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

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Design of Wood Members for Formwork 113
Many of the equations shown in this table were derived and illustrated
in previous sections. The symbols and units were also defined earlier in
this chapter. The span length l and deflection ∆ are measured in inches,
and the unit of measure for the uniformly distributed load w is lb per lin
ft. The concentrated load P and shear force V are measured in pounds.
Calculating Deflection by Superposition
Table 5-2 gives equations for various load conditions for calculating
bending stress, shear stress, and deflection. These equations are commonly
used to design wood members for formwork and temporary
structures. However, sometimes there are other load conditions that
may be applied to the beams shown in Table 5-2. The method of
superposition is a technique of determining the total deflection of a
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beam by superimposing the deflections caused by several simple
loadings. In essence, the total deflection is determined by adding the
deflections caused by several loads acting separately on a beam.
The method of superposition is restricted to beams with the same
length and end conditions. Also, this method is restricted to the theory
of small deformations, which means the effect produced by each
load must be independent of that produced by other loads. Each load
must not cause an excessive change in the original shape or length of
the beam. Also, the point of maximum deflection caused by the separate
loadings must occur at the same location on the beam.
The technique of superposition is applicable for combining the
types of loads shown in Table 5-2. The following examples illustrate
the method of superposition for calculating deflection.
Example 5-10
Use the method of superposition to calculate the total deflection of
the beam shown below. The single-span beam has four concentrated
loads, two 8-lb loads, and two 120-lb loads. A review of Table 5-2
shows there is no beam with this load condition. However, Beam 4 in
Table 5-2 is a single-span beam with two loads located at a distance a
from each end of the beam. Using Beam 4 in Table 5-2, the deflection
due to the two 80-lb loads can be calculated and then the deflection
due to the two 120-lb loads can be calculated. Then, by method of
superposition, the two deflections can be added together to obtain
the total deflection due to all four of the loads.
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