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

106 Chapter Five
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FIGURE 5-3 Single-span beam with concentrated load at the center.
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Deflection of Single-Span Beams with Concentrated Loads
For a single-span 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 5-3. The concentrated load will cause a bending
moment of Pl/4 as discussed previously in this chapter. The maximum
deflection will occur at the center of the beam, and can be calculated
by Eq. (5-20).
∆=Pl 3 /48EI (5-20)
When the concentrated load is not located at the center of the
single span beam, as shown in Figure 5-4, the deflection can be calculated
by Eq. (5-21).
∆=Pb[l 2 /16 – b 2 /12]/EI (5-21)
When there are three concentrated load as shown on the singlespan
beam in Figure 5-5, the deflection can be calculated by Eq. (5-22).
∆=P [l 3 + 6al 2 – 8a 3 ]/48EI (5-22)
FIGURE 5-4 Single-span beam with concentrated load off center.
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