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

102 Chapter Five
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Example 5-6
A 6-ft-long rectangular 4 × 6 beam will be used for temporary support
of formwork. The duration of the load will be less than 7 days and the
beam will be in a dry condition, moisture content less than 19%. The
beam will be grade No. 2 Spruce-Pine-Fir whose actual dimensions
are 3½ by 5½ in. If the beam supports a uniformly distributed load of
450 lb per lin ft over a single span, determine the values of the shear
force V and the applied horizontal shear stress f v
using the modified
method of determining shear. Also, check the bending capacity for
this beam.
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Check Shear Capacity
From Eq. (5-16), the modified shear force for a single-span beam with a
uniformly distributed load can be calculated by Eq. (5-16) as follows:
V = wL/2[1 – 2d/l]
= [(450 lb/ft × 6 ft)/2][1 – 2(5.5 in.)/72 in.]
= (1,350 lb)[1 – 0.153]
= 1,143.5 lb
From Eq. (5-17), the applied shear stress can be calculated:
f v
= w[l – 2d]/16bd
= 450 lb/ft[72 in. – 2(5.5 in.)]/[16(3.5 in.)(5.5 in.)]
= 27,450/308
= 89.1 lb per sq in.
Determine the allowable shear stress for a 4 × 6 No. 2 grade
Spruce-Pine-Fir with a 7-day load-duration as follows:
Table 4-3, reference design value for shear stress = 135 lb per sq in.
Table 4-4, adjustment factor for 7-day load-duration, C D
= 1.25
Allowable shear stress F v
= (135 lb per sq in.)(C D
)
= (135 lb per sq in.)(1.25)
= 168.8 lb per sq in.
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