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

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Design of Wood Members for Formwork 115
Using Beam 4 in Table 5-2 to calculate the deflection from the two
200-lb loads:
∆=Pa [3(l 2 )/4 – (a) 2 ]/6EI
= 200(36)[3(108) 2 /4 – (36) 2 ]/6(1,600,000)(79.39)
= 0.07 in.
Using Beam 8 in Table 5-2 to calculate the deflection from the 150 lb
per lin ft uniformly distributed load:
∆= 5wl 4 /4,608EI
ww.EasyEngineering.n
= 5(150)(108) 4 /4,608(1,600,000)(79.39)
= 0.17 in.
By superposition the total deflection is obtained by adding the
two deflections as follows:
Total deflection = deflection from 200-lb loads + deflection from the
150-lb per lin ft uniformly distributed load:
∆= 0.07 in. + 0.17 in.
= 0.24 in.
Allowable Span Length Based on Moment,
Shear, or Deflection
As illustrated in the preceding sections, many calculations are required
to determine the adequacy of the strength of structural members. It
requires considerable time to analyze each beam element to determine
the applied and allowable stresses for a given load condition,
and to compare the calculated deflection with the permissible deflection.
For each beam element, a check must be made for bending,
shear, and deflection. Thus, it is desirable to develop a method that is
convenient for determining the adequacy of the strength and rigidity
of form members.
For design purposes it is often useful to rewrite the previously
derived stress and deflection equations in order to calculate the permissible
span length of a member in terms of member size, allowable
stress, and loads on the member. The equations derived earlier in this
chapter can be rewritten to show the span length l in terms of the
bending and shear stresses and deflection.
The following sections show the method of determining the
length of span that is permitted for the stated conditions. The equations
presented in these sections are especially useful in designing
formwork.
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