### Simply-supported Beams - Steel 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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