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

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Design of Wood Members for Formwork 93
and because c = d/2 for a rectangular beam, the section modulus is
from which
S= I/c = bd 2 /6 (5-9)
f b
= M/S = 6M/bd 2 (5-10)
Equations (5-7) and (5-10) are used to determine the applied bending
stress in a beam of known size for a known bending moment.
For design purposes, the bending moment M and the allowable
bending stress F b
are known, with the required size of the beam to be
determined. Therefore, substituting the allowable bending stress F b
for the applied bending stress f b
, Eq. (5-7) can be written for design
purposes in the form:
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S = M/F b
(5-11)
For a rectangular section, substituting bd 2 /6 for S, we get
bd 2 = 6M/F b
(5-12)
When analyzing a beam, the magnitude of the load uniformly
distributed along the beam or the magnitude and location of the concentrated
load or loads are known. Also, the length of the span and
the type of supports (whether simple or continuous) are known.
Therefore, the bending moment M can be calculated. Also, for a given
grade and species of lumber, the allowable stress F b
is known. Using
this information, the required size (width and depth) of a beam can
be determined as illustrated in the following sections.
Stability of Bending Members
Equations (5-7) through (5-12) for bending stresses are based on
beams that are adequately braced and supported. The allowable
bending stresses for beams are based on beams that have adequate
lateral bracing and end supports to prevent lateral buckling of members
subject to bending. If the beam is not adequately braced and supported,
the reference design value is reduced in order to determine
the allowable bending stress.
The beam stability factor C L
in the NDS is a multiplier to reduce the
reference design value of bending stress based on the depth-tothickness
ratio (d/b) of the beam. When the conditions in Table 5-1
are satisfied, the beam stability factor C L
= 1.0; therefore, no adjustment
is required in the reference design value in order to determine
the allowable bending stress. The d/b ratios in Table 5-1 are based on
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