Formwork for Concrete Structures by R.L.Peurifoy and G.D- By EasyEngineering.net

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Design of Wood Members for Formwork 91
FIGURE 5-1 Simple span beam with concentrated load.
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For a simple beam supported at each end, with a concentrated
load P at its center, the reaction at each end of the beam will be P/2,
as illustrated in Figure 5-1. The maximum bending moment due to
the concentrated load will occur at the center of the beam and can be
calculated as the product of force times distance: M = P/2 × l/2 = Pl/4.
The following equations can be used to calculate the maximum bending
moment for a simple span beam for the stated loads.
For one concentrated load P acting at the center of the beam,
M = Pl/4 in.-lb (5-1)
For two equal loads P acting at the third points of the beam,
M = Pl/3 in.-lb (5-2)
For three equal loads P acting at the quarter points of the beam,
M = Pl/2 in.-lb (5-3)
For one concentrated load P acting at a distance x from one end of
the beam, the maximum bending moment will be:
M = [P(l – x)x]/l in.-lb (5-4)
Equation (5-4) can be used to determine the maximum bending
moment in a beam resulting from two or more concentrated loads
acting at known locations by adding the moment produced by each
load at the critical point along the beam. The critical point is that
point at which the combined moments of all loads is a maximum.
Analysis of Bending Moments in Beams with Uniformly
Distributed Loads
For a simple beam, supported at each end, with a uniform load distributed
over its full length, the total vertical load on the beam wL is
divided between the two supports at the end of the beam, as illustrated
in Figure 5-2.
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