o£ stresses in 

 struts and tie-rods which are subjected either to non-axial or 

 to lateral systems of loading. If the bending moment at 

 the point and the direct thrust in the column are known, the 

 intensity of stress at any point can be calculated from 

 the expression 



/_ I + A 



where M = Bending moment at section considered ; 

 I = Moment of inertia at that section ; 

 y=. Distance of the point from the neutral axis; 

 P- Direct thrust ; 

 A = Area of section. 



The direct thrust is always known, and the stress due to 

 this can therefore be obtained with no further difficulty. 

 With regard to the bending moment, however, matters are 

 complicated by the fact that owing to the deflexion caused 

 by the lateral loading, the moment will be increased in 

 amount by the presence of the end load which in its turn 

 again increases the deflexion, and so on until a balance is 

 obtained. 



For simple cases f expressions can be obtained which will 

 give the actual bending moment at any point in the beam. 

 A useful approximate method, suggested by Professor 

 Morley J, consists in first calculating the central deflexion 

 due to the lateral load alone, and then increasing the moment 

 by an amount equal to the product of the end load and this 

 deflexion. The reader is referred to Professor Morley's 

 paper in which he shows that the error involved in most 

 practical cases is negligible. 



When, however, the lateral loading is complicated by the 

 existence of several concentrated loads, due to the end load 

 being non-axial or to a distributed lateral load of non- 



* Communicated by Prof. J. E. Petavel, F.R.S. 

 t Perry, J., " Struts with Lateral Loads," Phil. Mag. March 1892. 

 ; X Morley, A., " Laterally Loaded Struts and Ties," Phil. Mag. June 

 1908. 



