C-F4F4 Buckling-restrained braced frames (BRBF)

F4.2a Brace Strength

Testing of braces is considered necessary for this system to ensure proper behavior. The applicability of tests to the designed brace is defined in Section K3.

Tests cited serve another function in the design of BRBF: The maximum forces that the brace can develop in the system are determined from test results. These maximum forces are used in the analysis required in Section F4.3.

F4.2b Adjustment Factors

The compression strength adjustment factor, $\beta$, accounts for the compression overstrength with respect to tension strength noted in testing of buckling-restrained braces (SIE, 1999a, 1999b). The strain hardening adjustment factor, $\omega$, accounts for strain hardening. Figure C-F4.3 shows a diagram of the bilinear force-displacement relationship in which the compression strength adjustment factor, $\beta$, and the strainhardening adjustment factor, $\omega$, are related to brace forces and nominal material yield strength. These quantities are defined as

(C-F4-1)

(C-F4-2)

where

$A_{\mathrm{sc}} \quad=$ cross-sectional area of the yielding segment of steel core, in. ${ }^{2}\left(\mathrm{~mm}^{2}\right)$

$\begin{aligned} F_{y s c} & =\text { actual yield stress of the steel core as determined from a coupon test, } \\ & \text { ksi (MPa) }\end{aligned}$

$P_{\max }=$ maximum compression force, kips (N)

$T_{\max }=$ maximum tension force within deformations corresponding to $200 \%$ of the design earthquake displacement (these deformations are defined as $2.0 \Delta_{b m}$ in Section K3.4c), kips (N)

Note that the specified minimum yield stress of the steel core, $F_{y}$, is not typically used for establishing these factors; instead, $F_{y s c}$ is used, which is determined by the coupon tests required to demonstrate compliance with Section K3. Braces with values of $\beta$ and $\omega$ less than unity are not true buckling-restrained braces, and their use is precluded by Sections F4.2b and K3.8.

The expected brace strengths used in the design of connections and of beams and columns are adjusted upward for various sources of overstrength, including amplification due to expected material strength, using the ratio $R_{y}$, in addition to the strain hardening, $\omega$, and compression adjustment, $\beta$, factors discussed previously. The amplification due to expected material strength can be eliminated if the brace yield stress is determined by a coupon test and is used to size the steel core area to provide the desired available strength precisely. Coupon testing, where used, should be performed at the point of manufacture on each plate used for the fabrication of BRB yielding cores. The use of mill test report results is not equivalent to a coupon test. Where core plates are fabricated from bar stock, coupons should be made at intervals of, at most, each 5 tons of material of the same heat and thickness. Other sources of overstrength, such as imprecision in the provision of the steel core area, may need to be considered; fabrication tolerance for the steel core is typically negligible.

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

In SCBF, V-bracing has been characterized by a change in deformation mode after one of the braces buckles. This is primarily due to the negative post-buckling stiffness, as well as the difference between tension and compression capacity of traditional braces. Because buckling-restrained braces do not lose strength due to buckling and have only a small difference between tension and compression capacity, the practical requirements of the design provisions for this configuration are relatively minor. Figure C-F4.4 shows the effect of beam vertical displacement under the unbalanced load caused by the brace compression overstrength. The vertical beam deflection adds to the deformation demand on the braces, causing them to elongate more than they compress due to higher compression strength compared to tension strength. Therefore, where V-braced frames are used, it is required that a beam be provided that has sufficient strength to permit the yielding of both braces within a reasonable story drift, considering the difference in tension and compression capacities determined by testing. The required brace deformation capacity must include the additional deformation due to beam deflection under this load. Because other requirements, such as the brace testing protocol addressed in Section K3.4c and the stability of connections addressed in Section F4.6, depend on this deformation, engineers will find significant incentive to avoid flexible beams in this configuration. Where the special configurations shown in Figure C-F2.3 are used, the requirements of this section are not relevant.

Figure description:

Key Entities:

• Columns
• Top beam
• Inverted-V braces

Deformation Stages:

• Top Diagram: Initial undeformed state of the inverted-V braced frame.
• Middle Diagram: Lateral drift deformation where the frame undergoes horizontal sway while the top beam remains straight.
• Bottom Diagram: Post-yield deformation mode showing significant lateral drift combined with downward vertical deflection of the top beam at the brace connection point.
• Significance: Illustrates how vertical beam deflection increases total brace deformation demand due to unbalanced forces between tension and compression braces.

Fig. C-F4.4. Post-yield change in deformation mode for inverted-V BRBF.

F4.4b K-Braced Frames

K-braced frames are not permitted for BRBF due to the possibility of inelastic flexural demands on columns.

F4.4d Multi-Tiered Braced Frames

Multi-tiered braced frames (MTBF) are defined as braced frame configurations with two or more tiers of bracing between diaphragm levels or locations of out-of-plane support. These tiers each incorporate a strut or beam at each tier of bracing and are therefore not classified as K-braced frames. The strut required by these Provisions spans between frame columns, though a strut exterior to the frame can be incorporated as part of the design of the frame to resist in-plane moments from the analysis requirements.

In the multi-tiered BRBF system (MT-BRBF), in-plane column demands are imposed by varying tier capacities and unbalanced brace loads created by the difference between the BRB overstrength in tension and compression. Studies done by Imanpour et al. (2015, 2016a, 2016b) have shown BRBF frames to be the most stable of the MTBF configurations explored to date. In these studies, the MT-BRBF has not demonstrated a single-tier mechanism, but some brace overstrength variation may occur from tier to tier. If the column or other resisting framework is not sufficient to support these loads, in-plane column yielding may occur. See Commentary Section F2.4e for additional information. Although this phenomenon was studied for the SCBF and demonstrated primarily during a concentration of drift in a critical tier, the same precautions are being recommended for the BRBF as have been proposed for the SCBF to mitigate the potential column instability. The requirement for column torsional bracing at each brace connection location satisfying the requirements developed by Helwig and Yura (1999), which may be provided by the flexural stiffness of the tier strut, is necessary to provide stability to the column. Previous editions of the Provisions included a separate requirement to consider the effects of out-of-plane forces due to the mass of the structure and supported items in combination with the forces obtained from the analyses required in this section. The consideration of forces in multiple directions and from multiple sources is a design requirement for all seismic force-resisting systems (SFRS) and is not specific to MT-BRBF systems. While required for all SFRS, consideration here could be particularly critical for multi-tiered braced frame systems.

The Provisions allow for the design of MT-BRB F using similar design requirements as are used for typical BRBF frames. Adjusted brace strengths are determined for each tier and used for design of the struts and columns in the frame. Unlike the typical building case, for multi-tiered braced frames, tiers with varied capacities or the possibility of an overstrength imbalance between tiers will require the column to work in flexure. Imanpour and Tremblay (2014) found that the application of adjusted brace strengths to the MT-BRBF frame overpredicts potential bending moments in the frame columns. However, the unique case where each tier is identical and braces are inclined in the same direction results in the applied moments in the columns being zero, a condition that would be unconservative. To address this, the minimum notional load requirement of 0.5% of the adjusted brace tier strength of each tier is included in the design provisions.

With an in-plane load at each tier level, the static-equilibrium method may then be followed with the columns treated as members spanning simply supported between the base and top of the MT-BRBF frame. The resulting method of adjusted brace strengths and the 0.5% minimum notional load provides for column moments that may be incurred due to a variation in the strains in the braces, tolerances on the core cut widths, and possible small variations between the independently tested core yield strengths and the final core yield strength. However, it may not provide for column moments that may be incurred due to tier capacity differences caused by $R_{y}$ or the specification of braces using a fixed area and a range of permitted yield strengths of the core material. Although there is no evidence that this material variation is detrimental to the MT-BRBF, a factor to account for the range of expected yield strengths of the braces has been included in the Provisions. The specification of the BRB by required capacity, $P_{y s c}$, rather than by core area, $A_{s c}$, is a simple method to control the capacity of each tier such that the tier capacities are similar in a given frame, and column bending moments in the plane of the frame are reduced.

In Figure C-F4.5, “ABS” indicates unbalanced loads applied to the columns due to variation in adjusted brace strengths, and “NOT” indicates the required notional loads. Only the first and the fourth tier levels in this example have unbalanced loads due to adjusted brace strengths alone, and these loads are greater than the minimum notional load. NOT loads are applied in the direction producing the maximum moment on the column and analysis considers seismic loads in each direction.

A series of columns may be used to support the loads from this analysis. In this case, these must be designed for the portion of in-plane loads at tier levels combined with the axial compression on the column.

F4.4e Overall Stability of BRB and Connection Assemblies

Recent testing in stability and fracture has demonstrated that overall stability of the BRB and connections is a critical aspect of the design of BRBF (Tsai et al., 2003; Lopez et al., 2004; Takeuchi et al., 2014). The tendency to instability may vary depending on the initial out-of-straightness of the BRB and gusset, amplification of this out-of-straightness due to the manufacturer’s debonding gap, the flexural stiffness of the connection portions of the BRB, the degree of their flexural continuity with the casing (which is dependent on the effectiveness of the BRB neck’s development into the casing), and the stiffness of the casing itself. Note that the geometric imperfections of the external casing tube are not necessarily equal to those of the encased steel core. As destabilizing demands are primarily generated in the axially loaded steel core, geometric imperfections of the steel core are of greater interest to global stability of BRB. This aspect of BRBF design is the subject of continuing investigation, and designers are encouraged to consult Zaboli et al. (2018) and other research publications as they become available. The global stability of BRB and their gussets may be demonstrated with calculations or finite element analyses that consider the items listed in this section or by testing if the test specimen adequately resembles the conditions in the building. It is worth noting that during an earthquake, the frame may be subjected to some out-of-plane displacement concurrent with the in-plane deformations, and considering this in design may be warranted.

F4.5a Basic Requirements

The 2005 and 2010 editions of these Provisions required highly ductile sections for beams and columns. The requirement was then changed to moderately ductile sections in the 2016 edition. Because columns in BRBF are not only subjected to high axial forces but are also likely to experience inelastic rotations at the design earthquake displacement (Palmer et al., 2014), it is prudent that columns be designed for highly ductile requirements, which is reflected in the current provisions. This revision also aligns the column ductility requirements across SCBF, EBF, and BRBF.

F4.5b Diagonal Braces

1. Assembly

• (a) Steel core

The steel core is composed of a yielding segment and steel core projections; it may also contain transition segments between the projections and

Figure description:

Key Information:

• Structure: MT-BRBF (Multi-Tiered Buckling Restrained Braced Frame elevation.
• Components:
  • Braces: Labeled as BRB1 (bottom tier and BRB2 (upper four tiers.
  • Frame: Five-tier vertical steel frame with horizontal struts and diagonal bracing.
  • Supports: Fixed/pinned base supports at the bottom of the main frame.
• Force/Analysis Diagram (Right:
  • ABS: Indicates "Adjusted Brace Stiffness" or similar applied force points.
  • NOT: Indicates "Notional" force points.
  • Boundary Conditions: Pinned supports at the top and bottom of the representative vertical line.
• Lateral Loading: Indicated by a horizontal arrow at the top-left corner of the frame.

Fig. C-F4.5. MT-BRBF elevation.

yielding segment. The cross-sectional area of the yielding segment of the steel core is expected to be sized so that its yield strength is fairly close to the demand calculated from the applicable building code. Designing all braces close to the required strengths will help facilitate distribution of yielding over multiple stories in the building. Conversely, over-designing some braces more than others (e.g., by using the same size brace on all floors) may result in an undesirable concentration of inelastic deformations in only a few stories. The length and area of the yielding segment, in conjunction with the lengths and areas of the nonyielding segments, determine the stiffness of the brace. The yielding segment length and brace inclination also determines the strain demand corresponding to the design earthquake displacement.

In typical brace designs, a projection of the steel core beyond its casing is necessary in order to accomplish a connection to the frame. Buckling of this unrestrained zone is an undesirable failure mode and must therefore be precluded.

In typical practice, the designer specifies the core plate dimensions as well as the steel material and grade. The steel stress-strain characteristics may vary significantly within the range permitted by the steel specification, potentially resulting in significant brace overstrength. This overstrength must be addressed in the design of connections as well as of frame beams and columns. The designer may specify a limited range of acceptable yield stress in order to more strictly define the permissible range of brace capacity. Alternatively, the designer may specify a limited range of acceptable yield stress if this approach is followed in order to more strictly define the permissible range of core plate area and the resulting brace stiffness. The brace supplier may then select the final core plate dimensions to meet the capacity requirement using the results of a coupon test. The designer should be aware that this approach may result in a deviation from the calculated brace axial stiffness. The maximum magnitude of the deviation is dependent on the range of acceptable material yield stress. Designers following this approach should consider the possible range of stiffness in the building analysis to adequately address both the building period and expected drift.

The strength of the steel core has been defined in terms of $F_{y s c}$, which is defined as either the specified minimum yield stress of the steel core, or actual yield stress of the steel core as determined from a coupon test. The use of coupon tests in establishing $F_{y s c}$ eliminates the necessity of using $R_{y}$ in calculating the adjusted brace strength (see Commentary Section F4.2a). This is in recognition of the fact that coupon testing of the steel core material is in effect required by the similitude provisions in Section K3, and such coupon tests can provide a more reliable estimation of expected strength.

(b) Buckling-restraining system

• This term describes those elements providing brace stability against overall buckling. This includes the casing as well as elements connecting the core. The adequacy of the buckling-restraining system must be demonstrated by testing.

F4.5b.2 Available Strength

The nominal strength of buckling-restrained braces is simply based on the core area and the material yield strength. Buckling is precluded, as is demonstrated by testing.

F4.5b.3 Conformance Demonstration

BRBF designs require reference to successful tests of a similarly sized test specimen and of a brace subassemblage that includes rotational demands. The former is a uniaxial test intended to demonstrate adequate brace hysteretic behavior. The latter is intended to verify the general brace design concept and demonstrate that the rotations associated with frame deformations do not cause failure of the steel core projection, binding of the steel core to the casing, or otherwise compromise the brace hysteretic behavior. A single test may qualify as both a subassemblage and a brace test subject to the requirements of Section K3; for certain frame-type subassemblage tests, obtaining brace axial forces may prove difficult and separate brace tests may be necessary. A sample test subassemblage is shown in Figure C-K3.1 (Tremblay et al., 1999).

References to successful tests must be within the limits specified for subassemblage and brace test specimens specified in Sections K3.2 and K3.3. The intent of these limits is to help make the design and configuration of the tested specimen representative of those that will be present in the prototype and that the extrapolation range is reasonably centered on the prototype test specimen. A requirement was added in the 2022 Provisions to provide a bottom end on the downward extrapolation for small-capacity braces where their behavior may become a concern and may differ more significantly from larger capacity test specimens. This addition results in a test specimen with a steel core axial yield strength that is no more than 120% of the prototype, effectively reducing the extrapolation range for these lower-capacity prototypes. In previous versions of the Provisions, the extrapolation range for all braces was limited in a similar manner, but this restricted limitation is not deemed to be necessary except at the lower limits of tested ranges.

F4.5c Protected Zones

The core, as the expected region of inelastic strain, is a protected zone along with all elements connecting the core to the beams and columns, which may include gusset plates and gusset connections.

F4.6a Demand Critical Welds

Inelastic strain in the weld material is likely at column base plates and column splices. Thus, these are required to be treated as demand critical welds. See Commentary Section F2.6a.

F4.6b Beam-to-Column Connections

See Commentary Section F2.6b.

F4.6c Diagonal Brace Connections

Bracing connections must not yield at force levels corresponding to the yielding of the steel core; they are therefore designed for the maximum force that can be expected from the brace (see Commentary Section F4.5b). The engineer should recognize that the bolts are likely to slip at forces 30% lower than their available strength. This slippage is not considered to be detrimental to behavior of the BRBF system and is consistent with the design approach found in Section D2.2.

Fahnestock et al. (2006) tested a connection, shown in Figure C-F4.6, that effectively provided a pin in the beam outside of the gusset plate via the splice with a WT section on each side. In addition to satisfying the requirements of Section F4.6b, this connection relieves the gusset plate of in-plane moments and the related destabilization effects.

Refer to Commentary Section F4.4e for discussion of the combined stability require- ment of the gusset plate and the BRB, as well as the interaction between these two elements.

F4.6d Column Splices

See Commentary Section F2.6d.