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

154 Chapter Five
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From Eq. (5-37a), l ∆
= [1,743EI/360w] 1/3 for ∆ =l/360
= [1,743(1,440,000)(12.51)/360(238)] 1/3
= 71.6 in.
From Eq. (5-37b), l ∆
= [1,743EI/16w] 1/4 for ∆ = ¹⁄16 in.
= [1,743(1,440,000)(12.51)/16(238)] 1/4
= 53.6 in.
Summary for 4 ë 4 S4S Joists
For bending, the maximum span length of joists = 71.9 in.
For shear, the maximum span length of joists = 150.6 in.
For deflection, the maximum span length of joists = 53.6 in.
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For this design, deflection governs the maximum span length of
the joists. Because the stringers must support the joists, the maximum
spacing of the wales must be no greater than 53.6 in. For constructability,
a spacing of 48.0 in. center to center will be used for stringers.
Stringers for Support of Joists
For this design, consider using 4-in.-thick stringers. Thus, the actual
size of a stringer will be 3½ in. Determine the unit stress in bearing
between joists and stringers.
Contact area in bearing, A = 3.5 in. × 3.5 in.
= 12.25 sq in.
The total load in bearing between a joist and a stringer will be the
unit pressure of the concrete acting on an area based on the joist and
stringer spacing. For this design, the area will be 20 in. wide by 48 in.
long. Therefore, the pressure acting between the joist and the stringer
will be
P= 143 lb per sq ft [20/12 × 48/12]
= 953 lb
The calculated applied unit stress in bearing, perpendicular to
grain, between a joist and a stringer will be
f c⊥
= 953 lb/12.25 sq in.
= 77.8 lb per sq in.
The allowable compression stress perpendicular to grain for
Douglas Fir-Larch can be obtained by multiplying the value tabulated
in Table 4-3 by the adjustment factor for a wet condition (C M
= 0.67).
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