Study of Some Geometries

Abstract

Let us consider (see Fig. 5.1) a beam of rectangular section (width b, height h) built in at x = L and supporting a load P at x = 0. Angles and moments will be positive if they are in the direction of rotation of Ox to Oy. At a point of abcissa x the bending moment is thus

$${M_f} = - {P_x}$$

and the shear force T = P. At a point 0 < x < L of the beam axis displayed in Fig. 5.1 the shear force is positive, the bending moment is negative and the curvature is positive. Consider a single element of the beam, of length dx. If pdx is the load acting on the element dx (p is the weight per unit length in N/m), the shear force and the bending moment at x + dx are given respectively by

$${M_f} = - {P_x}$$

.