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

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Design of Wood Members for Formwork 95
Examples of Using Bending Stress Equations for
Designing Beams and Checking Stresses in Beams
The following examples illustrate methods of designing and checking
bending stresses in rectangular wood beams for specified loading
conditions. The beams will have adequate lateral bracing and end
supports (C L
= 1.0) to allow the reference design values to be used for
the allowable bending stress.
Example 5-1
Determine the minimum-size wood beam, 8 ft long, required to support
three equal concentrated loads of 190 lb spaced at 2, 4, and 6 ft
from the ends of the beam. The beam will be used in a dry condition
with normal load-duration and temperature. Adequate bracing and
end supports will be provided.
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Because the loads are acting at the quarter points of the beam,
Eq. (5-3) will be used to calculate the applied bending moment.
M = Pl/2
= (190 lb × 96 in.)/2
= 9,120 in.-lb
Consider a 2 × 6 S4S (surfaced four sides) lumber of No. 2 grade
Southern Pine. Table 4-2 indicates an allowable bending stress of
1,250 lb per sq in. From Eq. (5-11), the required section modulus S can
be calculated:
S = M/F b
= (9,120 in.-lb)/(1,250 lb per sq in.)
= 7.29 in. 3
Thus, the required section modulus of the beam is 7.29 in. 3 . From
Table 4-1, the section modulus of a 2 × 6 S4S beam is 7.56 in. 3 , which
is greater than the required 7.29 in. 3 . Therefore, a 2 × 6 S4S No. 2 grade
Southern Pine is satisfactory provided it satisfies the requirements for
the allowable unit stress in shear and the limitations on deflection.
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