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

330 Chapter Eleven
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per square inch. The unit for allowable span length is inches. Because
joists are usually simply supported, the equations for single spans will
apply.
The examples that follow illustrate a method of determining each
of the three values previously listed. The results are based on resistance
to bending, shear, and deflection for a simple span that is supported
at each end. If a joist extends over more than two supports, it
can support a larger load than the one specified. It is assumed that the
joists are braced adequately. Table 11-6 provides the equations for
determining the allowable span lengths of wood members based on
bending, shear, and deflection. There equations can be used for single
span joists as illustrated in Figure 11-2.
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Example 11-2
Given the total load on the decking, the spacing of the joists, and the
size and grade of the joists, determine the maximum span for the
joist. For this example, the total load on the joist is 150 lb per sq ft and
the joist spacing is 20 in. on centers. The size and grade of the joists
are 4 × 4 S4S No. 1 grade Douglas Fir-Larch.
From Table 4-1 the physical properties of 4 × 4 lumber are
Section modulus, S = 7.15 in. 3
Moment of inertia, I = 12.51 in. 4
The decking will be attached to the top of the joists to stabilize the
joists. The lumber selected for the joists is No. 1 grade Douglas Fir-
Larch. Assume a dry condition and short load-duration, less than
7 days. Adjusting the reference design values in Table 4-3 for size C F
in Table 4-3a and short load-duration (C D
) in Table 4-4, the allowable
stresses will be:
Bending stress, F b
= C F
(C D
) (reference value for bending stress)
= 1.5(1.25)(1,000)
= 1,875 lb per sq in.
Shear stress, F v
= C D
(reference value for shear stress)
= 1.25(180)
= 225 lb per sq in.
Modulus of elasticity, E = 1,700,000 lb per sq in.
The uniform linear load transmitted from the decking to the joist
can be calculated by multiplying the slab load by the joist spacing as
follows:
w = (150 lb per sq ft)(20/12 ft)
= 250 lb per lin ft
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