A timber beam may consist of a single member or may be built up from two or more members, called built up beams. • Timber beams are designed to resist- 1. Maximum bending moment 2. Maximum horizontal shear stress 3. Maximum stress at bearing.
Maximum bending stress, f_{b} must not exceed allowable stress parallel to grain,
F'_{b} = F_{b}*C_{D}*C_{M}*C_{t}*C_{F}*C_{V}*C_{fu}*C_{r}*C_{c}*C_{f}
Where
F_{b} is allowable bending stress in NDS supplement.
C_{D} is load duration factor, (see NDS Table 2.3.2 reproduced below)
C_{M} is wet service factor, (use when moisture of timber is higher than 19%)
C_{t} is temperature factor, (when timber is used in temperature higher than 150°F)
C_{L} is beam stability factor, (See below)
C_{F} is size factor, (apply only to visually graded sawn lumber members, and to round timber bending members, not apply simultaneously with Cv for glued laminated timber)
C_{V} is volume factor, (apply only to glued laminated timber bending member)
C_{fu} is flat use factor, (when 2”-4” timber is loaded at wide face)
C_{r} is repetitive member factor, (apply to dimension bending member 2”-4” thick)
C_{c} is curvature factor (apply to curved glued laminated bending member)
C_{f} is form factor. (for round or diamond section)
Deflection should not exceed allowable limit. The elastic modulus shall be calculated as E'=E*C_{M}*C_{t}, Where E is modulus of elasticity in NDS supplement
Maximum shear stress, f_{v} shall not exceed allowable shear stress,
F'_{v} = F_{v}*C_{D}*C_{M}*C_{t}*C_{H}
Where F_{v} is allowable shear stress in NDS supplement and,
C_{H} is shear stress factor depends on length of split and shake. Value of C_{H} varies from 2 for no split to 1 with 1-1/2 split.
Load duration |
C_{D} |
Design load |
---|---|---|
Permanent |
0.9 |
Dead load |
Ten years |
1.0 |
Occupancy live load |
Two months |
1.15 |
Snow load |
Seven days |
1.25 |
Construction load |
Ten minutes |
1.6 |
Wind/Earthquake load |
Impact |
2.0 |
Impact load |
C_{L} = 1 for the following condition for member, with nominal depth, B and width, D.
D/B £ 2
2 < D/B £ 4 – solid blocking is provided at both ends of member.
D/B = 5, one edge (tension or compression) is fully supported.
D/B = 6, bridge, full depth blocking, cross bracing at 8 ft maximum, and both edges are fully supported or compressive edge is fully supported to prevent lateral displacement, and the ends at the point of bearing are laterally supported to prevent rotation;
D/B = 7, both edge fully supported.
When the conditions were not met, C_{L} is calculated based on a complicated equation in NDS section 3.3.3.7. Normally, it is easier to meet the requirement then to go through the complicated equation.
The size, C_{F}, for timber species other than southern pine are listed in Table 4-A. For southern pine 2” to 4” thick, size factor needs not be applied. For southern pine 4” thick, 8” and wider, C_{F} = 1.1. For dimension lumber, wider than 12”, C_{F} = 0.9 except Dense structural 86. 72, and 65. in which, C_{F} =0.9. When the depth of Dense structural 86, 72, and 65, dimension lumber exceeds 12”, C_{F} =(12/d)1/9.
C_{r} applies to dimension lumber 2” to 4” thick that subjected to bending. C_{r} =1.15 when members are used as joist, truss chords, rafters, etc and spacing is not exceed 24” and not less than 3”.
When the moisture of dimension lumber exceeds 19%, the design value Fb shall be multiplied by C_{M} = 0.85 except that when F_{b} * C_{M} £ 1500 psi, C_{M} =1.
Calculate design load and moment
Select timber species and cross section. Determine maximum bending stress, f”_{b}=M/S, where M is design moment with load duration factor, S is section modulus.
Determine allowable bending stress, with the rest of multiplication factors
F"_{b} = F_{b}*C_{D}*C_{M}*C_{t}*C_{F}*C_{V}*C_{fu}*C_{r}*C_{c}*C_{f}
Calculate elastic modulus
E'=E*C_{M}*C_{t}
Calculate deflection of beam with load without load duration factor.
Calculate shear stress, f”_{v} = VQ/Ib or for rectangular member, f”_{v} = 3V/2b
Where, V is shear force with load duration factor, Q is first moment of inertia, I is second moment of inertia, b is width of the member, d is depth of the member.
Calculate allowable shear stress with the rest of multiplication factors
F"_{v} = F_{v}*C_{D}*C_{M}*C_{t}*C_{H}
Solved Example: Design of 2x12 Timber Floor Joist with Douglas Fir-Larch
Solved Example: Design of 2x10 Timber Floor Joist with Southern Pine