Beam Stability Factor Using 2005 Dual Format NDS

Dual Calculation of Beam Stability Factor Using ASD and LRFD Provisions

DRAFT - Comments Welcome

Consider a 5-1/8 in. x 24 in. 24F-1.8E Douglas fir glulam beam subject to the following loads: 325 plf Dead load and 1060 plf Occupancy Live load. The beam is `simple' and spans 20 ft - 4 in. (20.33 ft) The stated loads do not include the weight of the beam itself. Let's do the flexure (bending) check for the beam using both the ASD and LRFD methods as presented in the 2005 Dual Format National Design Specification ®for Wood Construction (NDS). Assume the beam is held in place and prevented from rotation at the ends, but is not braced along its span to resist lateral torsional buckling. (Consider dry and normal temperature service conditions.)

Since the beam is not braced (in particular the top / compression zone of the beam), the Beam Stability Factor, C_L, must be considered.

First let's determine the self weight of the beam, since it must be added to the Dead load. Using a specific weight of 33 pcf (Timber Construction Manual, Table 2.2),

ω _{self weight} = (5.125/12 ft)(24/12 ft)(33 pcf) = 28 plf.

Thus the total Dead load for the beam is,

ω _{applied Dead + self weight} = 325 + 28 = 353 plf.

ASD

Using the ASD approach the loads combine as follows:

D + L = 353 plf + 1060 plf = 1413 plf Total load ...

The maximum bending moment in the beam is at mid-span and is,

M _max = ω L² / 8 = 1413 plf (20.33 ft)² /8 = 73,000 lb-ft = 876,000 lb-in.

The Section Modulus for the beam is,

S = bh²/6 = (5.125)(24)²/6 = 492 in.³ (or by Timber Construction Manual Table A.1.2.1, or NDS® Table 1C).

The extreme fiber bending stress is thus,

f_b = M/S = 876,000 lb-in./492 in.³ = 1780 psi.

This value is checked against the allowable bending stress, which is obtained by multiplying the reference design value for bending by all the appropriate adjustment factors. The allowable stress is,

F_b' = F_b C_D C_M C_t (the lesser of C_L and C_V) ...

Where, for this problem,

C_D = 1.00 (Normal Load Duration for Occupancy Live load), C_M = 1.00, C_t = 1.00, and C_L and C_V will be calculated. (You guessed it: `M' for moisture and `t' for `temp'.)

First, F_b = 2400 psi.

And note: in the 2005 Dual Format NDS, this F_b=2400 psi is for both methods.