DETERMINATION OF DISPLACEMENT OF A BEAM WITH ONE END OVERHANGING IN SYMMETRIC BENDING WITH CONVERSION METHOD

The Conversion Method is used to determine the displacement of a beam with one end overhanging in symmetric bending. According to the relation between angles and normal lines of the beam, the displacement equation of the conversion method (DECM) is derived to obtain the deflection and the slope of this type of beams. The variables of the equation are the deflections of the free end of the corresponding Conversion Beam, the length of the beam converted, and the coordinate of the axis of the beam. The deeetailed process of computation for a specific beam is shown. The deflections of the free ends of the left, right conversion beams are computed, then they are put in a unified formula of DECM. The complete solution of the equation of deflection and slope is obtained. Only the knowledge of the deflection curve and the superposition method is required, without differentiation and integration, and without the need to consult the table of deflections. The result is accurate. Some instances of calculation with engineering background are given.