Experimental and Finite Element Study of Polymer Infilled Tube-in-Tube Buckling Restrained Brace

Abstract

This study presents a tube-in-tube buckling-restrained brace (BRB) infilled with lightweight and rapid hardening polymer. The proposed BRB consists of a circular or square tube core encased with a tube of similar shape and polymer infill. The tube-in-tube arrangement minimizes the filler material volume and enables the use of rolled steel section as opposed to welded profiles commonly utilized when large BRB axial strength is required, although welded profiles suffer from low assembly accuracy resulting from welding deformation. The infilled polymer has a density of approximately half that of mortar and requires a curing time of 24 h, enabling weight and fabrication time reduction. The stability and inelastic deformation capability of the BRB were investigated through brace and subassembly tests of six circular and four-square full-scale specimens, followed by finite element analysis. The test results show that circular BRB designed with a P_cr/P_y ratio of 1.46 exhibited a stable hysteresis up to 1.42% and 1.06% core strain in tension and compression, respectively. Circular and square specimens designed with P_cr/P_y ratios ranging from 0.82 to 1.06 exhibited stable hysteresis before failing by global buckling at compressive core stains ranging from 0.86% to 1.09%. The slot weld detail adopted for welding core projection stiffener displayed a stable performance in circular BRB specimens, while it resulted in large plastic strain demand in square BRB specimens, leading to core fracture at tensile core strains ranging from 0.64% to 0.71%.

1. Introduction

Buckling-restrained braces (BRBs) have been widely utilized to enhance the seismic performance of new and existing buildings as well as for post-earthquake retrofitting [1,2,3,4,5,6]. BRBs differ from conventional braces because the BRB core yields under both tension and compression without buckling. Numerous BRB types have been proposed and tested [7,8,9,10,11]. A typical BRB consists of a steel core encased by a steel tube filled with mortar or concrete. A thin layer of debonding material or a small gap separates the steel core and infilled material. Hence, the core sustains axial tension and compression without buckling under the restraining effect of the casing and filler material. The long curing time and high density of concrete/mortar negatively affect the fabrication time and dead-weight of such BRBs. To address these drawbacks, and in a few cases to allow disassembly and inspection, several all-steel BRBs, including flat, cruciform, and H-section core BRBs, have been proposed and tested [12,13,14,15]. When large BRB axial strength is required, cruciform, H-section, or other core profiles are better alternatives to a thick flat plate core. However, core cross-sections assembled by welding multiple steel plates have low fatigue life and assembly accuracy, owing to welding deformation and residual stress [16].

This paper proposes polymer infilled tube-in-tube BRBs to eliminate the drawbacks of concrete/mortar-filled BRBs. Moreover, they utilize rolled steel sections to avoid defects that arise from the use of sections assembled by welding. The proposed BRB consists of a circular or square hollow section core encased by a larger hollow section of the same shape, as illustrated in Figure 1. The gap between the core and the casing is filled with a rapid-hardening lightweight polymer material produced by a chemically reacting diisocyanate and polyol mixture [17]. The development of polymer composites and engineered materials for structural application has been gaining popularity in the past few decades [17,18]. The infilled polymer is initially a yellowish-brown viscous fluid; it solidifies gradually and fully hardens within 24 h at room temperature. The polymer has a density of 1178 kg/m³ (about half that of mortar) in its hardened state [17]. The adequacy of the polymer for structural use in steel–polymer hybrid floor systems has been demonstrated [17].

The unconstrained segment of the core projecting out of the casing is subjected to large in-plane bending and prone to failure [19,20]. To minimize the number of such potential failure zones, the core projection is only on one end of the proposed BRB, as opposed to two ends such as in a conventional BRB. The core projection is stiffened, as shown in Figure 1.

Ten full-scale specimens were tested under brace and subassembly cyclic load tests. The test program investigated the buckling behavior and unconstrained length stiffener detail of the BRB. Nonlinear finite element analysis [21,22,23] was conducted to better understand the proposed BRB.

2. Test Program

2.1. Test Specimens

The test program consists of six circular and four square tube-in-tube full-scale specimens with varying stiffness and strength parameters. Figure 2 and Table 1 summarize the details of the test specimens fabricated using SRT275 and SJT275 steel, with a specified minimum yield strength of 275 MPa. The core of one square BRB specimen was fabricated using SRT 355 steel with a specified minimum yield strength of 355 MPa to examine the behavior of the BRB under different steel grades. The stiffeners and pin connectors at the BRB ends were fabricated using SM355 steel, with a specified minimum yield strength of 355 MPa. The average material properties with the respective coefficient of variation obtained from three coupon tests conducted on the components of the specimens are reported in Table 2. The yield strength obtained from the coupon test was higher than the specified nominal strength by a factor of 1.6 and 1.4 for circular and square specimens, respectively. The specimen and component (core and casing) names in Table 1 and Table 2 represent the respective shapes and sizes. C and S denote circular and square tubes, respectively, followed by the outside diameter or width of the tube and wall thickness in millimeters. For example, C216 t8 indicates a circular tube with 216 mm diameter and 8 mm wall thickness. The specimen names indicate the core size, followed by the casing size. The first two circular specimens were identical except for core wall thickness, while the third circular specimen was more slender compared to the first two. Similarly, the first two square specimens were identical except for core wall thickness and steel grade, while the third square specimen was more slender compared to the first two.

The infilled polymer, in its fully hardened state, has density, tensile strength, compressive strength, modulus of elasticity in tension, and modulus of elasticity in compression of 1178 kg/m³, 31.4 MPa, 23.1 MPa, 1277 MPa, and 461 MPa, respectively. To minimize friction and achieve a similar force strength in tension and compression, a 1.6 mm thick rubber was applied as a debonding layer between the core and infilled polymer [24].

Using the mechanical properties obtained from the coupon test, the global stability of the test specimens was estimated using Euler’s buckling theory. The critical buckling load (P_cr) and the bending moment at the center of the casing (M_center) [25,26] were calculated using Equations (1) and (2), respectively.

(1)$P_{cr}=\frac{{\pi }^{2}EI}{L^2}$

(2)$M_{center}=\frac{P{\nu }_0}{1-\frac{P}{P_{cr}}}$

where E, I, and L represent the modulus of elasticity, casing moment of inertia, and effective brace length, respectively. The modulus of elasticity was taken as 200 GPa for all specimens. To estimate the brace stability, P_cr was compared with the brace yielding force P_y, and ultimate force P_u, computed as the product of the core cross-sectional area, with the yield and ultimate stress, respectively. Watanabe et al. [27] recommended a P_cr/P_y ratio above 1.5 to provide sufficient constraint against global buckling. Moreover, flexural yielding of the casing should be prevented to avoid global buckling [14]. Thus, the casing moment (M_center) computed by Equation (2) was compared with the casing yield moment, (M_y) calculated as the product of the casing elastic section modulus and the casing yield strength. Here, P and ${\nu }_0$ are the brace axial force and brace initial imperfection amplitude, respectively. The initial imperfection was taken as 12 mm (L/500) [28]. For convenient comparison of P with M_center and M_y, P_cy in Equation (3) was defined as the brace axial force corresponding to casing flexural yield and computed by equating M_center to M_y in Equation (2). The computed strength and stiffness parameters are listed in Table 3.

(3)$P_{cy}=\frac{M_y}{{\nu }_0+\frac{M_y}{P_{cr}}}$

2.2. Test Setup

The BRB specimens were subjected to cyclic load through a 3000 kN actuator in the brace and subassembly setups, as illustrated in Figure 3. In the brace test setup, which subjects the specimens to axial tension and compression, the specimens were constrained at one end through a pin support connected to a reaction block and pin-connected to the actuator at the opposite end. The movement of the actuator was constrained to be in the axial direction of the test specimen through a guide frame and a set of rollers, as illustrated in Figure 3a. In the subassembly test setup, the BRB specimens were inclined at an angle of 33.69° and pin-connected to the column, as illustrated in Figure 3b, resulting in a 4 m story height and 6 m bay width configuration. The column base and the opposite end of the BRB specimen were pin-connected to the strong floor. The out-of-plane movement of the column was restrained by a lateral support frame and a set of rollers, as illustrated in Figure 3b. One of the four C216 t8–C267 t6 and one of the two S125 t9–S200 t9 BRB specimens were tested in the subassembly setup, while the other specimens were tested in the brace test setup.

2.3. Instrumentation

The brace’s axial deformation was monitored through displacement transducer 1, attached as illustrated in Figure 3. Moreover, the in-plane vertical and out-of-plane horizontal displacement of the BRB was monitored through displacement transducers 2 and 3, respectively, attached at the mid-length of the BRB. In addition, longitudinal and tangential strain components at the end of the stiffeners and BRB mid-length were monitored through strain gauges 1 to 10, arranged as illustrated in Figure 4. Strain gauges 1, 3, 4, 7, and 9 were adopted to measure longitudinal strain components, while strain gauges 2, 5, 6, 8, and 10 were adopted to measure tangential strain components.

2.4. Loading Protocol

The quasi-static cyclic loading protocol adopted from AISC seismic provision [29] and applied in the test is illustrated in Figure 5. The loading protocol starts with two cycles of loading, at Δ_by loading amplitude, followed by two cycles of 0.5Δ_bm, 1.0Δ_bm, 1.5Δ_bm, and 2.0Δ_bm. Here, Δ_by and Δ_bm indicate brace deformation at core yielding and design story drift, respectively [29]. Δ_bm indicates displacement amplitude at the design story drift and was set to be 1.0% of the story height [29], and Δ_by represents brace-yielding displacement. Following the 2.0Δ_bm cycle, the loading protocol continues with fatigue loading at 1.5 Δ_bm loading amplitude until the cumulative plastic deformation exceeds 200 Δ_by [29]. The fatigue loading is only required for the brace test setup [29].

The brace’s axial deformation (δ) and the story drift (d) were related by Equation (4). L and L_B are as defined in Figure 6. The brace’s axial deformation (δ) was monitored through displacement transducer 1 in all the tests. d and δ corresponding to 2.0Δ_bm were 80 mm and 66.56 mm, respectively, for the 4 m by 6 m subassembly utilized in the test.

(4)$\delta =\frac{L\times d}{L_B}$

3. Test Results

3.1. Circular Specimens

Figure 7 illustrates the brace’s axial deformation (δ), measured by displacement transducer 1 versus the applied force. Compressive force and displacement are indicated on the positive axis. To distinguish in which test setup the specimens were tested, “B” and “S” were added at the end of the specimen names to indicate brace and subassembly test setups, respectively. C216 t8–C267 t6-B1, C216 t8–C267 t6-B2, and C216 t8–C267 t6-B3 represent the three specimens of C216 t8–C267 t6 tested in the brace test setup.

As illustrated in Figure 7 and Figure 8, and summarized in Table 4, all the C216 t8–C267 t6 specimens tested in the brace and subassembly test setup failed by global buckling except C216 t8–C267 t6-S-B2, where the test was terminated for safety. Among the C216 t8–C267 t6 specimens, C216 t8–C267 t6-S and C216 t8–C267 t6-B1 failed prematurely at the first compressive loading of the 1.0Δ_bm cycle, while C216 t8–C267 t6-B2 and C216 t8–C267 t6-B3 exhibited stable hysteresis up to the first compressive loading of the 2.0Δ_bm cycle, achieving a maximum core strain of 1.46% and 1.10% in tension and compression, respectively. Similarly, the C216 t6–C267 t6-B specimen, which had the highest P_cr/P_y ratio among the circular specimens, did not fail by global buckling and exhibited a stable hysteresis up to a core strain of 1.42% in tension and 1.06% in compression. As illustrated in Figure 7e, C216 t6–C267 t6-B exhibited stable hysteresis until compressive strength loss occurred in the second 1.5Δ_bm loading cycle without any visible damage or global buckling, as illustrated in Figure 8d. Loading was continued to the next loading step, and the specimen exhibited a stable response up to 1.42% core strain in tension. However, its strength deteriorated in the next compressive loading step without global buckling or noticeable damage. To investigate the cause of failure, and inspect the core while preserving the polymer infill, specimen C216 t6–C267 t6-B was cut by a water jet. As illustrated in Figure 9, there was no local buckling or other defects on the core.

Specimen C165 t7–C216 t6-B, with the lowest P_cr/P_y ratio among the circular specimens, failed by global buckling at the first compressive loading of the 0.5Δ_bm loading cycle. At the onset of global buckling, P_max/P_cr and P_max/P_cy were 0.97 and 1.15, respectively. In the C216 t8–C267 t6 specimens, global buckling occurred at P_max/P_cr and P_max/P_cy ratios ranging from 0.82 to 0.93 and 0.99 to 1.14, respectively. In specimen C216 t6–C267 t6, where global buckling was not observed, the maximum axial compressive load was 68% and 82% of P_cr and P_cy, respectively.

Figure 10 illustrates the typical longitudinal casing strain, measured at the center of the BRB specimens with and without global buckling. Evident from the graphs, the casing provided sufficient restraint against global buckling until yielding occurred. Similar test results have been reported by Alemayehu et al. [14].

For the core and casing size combination of the tested circular BRBs, global buckling was the governing failure mode. Evident from the casing strain distribution and P_max/P_cy, global buckling resulted, owing to casing yielding at forces 3–18% lower than P_cr.

During all the tests, varying degrees of unsolidified filler material leakage were observed. Such a phenomenon was not present when the filler material was used as part of the composite slab in previous studies [17].

3.2. Square Specimens

Figure 11 illustrates the measured force in the square specimens versus the brace’s axial displacement. Specimens S125 t9–S200 t9-S, S125 t9–S200 t9-B, and S125 t7–S200 t9-B failed by core rupture in the first tension loading of the 1.0Δ_bm cycle, as illustrated in Figure 11a–c and Figure 12a. The rupture occurred at a core strain ranging from 0.42% to 0.71%. Comparison of the core strain gauge reading, as illustrated in Figure 13a, indicates the presence of stress concentration at the end of the core projection stiffener. The stress concentration was not exhibited in the circular specimens, as illustrated in Figure 13b. Table 5 summarizes the maximum force and core strain before rupture occurred.

The square specimen S100 t9–S175 t6-B, with P_cr/P_y and P_cy/P_y ratios of 0.9 and 0.76, respectively, failed by global buckling under a compressive force equal to 77% of $P_{cr}$. When global buckling occurred, the P_max/P_cy ratio was 0.92, suggesting that yielding of the casing resulted in global buckling, although the maximum force was lower than $P_{cr}$.

Figure 13 illustrates the comparison of strain at different core locations in square and circular specimens. Evident from the graphs, the strain at the end of the core projection stiffener was above the strain in the yielding portion of the BRB core, implying the existence of stress concentration. In contrast, stress concentration was not observed in the circular specimens up to core strains four times the core strain at the onset of rupture in square specimens.

4. Finite Element Analysis

To elucidate the behavior of the proposed BRB, an analytical model of C216 t8–C267 t6-B3 and S125 t9–S200 t9-B was formulated using the finite element program ABAQUS (Dassault Systemes Simulia Corp., Johnston, RI, USA) [30]. The interaction properties and adapted material models are summarized in Table 6. To reflect the cyclic response of the BRB, the material nonlinearity of the steel core and casing was considered using the Chaboche combined isotropic and kinematic hardening model. The Chaboche model parameters were independently calibrated for the square and circular specimens analyzed. The calibrated hardening parameters with three back stresses are listed in Table 7. Material properties of the stiffener and end connectors at the ends of the BRB were modeled using the Von-Mises yield criteria, using stress–strain relations obtained by the coupon test (Table 2). The weld filler material in the core-stiffener slot weld detail illustrated in Figure 2 was modeled as a bilinear material with a yield stress, ultimate stress, and maximum strain of 520 MPa, 580 MPa, and 0.29, respectively. The elastic modulus of steel adopted for all steel and weld components was 200 GPa. The polymer infill was modeled as an elastic material with elastic modulus and Poisson’s ratio of 461 MPa and 0.39. The finite element models were meshed using 20-node solid quadratic elements with reduced integration, C3D20R. Interaction between the steel core and filler material was modeled as hard contact, with no penetration in compression and allowing separation in tension. The interface was modeled as frictionless, owing to the presence of a slippery layer of unsolidified polymer on top of the debonding material layer. The interaction between the filler material and the casing was modeled as a tied surface, considering no relative slip was observed. The first buckling mode shape of the brace with 12 mm (L/500) amplitude [28] was adopted as an initial geometric imperfection. To replicate the boundary condition in the test, the ends of the BRB were modeled as pin connection with three direction translation restrained. The cyclic load shown in Figure 5 was applied as a displacement-controlled load on the BRB end with core projection. The nonlinear static analysis was conducted using the full Newton method as a solution technique.

Figure 14 illustrates a comparison of the test and analysis results. As can be observed from the hysteresis response, the cyclic response from the test and analysis are in good agreement. The stress concentration at the end of the core projection stiffener was investigated. Evaluation of core plastic strain (PEEQ) in the square and circular BRB indicated the presence of strain concentration at the end of the stiffener slot weld. While the strain concentration was localized at the slot weld end in the circular BRB, it resulted in a band of high strain in the square BRB. The plastic strain comparisons are illustrated in Figure 15. From these results, it can be concluded that the adopted stiffener slot welding detail is favorable for the circular BRB core but not for the square BRB core.

5. Conclusions

A tube-in-tube BRB with core projection only on one side was developed by restraining circular and square tubes with larger tubes of similar shapes, infilled with lightweight rapid-hardening polymer. Ten full-scale specimens were tested in brace and subassembly test setup, followed by finite element analysis. Circular specimens designed with P_cr/P_y, and P_cy/P_y ratios of 1.46 and 1.2 exhibited a stable hysteresis response up to 1.42% and 1.06% strain in tension and compression. The maximum compressive load developed was 68% and 82% of P_cr and P_cy, respectively. Circular specimens designed with P_cr/P_y, and P_cy/P_y, ranging from 0.82 to 1.06, and 0.7 to 0.87, respectively, and a square specimen designed with P_cr/P_y, and P_cy/P_y of 0.9 and 0.76 exhibited stable hysteresis before failing by global buckling, at compressive core strains ranging from 0.18% to 1.10%. Square specimens designed with P_cr/P_y and P_cy/P_y ranging from 1.39 to 1.50, respectively, failed by core rupture at tensile core strains ranging from 0.42% to 0.71%. Strain gauge readings and finite element analysis results indicated the presence of large plastic strain demand in square specimens because of the stiffener slot weld adopted. The same weld detail did not result in a similar plastic strain demand in the circular specimens. Based on the test results and the finite element analysis, the following conclusions can be drawn:

• Despite the leakage of unsolidified filler material, the infilled polymer provided sufficient restraint against strength or stiffness degradation due to local or global core deformation, up to a compressive core strain of 1.1%

• The slot weld detail adopted for welding stiffeners indicated a stable performance, up to a tensile core strain of 1.46% in circular BRBs. However, the slot weld resulted in a band of high plastic strain region in square BRBs, leading to a premature rupture at tensile core strains ranging from 0.42 to 0.71.

• In circular test specimens with P_cr/P_y = 1.06 and a square specimen with P_cr/P_y = 0.9, global buckling occurred at a compressive force equal to 77–82% of the critical buckling force when the casing moment reached 92–100% of the casing yield moment. This indicates that global buckling occurred owing to the yielding of the case, and both the stiffness and strength of the casing should be considered when proportioning a BRB.

Leakage of unsolidified filler material was observed during all the tests. Further research is needed to examine the influence of this phenomenon and investigate possible remedies.

Author Contributions

Conceptualization, R.W.A., Y.K., M.P. and Y.K.J.; methodology, R.W.A., Y.K., M.P. and Y.K.J.; software, R.W.A.; validation, R.W.A., Y.K., M.P., M.J.P. and Y.K.J.; formal analysis, R.W.A.; investigation, R.W.A., Y.K., M.P. and Y.K.J.; resources, Y.K., M.P. and Y.K.J.; data curation, R.W.A.; writing—original draft preparation, R.W.A.; writing—review and editing, R.W.A. and Y.K.J.; visualization, R.W.A., Y.K., M.J.P., M.P. and Y.K.J.; supervision, R.W.A., Y.K., M.J.P., M.P. and Y.K.J.; project administration, Y.K.J.; funding acquisition, Y.K., M.P. and Y.K.J. All authors have read and agreed to the published version of the manuscript.

Funding

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean Government (MSIT) (No. NRF-2020R1A2C3005687) and the Korea Agency for Infrastructure Technology Advancement (KAIA) (21AUDP-B121595-06, 21AUDP-B100343-07).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Data are contained within the article.

Conflicts of Interest

The authors declare no conflict of interest.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Figures and Tables

Figure 1. Polymer infilled tube-in-tube buckling-restrained brace.

Figure 2. Details of the proposed BRB. (All dimensions are in mm).

Figure 3. Test setup. (a) Brace test; (b) subassembly test. (All dimensions are in mm).

Figure 3. Test setup. (a) Brace test; (b) subassembly test. (All dimensions are in mm).

Figure 4. Strain gauge arrangement, orientation, and numbering.

Figure 5. Loading protocol.

Figure 6. Brace axial deformation and story drift correlation.

Figure 7. Hysteretic response of circular specimens: (a) C216 t8–C267 t6-S; (b) C216 t8–C267 t6-B1; (c) C216 t8–C267 t6-B2; (d) C216 t8–C267 t6-B3; (e) C216 t6–C267 t6-B; (f) C165 t7–C216 t6-B.

Figure 7. Hysteretic response of circular specimens: (a) C216 t8–C267 t6-S; (b) C216 t8–C267 t6-B1; (c) C216 t8–C267 t6-B2; (d) C216 t8–C267 t6-B3; (e) C216 t6–C267 t6-B; (f) C165 t7–C216 t6-B.

Figure 8. Deformed shape at the end of test: (a) C216 t8–C267 t6-S; (b) C216 t8–C267 t6-B1 and C216 t8–C267 t6-B3; (c) C216 t8–C267 t6-B2; (d) C216 t6–C267 t6-B; (e) C165 t7–C216 t6-B.

Figure 8. Deformed shape at the end of test: (a) C216 t8–C267 t6-S; (b) C216 t8–C267 t6-B1 and C216 t8–C267 t6-B3; (c) C216 t8–C267 t6-B2; (d) C216 t6–C267 t6-B; (e) C165 t7–C216 t6-B.

Figure 9. Cross-section of C216 t6–C267 t6-B after water jet cutting.

Figure 10. Typical casing longitudinal strain: (a) specimens that failed by global buckling; (b) specimens with no global buckling.

Figure 11. Hysteretic response of circular specimens: (a) S125 t9–S200 t9-S; (b) S125 t9–S200 t9-B; (c) S125 t7–S200 t9-B; (d) S100 t9–S175 t6-B.

Figure 11. Hysteretic response of circular specimens: (a) S125 t9–S200 t9-S; (b) S125 t9–S200 t9-B; (c) S125 t7–S200 t9-B; (d) S100 t9–S175 t6-B.

Figure 12. Failure mode of square specimens: (a) Core rupture at the end of unconstrained length stiffener in specimens S125 t9–S200 t9-S, S125 t9–S200 t9-B, and S125 t7–S200 t9-B; (b) global buckling of specimen S100 t9–S175 t6-B.

Figure 13. Typical core strain distribution: (a) square specimens; (b) circular specimens.

Figure 14. Comparison of finite element and results: (a) C216 t8–C267 t6-B3; (b) S125 t9–S200 t9-B.

Figure 15. Equivalent plastic strain (PEEQ) distribution: (a) S125 t9–S200 t9-B at 0.5Δbm; (b) C216 t8–C267 t6-B3 at 2.0Δbm.

Table 1

Test specimens.

Specimen	Shape	Number of Specimens	Core 1		Casing 1		PolymerThickness (mm)
			Size 1	Steel Type	Size 1	Steel Type
C216 t8–C267 t6	Circular	4	216.3 t8	SRT275	267.4 t6	SJT275	17.95
C216 t6–C267 t6		1	216.3 t6	SRT275	267.4 t6	SRT275	17.95
C165 t7–C216 t6		1	165.2 t7	SRT275	216.3 t6	SRT275	17.95
S125 t9–S200 t9	Square	2	125 t9	SRT275	200 t9	SRT275	26.90
S125 t7–S200 t9		1	125 t7	SRT335	200 t9	SRT275	26.90
S100 t9–S175 t6		1	100 t9	SRT275	175 t6	SRT275	29.90

¹ Outside tube diameter/width followed by wall thickness.

Table 2

Material properties.

Component	Steel Type	Yield Strength		Ultimate Strength		Elongation
		Average (MPa)	CV 3 (%)	Average (MPa)	CV 3 (%)	Average (%)	CV 3 (%)
C267 t6	SJT275	422	1.25	486	0.75	20.8	5.69
C216 t8	SRT275	437	0.35	476	0.59	16.8	6.33
C216 t6	SRT275	418	1.65	461	1.38	20.1	6.38
C165 t7	SRT275	441	1.06	475	0.56	16.1	9.12
S175 t6	SRT275	329	0.47	421	0.46	23.0	4.58
S125 t9	SRT275	386	0.79	423	0.80	18.1	6.33
S125 t7	SRT355	525	1.98	575	1.97	12.5	9.59
S100 t9	SRT275	377	1.33	426	1.66	16.0	5.24
Stiffener 1	SM355	349	1.52	524	0.84	25.9	3.85
Pin plates 2	SM355	397	1.87	534	0.23	26.9	1.53

¹ 20 mm thick. ² 30 mm thick. ³ Coefficient of variation.

Table 3

Strength and stiffness parameters.

Specimen	Core		Casing
	Py (kN)	Pu (kN)	Pcr (kN)	My (kN.m)	Pcy 1	Pcr/Py	Pcy/Py
C216 t8–C267 t6	2289	2494	2427	133	1991	1.06	0.87
C216 t6–C267 t6	1659	1826	2427	133	1991	1.46	1.20
C165 t7–C216 t6	1534	1652	1264	85	1072	0.82	0.70
S125 t9–S200 t9	1611	1765	2415	162	2048	1.5	1.27
S125 t7–S200 t9	1734	1899	2415	162	2048	1.39	1.18
S100 t9–S175 t6	1234	1396	1114	73	941	0.9	0.76

¹ Brace axial force that results in casing flexural yielding.

Table 4

Circular specimens test result.

Specimen	Pmax (kN)		δmax (mm)		εmax (%) 3		$\frac{{\mathit{P}}_{\mathit{m}\mathit{a}\mathit{x}}}{{\mathit{P}}_{\mathit{c}\mathit{r}}}$ 4	$\frac{{\mathit{P}}_{\mathit{m}\mathit{a}\mathit{x}}}{{\mathit{P}}_{\mathit{c}\mathit{y}}}$ 5	Failure Mode
	(+) 1	(−) 2	(+)	(−)	(+)	(−)
C216 t8–C267 t6-S	1987 6	2097 6	25.5	34.3	0.54	0.73	0.82	1.0	Global buckling
C216 t8–C267 t6-B1	1980	2096	15.6	29.7	0.33	0.63	0.82	0.99	Global buckling
C216 t8–C267 t6-B2	2183	2078	51.8	68.2	1.10	1.45	0.90	1.10	Test stopped for safety
C216 t8–C267 t6-B3	2267	2066	51.6	68.9	1.09	1.46	0.93	1.14	Global buckling
C216 t6–C267 t6-B	1640	1584	50.1	66.9	1.06	1.42	0.68	0.82	No global buckling
C165 t7–C216 t6-B	1231	1317	11.9	17.3	0.25	0.37	0.97	1.15	Global buckling

¹ Compression. ² Tension. ³ core strain. ⁴ Maximum compressive force to Euler buckling force ratio. ⁵ Maximum compressive force to casing yield force ratio. ⁶ Maximum brace axial force.

Table 5

Square specimens test results.

Specimen	Pmax (kN)		δmax (mm)		εmax (%) 3		$\frac{{\mathit{P}}_{\mathit{m}\mathit{a}\mathit{x}}}{{\mathit{P}}_{\mathit{c}\mathit{r}}}$ 4	$\frac{{\mathit{P}}_{\mathit{m}\mathit{a}\mathit{x}}}{{\mathit{P}}_{\mathit{c}\mathit{y}}}$ 5	Failure Mode
	(+) 1	(−) 2	(+)	(−)	(+)	(−)
S125 t9–S200 t9-S	1517 6	1589 6	17.4	30.4	0.40	0.71	0.63	0.74	Core rupture at the end of the core projection stiffener
S125 t9–S200 t9-B	1574	1546	17.9	27.4	0.42	0.64	0.65	0.77
S125 t7–S200 t9-B	1390	1362	18.0	18.1	0.42	0.42	0.58	0.68
S100 t9–S175 t6-B	863	1161	7.6	17.4	0.18	0.40	0.77	0.92	Global buckling

¹ Compression. ² Tension. ³ Core strain. ⁴ Maximum compressive force to Euler buckling force ratio. ⁵ Maximum compressive force to casing yield force ratio. ⁶ Brace axial force.

Table 6

Material model and interaction properties.

Component	Material Model	Interaction with Polymer Infill
Core	Chaboche combined isotropic and kinematic hardening	Frictionless hard contact with no penetration
Polymer infill	Elastic	-
Casing	Chaboche combined isotropic and kinematic hardening	Tie constraint
Weld	Bilinear	Frictionless hard contact with no penetration
Stiffeners and end connectors	Multilinear kinematic with true stress–true strain relation from coupon test	-

Table 7

Chaboche model parameters.

Model	${\mathit{\sigma }}_0$(MPa)	${\mathit{C}}_1$(MPa)	${\mathit{\gamma }}_1$	${\mathit{C}}_2$(MPa)	${\mathit{\gamma }}_2$	${\mathit{C}}_3$(MPa)	${\mathit{\gamma }}_3$	Q(MPa)	b
C216 t8–C267 t6-B3	190	64,515	680	123,830	9985	940	1	33.75	7.15
S125 t9–S200 t9-B	230	109,347	869	117,933	9985	4850	1	33.75	7.15