Analytical modelling of structural systems : an entirely new by Iain Alasdair MacLeod

By Iain Alasdair MacLeod

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From a consideration of the overall equilibrium of the beam (Fig. 17(a)) the support reactions are RA = Mn/L acting vertically upward and R, = Mn/L acting vertically downward. Note that RA and R , are independent of the point of application of Mn. Although there is a loading discontinuity at B it is a point moment and will not affect the distribution of shear force. Thus, by considering the vertical equilibrium of either AZ,in Fig. 17(b) or Z2Cin Fig. 17(c) we see that The shear force is therefore constant along the length of the beam as shown in Fig.

5 (continued) CHAPTER 3 Normal Force, Shear Force, Bending Moment and Torsion The purpose of a structure is to support the loads for which it has been designed. e. from the loading point to the supports. In Fig. 21, for example, the beam transmits the effects of the loads at B and C to the built-in end A. This it achieves by developing an internal force system and it is the distribution of these internal forces which must be determined before corresponding stress distributions and displacements can be found.

The complete bending moment diagram is therefore as shown in Fig. 16(e). Note that the value of zero shear force in AB coincides with the turning value of the bending moment. In this particular example it is not possible to deduce the displaced shape of the beam from the bending moment diagram. Only three facts relating to the displaced 52 Normal Force, Shear Force, Bending Moment and Torsion shape can be stated with certainty; these are, the deflections at A and B are zero and there is a point of contraflexure at D, 1 m from A.

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