F4Buckling-restrained braced frames (BRBF)

F4.2a Brace Strength

The adjusted brace strength shall be established on the basis of testing as described in this section.

Where required by these Provisions, brace connections and adjoining members shall be designed to resist forces calculated based on the adjusted brace strength.

The adjusted brace strength in compression shall be $\beta \omega R_{y} P_{y s c}$,

where

$P_{y s c}=$ axial yield strength of steel core, ksi (MPa)

$\begin{aligned} R_{y} & =\text { ratio of the expected yield stress to the specified minimum yield stress of } \\ & \text { steel core, } F_{y}\end{aligned}$

• $\beta \quad$ = compression strength adjustment factor
• $\omega \quad$ = strain-hardening adjustment factor

The adjusted brace strength in tension shall be $\omega R_{y} P_{y s c}$.

Exception: The factor $R_{y}$ need not be applied if $P_{y s c}$ is established using the yield stress determined from a coupon test.

F4.2b Adjustment Factors

Adjustment factors shall be determined as follows:

The compression strength adjustment factor, β, shall be calculated as the ratio of the maximum compression force to the maximum tension force of the test specimen measured from the qualification tests specified in Section F4.5b at strains corresponding to the expected deformations. The larger value of β from the two required brace qualification tests shall be used. In no case shall β be taken as less than 1.0.

The strain-hardening adjustment factor, $\omega$, shall be calculated as the ratio of the maximum tension force measured from the qualification tests specified in Section F4.5b at strains corresponding to the expected deformations to the measured yield force, $P_{y s c}$, of the test specimen. The larger value of $\omega$ from the two required qualification tests shall be used. Where the tested steel core material of the subassemblage test specimen required in Section K3.2 does not match that of the prototype, $\omega$ shall be based on coupon testing of the prototype material.

F4.2c Brace Deformations

The expected brace deformation shall be determined as specified in Section F4.2. Alternatively, the brace expected deformation is permitted to be determined from nonlinear analysis as defined in Section C3.

F4.4a V- and Inverted V-Braced Frames

V- and inverted V-braced frames shall satisfy the following requirements:

• (a) The required strength of beams and struts intersected by braces, their connections, and supporting members shall be determined based on the load combinations of the applicable building code assuming that the braces provide no support for dead and live loads. For load combinations that include earthquake effects, the vertical and horizontal seismic load effect, E, on the beam shall be determined from the adjusted brace strengths in tension and compression.
• (b) Beams and struts shall be continuous between columns. Beams and struts shall be braced to meet the requirements for moderately ductile members in Section D1.2a.1.

As a minimum, one set of lateral braces is required at the point of intersection of the V- or inverted V-braces, unless the beam or strut has sufficient out-of-plane strength and stiffness to ensure stability between adjacent brace points.

User Note: The beam has sufficient out-of-plane strength and stiffness if the beam bent in the horizontal plane meets the required strength and stiffness for column point bracing as prescribed in the Specification. $P_{r}$ may be taken as the adjusted brace strength in compression of the BRBF brace.

F4.4b K-Braced Frames

K-braced frames shall not be used for BRBF.

F4.4c Lateral Force Distribution

Where the compression strength adjustment factor, β, as determined in Section F4.2b, exceeds 1.3, the lateral force distribution shall comply with the following:

Along any line of braces, braces shall be deployed in alternate directions such that, for either direction of force parallel to the braces, at least 30%, but no more than 70%, of the total horizontal force along that line is resisted by braces in tension, unless the available strength of each brace is larger than the required strength resulting from the overstrength seismic load. For the purposes of this provision, a line of braces is defined as a single line or parallel lines with a plan offset of 10% or less of the building dimension perpendicular to the line of braces.

F4.4d Multi-Tiered Braced Frames

A buckling-restrained braced frame is permitted to be configured as a multi-tiered buckling-restrained braced frame (MT-BRBF) when the following requirements are satisfied.

• (a) Struts shall be provided at every brace-to-column connection location.
• (b) Columns shall meet the following requirements.
• (1) Columns of multi-tiered braced frames shall be designed as simply supported for the height of the frame between points of out-of-plane support and shall satisfy the greater of the following in-plane load requirements at each tier:
• (i) Loads induced by the summation of frame shears from adjusted brace strengths between adjacent tiers from the Section F4.3 analysis. The analysis shall consider variation in the permitted core strength.

User Note: Specifying the buckling-restrained brace (BRB) using the desired brace capacity, $P_{y s c}$, rather than a desired core area is recommended for the MT-BRBF to reduce the effect of material variability and allow for the design of equal or nearly equal tier capacities.

• (ii) A minimum notional load equal to 0.5% times the larger of the frame shear strengths of adjacent tiers as determined using adjusted brace strengths. The notional load shall be applied to create the greatest load effect on the column.
• (2) Columns shall be torsionally braced at every strut-to-column connection location.

User Note: The requirements for torsional bracing are typically satisfied by connecting the strut to the column to restrain torsional movement of the column. The strut must have adequate flexural strength and stiffness and have an appropriate connection to the column to perform this function.

• (c) Each tier in a multi-tiered braced frame shall be subject to the drift limitations of the applicable building code, but the drift shall not exceed 2% of the tier height.

F4.4e Overall Stability of BRB and Connection Assemblies

The design of a buckling-restrained brace (BRB) and its connections shall include consideration of combined buckling modes that include imperfections and flexibility of the gusset plate, casing, and other elements that significantly affect stability. At a minimum, the following shall be considered:

• (a) Initial imperfections in the brace and gusset plates
• (b) Flexibility of the core extension
• (c) Flexibility of the BRB core and casing interconnection
• (d) Casing flexibility

User Note: Global stability of the BRB and connections can be demonstrated through calculations or through testing that is representative of the project connection.

F4.5a Basic Requirements

Columns shall satisfy the requirements of Section D1.1 for highly ductile members. Beams shall satisfy the requirements of Section D1.1 for moderately ductile members.

F4.5b Diagonal Braces

F4.5b.1 Assembly

Braces shall be composed of a structural steel core and a system that restrains the steel core from buckling.

• (a) Steel core

Plates used in the steel core that are 2 in. (50 mm) thick or greater shall satisfy the minimum notch toughness requirements of Section A3.3.

Splices in the steel core are not permitted.

• (b) Buckling-restraining system

The buckling-restraining system shall consist of the casing for the steel core. In stability calculations, beams, columns, and gussets connecting the core shall be considered parts of this system.

The buckling-restraining system shall limit local and overall buckling of the steel core for the expected deformations.

F4.5b.2 Available Strength

The steel core shall be designed to resist the entire axial force in the brace.

The brace design axial strength, $\phi P_{y s c}$ (LRFD), and the brace allowable axial strength, $P_{y s c} / \Omega$ (ASD), in tension and compression, in accordance with the limit state of yielding, shall be determined as follows:

$P_{y s c}=F_{y s c} A_{s c}$

(F4-1)

$\phi=0.90$ (LRFD) $\quad \Omega=1.67$ (ASD)

where

$\begin{aligned} A_{s c} & =\text { cross-sectional area of the yielding segment of the steel core, in. }^{2} \\ & \left(\mathrm{mm}^{2}\right)\end{aligned}$

$F_{y s c}=$ specified minimum yield stress of the steel core, or actual yield stress of the steel core as determined from a coupon test, ksi (MPa)

F4.5b.3 Conformance Demonstration

The design of braces shall be based upon results from qualifying cyclic tests in accordance with the procedures and acceptance criteria of Section K3. Qualifying test results shall consist of at least two successful cyclic tests: One is required to be a test of a brace subassemblage that includes brace connection rotational demands complying with Section K3.2, and the other shall be either a uniaxial or a subassemblage test complying with Section K3.3. If the prototype has a lower axial yield strength, $P_{y s c}$, than all qualifying tests that meet the requirements of Section K3, the similarity limits specified in Section K3.3c(b) shall be restricted such that the axial yield strength of the steel core of the test specimen is no more than $120 \%$ of the prototype. Both test types shall be based upon one of the following:

(a) Tests reported in research or documented tests performed for other projects

(b) Tests that are conducted specifically for the project

Interpolation or extrapolation of test results for different member sizes shall be justified by rational analysis that demonstrates stress distributions and magnitudes of internal strains consistent with or less severe than the tested assemblies. In addition, the rational analysis shall address the adverse effects of variations in material properties. Extrapolation of test results shall be based upon similar combinations of steel core and buckling-restraining system sizes. Tests are permitted to qualify a design when the provisions of Section K3 are met.

F4.5c Protected Zones

The protected zone shall include the steel core of braces and elements that connect the steel core to beams and columns and shall satisfy the requirements of Section D1.3.

F4.6a Demand Critical Welds

The following welds are demand critical welds and shall satisfy the requirements of Sections A3.4b and I2.3:

• (a) Groove welds at column splices
• (b) Welds at the column-to-base plate connections

Exception: Welds need not be considered demand critical when both of the fol- lowing conditions are satisfied.

• (1) Column hinging at, or near, the base plate is precluded by conditions of restraint.
• (2) There is no net tension under load combinations including the overstrength seismic load.
• (c) Welds at beam-to-column connections conforming to Section F4.6b(c)

F4.6b Beam-to-Column Connections

Where a brace or gusset plate connects to both members at a beam-to-column connection, the connection shall satisfy one of the following requirements:

• (a) The connection assembly shall be a simple connection meeting the require- ments of Specification Section B3.4a, where the required rotation is taken to be 0.025 rad.
• (b) The connection assembly shall be designed to resist a moment equal to the lesser of the following:
• (1) A moment corresponding to the expected beam flexural strength, $R_{y} M_{p}$, multiplied by 1.1 and divided by $\alpha_{s}$, where

$M_{p}=$ plastic moment, kip-in. (N-mm)

• (2) A moment corresponding to the sum of the expected column flexural strengths, $\Sigma\left(R_{y} F_{y} Z\right)$, multiplied by 1.1 and divided by $\alpha_{s}$, where
• $Z=$ plastic section modulus about the axis of bending, in. ${ }^{3}\left(\mathrm{~mm}^{3}\right)$
• $\begin{aligned} \alpha_{s} & =\text { LRFD-ASD force level adjustment factor }=1.0 \text { for LRFD and } 1.5 \\ & \text { for ASD }\end{aligned}$

This moment shall be considered in combination with the required strength of the brace connection and beam connection, including the diaphragm collector forces determined using the overstrength seismic load.

• (c) The beam-to-column connection shall meet the requirements of Section E1.6b(c).

F4.6c Diagonal Brace Connections

F4.6c.1 Required Strength

The required strength of brace connections in tension and compression (including beam-to-column connections if part of the BRBF system) shall be the adjusted brace strength divided by $\alpha_{s}$, where the adjusted brace strength is as defined in Section F4.2a.

When oversized holes are used, the required strength for the limit state of bolt slip need not exceed $P_{y s c} / \alpha_{s}$.

F4.6c.2 Gusset Plate Requirements

Lateral bracing of gusset plates consistent with that used in the tests upon which the design is based shall be provided.

User Note: This provision may be met by designing the gusset plate for a transverse force consistent with transverse bracing forces determined from testing, by adding a stiffener to it to resist this force, or by providing a brace to the gusset plate. Where the supporting tests did not include transverse bracing, no such bracing is required. Any attachment of bracing to the steel core must be included in the qualification testing.

F4.6d Column Splices

Column splices shall comply with the requirements of Section D2.5. Where groove welds are used to make the splice, they shall be complete-joint-penetration groove welds. Column splices shall be designed to develop at least 50% of the lesser plastic moment of the connected members, $M_{p}$, divided by $\alpha_{s}$.

The required shear strength, $V_{r}$, shall be determined as follows:

(F4-2)

where

• $H_{c}$ = clear height of the column between beam connections, including a structural slab, if present, in. (mm)

$\Sigma M_{p}=$ sum of the plastic moments, $F_{y} Z$, at the top and bottom ends of the column, kip-in. (N-mm)