## T

Zipper column bracing

Figure 3.40a. Braced frame configurations.

• In detailing the SCBF's gusset plate, the potential restraint that occurs due to the floor slab must be considered. To keep the gusset plate as small as possible, it may be isolated from the slab to allow the yield line to extend below the concrete surface. Note that the entire gusset plate does not have to be isolated, just the area where the yield line occurs. A compressible material 2- to 3-in. thick on each side may be used to isolate the plate, as shown in Fig. 3.40b.

• Beams or columns of braced frames should not be interrupted at the brace intersections. This is to ensure out-of-plane stability of the bracing system at those locations. However, mere continuity of columns or beams at the brace intersections may not be sufficient to provide the required stability. Typical practice is to provide perpendicular framing that engages a diaphragm to provide out-of-plane strength and stiffness, and resistance to lateral torsional buckling of beams.

• SCBFs are expected to achieve trilinear hysteretic behavior in a large earthquake by going through three ranges of displacement of its brace: the elastic range, the postbuckling range, and the tensile yielding range.

• Basic design concept for an OCBF is to limit its response to an elastic behavior. Therefore, a higher seismic force (using a lower value of R = 5 versus R = 6 for an SCBF) and lower brace capacity are used in the design. Increase in capacity is achieved by limiting Kl/r < 720/^Fy versus 1000/^F for an SCBF.

• Compactness requirements for braces are the same for OCBFs and SCBFs.

• Basic design concept for an SCBF is to mitigate brittle modes of failure by controlling its behavior through better detailing. Therefore, connections are designed to develop yield capacity of brace.

• In a chevron-configured SCBF, instead of increasing earthquake load by 1.5, the beam is designed for unbalanced load requirements by assuming one brace at the beam intersection fails in compression. This is not a design requirement for an OCBF.

• Special requirements apply to the design of chevron-braced frames. Because braces meet at the midspan of beams, the vertical force resulting from the unequal compression and tension strengths of these braces can have a considerable impact on the cyclic behavior of the frame. That vertical force introduces flexure in the beam, and possibly a plastic hinge, producing a plastic collapse mechanism. Therefore, beams in chevron-braced frames must be continuous between columns.

• Seismic provisions require that beams in chevron-braced frames be capable of resisting their tributary gravity loads, neglecting the presence of the braces, and that each beam in an SCBF be designed to resist a maximum unbalanced vertical load calculated using full-yield strength or the brace in tension, and 30% of the brace buckling strength in compression. In an OCBF, this latter provision need not be considered. However, braces in the OCBF must be designed to have 1.5 times the strength required by load combinations that include seismic forces, which is equivalent to designing chevron-braced frames for a smaller value of R to compensate for their lower ductility. To prevent instability of a beam bottom flange at the intersection of the braces in a chevron-braced frame, the top and bottom flanges of beams in both SCBF and OCBF must be designed to resist a lateral force equal to 2% of the nominal beam flange strength (i.e., 0.02AfFy). This requirement is best met by the addition of a beam perpendicular to the chevron-braced frame. The preceding concepts explain why a K-type braced frame configuration is prohibited in high seismic regions. The unequal buckling and tension-yielding strengths of the braces would create an unbalanced horizontal load at the midheight of the columns, jeopardizing the ability of the column to carry gravity loads if a plastic hinge forms at the midheight of the column. Concentrically braced frames are expected to undergo inelastic response during large earthquakes. Specially designed diagonal braces in these frames can sustain plastic deformations and dissipate hysteretic energy in a stable manner through successive cycles of buckling in compression and yielding in tension. The preferred design strategy is, therefore, to ensure that plastic deformations only occur in the braces, leaving the columns, beams, and connections undamaged, thus allowing the structure to survive strong earthquakes without losing gravity-load resistance.

The plastic hinge that forms at midspan of a buckled brace may develop large plastic rotations that could lead to local buckling and rapid loss of compressive capacity and energy dissipation characteristic during repeated cycles of inelastic deformations. Locally buckled braces can also suffer low-cycle fatigue and fracture after a few cycles of severe inelastic deformations, especially when braces are cold-formed rectangular hollow sections. For these reasons, braces in SCBFs must satisfy the width-to-thickness ratio limits for compact sections. For OCBFs, braces can be compact or noncompact, but not slender. In particular, the width-to-thickness ratio of angles (b/t), the outside-diameter-to-wall-thickness ratio of unstiffened circular hollow sections (D/t), and the outside-width-to-wall-thickness ratio of unstiffened rectangular sections must not exceed 52/^Fy, 1300/ JFy, and 110/^F", respectively. Note that the AISC- Seismic provisions define b for rectangular hollow sections as the "out-to-out width," not the flat-width equal to b - 3t, as defined in the AISC Allowable Stress Design Specifications (AISC 1989).

When a brace is in tension, net section fracture and block shear rupture at the end of the brace must be avoided. Likewise, the brace connections to beams and columns must be stronger than the braces themselves. Using capacity design, calculation of brace strength must recognize that the expected yield strength of the brace, Fye, will typically exceed its specified minimum yield strength, Fy. Thus, connections must be designed to resist an axial force equal to RyFyAg , where Ry is the ratio of expected yield strength to specified yield strength Fy. See Table 3.1. Connections must also be able to resist the forces due to buckling of the brace. If strong connections permit the development of a plastic hinge at each end of a brace, they should be designed to resist a moment equal to 1.1RyMp of the brace in the direction of buckling. Otherwise, the connecting elements will themselves yield in flexure (such as gussets out of their plane); these must then be designed to resist the maximum brace compression force in a stable manner while undergoing the large plastic rotations that result from brace buckling. Providing a clear distance of twice the plate thickness between the end of the brace and the assumed line of restraint for the gusset plate permits plastic rotations and precludes plate buckling.

• Beams and columns in braced frames must be designed to remain elastic when braces have reached their maximum tension or compression capacity (1.LR, times the nominal strength) to preclude inelastic response in all components except the braces. This requirement could be too severe for columns of a multistory frame because the braces along the height of the frame do not necessarily reach their capacity simultaneously during an earthquake. AISC-Seismic provisions address this issue using special load conditions with the further specification that the maximum axial tension forces in columns need not be taken larger than the value corresponding to foundation uplift. For SCBFs, the provisions also require that columns satisfy the same width-to-thickness ratio limits as braces.

• Partial penetration groove welds in column splices have been observed to fail in a brittle manner. When a welded column splice is expected to be in tension under the loading combination, the AISC-Seismic provisions mandate that the partial joint penetration groove welded joints in SCBFs be designed to resist 200% of the strength required by elastic analysis using code-specified forces. Column splices also need to be designed to develop at least the nominal shear strength of the smaller connected member and 50% of the nominal flexural strength of the smaller connected section.

3.11.1.1. Ordinary Concentric Braced Frame (OCBF)

ASCE 7-02, Seismic Coefficients

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