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

116 Chapter Five
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Allowable Span Length for Single-Span Members with
Uniformly Distributed Loads
For a single-span beam with a uniformly distributed load over its
entire length (Beam 8 in Table 5-2) the allowable span length for bending,
shear, and deflection can be determined as follows.
Combining the applied bending moment M = wl 2 /96 with the
allowable bending stress F b
= M/S, and rearranging terms, provides
the following equation for allowable span length due to bending for
a single-span beam:
l b
= [96F b
S/w] 1/2 in. (5-30)
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Combining the applied shear force V = wl/24 with the allowable
shear stress F v
= 3V/2bd, the allowable span length due to shear
for a single-span beam is provided by the following equation:
l v
= 16F v
bd/w (5-31)
Combining the modified shear force V = wl/24(1 – 2d/l) with the
allowable shear stress F v
= 3V/2bd provides the following equation
for the allowable span length for modified shear:
l v
= 16F v
bd/w + 2d (5-32)
The general equation for calculating the allowable span length
based on the deflection of a single-span wood beam can be obtained
by rearranging the terms in Eq. (5-26) as follows:
l ∆
= [4,608EI∆/5w] 1/4 (5-33)
If the permissible deflection is l/360, substituting l/360 for ∆ in
Eq. (5-26) and rearranging terms, the allowable span length for single-span
beams will be:
l ∆
= [4,608EI/1800w] 1/3
(5-33a)
If the permissible deflection is ¹⁄16 in., substituting ¹⁄16 in. for ∆ in
Eq. (5-26) for a single-span beam, the allowable span length based on
a permissible deflection of ¹⁄16 in. is
l ∆
= [4,608EI/80w] 1/4
(5-33b)
Allowable Span Length for Multiple-Span Members with
Uniformly Distributed Loads
For a multiple-span beam with a uniformly distributed load over its
entire length (Beam 9 in Table 5-2), the allowable span length can be
determined as described in the following paragraphs.
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