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Extra info for Building Structures
Fig. 23 The figure shows two cantilevers that are exactly the same except the loads are being applied in opposite directions. Some agreement has to be made to distinguish the fact that cantilever A is being bent down, and cantilever B is being bent up! This could be done by deciding that cantilever A deforms in a negative way, causing negative bending moments and vice versa for cantilever B. Fig. 24 In this figure the bending moments have been drawn on the tension side of the beam. Although these decisions are supposed to aid clarification, this is not always the case!
Fig. 43 Because the slab is two dimensional, bending moments and shear forces can be considered as acting in two separate directions. For example a rectangular slab, supported on all sides and loaded by a central point load, will span in two directions. Internal forces 55 Fig. 44 A ‘strip’, AB, of the slab acts rather like a beam spanning from A to B. This strip will have bending moment and shear force distributions which can be represented by bending moment and shear force diagrams. Fig. 45 Similarly with strip CD.
A possible sign convention is shown in the following figure. Building structures 46 Fig. 25 Again this decision is made by personal whim! Using the stated sign conventions the bending moment and shear force diagrams can be drawn for a simple beam with point load, and these diagrams show the signs of the bending moments and shear forces. Fig. 26 It is sets of diagrams like this that give engineers pictures of what is happening inside a structure. The conceptual meaning of sets of bending moment and shear force diagrams is central to the understanding of structural behaviour.