2. W-Shape subject to combined axial compression and flexure (braced frame).
EXAMPLE 6.2. W-Shape subject to combined axial compression and flexure (braced frame).
Given: Check the adequacy of an ASTM A992 W14×176 with L x =L y =
14.0 ft in a symmetric braced frame subject to the loading P u = 1,400 kips, M ux = 200 kip-ft, M uy = 70 kip-ft. Assume reverse-curvature bending with equal end moments about both axes and no loads along the member.
F y 2 = 50 ksi A = 51.8 in. r x = 6.43 in.
F 3 u Rev. = 65 ksi Z x = 320 in. r y = 4.02 in. 11/1/02
y = 163 in.
I x = 2,140 in. =
Solution: For a braced frame, K = 1.0 and K x L x =K y L y = 14.0 ft. From Table 4-2,
φ c P n = 1,940 kips From LRFD Specification Section H1.2,
1,400 kips φ c P n = 1,940 kips
= 0.722 > 0.2 Therefore, LRFD Specification Equation H1-1a governs.
DESIGN EXAMPLES 6–7
From LRFD Specification Equations C1-2 and C1-3:
(1 − P u / P
where in this case (a braced frame with no transverse loading),
C m = 0.6 − 0.4(M 1 / M 2 ) For reverse curvature bending and equal end moments: M 1 / M 2 = +1.0
C m = 0.6 − 0.4(1.0) = 0.2
π 2 EI P e 1 = Rev. (KL) 2 11/1/02
From Table 4-2, P
e 1x = 61,300 kip-in. × 10 / (14.0 ft × 12 in./ft)
= 21,700 kips
2 1y
e = 24,000 kip-in. × 10 /
(14.0 ft × 12 in./ft)
(1 − 1,400 kips/21,700 kips) = 0.214 ≥ 1 =1
(1 − 1,400 kips/8,500 kips) = 0.239 ≥ 1 =1
M ux = 1.0 × 200 kip-ft M uy = 1.0 × 70 kip-ft
From LRFD Specification Equation F1-4,
DESIGN TABLES 7–19
Table 7-1.
Dimensions of High-Strength Fasteners, in.
Nominal Bolt Diameter d b , in. Measurement
1 / 2 5 / 8 3 / 4 7 / 8 1 1 1 / 8 1 1 / 4 1 3 / 8 1 1 / 2 Width Across
Flats, F
A490 a Height, H
and Bolts Thread Length
A325
Grip +− > 2 1 5 / 8 1 3 / 4 1 7 / 8
Bolt Length f =
b Width Across
8 1 1 / 16 1 Nuts 1 / 4 1 7 / 16 1 5 / 8 1 13 / 16 2 2 3 / 16 2 3 / 8
Flats, W
31 / 64 39 / 64 47 / 64 55 / 64 63 / 64 1 7 / 64 1 7 / 32 1 11 / 32 1 15 / 32 Rev.
A563 Height, H
Nom. Outside
Diameter, OD
c s Diameter, ID
cular
Cir asher Thckns., Min.
W F436
T Max.
Min. Edge
1 1 3 / 1 7 / 1 5 / Distance, E d 16 16 32 32 8 32 32 16
Dimension, A
or c ,e s Mean Thckns.,
Square asher W
Taper in
Thickness F436
Rect. Min. Edge
d 7 / 16 9 / 16 21 /
Distance, E
a b Tolerances as specified in ASTM A325 and A490. c ASTM F436 Washer Tolerances, in.: Tolerances as specified in ASTM A563.
DESIGN TABLES 7–35
Table 7-13.
Design Bearing Strength at Bolt Holes for Various Edge Distances a
kips/in. thickness
Hole Edge Distance
F u , ksi
Nominal Bolt Diameter d b , in.
Type L e , in. 5 / 8 3 / 4 7 / 8 1 1 1 / 8 1 1 / 4 1 3 / 8 1 1 / 2
STD, SSLT,
SSLP, L e ≥ L OVS,
e full
LSLP LSLT
L e ≥ L e full
STD, SSLT,
Edge distance for 5 1 / 8 1 15 / 16 2 1 / 4 2 9 / 16 2 7 / 8 3 3 / 16 3 1 / 16 3 13 / 16
full bearing LSLT
11 5 5 5 5 15 Rev.
strength L b , in. OVS
2 1 / 16 2 7 / 16 2 7 / 8 3 1 / 4 3 11 / 16 4 1 / 16 4 1 / 2 4 7 / 8 LSLP = Long-Slotted Hole oriented parallel to the line of force.
LSLP
LSLT = Long-Slotted Hole oriented transverse to the line of force. OVS = Oversized Hole. SSLP = Short-Slotted Hole oriented parallel to the line of force. SSLT = Short-Slotted Hole oriented transverse to the line of force. STD = Standard Hole. –indicates edge distance is inadequate for this hole size. a
Edge distance indicated is from the center of the hole or slot to the edge of the material in the line of force. Hole deformation is b considered. When hole deformation is not a consideration, see LRFD Specification Section J3.10. Decimal value has been rounded to the nearest sixteenth of an inch.
Table 7-14.
Design Tensile Strength of Bolts, kips
DESIGN TABLES 7–37
φ = 1.0 STD
Table 7-16.
φ = 0.85 OVS & SSL
Slip-Critical Connections
φ = 0.7 LSLT
Design Resistance to Shear at Service
φ = 0.6 LSLP
Loads Using Service Loads, φR n , kips 1 (Class A Faying Surface, µ = 0.33) 2
Nominal Bolt Diameter d b , in.
ASTM Hole 5 Loading 3 / 8 / 4 7 / 8 1 1 1 / 8 1 1 / 4 1 3 / 8 1 1 / 2 Desig.
Type
Nominal Bolt Area, in. 2
A325 SSL
D 9.20 13.3 18.0 23.6 29.8 36.8 44.5 53.0
F1852 LSLT S
3.68 5.30 7.22 9.42 11.9 14.7 17.8 21.2 D 7.36 10.6 14.4 18.8 23.9 29.5 35.6 42.4
LSLP S
A490 SSL
D 11.0 15.9 21.6 28.3 35.8 44.2 53.5 63.6
LSLT S
4.60 6.63 9.02 11.8 14.9 18.4 22.3 26.5 D 9.20 13.3 18.0 23.6 29.8 36.8 44.5 53.0
LSLP S
3.99 5.74 7.82 10.2 12.9 16.0 19.3 23.0 D 7.98 11.5 15.6 20.4 25.8 31.9 38.6 45.9
STD = Standard Hole. OVS = Oversized Hole. SSL = Short-Slotted Hole. LSLP = Long-Slotted Hole parallel to line of force. LSLT = Long-Slotted Hole transverse to line of force. S = Single Shear.
D = Double Shear. 1 2 For design slip resistance using factored loads, refer to Table 7-15.
Rev. For Class B faying surfaces, multiply the tabled design resistance by 1.52.
11/1/02 For Class C faying surfaces, multiply the tabled design resistance by 1.06.
YIELDING LIMIT STATES 9–3