✔Homework 4 (Due Monday, October 1)

What reference design values for wood, if any, are not subject to adjustment for duration of loading (ASD)? For time effect (LRFD)?

For sawn lumber, F_c^⊥, E, and E_min are not adjusted for the ASD load duration factor, while only E and E_min are not adjusted for the LRFD time effect.

Above what moisture content is it necessary to reduce the reference design values for most species of…

(a) sawn lumber: 19%
(b) glulam: 16%

Should lumber be pressure-treated if it is to be used in an application where it will be continuously submerged in

fresh water? No
Salt water? Yes

Explain. When continuously submerged in fresh water, wood does not decay appreciably. However, according to the text, page 4.23, “Pressure treated piles have an extensive record in resisting attack by marine borers.”

Determine the ASD reference and adjusted design values for the following members and loading conditions. All members are No. 2 Hem-Fir and are fully braced to prevent lateral-torsional buckling. Bending occurs about the strong axis.

a. Roof joists are 2 x 10 at 16 in. o.c. which directly support the roof sheathing. Loads are (D + S).

Symbol	Reference Design Value	C_D	C_M	C_t	C_L	C_F	C_fu	C_i	C_r	C_P	C_T	C_b	Adjusted Design Value
F_b	850	1.15	1	1	1	1.1	1	1	1.15	–	–	–	1237
F_t	525	1.15	1	1	–	1.1	–	1	–	–	–	–	664
F_v	150	1.15	1	1	–	–	–	1	–	–	–	–	173
F_c⊥	405	–	1	1	–	–	–	1	–	–	–	1.19	782
F_c	1300	1.15	1	1	–	1.0	–	1	–	1	–	–	1495
E	1.3e6	–	1	1	–	–	–	1	–	–	–	–	1.3e6
E_min	0.47e6	–	1	1	–	–	–	1	–	–	1	–	0.47e6

b. A 6 x 14 carries an equipment load that can be considered a permanent load.

Assuming temperatures 100-125ºF.

$C_F=(12/d)^{1/9}=root{9}{12/14}=$ 0.98

Symbol	Reference Design Value	C_D	C_M	C_t	C_L	C_F	C_fu	C_i	C_r	C_P	C_T	C_b	Adjusted Design Value
F_b	375	0.9	1	0.8	1	0.98	1	1	1	–	–	–	265
F_t	325	0.9	1	0.9	–	0.98	–	1	–	–	–	–	258
F_v	135	0.9	1	0.8	–	–	–	1	–	–	–	–	97
F_c⊥	405	–	1	0.8	–	–	–	1	–	–	–	1.00	324
F_c	475	0.9	1	0.8	–	0.98	–	1	–	1	–	–	335
E	1.1e6	–	1	0.9	–	–	–	1	–	–	–	–	0.99e6
E_min	0.4e6	–	1	0.9	–	–	–	1	–	–	1	–	0.36e6

c. Purlins in a roof are 4 x 14 at 8 ft o.c. Loads are (D + L_r).

Assuming temperatures 100-125ºF.

Symbol	Reference Design Value	C_D	C_M	C_t	C_L	C_F	C_fu	C_i	C_r	C_P	C_T	C_b	Adjusted Design Value
F_b	850	1.25	1	0.8	1	1.0	1	1	1	–	–	–	850
F_t	525	1.25	1	0.9	–	0.9	–	1	–	–	–	–	532
F_v	150	1.25	1	0.8	–	–	–	1	–	–	–	–	150
F_c⊥	405	–	1	0.8	–	–	–	1	–	–	–	1.10	356
F_c	1300	1.25	1	0.8	–	0.9	–	1	–	1	–	–	1170
E	1.3e6	–	1	0.9	–	–	–	1	–	–	–	–	1.17e6
E_min	0.47e6	–	1	0.9	–	–	–	1	–	–	1	–	0.42e6

d. Floor beams are 4 x 6 at 4 ft o.c. Loads are (D + L). High-humidity conditions exist, and the moisture content may exceed 19 percent.

Symbol	Reference Design Value	C_D	C_M	C_t	C_L	C_F	C_fu	C_i	C_r	C_P	C_T	C_b	Adjusted Design Value
F_b	850	1	1.00*	1	1	1.3	1	1	1	–	–	–	1105
F_t	525	1	1.00	1	–	1.3	–	1	–	–	–	–	683
F_v	150	1	0.97	1	–	–	–	1	–	–	–	–	146
F_c⊥	405	–	0.67	1	–	–	–	1	–	–	–	1.10	298
F_c	1300	1	0.80†	1	–	1.1	–	1	–	1	–	–	1144
E	1.3e6	–	0.90	1	–	–	–	1	–	–	–	–	1.17e6
E_min	0.47e6	–	0.90	1	–	–	–	1	–	–	1	–	0.42e6

*≤ 1150 psi
†> 750 psi

Determine the LRFD nominal and adjusted design values and adjusted design resistances for the following members and loading conditions. All members are No. 2 Hem-Fir and are fully braced to prevent lateral-torsional buckling. Bending occurs about the strong axis.

a. Roof joists are 2 x 10 at 16 in. o.c. which directly support the roof sheathing. Loads are 1.2D + 1.6S.

A=13.88 in² ; S=21.39 in³

Symbol	Reference Design Value	C_M	C_t	C_L	C_F	C_fu	C_i	C_r	C_P	C_T	C_b	K_F	φ_x	λ	Adjusted Design Value	A or S	Adjusted Design Resistance
F_b	850	1	1	1	1.1	1	1	1.15	–	–	–	2.54	0.85	0.8	1858	21.39	39.7 kip-in
F_t	525	1	1	–	1.1	–	1	–	–	–	–	2.70	0.80	0.8	998	13.88	13.9 k
F_v	150	1	1	–	–	–	1	–	–	–	–	2.88	0.75	0.8	259	13.88	3.6 k
F_c⊥	405	1	1	–	–	–	1	–	–	–	1.19	2.08	0.90	0.8	723	13.88	10.0 k
F_c	1300	1	1	–	1	–	1	–	xx1x	–	–	2.40	0.90	0.8	2246	13.88	31.2 k
E	1.3e6	1	1	–	–	–	1	–	–	–	–	–	–	–	1.3e6	–	–
E_min	4.7e6	1	1	–	–	–	1	–	–	1	–	1.76	0.85	–	0.71e6	–	–

b. A 6 x 16 carries an equipment load that can be considered storage using 1.2D + 1.6L.

A=85.25 in² ; S=220.2 in³ ; assume temperature < 100ºF

$C_F=(12/d)^{1/9}=root{9}{12/16}=$ 0.97

Symbol	Reference Design Value	C_M	C_t	C_L	C_F	C_fu	C_i	C_r	C_P	C_T	C_b	K_F	φ_x	λ	A justed Design Value	A or S	Adjusted Design Resistance
F_b	375	1	1	1	0.97	1	1	1	–	–	–	2.54	0.85	0.7	550	220.2	121.1 kip-in
F_t	325	1	1	–	0.97	–	1	–	–	–	–	2.70	0.80	0.7	477	85.25	40.6 k
F_v	135	1	1	–	–	–	1	–	–	–	–	2.88	0.75	0.7	204	85.25	17.4 k
F_c⊥	405	1	1	–	–	–	1	–	–	–	1	2.08	0.90	0.7	532	85.25	45.3 k
F_c	475	1	1	–	0.97	–	1	–	1	–	–	2.40	0.90	0.7	697	85.25	59.4 k
E	1.1e6	1	1	–	–	–	1	–	–	–	–	–	–	–	1.1e6	–	–
E_min	0.4e5	1	1	–	–	–	1	–	–	1	–	1.76	0.85	–	0.6e6	–	–

c. Purlins in a roof are 4 x 14 at 8 ft o.c. Loads are 1.2D + 1.6L_r.

Assume fairly hot.

A=46.38 in² ; S=102.4 in³

Symbol	Reference Design Value	C_M	C_t	C_L	C_F	C_fu	C_i	C_r	C_P	C_T	C_b	K_F	φ_x	λ	Adjusted Design Value	A or S	Adjusted Design Resistance
F_b	850	1	0.8	1	1	1	1	1	–	–	–	2.54	0.85	0.8	1175	102.4	120 kip-in
F_t	525	1	0.9	–	0.9	–	1	–	–	–	–	2.70	0.80	0.8	735	46.38	34.1 k
F_v	150	1	0.8	–	–	–	1	–	–	–	–	2.88	0.75	0.8	207	46.38	9.6 k
F_c⊥	405	1	0.8	–	–	–	1	–	–	–	1.1	2.08	0.90	0.8	535	46.38	54.8 k
F_c	1300	1	0.8	–	0.9	–	1	–	1	–	–	2.40	0.90	0.8	1617	46.38	75.0 k
E	1.3e6	1	0.9	–	–	–	1	–	–	–	–	–	–	–	1.17e6	–	–
E_min	0.47e6	1	0.9	–	–	–	1	–	–	1	–	1.76	0.85	–	0.63e6	–	–

d. Floor beams are 4 x 6 at 4 ft o.c. Loads are 1.2D + 1.6L with L from occupancy. High-humidity conditions exist, and the moisture content may exceed 19 percent.

A=19.25 in² ; S=17.65 in³

Symbol	Reference Design Value	C_M	C_t	C_L	C_F	C_fu	C_i	C_r	C_P	C_T	C_b	K_F	φ_x	λ	Adjusted Design Value	A or S	Adjusted Design Resistance
F_b	850	1	1	1	1.3	1	1	1	–	–	–	2.54	0.85	0.8	1909	17.65	33.7 kip-in
F_t	525	1	1	–	1.3	–	1	–	–	–	–	2.70	0.80	0.8	1179	19.25	22.7 k
F_v	150	0.97	1	–	–	–	1	–	–	–	–	2.88	0.75	0.8	251	19.25	4.8 k
F_c⊥	405	0.67	1	–	–	–	1	–	–	–	1.1	2.08	0.90	0.8	448	19.25	8.6 k
F_c	1300	0.8	1	–	1.1	–	1	–	1	–	–	2.40	0.90	0.8	1977	19.25	38.0 k
E	1.3e6	0.9	1	–	–	–	1	–	–	–	–	–	–	–	1.17e6	–	–
E_min	0.47e6	0.9	1	–	–	–	1	–	–	1	–	1.76	0.85	–	0.64e6	–	–

Estimate the total shrinkage that will occur in a four-story building similar to the one in Example 4.3. Floor joists are 2 x 10's instead of 2 x 12's. The initial moisture content can be taken as 19 percent, and the final moisture content is assumed to be 9 percent. All other information is the same as in Example 4.3.

SV = 0.002 , $Delta_{MC}=19-9=$ 10 %

$S_{floor}=SV d Delta_{MC} = 0.002*9.25*10=/m>0.185 in <m>S_{plate}=SV d Delta_{MC} =0.002*1.5*10=$ 0.03 in

$S = Sigma S = 3*S_{floor} + (4+8)*S_{plate}=3*0.185+12*0.03 =0.555+.36=$ 0.915

Total S = 0.915 in. ≈ 1 in.

What is the usual thickness of lamination used to fabricate glulam members from

a. Western Species: 1½” b. Southern Pine: 1 3/8”

c. Under what conditions would thinner laminations be used?

Thinner laminations are used to construct sharply-curved members.

What are the usual widths of glulam members fabricated from

a. Western Species: 3 1/8, 5 1/8, 6 3/4, 8 3/4, 10 3/4 b. Southern Pine: 3, 5, 6 3/4, 8½, 10½

Given: 5 1/8 x 28.5 24F-1.8E Douglas Fir glulam is used to span 32 ft, carrying an ASD load combination of (D + S). The load is a uniform load over a simple span, and the beam is supported so that buckling is prevented.

a. Sketch the beam and the cross section. Show calculations to verify the section properties S_x and I_x for the member, and compare with values in NDS Supplement Table 1C.

$S_x = {bh^2}/6 = {5.125*28.5^2}/6 =693.8 approx$ 693.8 in table 1C

693.8 in3

$I_x = {bh^3}/12 = {5.125*28.5^3}/12 =9886.6 approx$ 9887 in table 1C

9886.6 in4

b. Determine the adjusted ASD values associated with the section properties in part a. These include F+'bx F'ux and F'x.

Assume normal temperatures.

$C_V = root{10}{{21*12*5.125}/{Ldb}} =root{10}{1291.5/{32*5.125*28.5}}root{10}{0.2763}=0.8793 approx$ 0.88 <1✔

Symbol	Reference Design Value	C_D	C_M	C_t	C_L	C_V	C_fu	C_c	C_P	C_b	Adjusted Design Value
F_bx⁺	2400	1.15	1	1	1	0.88	1	1	–	–	2429
F_bx^-	1450	1.15	1	1	1	0.88	1	1	–	–	1467
F_c⊥x	650	–	1	1	–	–	–	–	–	–	650
F_vx	265	1.15	1	1	–	–	–	–	–	1	305
Ex	1.8e6	–	1	1	–	–	–	–	–	–	1.8e6
E_x~min	0.93e6	–	1	1	–	–	–	–	–	–	0.93e6
F_by^-	1450	1.15	1	1	1	1	1	1	–	–	1668
F_c⊥y	560	–	1	1	–	–	–	–	–	1	560
F_vy	230	1.15	1	1	–	–	–	–	–	–	265
Ey	1.6e6	–	1	1	–	–	–	–	–	–	1.6e6
E_y~min	0.83e6	–	1	1	–	–	–	–	–	–	0.83e6
F_t	1100	1.15	1	1	–	1.1	–	–	–	–	1392
F_c	1600	1.15	1	1	–	1.0	–	–	1	–	1840
E_axial	1.7e6	1.15	1	1	–	1.0	–	–	–	–	1.96e6

c. Repeat part b except the moisture content of the member may exceed 16 percent.

Symbol	Reference Design Value	C_D	C_M	C_t	C_L	C_V	C_fu	C_c	C_P	C_b	Adjusted Design Value
F_bx⁺	2400	1.15	0.8	1	1	0.88	1	1	–	–	1943
F_bx^-	1450	1.15	0.8	1	1	0.88	1	1	–	–	1174
F_c⊥x	650	–	0.53	1	–	–	–	–	–	–	345
F_vx	265	1.15	0.875	1	–	–	–	–	–	1	267
Ex	1.8e6	–	0.833	1	–	–	–	–	–	–	1.5e6
E_x~min	0.93e6	–	0.833	1	–	–	–	–	–	–	0.78e6
F_by^-	1450	1.15	0.8	1	1	1	1	1	–	–	1334
F_c⊥y	560	–	0.53	1	–	–	–	–	–	1	297
F_vy	230	1.15	0.875	1	–	–	–	–	–	–	231
Ey	1.6e6	–	0.833	1	–	–	–	–	–	–	1.3e6
E_y~min	0.83e6	–	0.833	1	–	–	–	–	–	–	0.69e6
F_t	1100	1.15	0.8	1	–	1.1	–	–	–	–	1113
F_c	1600	1.15	0.73	1	–	1.0	–	–	1	–	1343
E_axial	1.7e6	1.15	1	1	–	1.0	–	–	–	–	1.96e6

Repeat problem 5.11 using LRFD. The applicable load combination is (1.2D + 1.6S).

a. Sketch the beam and the cross section. Show calculations to verify the section properties S_x and I_x for the member, and compare with values in NDS Supplement Table 1C.

$S_x = {bh^2}/6 = {5.125*28.5^2}/6 =693.8 approx$ 693.8 in table 1C

693.8 in3

$I_x = {bh^3}/12 = {5.125*28.5^3}/12 =9886.6 approx$ 9887 in table 1C

9886.6 in4

b. Determine the adjusted [LRFD] values associated with the section properties in part a. These include F+'bx F'ux and F'x.

Assume normal temperatures.

$C_V = root{10}{{21*12*5.125}/{Ldb}} =root{10}{1291.5/{32*5.125*28.5}}root{10}{0.2763}=0.8793 approx$ 0.88 <1✔

Symbol	Reference Design Value	C_M	C_t	C_L	C_V	C_fu	C_c	C_P	C_b	K_F	φ_x	λ	Adjusted Design Value
F_bx⁺	2400	1	1	1	0.88	1	1	–	–	2.54	0.85	0.8	3650
F_bx^-	1450	1	1	1	0.88	1	1	–	–	2.54	0.85	0.8	2205
F_c⊥x	650	1	1	–	–	–	–	–	–	2.08	0.90	0.8	975
F_vx	265	1	1	–	–	–	–	–	1	2.88	0.75	0.8	458
Ex	1.8e6	1	1	–	–	–	–	–	–	–	–	–	1.8e6
E_x~min	0.93e6	1	1	–	–	–	–	–	–	1.76	0.85	0.8	1.1e6
F_by^-	1450	1	1	1	1	1	1	–	–	2.54	0.85	0.8	2506
F_c⊥y	560	1	1	–	–	–	–	–	1	2.08	0.90	0.8	840
F_vy	230	1	1	–	–	–	–	–	–	2.88	0.75	0.8	397
Ey	1.6e6	1	1	–	–	–	–	–	–	–	–	–	1.6e6
E_y~min	0.83e6	1	1	–	–	–	–	–	–	1.76	0.85	0.8	0.10e6
F_t	1100	1	1	–	1.1	–	–	–	–	2.70	0.80	0.8	2091
F_c	1600	1	1	–	1.0	–	–	1	–	2.40	0.90	0.8	2465
E_axial	1.7e6	1	1	–	1.0	–	–	–	–	–	–	–	1.36e6

c. Repeat part b except the moisture content of the member may exceed 16 percent.

Symbol	Reference Design Value	C_M	C_t	C_L	C_V	C_fu	C_c	C_P	C_b	K_F	φ_x	λ	Adjusted Design Value
F_bx⁺	2400	0.8	1	1	0.88	1	1	–	–	2.54	0.85	0.8	2920
F_bx^-	1450	0.8	1	1	0.88	1	1	–	–	2.54	0.85	0.8	1764
F_c⊥x	650	0.53	1	–	–	–	–	–	–	2.08	0.90	0.8	517
F_vx	265	0.875	1	–	–	–	–	–	1	2.88	0.75	0.8	401
Ex	1.8e6	0.833	1	–	–	–	–	–	–	–	–	–	1.5e6
E_x~min	0.93e6	0.833	1	–	–	–	–	–	–	1.76	0.85	0.8	0.93e6
F_by^-	1450	0.8	1	1	1	1	1	–	–	2.54	0.85	0.8	2004
F_c⊥y	560	0.53	1	–	–	–	–	–	1	2.08	0.90	0.8	445
F_vy	230	0.875	1	–	–	–	–	–	–	2.88	0.75	0.8	348
Ey	1.6e6	0.833	1	–	–	–	–	–	–	–	–	–	1.3e6
E_y~min	0.83e6	0.833	1	–	–	–	–	–	–	1.76	0.85	0.8	0.83e6
F_t	1100	0.8	1	–	1.1	–	–	–	–	2.70	0.80	0.8	1672
F_c	1600	0.73	1	–	1.0	–	–	1	–	2.40	0.90	0.8	2018
E_axial	1.7e6	1	1	–	1.0	–	–	–	–	–	–	–	1.4e6

✔Homework 4 (Due Monday, October 1)

✔4.23(0.5 points)

✔4.24(0.5 points)

✔4.27(0.5 points)

✔4.30(1.5 points)

✔4.31(1.5 points)

✔4.35(1.5 points)

✔5.1(0.5 points)

✔5.2(0.5 points)

✔5.11(1.5 points)

✔5.12(1.5 points)

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