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