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0.9^Es / Fy aFor hybrid beams, use the yield strength of the flange Fyt instead of Fy. bRequired for beams in SMF, Section 9.

"Required for columns in SMF, Section 9, unless the ratios from Eq. (9.3) are greater than 2.0

where it is permitted to use 1p in LRFD Specification Table B5.1 dRequired for beams and braces in SCBF, Section 13.

eIt is permitted to use 1p in LRFD Specification Table B5.1 for columns in STMF, Section 12 and

EBF, Section 15. fRequired for link in EBF, Section 15.

gDiagonal web members within the special segment of STMF, Section 12. hChord members of STMF, Section 12. (From AISC 341-02 Table I-8-1.)

Figure 3.41. Special concentric brace frame (SCBF) example.

• Width-thickness ratios of columns shall meet the requirements specified for bracing members of an SCBF.

• Column splices must develop

1. At least the nominal shear strength of the smaller column.

2. At least 50% of the nominal flexural strength of the smaller column.

Design Example

Given. A three-story, two-bay SCBF shown in Fig. 3.41. It is part of a building frame system of a structure in seismic design category (SDC) D with a redundancy coefficient p = 1.20. The building is on a site with a short period mapped acceleration response SDS = 0.90. The axial loads acting on the second story brace B2 are

Dead load D = 40 kips Live load L = 12 kips Snow load S = 0 kips Hydrostatic load H = 0 kips Seismic force QE = ±90 kips

Required. Select an appropriate tube section for the second-floor brace B2. Use ASTM A 500, Grade B, Fy = 42 ksi, Fu (minimum tensile stress) = 58 ksi, steel. Solution. The factored compression load Puc in the brace is

= 1.2 x 40 + 0.5 x 12 + 0 + 1.2 x 90 + 0.2 x 0.9 x 40 = 169.2 kips, compression ^ governs.

The factored tensile load Put on the brace is

= 0.9 x 40 + 0 - 1.2 x 90 - 0.2 x 0.9 x 40 = -144 kips, tension

The unbraced length of the brace, using centerline dimensions, is l = H/sin e = H/sin 43° = 21.9 ft, use 22 ft

The effective length factor for the brace, assuming hinged ends, is given by LRFD Table C-C2.1, item (d), as

The effective length of the brace is Kl = 1 x 22 = 22 ft

From LRFD Table 4.7, select a round HSS 8.625 x 0.322 in. with a design strength in axial compression of 171 kips for an effective length of 22 feet.

The section properties of an HSS 8.625 x 0.332 in. are given in LRFD Table 1.13 as

t = 0.3 in. (Note: Design thickness = 0.93 x nominal wall thickness) D = 8.625 in.

The diameter-to-thickness ratio of a hollow section is limited by Table 3.2 to a maximum value of

The actual diameter-to-thickness ratio is

AISC-Seismic requires bracing members in a chevron configuration to be designed with a slenderness ratio net exceeding l/r = 1000/( Fy )0

The actual slenderness ratio is l/r = (22 x 12)/2.95 = 89.5

Hence, an HSS 8.625 x 0.332-in. brace satisfies all bracing requirements.

Figure 3.42. Built-up brace detail for use in an SCBF. (Courtesy of Louis Choi, S.E., John A. Martin & Assoc. Structural Engineers, Los Angeles, CA.)

In some practical applications, the ratio D/t of available hollow sections for a given load may not be able to satisfy the design criteria. In such cases, doubling of hollow structural sections, HSS, as shown in Fig. 3.42, may provide the required section properties. Figures 3.43 through 3.50 show some typical details for braced frames.

Figure 3.43. Braced frame with story-high chevron inverted-V braces. (Courtesy of Louis Choi, S.E., John A. Martin & Assoc. Structural Engineers, Los Angeles, CA.)
Figure 3.44. Schematic elevation of an OCBF showing gusset plates. (Courtesy of Louis Choi, S.E., John A. Martin & Associates Structural Engineers, Los Angeles, CA.)

Typical procedure for connection design is to use the Uniform Force Method (UFM, AISC, LRFD, Vol. II). The gusset dimensions are configured such that there are no moments at the connection interfaces: gusset-to-column and gusset-to-beam. Then, the plate and connection capacities are calculated and compared with the required capacities.

The gusset plate is designed to carry the compressive strength of the brace without buckling. Using the Whitmore method (UFM, AISC, LRFD, Vol. II), the effective plate width Ww at the critical section is calculated. The unsupported plate length Lu is taken as centerline length from the end of the brace to the edge of beam or column. An effective length factor, K, representative of the plate boundary conditions, is used to calculate KLu/r.

Figure 3.45. Schematic elevation of an SCBF showing imaginary yield lines in gusset plates. Also shown are the gusset plates for an OCBF. Observe the substantial increase in gusset plate sizes required for the SCBF. (Courtesy of Louis Choi, S.E., John A. Martin & Assoc. Structural Engineers, Los Angeles, CA.)

Figure 3.45. Schematic elevation of an SCBF showing imaginary yield lines in gusset plates. Also shown are the gusset plates for an OCBF. Observe the substantial increase in gusset plate sizes required for the SCBF. (Courtesy of Louis Choi, S.E., John A. Martin & Assoc. Structural Engineers, Los Angeles, CA.)

Figure 3.46. An SCBF connection detail at column. (Courtesy of Louis Choi, S.E., John A. Martin & Associates Structural Engineers, Los Angeles, CA.)

Figure 3.46. An SCBF connection detail at column. (Courtesy of Louis Choi, S.E., John A. Martin & Associates Structural Engineers, Los Angeles, CA.)

Based on the yield strength Fy of the plate, the allowable axial stress Fa is obtained from AISC tables. The axial capacity is calculated as

Pplate = 1.7 X t X Ww X Fa and compared with the lesser of

The strength of the brace in axial tension, Pst.

• The maximum force that can be transferred to the brace by the system.

Figure 3.47. Typical bracing-to-column connection, SCBF.

Notes: 1. Yield line intersects free edge of gusset plate and not beam flange.

2. Whitmore effective width Ww = tube width + 2lw (tan 30).

3. Welding of beam flanges is for resisting drag forces.

(Courtesy of Louis Choi, S.E., John A. Martin & Associates Structural Engineers, Los Angeles, CA.)

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