BUCKLING RESTRAINED BRACE WITH LIGHTWEIGHT CONSTRUCTION

Abstract

A buckling restrained brace comprises a core member, core restrainer member sections and a jacket member. The core member has two opposite ends. The core restrainer member sections are configured to be arranged around the core member. The jacket member comprises fiber reinforced polymers configured to be wrapped around the core restrainer member sections and core member to couple the core restrainer member sections to the core member such that the core restrainer member sections and jacket member cooperate to provide greater resistance to buckling of the core member when the brace is subjected to compression. In some implementations, the brace has a weight less than about 50% of a weight of a conventional buckling restrained brace of similar length and having a steel core and mortar-filled tubular core restrainer member of comparable cross-sectional areas, respectively.

Description

CROSS-REFERENCE TO RELATED APPLICATION

The present application claims the benefit of U.S. Provisional Application No. 61/584,066, filed Jan. 6, 2012, which is incorporated herein by reference.

ACKNOWLEDGMENT OF GOVERNMENT SUPPORT

This invention was made with government support under DTRT06-G-0017 awarded by the Department of Transportation. The government has certain rights in the invention.

BACKGROUND

A buckling-restrained brace (BRB) is a structural element designed to withstand cyclic loading in the form of repeated tensile and compressive forces such as from an earthquake or an explosive blast. BRBs add reinforcement and energy dissipation to steel frame buildings to protect them from large deformations by yielding in tension and compression, while at the same time resisting failure due to buckling.

Conventional BRBs have a steel core member and a surrounding tubular member filled with mortar that is designed to resist buckling of the core member when the core member is subjected to compression loading. Although conventional BRBs are adequate in some situations, it would be desirable to provide BRBs having the same energy dissipating performance while having a lower overall weight, which among other advantages makes handling and installation easier.

SUMMARY

Described below are embodiments of a buckling restrained brace having a light-weight construction.

In an exemplary embodiment, a buckling restrained brace comprises a core member, core restrainer member sections, and a jacket member. The core member has two opposite ends. The core restrainer member sections are configured to be arranged around the core member. The jacket member comprises fiber reinforced polymers configured to be wrapped around the core restrainer member sections and core member to couple the core restrainer member sections to the core member. The core restrainer member sections and jacket member cooperate to provide greater resistance to buckling of the core member when the brace is subjected to compression.

The brace can have a weight less than 50% of a weight of a conventional buckling restrained brace of similar length and having a steel core and mortar-filled tubular core restrainer member of comparable cross-sectional areas, respectively.

The core member can have a cross section defining at least one pair of opposed spaces configured to receive a respective number of core restrainer member sections. The core member can have a T-shaped cross section defining two opposed spaces, wherein each of the two spaces is configured to receive one of the core restrainer sections. The core member can be comprised of two-angled sub-members defining a T-shape when positioned adjacent each other. The core member can have a cross-section defining at least four separated spaces, wherein each of the spaces is configured to receive one of the core restrainer sections. The core member can be comprised of four angled sub-members, and the angled sub-members can be arranged such that the vertices thereof are adjacent but spaced apart from each other in a cross section of the core member.

The core member can be comprised of two T-shaped sub-members arranged opposite to each other. The core restrainer members can be tubular and have a rectangular cross section or a circular cross section, and are sometimes referred to herein as “tubes”.

The jacket member can be sized to extend over an intermediate portion of the core member between the two opposite ends.

The core member can be formed of a ductile material, such as an aluminum alloy. The core member can comprise at least two core member sections and at least one spacer member positioned between the core member sections. The spacer member can be formed of a plastic material or fiber reinforced polymers.

The jacket member can comprise at least one layer of material applied at different angles relative to the core member. In some implementations, two or more layers are used. The jacket member can comprise at least one layer of material applied at an angle of about 30 degrees relative to an axis of the core member. The core member can be configured to dissipate seismic energy through substantially reversible cyclic plastic strain. The core member, core restrainer member sections, and jacket member can be constructed of materials selected to reduce corrosion from exposure to environmental conditions.

The core member, core restrainer sections, and jacket member are configured to allow the core and the core restrainer sections to translate relative to each other under pre-defined loading conditions imposed on the brace.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1(a) is a perspective view of an implementation of a buckling restrained brace having a light weight construction with an intermediate portion of the brace cut away to show the relative positions of various components.

FIG. 1(b) is an enlarged perspective view of a portion of the brace of FIG. 1(a).

FIGS. 1(c), 1(d), 1(e) and 1(f) are end elevation views of representative braces having different core member and core restrainer member configurations.

FIG. 1(g) is a perspective view similar to FIG. 1(a) of another implementation of a buckling restrained brace.

FIG. 1(h) is an enlarged perspective view of a portion of the brace of FIG. 1(g).

FIGS. 2(a) and 2(b) are side elevation views of a representative brace identifying various dimensions used in modeling.

FIG. 2(c) is an end view of the brace of FIGS. 2(a) and 2(b) showing bolted connections to gusset plates.

FIG. 3(a) is a set of diagrams showing a single degree of freedom mechanical model for modeling the brace.

FIG. 3(b) is a drawing showing another model of the brace.

FIG. 4 is a scatter plot of required restrainer stiffness vs. restrainer length providing a comparison between analytical and numerical results.

FIG. 5(a) is a drawing showing dimensions for two test coupons.

FIG. 5(b) is a perspective view showing a test apparatus for subjecting a test coupon to a predetermined loading.

FIG. 6 is a graph of stress versus axial strain showing the brace's response to predetermined loading.

FIG. 7 is a graph showing maximum cyclic stress versus a number of reversals for the brace of FIG. 6.

FIG. 8(a) is a graph of normalized stress versus axial strain based on testing of another representative coupon.

FIG. 8(b) is a side elevation view of the representative coupon tested in FIG. 8(a).

FIG. 9(a) is a perspective view of a core member showing how it is modeled using finite element analysis.

FIG. 9(b) is a graph of axial load versus axial displacement for the model of FIG. 9(a).

FIG. 10(a) is a cross section of a core member at an intermediate point showing various dimensions used in modeling brace end moments.

FIG. 10(b) is a diagram illustrating end moments or rotations that the brace of FIG. 10(a) may experience during severe seismic loading.

FIGS. 11(a) through 11(f) show axial load versus log-displacement relationships for six groups of simulations.

FIG. 11(g) is a graph of the required restrainer stiffness versus the end moment ratio for two groups of braces.

FIG. 12(a) is a perspective view of a brace showing yielding prior to buckling.

FIG. 12(b) is a perspective view of the brace of FIG. 12(a) showing its deformed shape after buckling.

FIG. 12(c) is an enlarged view of a portion of the brace of FIGS. 12(a) and 12(b) that has been subjected to buckling showing that a plastic hinge is created in the area of junction between its full section and its intermediate section.

FIGS. 13(a) and FIG. 13(b) are graphs of axial load versus axial displacement for one prototype.

FIGS. 13(c) and FIG. 13(d) are graphs of axial load versus axial strain at mid-length for the prototype of FIGS. 13(a) and 13(b).

FIG. 13(e) is a plot of normalized cumulative-displacement versus restrainer stiffness for the prototype of FIGS. 13(a) and 13(b).

DETAILED DESCRIPTION

Small to medium size concrete or steel buildings constructed according to deficient legacy codes constitute a large portion of today's backlog of structures requiring seismic retrofit. A number of retrofit solutions are available to address these deficient structures. However, many solutions impose great difficulties for material handling and installation of traditional lateral elements such as shear walls or conventional steel braces due to limited access for heavy lifting equipment such as cranes and forklifts Therefore, an ultra-lightweight lateral bracing system is desired that allows for easy manual transport, lifting, erection, and connection of required components to the existing structure without deconstruction of exterior walls for access. By minimizing disruption to building occupants, the building may remain partially viable during construction resulting in decreased cost and thus increasing the feasibility of elective upgrades. Described herein is a new BRB, having an aluminum core member for seismic force dissipation, and fiber reinforced polymers (FRP) arranged to couple tubular core restrainer sections to the core, thus accomplishing the goals of decreased installation weight, increased system compactness and efficient energy dissipation.

Attempts to refine metallic seismic dissipaters originally proposed by Skinner et al. (1975) have recently strayed from the traditional steel core and mortar-filled steel tube restrainer BRBs developed throughout the 1980s and 1990s (Watanabe et al. 1988; Wada et al. 1989; Watanabe and Nakamura 1992; Black et al. 2002; Black et al. 2004). Many variations have been presented (Xie 2005), but those termed “lightweight” and constructed of bolted or welded all-steel components for both the core and restrainer are the most numerous (Mazzolani et al. 2004; Tremblay et al. 2006; Usami et al. 2008; D'Aniello et al. 2008; D'Aniello et al. 2009; Chao and Chen 2009; Ju et al. 2009; Mazzolani et al. 2009). Competing concepts have been characterized as beneficial due to decreased installation cost, having replaceable cores, ability to use low-skilled labor for installation, compact for installation confined spaces, and use in existing building retrofits.

Aluminum as an industrial material has been around for more than a century but its incorporation into the primary structural elements of buildings has been relatively slow with uses limited to secondary systems such as curtain walls and auxiliary structures such as awnings, canopies or similar structures. However, attempts to utilize its high ductility and absence of cyclic hardening in seismic force dissipating systems have begun to appear. Shape memory braces constructed with super-elastic aluminum alloys that allow a structure to re-center after a seismic event with little permanent deformation (Mazzolani et al. 2004), replaceable shear links constructed of low yield point aluminum installed in concentrically braced frames or special truss moment frames (Rai and Wallace 2000) and replaceable aluminum plate shear panels (Rai 2002, Mazzolani et al. 2004, Brando et al. 2009) have all been proposed and tested with moderate success.

FRP has successfully been used in structures since the 1970s and has been commonly employed in applications bonded to concrete or steel members requiring strengthening or repair (Zhao and Zhang 2007). More pertinent applications recently have been developed that increase ductility of steel members. For instance, bonded unidirectional sheets wrapped around special truss moment frame chord members enhanced cyclic response of plastic hinge behavior (Ekiz et al. 2004). FRP strips bonded to compression elements of flexural members (Accord and Earls 2006), webs of WT compression members (Harries et al. 2009), and HSS columns (Shaat and Fam 2006, 2007, 2009) have also been reported to delay local buckling of elements subjected to compression. Although applications where the FRP is not bonded to the substrate that it serves to reinforce are rare, they are emerging as an effective method for precluding compression buckling. Pilot tests of a single steel angle fit with a pultruded FRP square tube and wrapped with GFRP (glass fiber reinforced polymer) fabric was experimentally loaded in cyclic push-pull testing and achieved an ultimate compressive strength of 35% of the tensile strength before global buckling (Dusicka and Wiley 2008). Small-scale monotonic experiments and finite element modeling of rectangular steel bars surrounded by PVC or mortar blocks and wrapped with CFRP (carbon fiber reinforced polymer) fabric have achieved compression loads up to P_max/P_y=1.53 (Ekiz and El-Tawil 2008). Experimental full-scale cyclic tests of pinned and semi-fixed end steel angles similarly wrapped with mortar blocks and CFRP fabric achieved up to a 270% increase in energy dissipation over bare steel angles and compression loads up to P_max/P_y=0.90 (El-Tawil and Ekiz 2009).

Described below are developments of high-performance BRBs, and specifically, a new ultra-lightweight BRB, designed for a typical model building using analytical models developed from established buckling theory and experimental cyclic coupon testing of a candidate 6061-T6511 aluminum alloy for development of a calibrated constitutive model and finite element simulations. Analytical models considered both a single degree of freedom (SDOF) and an established Euler buckling model which provided an initial required restrainer stiffness and strength for a given axial design force and core length. Monotonic numerical simulations of a prototype brace were performed to examine the effect of restrainer stiffness with two different core reduced section lengths and three degrees of applied end moment. Cyclic simulations were used to assess if a predictable and reliable cumulative plastic ductility and energy dissipation was possible at a considerable story drift ratio. As part of the parametric investigation, end moment effect due to frame drift was considered by using an upper bound approach which considers plastic hinging of the unrestrained section of core.

The new brace utilizes materials readily available in many sizes and profiles to allow customization of the core-restrainer configuration as shown in FIG. 1(a). Although not directly a part of research, a review of past literature and practicality led to the following considerations for development: (1) stock extruded aluminum profiles for the core members should lower procurement and fabrication costs; (2) bi-planar symmetry of the brace cross-section should eliminate potential for global buckling in a weak direction; (3) non-tapered core cross section dimensions should allow a tight fit to the restrainer tubes without shimming; (4) back to back core elements should be continuously supported by high modulus FRP spacers to prevent core rippling; (5) sufficient space should be provided at the tip of core elements to allow Poisson expansion; (6) unrestrained sections of the core should be sufficiently robust to prevent local or torsional buckling modes; (7) the core should be fabricated without welding to prevent material embrittlement and fatigue notching; (8) a reduced core section should be used to direct plastic straining to the mid-length of the brace away from the vulnerable unrestrained areas; (9) axial independence between the core and restrainer should be maintained using a frictionless interface of grease or other lubricant between the FRP tubes and aluminum; and lastly (10) GFRP should be used to prevent galvanic reaction as is present with CFRP and aluminum.

Brace Geometry and Estimate of Strain Demands

Seismic forces, story drift, axial displacement, frame geometry and end connections were established within the context of a model building based on the SAC 3-story office building located in Los Angeles, Calif. (FEMA 2000). The building consisted of 9.14 m [30 ft] square bays and measured 36.6 m by 54.9 m [120 ft by 180 ft] with a story height h_i=3.96 m [13 ft]. Seismic design criteria were taken from the current edition of the building code as follows: S_s=2.15 g, S_ds=1.43 g, R=7 and C_d=5.5 (ASCE 2005). Two adjacent BRB frames (BRBFs) in an inverted v-brace configuration were centered on each of the four perimeter column lines. An equivalent lateral force procedure with 5% minimum eccentricity was used to determine the seismic base shear and distribution to the individual stories and frames. A brace design force of P_u=1070 kN [241 k] at the first level was calculated using the assumption of equal tension and compression stiffness of the BRBs.

FIGS. 2(a)-(c) show a definition of the brace geometry with a two-step core profile. An end to end core length L_b=4.83 m [190 in] was generated using assumed W21×111 beams and W14×176 columns to remain consistent with previous literature reports on testing of full-scale BRBFs (Fahnestock et al. 2007). Selection of the brace reduced section length L_c was subsequently made by considering axial stiffness of the brace required to limit the inelastic story drift to 2.5%, the maximum allowed by code for a regular structure (ASCE 2005). Calculation of the elastic story drift ratio D_ie/h_i for a non-prismatic core neglecting the contribution of the much stiffer beams and columns was previously cited by Tremblay et al. (2006) in Eq. (1) where γ=L_c/L_b and η=A₁/A₃, F_y=core nominal specified yield strength, E_c=core Young's modulus and θ=brace angle with horizontal.

$\begin{array}{cc}\frac{D_{\mathrm{ie}}}{h_i}=\frac{\phi F_y}{E_c}\left[\frac{\gamma +\eta \left(1-\gamma \right)}{\sin \theta \cos \theta }\right]& \left(1\right)\end{array}$

By rearranging Eq. (1) algebraically to solve for γ, Eq. (2) is given. D_ie/h_i=0.45% was calculated by dividing the inelastic story drift of 2.5% by the deflection amplification factor C_d. Using the variables θ=42°, E_c=69.6 GPa [10,100 ksi], φ=0.9, F_y=241 MPa [35 ksi] and η=0.456, γ=0.481 was calculated which represents a 2.31 m [91.4 in] long reduced section. The final reduced section length was increased to 2.44 m [96 in] to give γ=0.5 which is termed the Group B brace. Another geometry was created for the parametric study to examine higher expected axial strain and stiffness with L_c=1.47 m [58 in], or γ=0.3, which is termed the Group A brace.

$\begin{array}{cc}\gamma ={\left(1-\eta \right)}^{-1}\left[\left(\frac{D_{\mathrm{ie}}}{h_i}\right)\frac{E_c\sin \theta \cos \theta }{\phi F_y}-\eta \right]& \left(2\right)\end{array}$

Table 1 shows all prototype brace dimensions.

TABLE 1
Brace prototype dimensions
	Lb	Lc	Lc2	Lc3	Lr	Lo	Ls	Ltr	A1	A2	A3
	m	m	cm	cm	m	cm	cm	cm	cm2	cm2	cm2
Group	[in]	[in]	[in]	[in]	[in]	[in]	[in]	[in]	[in2]	[in2]	[in2]
A	4.83	1.47	119	48.3	3.40	78.7	25.4	15.2	51.1	78.7	112
	[190]	[58]	[47]	[19]	[134]	[31]	[10]	[6]	[7.92]	[12.2]	[17.4]
B	4.83	2.44	71.1	48.3	3.40	33.0	25.4	15.2	51.1	78.7	112
	[190]	[96]	[28]	[19]	[134]	[13]	[10]	[6]	[7.92]	[12.2]	[17.4]

Approximation of the average inelastic strain in the two-step core at maximum story drift is required to determine material strain demand. Using Eq. (3) and the previously defined variables, ε_c=3.22% and 2.25% was calculated for the Group A and B braces at 2.5% story drift, respectively. These values fall within strain amplitudes reported for previous BRB tests of 1% to 2% for longer core lengths and 3% to 5% for shorter core lengths (Tremblay et al. 2006). Selection of L_c should target an appropriate inelastic strain suitable for use with established cyclic properties of the core material as well as brace stiffness required to meet a target design story drift. Typically, connection details, intermediate section overlap length and axial shortening requires γ≦0.5 as a practical limit. In the prototype, γ was maximized by extension of the unwrapped tubes a distance of L_s to prevent local buckling of the intermediate section while still allowing the full section to slide through the restrainer.

$\begin{array}{cc}{\varepsilon }_c=\frac{C_d}{L_c}\left[D_{\mathrm{ie}}\cos \theta -\left(\frac{n\phi F_y\left(L_b-L_c\right)}{E_c}\right)\right]& \left(3\right)\end{array}$

SDOF System Analytical Model

Transverse displacement of the slender core member during buckling imparts flexural demand on the restrainer through application of a force with an unknown distribution function w(x). Effort to resist this displacement was conservatively modeled as a simple span restrainer beam pinned at the end of length L_r assuming the full section of the core rigidly cantilevers from the firmly bolted gusset plate as shown in FIG. 2(c). Force interaction between the core and the restrainer was then established using a SDOF mechanical model with axially inextensible truss members in which an assumed plastic hinge exists at the mid-length as shown in FIG. 3(a). Flexural stiffness of the elastic restrainer serves to prevent transverse bifurcation of the core hence increasing the critical buckling load P_cr. The plastic hinge was justified by first considering the internal core moment by combining elastic column Eqs. (4) and (5) for a pinned-pinned column and solving for the internal moment at mid-length M_int^p at a given transverse displacement Δ_t in Eq. (6). Tangent modulus theory was used to account for core material non-linearity by replacing E_c with E_ct.

$\begin{array}{cc}{M}_{\mathrm{int}}=E_cI_c\stackrel{″}{y}& \left(4\right)\\ y\left(x\right)={\Delta }_t\sin \left(\frac{\pi x}{L_r}\right)& \left(5\right)\\ M_{\mathrm{int}}^p\left(\frac{L_r}{2}\right)=\frac{{\pi }^2{\Delta }_t}{L_r^2}E_{\mathrm{ct}}I_c& \left(6\right)\end{array}$

The resisting moment M_res provided by the bundled tube restrainer was calculated from equilibrium on the column half-length shown in FIG. 3a and Eq. (7) where E_r and I_r are the Young's modulus and moment of inertia of the restrainer, respectively. Comparison of M_int^p to M_res showed approximately two orders of magnitude difference at a common transverse displacement Δ_t. For this exercise, the modulus of elasticity for the pultruded composite tubes was taken as E_r=19.3 GPa [2800 ksi] and I, was calculated from four 10.8 cm by 6.35 mm [4.25 in by ¼ in] square tubes acting compositely. Tangent modulus E_ct of the core was taken as 1% of Young's modulus to account for strain hardening. The sharp transition between elastic and plastic behavior negates the need for an incremental approach accounting for material non-linearity.

$\begin{array}{cc}{M}_{\mathrm{res}}=\frac{48E_rI_r{\Delta }_t}{L_r^3}\sqrt{{\left(\frac{L_r}{2}\right)}^2-{\Delta }_t^2}& \left(7\right)\end{array}$

Effect of the restrainer was simulated by an elastic spring with stiffness k_s providing a force F exerted at the mid-length of the core. The spring stiffness is taken from the elastic deflection of a beam loaded at mid-span as F/Δ_t=48E_rI_r/L_r³. This relationship is substituted for k_s in Eq. (8) and gives the critical buckling load all in terms of known variables after using the classical eigenvalue solution for the SDOF system. Eq. (9) solves for the required restrainer stiffness E_rI_r/L_r³ which can be used for intial restrainer sizing.

$\begin{array}{cc}{P}_{\mathrm{cr}}=\frac{k_sL_r}{4}=\frac{12E_rI_rL_r}{L_r^3}& \left(8\right)\\ \frac{E_rI_r}{L_r^3}=\frac{P_u}{12L_r}& \left(9\right)\end{array}$

Euler Analytical Model

Previous research by Black et al. (2002) has used the Euler column with a distributed force interaction w(x) between the core and restrainer assuming Hooke's law, geometric perfection, concentric load application and small displacements. Introduction of a continuous support is shown diagrammatically in FIG. 3(b) as a pinned-pinned column of length L_r supported by an infinite number of axially rigid connector bars connected to the restrainer also spanning length L_r. By beginning with force equilibrium on an arbitrary length of column x and introducing sinusoidal displacement functions originating from Eq. (5), Eq. (10) was achieved. Eq. (11) arrives from solution of the differential equation for the critical buckling load P_cr where an undetermined additional factor of safety is proposed by Black (2002) to account for geometric imperfections and material non-linearity of the core. The E_cI_c term for the core can be omitted due to the much lower contribution as compared with E_rI_r as previously explained and the effective length factor K=1 for the pinned-pinned column. Removal of the E_cI_c term likewise removes the need for incremental analysis considering material non-linearity of the core. Eq. (12) similarly solves for the required restrainer stiffness.

$\begin{array}{cc}p\frac{{}^2y\left(x\right)}{x^2}+E_cI_c\frac{{}^4y\left(x\right)}{x^4}+E_rI_r\frac{{}^4y\left(x\right)}{x^4}=0& \left(10\right)\\ P_{\mathrm{cr}}=\frac{{\pi }^2}{{\left({\mathrm{KL}}_r\right)}^2}\left(E_cI_c+E_rI_r\right)& \left(11\right)\\ \frac{E_rI_r}{L_r^3}=\frac{P_u}{{\pi }^2L_r}& \left(12\right)\end{array}$

The SDOF and Euler analytical design methods are plotted in FIG. 4 as continuous functions illustrating required E_rI_r/L_r³ for lengths ranging from L_r=2 m [78.6 in] to 4.25 m [167 in] and loads P_u=225 kN [50 k] to 1350 kN [300 k]. If no degree of conservatism is provided, the present prototype brace requires E_rI_r/L_r³=30.1 kN/m [0.172 k/in] and 36.6 kN/m [0.209 k/in] for the SDOF and Euler methods, respectively. The prototype to be considered in the numerical simulations, used a restrainer stiffness of 33.4 kN/m [0.191 lain] provided by four 4.25 in×0.25 in bundled tubes. The SDOF model resulted in required stiffness values equal to 82% of the Euler model, indicating that it may be unconservative. However, restrainer stiffness was selected to fall in between these values.

Coupon Testing

Alloy 6061-T6511 is a relatively inexpensive heat-treated structural aluminum that is available in many extruded profiles that are conformable to square or round FRP tubes. This alloy has proven to be reliable when limited to the elastic range, but reversed cyclic behavior has not been reported for Δε_r/2≧4% and required investigation to determine its cyclic behavior such as is reported for plate steels (Dusicka et al. 2007). FIGS. 5(a) and 5(b) define the monotonic tension and cyclic push-pull coupons machined from 0.875 inch round bar and test setup which used a MTS load frame with a +/−445 kN [+/−110 k] capacity. The apparatus was manually controlled using a LVDT at a constant strain rate dε/dt for both the monotonic and cyclic tests. Cyclic tests were performed with a triangular waveform load history and began with a tensile excursion. Individual cyclic tests subjected the coupon to constant total strain amplitudes Δε_r/2=2, 3 and 4% at a cyclic strain ratio R_ε=−1. Table 2 summarizes experimental results for each of the specimens.

TABLE 2
6061-T6511 coupon test results
	Coupon ID
Material Property	T1	C1	C2	C3	C4
f0.2, MPa [ksi]	296 [42.9]	297 [43.0]	283 [41.1]	289 [41.9]	297 [43.0]
fu, MPa [ksi]	317 [46.0]	321 [46.5]	—	—	—
εy, %	0.38	0.33	0.481	0.427	0.464
εu, %	21.9	22.3	—	—	—
Af, mm2 [in2]	53.6 [0.0831]	53.1 [0.0823]	—	—	—
σtrue, MPa [ksi]	414 [60.1]	378 [54.8]	—	—	—
μ	0.816	0.805	0.852	0.835	0.814
Δεt/2, %	—	—	2.0	3.0	4.0
dε/dt, × 103 s−1	0.05	0.10	0.10	0.10	0.10
2Nf	—	—	48	36	22
Notes:
Af = measured cross sectional area at failure surface
σtrue = true fracture stress (Pu/Af)
μ = ratio of core nominal specified yield strength/experimental yield strength (Fy/f0.2)
2Nf = number of reversals to fracture

Since experimental yield strength exceeded nominal specified yield strength by approximately 25%, a normalization factor μ=F_y/f_0.2 was introduced. This value was used in creation of the material constitutive model in order to remain consistent with the material yield strength assumptions made during analytical modeling.

Monotonic results indicated strain hardening equal to 0.89% of Young's modulus until 5% elongation followed by 0.43% softening until tensile fracture (FIG. 6). Cyclic loops have a bi-asymptotic shape and are comprised of a linear elastic, smooth non-linear elastic-plastic transition and an approximately linear plastic region (FIG. 7). Transitions between the elastic and plastic regions were less abrupt for the cyclic tests as compared to the monotonic primarily due to the Bauschinger effect. Anomalies at the zero stress level can be attributed to looseness in the double nuts holding the specimens in the fixture. Closeness of the loops indicated that cyclic softening occurred at a very low rate, especially for the 2% test. This is better illustrated in FIG. 7 as a plot of maximum cyclic stress versus number of reversals where cyclic softening is negligible after an initial cycle of hardening. Cyclic softening increased minimally as the strain amplitude was increased from 2% to 4%. Consequently, isotropic cyclic hardening was relatively slow compared to kinematic hardening. This absence of isotropic hardening has been witnessed in similar tests on 6060-T6 aluminum tested to strain amplitudes of 0.4%, 0.8%, and 1.2% (Hopperstad et al. 1995).

Cyclic coupon tests on 6061-T651 alloy have been reported that achieved 2N_f=142 at Δε_i/2=2.5% and R_ε=−1 (Brodrick and Spiering 1972). This is up to 3 times greater than was achieved in the present tests at similar strain amplitudes. Slight bending in the 4% strain coupon was witnessed and is manifested in the hysteresis plots by a bend in the linear portion of the loop beginning at zero stress. Uniaxial stress may have been similarly compromised in the 2% and 3% coupons leading to premature fatigue failure due to non-uniform cross section strain distribution. Therefore, use of an hourglass shaped coupon without a prismatic center section is recommended for strain ranges greater than 2% to control buckling (ASTM 2004). Use of the current data for definition of a cyclic material model is not anticipated to significantly affect results since the linear portion of the curve is not used in its definition. However, suitability of the candidate alloy for use in high cyclic strain applications requires further experimental study.

Numerical Simulations

Cyclic Material Constitutive Model

Representative prediction of cyclic material behavior uses a calibrated general nonlinear combined kinematic-isotropic constituitive model. This model has proven to be capable of simulating the Bauschinger effect, cyclic hardening with plastic shakedown and relaxation of the mean stress (Simulia 2010). Experimental data from coupon C3 normalized by μ_ave=0.810 was selected which is in between the approximate inelastic core strains of 2.25% and 3.22%. The calibration procedure used a 3D finite element model of the test coupon comprised of C3D4 tetrahedral continuum elements as depicted in FIG. 8(b). Convergence of the fine mesh was studied by varying the number of degrees of freedom and the element polynomial. Coupon simulations were set to run in displacement control for two full cycles to verify calibration. Superposition of three backstresses effectively captured the shape of the experimental hysteresis plots in the Bauschinger region by accounting for strain ratcheting effects. Superposition of the experimental and numerical results for the 2%, 3% and 4% strain amplitudes are illustrated in FIG. 8(a) with reasonable correlation. Isotropic hardening was not used due to its negligible influence on cyclic behavior as shown by the stable maximum cyclic stress plots.

Finite Element Model Configuration

Numerical models were created using commercially available finite element analysis and post-processor software (Simulia 2010) and configured as shown in FIG. 9(a). Core angles were modeled as four separate 3D planar extrusions meshed with fully integrated, general purpose 4-node shell (S4) elements capable of modeling large membrane strains and the restrainer was modeled as a single 1D beam meshed with Timoshenko (B31) elements. Beam element section properties were assigned using equivalent square tubes representative of the x-x and y-y flexural stiffness of the bundled restrainer tubes acting compositely. Core and restrainer nodes were connected with slide-plane connectors to the angle tips and slot connectors to the angle vertex to decouple axial interaction and allow Poisson deformation. The spacing between slotted connectors was kept at a constant 25.4 mm [1 in] leaving one unsupported node in between the connector nodes. However, in the present study no local buckling imperfections were assigned to promote rippling between the connectors. Boundary conditions were assigned to reference points (RP) positioned at the end of the gusset plate a distance L_c3 from the end of the brace. Load eccentricity for end moments was introduced by offsetting the RP from the centroid a distance e_l in the positive y-direction to simulate gusset plate rotation from frame drift and single curvature of the brace. The applied end moment was directly proportional to axial load.

Consideration of thin and thick shell formulations on elastic buckling behavior was made by examining load vs. axial displacement behavior of braces loaded monotonically to an enforced axial displacement of 50.8 mm [2 in] with adequately and inadequately restrained cores. For these simulations, a nominal material yield strength F_y was used along with a nominal 1% post-yield hardening. The difference between tension and compression yield load, buckling load and post-buckling path are shown to be negligible in FIG. 9(b), indicating that transverse shear flexibility is not important for global buckling modes with thickness to characteristic length ratios less than 1/15. Model convergence was also studied by examining element strains at both the elastic and plastic regions for varying number of degrees of freedom. To stimulate global buckling, geometric imperfections were introduced into the mesh from the first four buckling modes. Maximum global out-of-straightness of L_b/1000 was assigned for modes 1 & 2 and L_b/4000 for modes 3 & 4.

Effect of Brace End Moments

BRBF in-plane drift may introduce end moments or rotations into the brace during severe seismic loading as shown in FIG. 10(b) for an inverted v-brace configuration. This effect causes additional flexural demand on the restrainer above those caused by ideal column buckling models. An upper bound end moment that utilizes the available plastic moment of the core's intermediate section M_p′ was used to quantify this effect which can be determined by performing a rigorous non-linear push-over analyses of the BRB/BRBF assembly which is beyond the scope of this research. The available plastic moment of the axially loaded member is reduced below the value of F_yZ as is shown diagrammatically in FIG. 10(a) when all four core angles act compositely by shear transfer occurring at the bolted connections. Using this interaction of axial load and moment with an axial load equal to the core nominal yield load P_yc=A₁F_y, the following values were calculated: d₁=8.43 cm [3.32 in], d₂=15.7 mm [6.16 in], Z=215 cm³ [13.1 in³] and M_p′=5186 kN-cm [459 k-in]. To express this moment as a ratio of the upper bound, the variable Ψ=M_app/M_p′ was introduced where M_app=maximum applied end moment and Ψ<1. Additionally, the relationship ΨM_p′ can be converted to a load-eccentricity relationship for use in numerical simulations as shown in Eq. (13) where the core nominal yield load is used neglecting the contribution of post-yield hardening and e₁ is calculated for a desired end moment effect.

$\begin{array}{cc}e1=\frac{\psi M_p^{\prime }}{P_{\mathrm{yc}}}& \left(13\right)\end{array}$

Monotonic Simulations

Parametric numerical simulations of monotonically loaded prototypes were studied in displacement control for comparison with the proposed analytical models. Variables used were L_c, E_rI_r/L_r³ and ΨM_p′ as shown in Table 3.

TABLE 3
Numerical simulation parameters and results
		General Parameters		Cyclic Results
Simulation	Simulation	Mono/	Lc	ErIr/Lr3		Monotonic Results	ΣPΔa	ΣPΔa
Group	ID	Cyclic	m [in]	kN/m [k/in]	ψ	Pe/Pyc	Pmax/Pyc	Δa/Δt	kN/m	ΣPoΔo
1A	58-R1-M0	M	1.47 [58]	31.5 [0.180]	0	0.859	0.730	0.341
γ = 0.3	58-R2-M0	M	1.47 [58]	42.2 [0.241]	0	1.15	0.934	0.362
	58-R3-M0	M	1.47 [58]	74.6 [0.426]	0	2.04	1.43	2.34*
2A	58-R1-M1	M	1.47 [58]	42.2 [0.241]	0.25	1.15	0.908	0.370
γ = 0.3	58-R2-M1	M	1.47 [58]	55.1 [0.315]	0.25	1.50	1.13	0.398
	58-R3-M1	M	1.47 [58]	83.6 [0.477]	0.25	2.28	1.42	1.78*
3A	58-R1-M2	M	1.47 [58]	55.1 [0.315]	0.5	1.50	0.883	0.379
γ = 0.3	58-R2-M2	M	1.47 [58]	70.4 [0.402]	0.5	1.92	1.09	0.407
	58-R3-M2	M	1.47 [58]	93.2 [0.532]	0.5	2.54	1.39	1.66*
1B	96-R1-M0	M/C	2.44 [96]	31.5 [0.180]	0	0.859	0.720	0.340	3990	0.529
γ = 0.5	96-R2-M0	M/C	2.44 [96]	42.2 [0.241]	0	1.15	0.923	0.362	5100	0.677
	96-R3-M0	M/C	2.44 [96]	66.4 [0.379]	0	1.81	1.29	3.59*	6740	0.895
2B	96-R1-M1	M/C	2.44 [96]	42.2 [0.241]	0.25	1.15	0.898	0.371	4884	0.649
γ = 0.5	96-R2-M1	M/C	2.44 [96]	55.1 [0.315]	0.25	1.50	1.12	0.401	6019	0.799
	96-R3-M1	M/C	2.44 [96]	74,6 [0.426]	0.25	2.04	1.29	2.01*	6653	0.883
3B	96-R1-M2	M/C	2.44 [96]	42.2 [0.241]	0.5	1.15	0.873	0.379	4700	0.624
γ = 0.5	96-R2-M2	M/C	2.44 [96]	55.1 [0.315]	0.5	1.50	1.08	0.409	5760	0.765
	96-R3-M2	M/C	2.44 [96]	83.6 [0.477]	0.5	2.28	1.28	1.82*	6630	0.880
Notes:
Pe = restrainer buckling load = π2 ErIr/Lr2
Pmax = maximum compressive axial load
ΣPΔa = cumulative load-displacement
ΣPoΔo = area of ideal trapezoidal hysteresis
*indicates successful BRB simulation

Target axial displacement Δ_bm relating to 2.5% story drift as calculated from the model building was multiplied by two as specified by the cyclic loading protocol for “Qualifying Cyclic Tests of Buckling-Restrained Braces” (AISC 2005).

FIGS. 11(a)-(f) show axial load vs. log-displacement relationships for the six groups of simulations. Each dual plot illustrates the ability of the trial to meet the target axial displacement before reaching the failure criteria. The failure criteria were defined as buckling or reaching a limiting transverse displacement at the mid-length of the brace. Maximum transverse displacement Δ_t^max=8.79 cm [3.47 in] is denoted as a dashed line and was calculated by considering f_b=206 MPa [30 ksi] and c=11.8 cm [4.63 in] as measured from the baseline four 10.8 cm by 6.35 mm [4.25 in by 0.25 in] tube configuration. The relationship given in Eq. (14) was derived from M_r=FL_r/4, f_b=M_r/S_r, S_r=I_r/c and Δ_t=FL_r³/48E_rI_r where M_r and S_r are the flexural moment when flexurally loaded by a point load at mid-span and elastic section modulus of the restrainer, respectively.

$\begin{array}{cc}{\Delta }_t^{\max }=\frac{f_bL_r^2}{12{\mathrm{cE}}_r}& \left(14\right)\end{array}$

Failure points of inadequately restrained braces are denoted by white markers on the plots while end of simulation points for adequately restrained braces are denoted by black markers. Inadequately restrained braces generally exhibited a failure progression in compression as shown in FIGS. 12(a) to 12(c) and described as follows: 1) uniform axial stress and yielding at the reduced section with transverse bending; 2) increasing transverse displacement and bending stress at the ends of the restrainer; 3) plastic local buckling of the core angle legs leading to hinging; and 4) overall global buckling.

Numerical results are given in Table 3 for each simulation. Restrainer stiffness used in the third simulation for each group was determined by an iterative process of increasing E_rI_r/L_r³ to achieve stable BRB performance with P_max/P_yc>1 and Δ_a/Δ_t>1.28 which represents target axial displacement over Δ_t^max. Application of end eccentricity had a degradation effect on the Δ_a/Δ_t ratio, but successful simulations were able to remain in relatively straight axial alignment. FIG. 11(g) shows the linear effect of application of end eccentricity on required E_rI_r/L_r³. Slope of the lines remained constant between the Group A and B braces demonstrating that reduced section length has insignificant effect. Furthermore, end eccentricity may be accounted for by superimposing from 34.4 to 37.2 kN/m of additional stiffness per unit of Ψ which effectively doubles required E_rI_r/L_r³ for this prototype. FIG. 4 illustrates scatter plot comparison between analytical and numerical results. Numerical simulations resulted in approximately two times greater required E_rI_r/L_r³ than analytical for the examined brace length indicating that a degree of conservatism of two or greater may be required to account for material non-linearity, load eccentricity, reasonable transverse displacement as well as possible local buckling effects near the end of the restrainer. Although, it is recognized that further study is required to determine the degree of conservatism required for other brace lengths since only one length was considered in this research. Accounting for this larger required stiffness, four 5 in by 5/16 in or 5½ in by 5/16 bundled tubes would be required for Ψ=0 and Ψ=0.5, respectively. This is within reasonable practical limits for brace compactness and promotes the notion that the described brace is a viable concept.

Cyclic Simulations

The objectives included to assess energy dissipation potential and assert numerical model stability and repeatability when subjected to cyclic axial force and rotational demand when subjected to a minimum cumulative inelastic axial deformation of 200 times the yield deformation (AISC 2005). Numerical formulation used the calibrated cyclic constitutive model and did not include simulation of material fatigue failure.

Table 3 shows test parameters for the Group B brace. Representative hysteresis plots for Group 1B prototypes for load vs. axial displacement and load vs. transverse displacement are given in FIGS. 13(a)-13(d). Inadequately restrained braces exhibited large transverse displacement along with pinched hysteresis loops on the compression excursions while adequately restrained braces exhibited full symmetrical loops with minimal transverse displacement. Group 1B hysteresis plots of load vs. axial strain at the mid-length of the reduced section demonstrate tension side strain ratcheting for the inadequately restrained brace (96-R1-M0) and nearly symmetrical loops for the adequately restrained brace (96-R3-M0). A strain shift of approximately 2.5% is witnessed toward the tension side due to incomplete strain reversal during compression excursions due to transverse displacement. Average achieved material strain over a gage length of 2.54 cm [1 in] at the mid-length of the reduced section was numerically measured at the 1.0Δ_bm cycle as +2.89% to −1.72% and +3.20% to −2.52% for the R1 and R3 braces, respectively. This correlates reasonably well with ε_t=+/−2.25% as calculated from Eq. (3) with the caveat that positive tension strains are approximately 25% greater than compression strains in an adequately restrained brace due to the strain ratchetting.

Cumulative energy dissipation ΣPΔ_a and load-strain ΣPε_t were determined by numerically integrating the area under the curve for each of the nine simulations. Table 3 shows these results along with those normalized by an ideal trapezoidal hysteresis plot ΣP_oΔ_o=7530 kN-m [66,700 k-in]. Adequately restrained braces achieved nearly 90% of the energy dissipation of the idealized hysteresis. Inadequately restrained braces ranged from 53% to 83% showing a marked improvement. End eccentricity also had a significant effect on cumulative displacement and strain demand as witnessed in FIG. 13(e) where a steeper slope is present at higher values of Ψ up to the plateau of ΣPΔ_a=6600 kN/m [58,500 k-in]. ΣPε_t plots exhibit a lower slope reaching a plateau of 2900 kN-m/m [652 k-in/in].

FRP Wrap Design

Bundled FRP tubes should work compositely to achieve greatest strength and stiffness. Maximum expected shear flow q_max between the tubes was approximated by utilizing the same Euler column buckling model and force equilibrium method. Since failure of the bundled tube assembly should be controlled by the flexural moment of the tubes and not shear failure of the wrap, shear flow was determined using the previously related Δ_t^max. Previously defined values of c, f_b and L_r were used with the tube arrangement to calculate q_max=8.60 kN/cm [4.91 k/in] at the end of the restrainer. A multi-layer wet layup GFRP uniaxial fabric can resist this shear flow. Proprietary wrap systems are common and typically exhibit ultimate tensile strengths of 582 MPa [84.4 ksi] in the primary fiber direction and have an effective laminate thickness of 1.27 mm [0.05 in]. A truss-like mechanism was conceived using two layers of wrap along the entire length of the restrainer oriented at +/−30° from the longitudinal axis to resist shear flow in tension through the primary fibers. The allowable shear strength of the wrap was calculated as 9.85 kN/cm [5.63 k/in] using a degree of conservatism of 1.5 to account for additional extreme fiber longitudinal stress imparted by bending of the restrainer assembly. Although, additional stress in the wrap from bending is expected to be minimal since the modular ratio of the fabric and tubes is unity.

Weight Reduction

The described prototype brace was calculated to weigh 200 kg [440 lb] or 27% and 41% the weight of a traditional mortar-filled tube and all-steel BRB of similar length, core area and restrainer dimensions. Thus, the described prototype brace weighs less than 50% of a comparable conventional brace. For the mortar-filled tube, a single square tube of comparable size (8 in×¼ in) was used. Since the nominal yield strength of common steel and 6061-T6 aluminum are almost identical, similar core sizes were considered fair comparison. Nominal unit weight for mild steel, aluminum and concrete mortar were taken as 7860 kg/m³ [490 lbs/ft³], 2650 kg/m³ [165 lbs/ft³] and 2410 kg/m³ [150 lbs/ft³], respectively. This comparison serves to highlight the considerable weight savings that can be realized with the described brace.

Notation

A1 = core reduced cross sectional area
A2 = core intermediate cross sectional area
A3 = core full cross sectional area
c = distance from NA to restrainer extreme
fiber
Cd = deflection amplification factor
Die = elastic story drift
Ec = core Young's modulus
Ect = core tangent modulus
Er = restrainer Young's modulus
f0.2 = experimental 0.2% offset yield strength
fb = restrainer ultimate bending stress
F = transverse restrainer force
Fy = core nominal specified yield strength
hi = story height, level “i”
Ic = core moment of inertia
Ir = restrainer moment of inertia
ks = equivalent restrainer spring stiffness
K = effective length factor
Lb = brace end to end length
Lc = core reduced section length
Lr = restrainer length
Mapp = maximum applied end moment
Mintp = core internal moment
Mp′ = available plastic moment of
intermediate section
Mr = restrainer moment at mid-length
Mres = restrainer resisting moment
P = brace applied axial load
Pcr = critical buckling load
Pu = design axial force
Pyc = core nominal yield load
qmax = maximum wrap shear flow
Rε = cyclic strain ratio
γ = Lc/Lb
Δa = core axial displacement
Δbm = brace disp. at design story drift
Δt = restrainer transverse displacement at
mid-length
Δtmax = max. transverse disp. of restrainer
εc = core inelastic strain
εt = total experimental strain
η = A1/A3
θ = brace angle with horizontal
μ = Fy/f0.2
Ψ = Mapp/Mp′

EXEMPLARY EMBODIMENTS

Referring to FIGS. 1(a) and 1(b), an exemplary embodiment of a buckling restrained brace 10, sometime referred to as a “full cruciform” type, is shown. The brace has an elongate core member 12 with opposite ends 14, 16. At least one spacer member 18 is positioned on the core member 12. In the illustrated implementation, there is a first spacer member 18 oriented along one plane of the core member 12 and a second space member oriented perpendicular to the first spacer member. There are one or more core restrainer member sections 20 arranged adjacent the spacer member and around the core member 12. The core restrainer member sections 20 are coupled together with the spacer member 18 and the core member 12 by a jacket 19 comprising fiber reinforced polymer fabric that is configured to be wrapped around the assembled core member and core restrainer member sections with the spacer member sandwiched therebetween.

In exemplary embodiments, the core member is made of aluminum, although other materials with suitable ductility could be used. In the illustrated embodiments, the ends 14, 16 of the core member 12 are exposed.

In the embodiment of FIGS. 1(a) and 1(b), there are four core restrainer member sections 20, but any suitable number of sections may be used. The core restrainer member sections 20 can have a rectangular (or square) cross-section as shown in FIGS. 1(a), 1(b), 1(c) and 1(e), a circular cross section as shown for the core restrainer members 24 in FIGS. 1(d) and 1(f), or any other suitable cross-section. As illustrated, the core restrainer sections may have a hollow tubular configuration over at least a portion of their length.

The core member may be comprised of a single member or several sub-members. In the illustrated implementation, the core member 12 is comprised of comprised of four angles 22a, 22b, 22c, and 22d arranged such that adjacent side surfaces are in contact with each other and the vertices are adjacent each other and oriented toward the center as shown. As shown in FIGS. 1(e) and 1(f), the core member 12 can be comprised of two tee members 26a, 26b arranged opposite each other, i.e., with the respective uninterrupted side surfaces facing each other. In some embodiments, the multiple sub-members are separated from each other, e.g., by the interposed spacer member(s), over at least an intermediate portion of the length of the brace 10. Also, exemplary configurations define at least one pair of separated spaces (such as two pair or four spaces as shown in FIGS. 1(c)-1(f)) for receiving the core restrainer member sections.

In some embodiments, a debonding material such as PTFE can be applied between adjacent surfaces of the core restrainer member sections 20 and the core member 12 to ensure that there is no coupling or bonding between the adjacent surfaces. In some embodiments, no such debonding material is used.

Referring to FIGS. 1(g) and 1(h), another exemplary embodiment of a buckling restrained brace 210 is shown. The brace 210 is similar to the brace 10 of FIGS. 1(a) and 1(b), except the brace 210 has an elongate core member 212 formed in a T-shape (shown inverted in the figures), and there are two core restrainer member sections 220 received in the spaces defined on either side of the core member 212. As in the case of the brace 10, a jacket 219 of fiber reinforced polymer fabric is wrapped around the core restrainer member sections 220 and the core member 212.

In specific implementations, the core restrainer member sections 20, 200 are made of fiber reinforced polymers. The core member 12, 212 is made of a suitable material, such as, e.g., an aluminum alloy.

In the illustrated embodiment, the brace 210 does not include any spacer member, but one or more spacer members can be provided if desired or if required in certain circumstances.

This analytical and numerical study focusing on global buckling demonstrated the ability to develop a new ultra-lightweight buckling-restrained brace for potential application in existing building seismic retrofit situations similar to a representative 3-story office model building. Calculated required restrainer stiffness from a newly developed SDOF model and previously established Euler buckling model was compared with monotonic and cyclic numerical simulations of prototypes with varying restrainer stiffness, reduced section length and applied end moment. The following presents a summary of results:

(1) A common structural aluminum coupon was tested cyclically to develop a hysteresis for use in creation of a constitutive model for cyclic numerical modeling. Excellent correlation was illustrated with a general nonlinear combined hardening model using finite element simulations. Test results indicated that low monotonic strain hardening and negligible cyclic hardening make 6061-T6511 a potentially suitable candidate for seismic applications.

(2) An important contribution was made to modeling BRB behavior using numerical finite element simulations to verify existing analytical based design methods. Monotonic numerical results indicated that a degree of conservatism of two or greater was required for the considered brace length when using proposed analytical methods to account for geometric and material non-linearity, local buckling at the unrestrained core and limiting transverse bending stress on the restrainer. SDOF and Euler buckling models achieved similar results with only 13% difference. Further research was recommended to examine the effect different brace lengths have on the degree of conservatism required to achieve BRB performance.

(3) BRB applied end moment was quantified using an upper bound approach in lieu of performing specific frame analyses in order to account for story drift two times greater than the maximum 2.5% given in typical building codes. The restrainer demand from applied end moment was determined by monotonic simulations to be one of linear superposition with conventional buckling demand. Additional required stiffness of 34.4 to 37.2 kN/m per unit of Ψ was required for the brace length examined. This relationship was shown to hold for restrainer length ratios of γ=0.3 and 0.5 indicating that there may be potential for using the method as a quick and easy design aid to account for end moment effects on BRB performance.

(4) Cyclic simulations indicated that reliable BRB performance was achieved with approximately 90% efficiency as compared to an ideal trapezoidal hysteresis if adequate restrainer stiffness was provided. Lower values of 53% to 83% were typical with inadequate restraint with most of the cumulative ductility occurring from yielding in the tension excursions. Material strains achieved in the simulations correlated reasonably well with those estimated by simple analytical methods and were approximately +3.2% to −2.52% for the design story drift. Material strains were shown to be asymmetrical due to strain ratcheting caused by transverse bending.

In view of the many possible embodiments to which the disclosed principles may be applied, it should be recognized that the illustrated embodiments are only preferred examples and should not be taken as limiting in scope. Rather, the scope of protection is defined by the following claims.

Claims

1. A buckling restrained brace, comprising:

a core member having two opposite ends;

core restrainer member sections configured to be arranged around the core member;

a jacket member comprising fiber reinforced polymers configured to be wrapped around the core restrainer member sections and core member to couple the core restrainer member sections to the core member, wherein the core restrainer member sections and jacket member cooperate to provide greater resistance to buckling of the core member when the brace is subjected to compression.

2. The buckling restrained brace of claim 1, wherein the brace has a weight less than about 50% of a weight of a conventional buckling restrained brace of similar length and having a steel core and mortar-filled tubular core restrainer member of comparable cross-sectional areas, respectively.

3. The buckling restrained brace of claim 1, wherein the core member has a cross section defining at least one pair of opposed spaces configured to receive a respective number of core restrainer member sections.

4. The buckling restrained brace of claim 1, wherein the core member has a T-shaped cross section defining two opposed spaces, wherein each of the two spaces is configured to receive one of the core restrainer sections.

5. The buckling restrained brace of claim 4, wherein the core member is comprised of two angled sub-members defining a T-shape when positioned adjacent each other.

6. The buckling restrained brace of claim 1, wherein the core member has a cross section defining at least four separated spaces, wherein each of the spaces is configured to receive one of the core restrainer sections.

7. The buckling restrained brace of claim 1, wherein the core member is comprised of four angled sub-members, and the angled sub-members are arranged such that the vertices are adjacent each other in a cross section of the core member.

8. The buckling restrained brace of claim 1, wherein the core member is comprised of two T-shaped sub-members, and the T-shaped sub-members are arranged opposite to each other in a cross section of the core member.

9. The buckling restrained brace of claim 1, wherein the core restrainer members are tubular and have a rectangular cross section.

10. The buckling restrained brace of claim 1, wherein the core restrainer members are tubular and have a circular cross section.

11. The buckling restrained brace of claim 1, wherein the jacket member is sized to extend over an intermediate portion of the core member between the two opposite ends.

12. The buckling restrained brace of claim 1, wherein the core member is formed of a ductile material.

13. The buckling restrained brace of claim 1, wherein the core member is formed of an aluminum alloy.

14. The buckling restrained brace of claim 1, wherein the core member comprises at least two core member sections, further comprising at least one spacer member positioned between the core member sections.

15. The buckling restrained brace of claim 14, wherein the at least one spacer member is formed of at least one of a plastic material and fiber reinforced polymers.

16. The buckling restrained brace of claim 1, wherein the jacket member comprises at least one layer of fabric material applied at different angles relative to the core member.

17. The buckling restrained brace of claim 1, wherein the jacket member comprises at least one layer of fabric material applied at an angle of about 30 degrees relative to an axis of the core member.

18. The buckling restrained brace of claim 1, wherein the core member is configured to dissipate seismic energy through substantially reversible cyclic plastic strain.

19. The buckling restrained brace of claim 1, wherein the core member, core restrainer member sections, and jacket member are constructed of materials selected to reduce corrosion from exposure to environmental conditions.

20. The buckling restrained brace of claim 1, wherein the core member, core restrainer sections and jacket member are configured to allow the core and the core restrainer sections to translate relative to each other under predefined loading conditions imposed on the brace.