# Design Methodology and Design Equations

In selecting the sizes of plywood, joists, and stringers for given spans and loads, the following requirements must be considered.

1. The allowable working stresses for bending and for shear must not be exceeded.

2. The allowable limits for deflection must not be exceeded.

3. The sizes of the joists and stringers should be easily ob­tained in the local markets.

1. Design for bending:

a. For single span: 96Fb(KS)
11

b. For two spans: 96Fb(KS)

11

c. For three or more spans:

 120Fb (KS) 11

 Wb where

 Wb = uniform load for bending, lb/ft F’b = adjusted allowable bending stress, psi KS = effective section modulus, in.3/ft 11 = span center to center of supports, in.

 2. Design for shear: a. For a single span:  where

 ws = uniform load for shear, lb/ft F’s = adjusted allowable rolling shear stress, psi Ib/Q = rolling shear constant, in.2/ft І2 = clear span, in. (center to center span minus support width) 3. Design to satisfy deflection requirements: a. Bending deflection: i. For a single span:

 wl 3 = 921.6 EI  where

Ab = bending deflection, in. w = uniform load for bending, psf E = modules of elasticity, psi I = effective moment of inertia, in. Vft l3 = clear span + SW (support width factor) SW = 0.25 in. for 2-in. nominal framing, and = 0.625" for 4-in. nominal framing  b. Shear deflection: The shear deflection may be closely approximated for all span conditions by the following formula:

where

AS = shear deflection, in. w = uniform load, psf

C = constant, equal to 120 for panels with face grain parallel to supports and 60 for panels with face grain perpendicular to supports t = nominal panel thickness, in.

E = modulus of elasticity, psi I = effective moment of inertia, in.4/ft

For cases when shear deflection is computed separately and added to bending deflection to obtain the total deflection, E for these bending-deflection equations should be increased by 10 per­cent. In this case the total deflection will be A = Ab + AS.