Simply-supported Beams - Steel Structures.

The calculations required to obtain the shear forces (SF) and bending moments (BM) in simply-supported beams form the basis of many other calculations required for the analysis of built-in beams, continuous beams and other indeterminate  structures.

Appropriate formulae for simple beams and cantilevers under various types of loads are presented in the Appendix Bending moment, shear and deflection tables for cantilevers and simply-supported beams.

In the case of simple beams it is necessary to calculate the support reactions before the bending moments can be evaluated; the procedure is reversed for built- in or continuous beams. The following rules relate to the SF and BM diagrams for beams:

(1) the shear force at any section is the algebraic sum of normal forces acting to one side of the section
(2) shear is considered positive when the shear force calculated as above is upwards to the left of the section
(3) the BM at any section is the algebraic sum of the moments about that section of all forces to one side of the section
(4) moments are considered positive when the middle of a beam sags with respect to its ends or when tension occurs in the lower fibres of the beam
(5) for point loads only the SF diagram will consist of a series of horizontal and vertical lines,while the BM diagram will consist of sloping straight lines, changes of slope occurring only at the loads
(6) for uniformly distributed loads (UDL) the SF diagram will consist of sloping straight lines, while the BM diagram will consist of second-degree parabolas
(7) the maximum BM occurs at the point of zero shear, where such exists, or at the point where the shear force curve crosses the base line.

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