columns with balcony loads

this paper deals with the solution of a column with balcony loads. it is intended to determine the expressions for deflections and bending moments of the sections of a column under the action of transmitted loads from a balcony loaded at its free end by a force «p» and rigidly connected to the column somewhere between its ends. the action of this load on the column is equivalent to that of the intermediate compre_ssion force « p» and that of the moment «pe» applied at the conjunction of the balcony and the column. the eccentricity « e s of the force « p» indicates the length of the balcony. as far as the author of this article has investigated, this problem has not been previously treated in any technical literature ; however its lengthy solution is a straight. forward one. it seems that, in the past, the designers were probably satisfied with the application of the inexact, but simple combined stress formula, in this respect. no doubt that this kind of computation of stresses in this problem may, some time, lead to some erroneous results which should be avoided. therefore, a more rigorous solution, especially in this time of optimum design, is in order. although, this solution is lengthy, answers can be found «painlessly» with the electronic computer. the nature of this problem is so that, it can be considered as a beam _column problem. first of all the euler - bernoulli's differential equations for the top and the bottom segments of the column are written and the expressions for deflections are obtained. then, the boundary conditions and the continuity of the deflections and slopes at the point. of application of the balcony loads are taken into account and the constants of integration are calculated. at this point, the discontinuity in the curvatures is also verified, and the expression for the deflection of the column is given. in this way it is possible to find the exact values of deflection, bending moment and shear force any secrion of the column, as explained in this paper. with the help of the electronic computer of tehran university, the author has obtained many figures, based on the variation of some parameters, and it is the intention of the writer in a time opportune to draw some graphs for deflections and bending moments of sections of the column, in order to facilitate the task of the structural designers, at the end, the solutions of some particular cases are derived from the general solution , and the criteria for the computation of buckling load in a column with intermediate compression forces, i. c. when e = 0 but e 0 , has resulted.