ASD/LRFD Manual - American Wood Council

ASD/LRFD MANUAL FOR ENGINEERED Wood Construction
157
c = 0.9 for structural glued laminated timbers (NDS 3.7.1.5)
C
P
* *
2
*
c c c
1
= + F ⎡ + ⎤
cE/F 1 F
cE/F −
2c ⎢
⎣ 2c ⎥ − F
cE/F
⎦ c
1
= + 0.
7190
−
2( 0. 9)
⎛1+
0.
7190⎞
0 7190
⎝
⎜
2 0 9 ⎠
⎟ − .
( . ) 0.
9
= 0. 626
(NDS 3.7.1.5)
F′ c = F c * (C p ) = 2,530 (0.626) = 1,583 psi (NDS 5.3.1)
Calculate the resisting column compression capacity:
P′ = F′ c A s = (1,583)(81.81) = 129,469 lbs
Structural Check: P′ ≥ P load
129,469 lbs ≥ 22,000 lbs OK
For the fire design of the wood column, the loading
is unchanged. Therefore, the total load is unchanged. The
fire resistance must be calculated.
Calculate column area, A, and moment of inertia, I, for
column exposed on four sides:
A f = (b – 2a)(d – 2a) = (9.625 – 3.6)(8.5 – 3.6)
= 29.52 in. 2
I f = (b – 2a)(d – 2a) 3 /12 = (9.625 – 3.6)(8.5 – 3.6) 3 /12
= 59.07 in. 4
Calculate the adjusted allowable compression stress
(assuming C D = N/A; C M = N/A; C t = N/A):
2
F cE = (2.03) 0.822 E min ′ / (< e /d) 2
= (2.03)(0.822)(880,000) / (168/(8.5 – 3.6)) 2
= 1,249 psi ft-lbs (NDS 16.2.2)
F* c = (2.58) F c = (2.58)(2,200)
= 5,676 psi ft-lbs (NDS 16.2.2)
F cE /F* c = 1,249/5,676 = 0.22
1
C P
= + 0.
22
−
2( 0. 9)
F′ c = 5,676 (0.214) = 1,216 psi
2
⎛1+
0.
22⎞
⎝
⎜
2 0 9 ⎠
⎟ − 0.
22
0 9
= 0.
214
( . ) .
Calculate the resisting column compression capacity:
P′ = F′ c A f = (1,216)(29.52) = 35,884 lbs
Fire Check: P′ ≥ P load
35,884 lbs ≥ 22,000 lbs OK
Design Aid
Calculate structural design load ratio:
r s = M max /M′ = 22,000/128,043 = 0.17
Select the maximum design load ratio (buckling) limit
from Table M16.2-5A or calculate using the following
equation:
R
s
2. 03I
f ( 2. 03)( 59. 07)
= = = 0.
24
I C C ( 492. 6)( 1. 0)( 1. 0)
s M t
Fire Check: R s ≥ r s 0.24 ≥ 0.17 OK
Example 16.2-3
Exposed Tension Member Example - Allowable Stress Design
Solid sawn Hem-Fir timbers used as heavy timber
truss webs. The total design tension loads from a roof live
and dead load are P total = 3,500 lbs. Calculate the required
section dimensions for a 1-hour fire resistance time.
For the structural design of the wood timber, calculate
the maximum induced tension stress, f t .
Calculate tension load: P total = 3,500 lbs
Select a nominal 6x6 (5-1/2" x 5-1/2") Hem-Fir #2
Posts and Timbers grade with a tabulated tension stress,
F t , equal to 375 psi.
Calculate timber area: A s = bd = (5.5)(5.5) = 30.25 in. 2
Calculate the adjusted allowable tension stress
(assuming C D = 1.25; C M = 1.0; C t = 1.0):
F′ t = F t (C D )(C M )(C t )
= 375 (1.25)(1.0)(1.0) = 469 psi (NDS 4.3.1)
Calculate the resisting tension capacity:
P′ = F′ c As = (469)(30.25) = 13,038 lbs
Structural Check: P′ ≥ P load
14,180 lbs ≥ 3,500 lbs OK
M16: FIRE DESIGN
16
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