A10 Determine preliminary member sizes for gravity load effects.
Roof Purlins

Assume simply supported, compression flange supported by roof deck along entire length

Tributary width = spacing = 10'(3.05m)

Strength reduction factor, φ= 0.9 (AISC LRFD Section F1.2)
Loads:
Live loads:
Lr =20R1R2
ASCE 795 Eq. 42
At = (10' (18' = 180 ft. (16.7 m2)
2
)
)
R1 = 1 (At < 200 ft.2 or 18.6 m2)
R2 = 1 (Rise of roof = 4" per foot or 3.33 cm per 10 cm)
Lr = (20 psf)(1)(1) = 20 psf (958 N/m2)
Dead loads:
Finish
1.0 psf
Metal Decking
2.0 psf
1.5 psf
Ceiling / Covering 1.0 psf
Misc.
3.0 psf
8.5 psf (407 N/m2)
Total:
(8.5)(12.65/12) = 8.96 plf (429 N/m2)
Adjust for slope:
Load Combination:
1.2 D + 1.6 Lr
wu = (10' [(1.2)(8.96psf) + (1.6)(20psf)] = 428 plf (6.25 KN/m)
)
Zreq = Mu / φ y,
F
Mu = wuL /8 = (428 plf)(18' 2/8 = 17.3 kipft (23.46 KNm)
2
)
Zreq = (17.3)(12)/(0.9)(36) = 6.41 in.3 (105 cm3)
Try C8x11.5, Zx = 9.55 in.3 (156 cm3) > 6.41 in.3
Check shear;
Vu = (428 plf)(18' /2 = 3.9 kips (17.35 KN)
)
h/tw = 6.125/.22 = 27.8 < 418/(36)1/2 = 70, use AISC LRFD Eq. F21
φVn = 0.6FywAw = 0.6(36ksi)(0.22")(8.0") =38.0 kip (169 KN) > 3.9 kips (17.35KN), O.K.
v
Beams along grid line 8

Assume simply supported, compression flange supported by roof deck

Tributary width = 5'(1.53m)
Loads:
Live Loads:
Lr =20R1R2
ASCE 795 Eq. 42
2
2
At = (5' (20' = 100 ft. (9.3m )
)
)
R1 = 1 (At < 200 ft.2)
R2 = 1 (Rise of roof = 4" per foot)
Lr = (20 psf)(1)(1) = 20 psf (958 N/m2)
(10.5)(12.65/12); Same as for purlins but add 2 psf (96 N/m2) for selfweight
Dead Loads:
= 11.07 psf (530 N/m2)
Load Combination: 1.2D + 1.6Lr
wu = (5)[1.2(11.07)+1.6(20)] = 226 plf (3.30 KN/m)
2
Mu = (226)(20) /8 = 11.3 kipft (15.32 KNm)
Zreq = (11.3)(12)/(0.9)(36) = 4.2 in.3 (68.8 cm3)
Try W12x14, Zx = 17.4 in.3 (285 cm3) > 4.2 in.3 (68.8 cm3)
Check shear;
Vu = (428 plf)(18' /2 = 3.9 kips (17.3 KN)
)
h/tw = 54.3 < 418/(36)1/2 = 70, use AISC LRFD Eq. F21
H38