APPLYING WOOD ADJUSTMENT FACTORS TO DETERMINE STRESSES Solution Example 6.6 A glued laminated 6¾ × 30 beam of stress class 24F-1.7E western species is simply supported over a span of 40 ft. The governing load combination is a uniformly distributed dead plus live load, and the beam is laterally braced at midspan. Determine the adjusted allowable bending stress and the adjusted factored bending stress. C M 1.0, Ct 1.0, Cc 1.0, C fu 1.0, C I 1.0 From NDS Supp. Table 5A. Fb 2400 lbf/in 2 Ey (min) 0.69 106 lbf/in 2 From Ex. 6.4, the volume factor is CV 0.832 The distance between lateral restraints is lu 40 ft 2 20 ft in (20 ft) 12 ft lu d 30 in 8.0 7 For a uniformly distributed load and an 𝑙𝑙𝑢𝑢 ⁄𝑑𝑑 ratio > 7, the effective length is obtained from Fig. 6.1 as ASD Method The adjusted modulus of elasticity for stability calculations with CM = Ct = 1.0 is le 1.63lu 3d in (1.63)(20 ft) 12 (3)(30 in) ft = 481 in The slenderness ratio is given by NDS Eq. 3.3-5. RB 0.69 106 lbf/in 2 b2 (481 in)(30 in) (6.75 in)2 17.80 50 [satisfies criteria of NDS Sec. 3.3.3] The critical buckling design value is FbE Ey (min)C MCt Emin lbf 0.69 106 (1.0)(1.0) 2 in led 1.20Emin 2 RB 1.200.69 106 lbf in 2 2 17.80 2613 lbf/in 2 The load duration factor for occupancy live load is C D 1.00 The reference flexural design value multiplied by all applicable adjustment factors except 𝐶𝐶𝐿𝐿, 𝐶𝐶𝑉𝑉, and 𝐶𝐶𝑓𝑓𝑓𝑓 is Fb* FbC MCtCcC I lbf 2400 (1.0)(1.0)(1.0)(1.0)(1.0) 2 in The beam stability factor is given by NDS Sec. 3.3.3 as 1.0 F CL 1.9 2400 lbf/in 2 F FbE Fb* 2613 2400 1.0 1.09 1.9 2 1.0 F F 0.95 1.9 1.0 1.09 2 1.09 1.9 0.95 lbf 0.85 in 2 1.09 lbf volume factor derived in Ex. 6.4 in 2 The volume factor governs. The adjusted allowable flexural stress is Fb FbC DC MCtC fuCcC ICV lbf 2400 (1.0)(1.0)(1.0)(1.0)(1.0)(1.0)(0.832) 2 in 1997 lbf/in 2 LRFD Method The critical buckling LRFD design value is From Table 6.4, the time effect factor for dead load plus occupancy live load is 0.8 FbE The adjusted modulus of elasticity for LRFD stability calculations with 𝐶𝐶𝑡𝑡 = 𝐶𝐶𝑀𝑀 = 1.0 is 1.20Emin 2 RB lbf (1.2) 1.032 106 2 in (17.80)2 EminC MCt KF s Emin 3909 lbf/in 2 lbf 0.69 106 (1.0)(1.0)(1.76)(0.85) 5 in 1.032 106 lbf/in 2 The reference flexural design value multiplied by all applicable LRFD adjustment factors except 𝐶𝐶𝑉𝑉, 𝐶𝐶𝐿𝐿, and C𝑓𝑓𝑓𝑓 is Fb* FbC MCtCcC I KF b lbf 2400 (1.0)(1.0)(1.0) in 2 (1.0)(2.54)(0.85)(0.8) 4145 lbf/in F FbE Fb* 2 3909 4145 The LRFD beam stability factor given by NDS Sec. 3.3.3 is 1.0 F 2 F 1.0 F CL 1.9 0.95 1.9 1.0 0.943 1.9 0.792 0.832 2 1.0 0.943 0.943 1.9 0.95 [volume factor derived from Ex. 6.4] lbf in 2 0.943 lbf in 2 Note: The CL equation given is actually a modified version from SE Structural Engineering Reference Manual and not the equation from NDS Sec. 3.3.3. The stability factor governs, and the adjusted factored bending stress is Fb FbC MCtC LC fuCcC I KF b lbf 2400 (1.0)(1.0)(0.792)(1.0)(1.0)(1.0)(2.54)(0.85)(0.8) 2 in 3283 lbf/in 2 DESIGN OF WOOD DEMAND/CAPACITY RATIO A beam is subjected to a dead load stress of 800 lbf/in2, a live load stress of 600 lbf/in2, and a wind load stress of 500 lbf/in2. The beam is made from lumber with a reference design strength value of 1500 lbf/in2, and is used in a situation where all adjustment factors except the load duration factor are 1.0. Find the demand/capacity ratio for all applicable IBC load combinations. Solution From Table 6.1, the load duration factor for dead load is 0.9. The allowable strength design value for the dead load loading condition is lbf Fb 0.90Fb (0.90) 1500 in 2 1350 lbf/in 2 The demand/capacity ratio for the dead load loading condition is fb Fb lbf in 2 600 lbf in 2 For the dead load plus live load plus wind load loading condition, the total applied stress is fb D 0.45W 0.75L lbf (0.45) 500 in in 2 lbf (0.75) 600 in 2 lbf 2 1475 lbf/in 2 The load duration factor for a wind load is 1.60, and the largest load duration factor governs, so the allowable design value for 1350 in 2 0.593 lbf in 2 1500 lbf/in 2 1400 lbf/ft2 The load duration factor for an occupancy live load is 1.0, and the largest load duration factor governs, so the allowable design value for the dead load plus live load loading condition is 800 lbf lbf Fb 1.0 fb (1.0) 1500 in 2 For dead load plus live load loading condition, the total applied stress is fb 800 800 The demand/capacity ratio for the dead load plus live load loading condition is fb Fb 1400 1500 lbf in 2 0.933 lbf in 2 the dead load plus live load plus wind load loading condition is lbf Fb 1.60Fb (1.60) 1500 in 2 2400 lbf/in 2 The demand/capacity ratio for the dead load plus live load plus wind load loading condition is fb Fb 1475 2400 lbf in 2 0.61 lbf in 2 DESIGN OF WOOD SHEAR Example 6.8 A glued laminated 6¾ × 30 beam of stress class 24F-1.7E western species is notched and loaded as shown. The beam has a moisture content exceeding 16% and is subjected to sustained temperatures between 100°F and 125°F. The governing load combination is dead plus occupancy live load. Determine the maximum allowable shear force at each support and at the hanger connection. Solution The reference design value for shear stress, tabulated in NDS Supp. Table 5A, is Fv 210 lbf/in 2 The applicable shear reduction factor for the design of members at a notch is From Table 6.7, the applicable temperature factor for wet conditions between 100°F and 125°F is Ct 0.7 From Table 6.6, the applicable wet service factor for moisture content exceeding 16% is C vr 0.72 ASD Method For normal occupancy live load, the load duration factor given in Table 6.5 is C D 1.00 The adjusted allowable shear stress is Fv FvC DC MCtC vr lbf 210 (1.00)(0.875)(0.7)(0.72) in 2 93 lbf/in 2 At the right support, 𝑒𝑒 < 𝑑𝑑𝑛𝑛′ and from NDS Eq. 3.4-5, the allowable shear force is d d 2 n e Vr Fvb d 3 dn lbf (2) 93 (6.75 in) in 2 3 30 in 27 in (12 in) 30 in 27 in 11,997 ibf C M 0.875 At the left support and from NDS Eq. 3.4-3, the allowable shear force is 2 2 d n Vr Fvbdn 3 d lbf (2) 93 2 (6.75 in)(27 in) 27 in 2 in 30 in 3 9153 lbf The hanger connection is less than 5𝑑𝑑 from the end of the beam, and from NDS Eq. 3.4-6, the allowable shear force is 2 2 d e Vr Fvbde 3 d lbf (2) 93 (6.75 in)(27 in) 2 in 2 27 in 30 in 3 9153 lbf LRFD Method From Table 6.4, the applicable time effect factor for dead load plus occupancy live load in 0.8 From Table 6.3, the applicable resistance factor for shear is The adjusted factored shear stress is Fv FvC MCtC vr KF v lbf 210 (0.875)(0.7)(0.72) 2 in (2.88)(0.8)(0.75) From Table 6.2, the applicable format conversion factor for shear is 160 lbf/in 2 KF 2.88 At the left support and from NDS Eq. 3.4-3, the allowable shear force is 2 2 d Vr Fvbdn n 3 d (2) 160 lbf (6.75 in)(27 in) 2 27 in 2 in 30 in 3 At the right support, 𝑒𝑒 < 𝑑𝑑𝑛𝑛, and from NDS Eq. 3.4-5, the allowable shear force is d d 2 n e Vr Fvb d 3 dn (2) 160 lbf (6.75 in) in 2 3 30 in 27 in (12 in) 30 in 27 in 15,747 lbf 20,640 lbf The hanger connection is less than 5d from the end of the beam, and from NDS Eq. 3.4-6, the allowable shear force is 2 2 d e Vr Fvbde 3 d (2) 160 lbf (6.75 in)(27 in) 27 in 2 2 in 30 in 3 15,747 lbf DESIGN OF WOOD AXIAL + BENDING Example 6.9 The select structural 2 × 6 Douglas fir-larch top chord of a truss is loaded with the service level loads shown in the illustration. The governing load combination consists of dead plus occupancy live load, and the moisture content exceeds 19%. The chord is laterally braced at midlength about the weak axis, and the self-weight of the chord and bracing members may be neglected. Determine whether the member is adequate. Solution The reference design values for compression and modulus of elasticity are tabulated in NDS Supp. Table 4A and are Fc 1700 lbf/in 2 Emin 0.69 106 lbf/in 2 CT 1.0 Ct 1.0 The applicable adjustment factors for compression and modulus of elasticity are as follows. C M wet service factor from Table 6.6 = 0.8 [compression member] = 0.9 [modulus of elasticity] C F size factor from NDS Supp. Table 4A =1.1 [compression member] C i 1.0 From the illustration, the slenderness ratio about the strong axis is in (1.0)(8 ft) 12 ft Kel1 5.5 in d1 17.46 From the illustration, the slenderness ratio about the weak axis is in (1.0)(4 ft) 12 ft Kel2 d2 1.5 in 32.00 [governs] ASD Method The reference compression design value multiplied by all applicable adjustment factors except CP is given by The adjusted modulus of elasticity for stability calculations is lbf EminC M 0.69 106 Emin (0.9) in 2 6 0.62 10 lbf/in Fc* FcC DC MC F lbf 1700 (1.00)(0.8)(1.1) in 2 2 1496 lbf/in 2 The load duration factor for dead load plus occupancy live load from Table 6.5 is C D 1.00 The critical buckling design value is FcE 2 0.822Emin 2 l e 2 d2 498 lbf/in The ratio of FcE 2 to Fc* is lbf (0.822) 062 106 in 2 F 2 in (4 ft) 12 ft 1.5 in 2 FcE 2 Fc* 498 1496 lbf in 2 lbf in 2 0.333 The column parameter is obtained from NDS Sec. 3.7.1.5 as c 0.8 [for sawn lumber] The column stability factor is specified by NDS Sec. 3.7.1 as CP 1.0 F 2c 2 1.0 F F 2c c 1.0 0.333 (2)(0.8) 1.0 0.333 2 0.333 (2)(0.8) 0.8 0.31 The allowable compression design value parallel to grain is Fc FcC MC FC P lbf 1700 (0.8)(1.1)(0.31) in 2 464 lbf/in 2 Applying IBC Eq. 16-9, the factored load is P D L 1000 lbf + 1800 lbf = 2800 lbf The actual compression stress on the chord is given by fc 2800 lbf P A (1.5 in)(5.5 in) 339 lbf/in 2 Fc The chord is adequate. DESIGN OF WOOD AXIAL + BENDING Example 6.10 The select structural 2 × 6 Douglas fir-larch top chord of a truss is loaded with the service level loads shown in the illustration. The governing load combination consists of dead plus live load, and the moisture content exceeds 19%. The chord is laterally braced at midlength about the weak axis, and the self-weight of the chord and bracing members may be neglected. Determine whether the member is adequate. Solution The distance between lateral restraints is The reference design values for bending and modulus of elasticity are tabulated in NDS Supp. Table 4A, and they are Fb 1500 lbf/in 2 Emin 0.69 106 lbf/in 2 C fu 1.0, C i 1.0, C r 1.0, Ct 1.0 lu 8 ft 2 4 ft From Fig. 6.1, for a concentrated load at midspan and with lateral restraint at midspan, the effective length for flexure is le 1.11lu in (1.11)(4 ft) 12 ft 53.28 in The slenderness ratio for flexure is given by NDS Sec. 3.3.3 as RB led1 d22 (53.28 in)(5.5 in) (1.5 in)2 11.41 50 satisfies criteria of NDS Sec. 3.3.3 From Table 6.6, the applicable wet service factor for flexure is C M 0.85 From NDS Supp. Table 4A, the applicable size factor for flexure is C F 1.3 ASD Method From Table 6.5, the load duration factor for dead load plus occupancy live load is The critical buckling design value for flexure is C D 1.00 From Ex. 6.9, the adjusted modulus of elasticity for stability calculations is EminC M Emin FbE 1.20Emin 2 RB lbf (1.20) 0.62 106 in 2 (11.41)2 5715 lbf/in 2 lbf 0.69 106 (0.9) 2 in 0.62 106 lbf/in 2 The reference flexural design value multiplied by all applicable adjustment factors except CL is Fb* FbC MC F lbf 1500 (0.85)(1.3) 2 in 1657 lbf/in 2 F FbE Fb* 5715 1657 lbf The beam stability factor is given by NDS Sec. 3.3.3 as 1.0 F 2 1.0 F F CL 1.9 1.9 0.95 1.0 3.45 1.9 2 1.0 3.45 3.45 1.9 0.95 0.98 in 2 3.45 lbf in 2 The allowable flexural design value for load applied to the narrow face is Fb1 FbC MC LC F lbf 1500 (0.85)(0.98)(1.3) in 2 1626 lbf/in 2 Applying IBC Eq. 16-9, the factored vertical load is W 1.0L (1.0)(200 lbf) 200 lbf The actual edgewise bending stress is fb 1 WL 4S in (200 lbf)(8 ft) 12 ft (4)(7.56 in 3 ) 635 lbf/in 2 From Ex. 6.9, Kel1 d1 FcE 1 17.46 0.822Emin l 2 e 1 d 1 lbf (0.822) 0.62 106 2 in Fc 464 lbf/in 2 fc 339 lbf/in 2 2 (8 ft) 12 in ft 5.5 in The critical buckling design value, in the plane of bending, for load applied to the narrow face is 1672 lbf/in 2 The moment magnification factor for axial compression and flexure with load applied to the narrow face is C m 3 1.0 fc The interaction equation for bending load applied to the narrow face of the member and concentric axial compression load is given in NDS Sec. 3.9.2 as f 2 c fb 1 1.0 Fc Fb1C m 3 FcE 1 339 1.0 1672 lbf in 2 lbf in 2 0.797 The left side of the expression is 635 lbf 2 339 lbf in 2 in 2 0.535 0.490 lbf 464 lbf 1626 (0.797) 2 2 in in 1.025 1.0 The chord is adequate. DESIGN OF WOOD POST AXIAL + BENDING A short post is subject to an axial wind load and a compressive dead load, as shown. The post is made from select structural 4×10 Douglas fir-larch members (actual dimensions: 3.5 in × 9.25 in) and is fixed at the base and free at the top. The post is used such that all adjustment factors except the load duration factor and column stability factor are 1.0. Does the post satisfy the NDS interaction equations for combined axial compression and flexure? Determine the applied stresses. fc The reference design values for select structural Douglas fir-larch members are 20,000 lbf P A (3.5 in)(9.25 in) Fb 1500 lbf/ft2 Fc 1700 lbf/ft2 618 lbf/in 2 Emin 690,000 lbf/ft2 25,000 in-lbf M fb 1 S (3.5 in)(3.5 in)(9.25 in) 6 Find the effective length. The post is a cantilever from the ground, so K = 2.1 in. le Kl (2.1 in)(30 in) = 63 in 1323 lbf/in 2 Find the compressive design value of the member. The load duration factor for a dead load plus wind load loading condition is 1.60. Find the critical buckling design value. The shortest dimension of the cross section will buckle, so d = 3.5 in. Fc* FeC DC M lbf 1700 (1.60)(1.0) in 2 2720 lbf/in 2 FcE 0.822Emin l 2 e d lbf (0.822) 690,000 2 in 1751 lbf/in 2 63 in 2 3.5 in The ratio of the compressive design value and the critical buckling design value is F FcE Fc* 1751 2720 CP lbf 1.0 F 2c 1.0 F 2 F 2c c 1.0 0.644 (2)(0.8) 2 in 0.644 lbf 1.0 0.644 2 0.644 (2)(0.8) 0.8 0.526 in 2 The allowable compression design value is Find the column stability factor. Select structural Douglas fir-larch is a sawn lumber, so c = 0.8. lbf F Fc*C P 2720 (0.526) in 2 1431 lbf/in 2 Find the moment magnification factor. C m 1 1.0 fc FcE 1 618 1.0 Check the interaction equation. There is no biaxial bending, so disregard the biaxial bending ratio. f 2 c fb 1 fb 2 1.00 F Fb1C m 1 Fb2C m 2 c 2 f fb 1 c Fb1C m 1 Fc 1751 lbf in 2 0.647 lbf in 2 2 lbf 617 lbf 1323 2 in in 2 1431 lbf 1500 lbf (0.647) (1.6) in 2 in 2 1.04 [ 1.00, not acceptable] DESIGN OF WOOD CONNECTION WITH BOLTS Example 6.12 A bolted connection in tension consists of a single row of eight ¾ in diameter bolts in two select structural 2 × 6 Douglas fir-larch members in single shear. The governing load combination consists of dead plus occupancy live load, and the moisture content exceeds 19%. The bolt spacing and end distance are 4 in. Determine the capacity of the connection. Solution The ¾ in diameter bolt reference design value for single shear is tabulated in NDS Table 12A as The specified minimum end distance for the full bolt design value is specified in NDS Sec. 12.5.1 as a p 7D Z 720 lbf Ct 1.0 (7)(0.75 in) As Am 8.25 in 2 = 5.25 in The applicable adjustment factors for the bolts are as follows. C M 0.7 [wet service factor from NDS Table 11.3.3] C g 0.71 [group action factor from NDS Table 11.3.6A] C actual end distance specified minimum end distance 4 in 5.25 in 0.76 [geometry factor from NDS Sec. 12.5.1] ASD Method From Table 6.5, The allowable capacity for eight bolts is C D 1.00 From Ex. 6.11, the allowable tension capacity of the members is T FtAn 1 FtA D b 16 3 lbf 1 in (1.5 in) 1300 8.25 in 2 in 4 16 in 2 9140 lbf T nZC MC gC C DCt (8)(720 lbf)(0.7)(0.71) (0.76)(1.00)(1.0) = 2176 lbf [governs] Example 6.16 DESIGN OF WOOD SHEAR RINGS The Douglas fir-larch select structural members shown in the illustration are connected with 2 5/8 in shear plate connectors. The governing load combination consists of dead plus occupancy live loads. The connector spacing and end distances are as shown. Determine the capacity of the connection. Solution The specific gravity of Douglas fir-larch is obtained from Table 12.3.3A as G = 0.5. From NDS Table 13A, the species group is B. The reference 2 5/8 in shear plate design value for the 2½ in thick main member of group B species with a connector on two faces is tabulated in NDS Table 13.2B as Pmain 2860 lbf The reference 2 5/8 in shear plate design value for a 1½ in thick side member of group B species with a connector on one face is tabulated in NDS Table 13.2B as Pside 2670 lbf CM 1.0, Ct 1.0 As (2)(8.5 in 2 ) 16.5 in 2 Am 18.13 in As Am The specified minimum spacing for the full shear plate design value is given in NDS Table 13.3 as s 6.75 in The applicable adjustment factors for the bolts are as follows. C g group action factor from NDS Table 11.3.6B = 0.98 [governs] 0.91 C geometry factor from NDS Sec. 13.3.2.1 for a spacing of 6 in = 0.5 + 0.885 (0.5)(6 in 3.5 in) 6.75 in 3.5 in ASD Method From Table 6.5, the load duration factor is C D 1.0 The allowable design value for four shear plates is T nPsideC gC C DC MCt (4)(2670 lbf)(0.98)(0.885)(1.0)(1.0)(1.0) 9263 lbf LRFD Method From Table 6.4, the time effect factor for occupancy live load is The format conversion factor from NDS Table 11.3.1 is The strength level design value for four shear plates is T nPsideC gC C MCt KF (4)(2670 lbf)(0.98)(0.885) (1.0)(1.0)(3.32)(0.8)(0.65) 15,991 lbf The resistance factor given by NDS Table 11.3.1 is DESIGN OF WOOD NAIL CONNECTIONS Example 6.19 Determine the lateral design value for the 3 in long 10d common wire nail in the toe-nailed connection shown. Loading applied to the connection is due to wind load, and all members are Douglas firlarch. As specified in NDS Sec. 12.1.5, toe nails are driven at an angle of 30 degrees from the face of the member, with the point of penetration one-third the length of the nail from the member end. In accordance with NDS Comm. Sec. C12.1.5, the side member thickness is taken to be equal to this end distance and ts C M 1.0 Ct 1.0 Z 118 lbf L 3 in 1 in 3 3 The applicable adjustment factors for the nail are as follows. • The nominal design value for single shear is tabulated in NDS Table 12N as The penetration of the nail into the main member, in accordance with NDS Comm. Sec. C12.1.6, is taken as the vertically projected length of the nail in the member and p L cos 30 L 3 (3 in)(0.866) 1.60 in 3 in 3 • This is greater than 10D, and from NDS Table 12N, the penetration depth factor is Cd 1.0 • Ctn = toe-nail factor from NDS Sec. 12.54 Ctn 0.83 ASD Method From Table 6.5, the load duration factor is C D 1.60 The allowable lateral design value for the nail is Z ZC DCdCtnC MCt (118 lbf)(1.60)(1.0)(0.83)(1.0)(1.0) = 157 lbf LRFD Method From Table 6.4, the time effect factor for wind load is 1.0 The format conversion factor given in NDS Table 11.3.1 is KF 3.32 The resistance factor given in NDS Table 11.3.1 is 0.65 The strength level lateral design value for the nail is T ZC MCtCdCtn KF (118 lbf)(1.0)(1.0)(1.0) (0.83)(3.32)(1.0)(0.65) = 211 lbf