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Mega columns with several reinforced steel profiles – Experimental and numerical investigations
Structures 21 (2019) 3–21
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Mega columns with several reinforced steel profiles – Experimental and numerical investigations
T
T. Bogdana, , M. Chrzanowskib, C. Odenbreitb ⁎
a b
ArcelorMittal Global R&D, Construction and Infrastructure Application Department, 66, rue de Luxembourg, L-4009 Esch-sur-Alzette, Luxembourg ArcelorMittal Chair of Steel and Façade Engineering, FSTC, RUES, University of Luxembourg, 6, rue Richard Coudenhove-Kalergi, L-1359 Luxembourg, Luxembourg
ARTICLE INFO
ABSTRACT
Keywords: Steel concrete composite mega column Separate steel sections Down-scaled experimental tests Plastic strain distribution method
Steel reinforced concrete (SRC) columns are widely used in super high-rise buildings, since they can provide larger load bearing capacity and better ductility than traditional reinforced concrete (RC) columns. Current design code like EN 1994-1-1 (EN 1994-1-1, 2004 [1]) (limited to one single encased profile), while AISC 360-16 (ANSI/AISC 360-16, 2016 [2]) allows the design of composite sections with two or more encased sections, although the way to perform such design is not detailed. To understand better the structural behaviour of such composite mega columns and provide a easy to use design method, a two-phase experimental campaign was conducted on scaled isolated steel reinforced concrete (ISRC) columns. Phase 1 of the study includes six 1/4scaled ISRC columns under static loads: every two of the specimens are loaded statically with the eccentricity ratio of 0, 10%, and 15%, respectively. Phase 2 of the study includes four 1/6-scaled ISRC columns under quasistatic loads: every two of the specimens were loaded under simulated seismic loads with the equivalent eccentricity ratios of 10% and 15%, respectively. A finite element analysis was conducted as a supplement to the physical tests to provide a deeper insight into the behaviour of SRC columns. It is concluded from these experiments that sufficient composite action exists between the concrete and the steel sections for the tested SRC specimens, and that the current code provisions are applicable for the considered configuration, in predicting the flexural capacity of SRC columns when the eccentricity ratio is less than or equal to 15%. The present paper summarizes the principles and an application method for the design of such columns under combined axial compression and bending. The method is based on simplifications provided in EN 1994–1-1. The validation of the method is made using experimental and numerical results.
1. Introduction Composite columns are frequently used in high rise buildings. Two commonly used types of composite columns for tall buildings are concrete encased composite columns and concrete filled steel tube columns. The concrete-encased composite column contains a structural steel with or without shear connectors and the surrounding concrete which is further reinforced by longitudinal bars and transverse bars. By utilizing the composite action between the concrete and the steel section, the capacity of the composite column is higher than the summation of the capacities of the concrete and the steel section [3]. A substantial number of experimental tests have been conducted to observe the behaviour of concrete encased composite columns subjected to axial and eccentric loads [4–10].
⁎
The current design codes, [1,2] consider composite structural elements but they do not offer specific provisions on the design of composite sections with two or more encased steel sections. The lack of knowledge on the axial, bending and shear behaviour of composite mega columns, along with the resulting lack of clarity in the codes, leads to the need for experimental performance tests. These tests provide a base for the simplified design approach and are used to calibrate numerical models to describe the designs and to validate the results. The experimental campaign took place within CABR Laboratories and the Laboratories of Tsinghua University, Beijing [11,12]. Experimental results are validated by finite element models (FEM) in accordance with the experimental values. FEM allow also for a deeper insight on steel-concrete interaction forces and stress distribution.
Corresponding author. E-mail address: [email protected] (T. Bogdan).
https://doi.org/10.1016/j.istruc.2019.06.024 Received 30 November 2018; Received in revised form 28 June 2019; Accepted 28 June 2019 Available online 10 July 2019 2352-0124/ © 2019 Institution of Structural Engineers. Published by Elsevier Ltd. All rights reserved.
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Polystyrene t=10mm
25
450 180
630
80
Endplate
130
220
900
1000
225
Lateral Plate t=8mm Q235
225
a)
10
25.5
53
55
(4)HEM100(H120X106X12X20)
53
25.5
450
3.25mm @ 80mm Yield strength = 500Mpa
450
60
b)
60
c)
Fig. 1. Details of the static tests: a) steel layout – longitudinal view; b) Cross-section details; c) Shear studs layout (Units: mm).
Finally, simplified design methods based on European, Chinese, and US codes are suggested and the results are compared to the numerical and experimental values. Then, through three examples of application to selected mega column cross-sections, the given simplified design methods are proven to be an effective and handy design tool.
2. Experimental program The column specimens' overall layout and geometry have been based on suggested sections of representative full-scale composite columns used for high-rise buildings, from Magnusson Klemencic
Fig. 2. Phase 1: Specimens fabrication: a) overview; b) longitudinal bar details; d) concrete mold.
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Fig. 3. Phase 1: Test setup: a) static setup in laboratory b) boundary conditions; c) load application.
concentrated load, using a 200-tons servo system at Tsinghua University [11]. The experimental setup consists in two hinges, as shown in Fig. 3. One hinge is placed on the ground and fixed by blocks to avoid any horizontal displacements. The other one is placed on the top of the test specimen, connected to a transition beam that serves as a connector between the hinge, the horizontal actuator and the vertical actuator. Sand layers are placed between the test specimen and the hinge, and polytetrafluoroethylene (PTFE) plates are placed under the end plates of the steel sections, to make sure that the steel – concrete interface slip can be developed near the test specimen ends to simulate real boundary conditions. In real structures, relative slip may occur along the composite column at any point. If the sand layers and PTFE plates are not provided, the rigid surface of the hinge will force the test specimen end to stay in the same plane. Consequently, relative displacement between the concrete and the steel sections near the test specimen ends will be limited. Fig. 2 shows different stages of specimens' fabrication. The loading rate is slow enough to avoid dynamic effects. Loads are increased to peak value until the specimens failed. Each two of specimens were loaded under the same eccentricity ratio e/h: 0% (E00-1, E00-2), 10% (E10-1, E10-2), and 15% (E15-1, E15-2), where: “h” is the cross section height and “e” is the distance between the neutral axis and the load application (Fig. 3). Due to second order effects, the actual eccentricity ratios got larger. The exact values of these eccentricities are presented in Table 2. During the test, the lateral displacement of the transition beam is strictly controlled by the horizontal actuators to
Table 1 Phase 1: Selected materials for the tests. Concrete Hot rolled jumbo sections Longitudinal reinforcement Stirrups Shear studs
C60 (fck = 60 MPa) according to Chinese Code, with 5 mm aggregate maximum size HEM100 (120x106x12x20) ASTM A572 Gr.50/S355 (fyk = 355 MPa = 50ksi) 8 mm dia HRB400 (ASTM A615), (fyk = 400 MPa) 3.25 mm dia @ 80 mm HRB500 (fyk = 500 MPa) 6 mm DIA × 25 mm Nelson headed Studs; ASTM A108 @ 144 mm O·C. 5 mm DIA × 20 mm Nelson headed Studs; ASTM A108 @ 144 mm O.C. Grade 4.8
Associates, Seattle (MKA). Overall dimensions of the columns are 1800 × 1800 mm, with a height of 9 m at the lobby level (base of the tower) and 4.5 m at the typical floor. The experimental campaign is divided in 2 phases: 6 static tests and 4 quasi-static tests [13]. 2.1. Phase 1 – static tests Phase 1 contains 6 specimens with the same geometry configuration, detailed in Fig. 1. The specimens are tested to failure by applying Table 2 Phase 1: Obtained material strengths (Units: MPa). Specimen ID
Actual eccentricities e/h [%]
Concrete cubic strength
Yield strength of steel section flange
Yield strength of steel section web
Yield strength of longitudinal bar
Yield strength of transverse bar
E00-1 E00-2 E10-1 E10-2 E15-1 E15-2
0.0 0.0 12.4 12.9 19.9 17.9
61.17 56.62 59.75 68.40 67.50 75.17
408 398 423 383 377 389
523 411 435 415 404 405
438
597
5
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Fig. 4. Phase 1: Configuration of strain and displacement gauges.
corner cracks
corner cracks crush of the concrete
vertical crack
vertical crack
new crack
corner cracks
a)
corner cracks
b)
c)
Fig. 5. Phase 1: Fig. 4. Crack development of specimens subjected to eccentric loads.
ensure that the lateral displacement of the top end has zero value. The selected materials for the static tests are presented in Table 1. Since the concrete strength is sensitive to its age, concrete cubes were tested or each specimen before and after the tests. Table 2 presents the
actual material strengths. The data in this test program include measuring the strain on the profiles, longitudinal bars, ties and concrete surface. The strain sensors are placed on four sections for each specimen, as shown in Fig. 4. The
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vertical cracks
initial cracks
crush of the concrete
horizontal cracks
a)
b)
Fig. 6. Phase 1: Crack development of specimens subjected to eccentric loads: a) 70% of the maximum load; b) failure load.
Table 3 Phase 1: Specimen capacities (Units: kN,m). Spec.
Nmax
Mmax
Ecc Ratio
efailure/einitial
E00-1 E00-2 E10-1 E10-2 E15-1 E15-2
17,082 15,325 14,360 13,231 12,041 12,759
143 52 803 767 1076 1026
1.9% 0.8% 12.4% 12.9% 19.9% 17.9%
– – 1.24 1.29 1.33 1.19
Fig. 7. Phase 1: a) Moment vs. rotation at mid-section; b) bending moment – axial force interaction curves.
Fig. 8. Phase 1: Curvature development at mid-height of specimens. a) Specimen E10-1; b) Specimen E15-1.
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7
130 140 30 300
3.25@36
300
200
2.95@55
(4)HEM80(H80X70X12X12)
300
292
b)
300
292
300
35
20
25
20
Lateral Plate t=8mm Q235 Polystyrene t=5mm
35
300
30
300
100
Steel Endplate
40
a)
40
c)
Fig. 9. Phase 2: Quasi-static tests: a) steel layout – longitudinal; b) steel layout – cross-section; c) shear studs layout.
Table 4 Phase 2: Selected materials for the tests (Units: MPa). Concrete Hot rolled jumbo sections
C60 (fck = 60 MPa), with 5 mm aggregate maximum size Horizontal: 140x73x4.7 × 6.9 mm Vertical: HEM80 (80 × 60 × 12 × 12 mm) S235 (fyk = 235 MPa) 6/8 mm dia - HRB400 (ASTM A615), (fyk = 400 MPa) 3.25 mm dia @ 36 mm HRB500 (fyk = 500 MPa) 5 mm DIA × 25 mm Nelson headed Studs; ASTM A108 @ 150 mm O.C. 5 mm DIA × 15 mm Nelson headed Studs; ASTM A108 @ 150 mm O.C Grade 4.8
Longitudinal reinforcement Stirrups Shear studs
N-Axial Force
100
300
600
900
V-Shear Force
Critical Section
2V-Shear Force 100
1900
(3.25mmDIA@36mm (Yield strength = 500Mpa)
150
3.25@36
Critical Section
V-Shear Force
a)
b)
N-Axial Force
Fig. 10. Phase 2: Quasi-static tests: a) laboratory setup; b) boundary conditions; c) test setup.
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c)
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Table 5 Phase 2: Obtained material strengths (Units: MPa). Specimen ID
Eccentricities e/h [%]
D10-1 D10-2 D15-1 D15-2
Concrete cubic strength
10.0 10.0 15.0 15.0
Steel section Ultimate strength
Yield strength
Ultimate strength
Yield strength
Ultimate strength
457
603
459
689
572
638
70.3 70.6 76.3 67.3
Spec.
Design values
Experimental values
Ratio (%)
E00-1 E00-2 E10-1 E10-2 E15-1 E15-2
17,392
17,082 15,325 14,360 13,231 12,041 12,759
102% 114% 99% 108% 99% 94%
11,924
The static test results confirm the composite mega column expected behaviour, and provide additional evidence of vertical and lateral displacements, curvature and ductility, axial and bending stiffness, and relative displacements between steel sections and concrete. As the axial load increases, cracks develop – at first vertically, where the concrete cover is limited, and then horizontally, when the specimen is reaching failure. When the deflections are large, the axial load decreases in value and the test stops. On purely axial specimens, the axial load starts decreasing after reaching the peak value due to an increased vertical deflection. The second load drop occurs when the column fails, when sudden, significant deflections and damage occurs, Fig. 25a). Eccentric specimens do not experience a sudden drop of applied load, as the axial load gradually decreases after the peak point. Meanwhile, the horizontal deflection and concrete damage continuously develop, especially on areas of the concrete under tension. On purely axial specimens, buckling of the longitudinal rebar and breakage of ties are observed. Figs. 5 and 6 present the crack development during the loading phase. Steel profiles yield, but do not buckle. No significant deformations of the profiles are registered. Fig. 7a) present the bending moment vs. rotation at the mid-section of the specimens. It can be observed that the bending moment of the mid-section remains constant as the curvature develops. The slopes of the curves become smaller with the increase of rotation, suggesting that the bending stiffness decreases as the load increases. The area under the curve can be expressed in absorbed energy by the specimen, since the energy can be expressed as the moment times the angle. Thus, for columns with an eccentricity ratio less than 15%, the ductility of the column in terms of ‘moment vs. rotation’ is satisfactory. The N-M interaction points from Fig. 7b) were evaluated using the Plumier et al. method [14]. Average material strengths of the 6 tests specimens were used., creating divergences between the design curves and recorded data points. For specimens subjected to eccentric loads,
Table 7 Axial force capacity – comparisons (Units: kN, mm). Spec.
E00-1 E00-2 E10-1 E10-2 E15-1 E15-2
Experimental values
Transverse rebar
Yield strength
Table 6 Phase 1: Axial force capacity – comparisons (Units: kN).
14,227
Longitudinal rebar
Design values
Nexp
Δexp
Ndesign
Δdesign
17,082 15,325 14,360 13,231 12,041 12,759
4.17 3.43 3.55 3.46 2.79 2.70
17,006 15,879 14,500 14,031 12,521 13,012
3.98 4.25 3.60 3.34 3.35 3.43
displacement sensor consists in two parts: a slide rheostat and a steel box. The slide rheostat is stuck on the surface of the steel section, surrounded by the steel box and the steel box is surrounded by concrete. During the test, the slide rheostat will move with the steel section and the box will move with the concrete, so the relative displacement can be detected.
Fig. 11. Phase 2: Load introduction: a) axial load history; b) horizontal load history.
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Fig. 12. Phase 2: Load introduction: a) strain sensor on concrete; b) strain sensor on critical Section 1; c) strain sensor on critical Section 2.
test results show good correlation with the curves. For specimens subjected to axial loads, test results are smaller than predictions since the concrete strengths of E00-1 and E00-2 specimens are lower than the average value of the six, and the calculated results have not considered
yet the buckling and P-Δ effects. Comparisons between the design values and experimental ones are given in Table 6. Table 3 lists the capacities and the corresponding bending moments on the mid-height cross-section of the columns. The bending moment
Fig. 13. Phase 2: Crack distribution and failure modes of specimens: a) Specimen D10-1; b) Specimen D15-1.
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Fig. 14. Phase 2: Strain distribution: a) Specimen D10-1; b) Specimen D15-1.
was determined by Eq. (1):
M = N (ei + )
(1)
where ei is the initial eccentricity of the specimen, and δ is the horizontal deflection of the mid-height cross-section due to the second order effect. Although the initial eccentricity of specimen E00-1 and E00-2 was zero, horizontal deflections of these two columns were recorded during the test. Nevertheless, the eccentricities were very small under the maximum load level, so that the axial resistances of these two specimens were not significantly influenced. For specimens subjected to eccentric loads, the eccentricities under the maximum load level were 19%~33% larger than the initial eccentricities due to the second order effect. Since this paper deals with short columns, the second order effect will not be discussed in detail. Fig. 8 represents the curvature development for specimens E10-1 and E15-1. Similar behaviour was observed for specimens E10-2 and E15-2. A linear regression is created using points of normal stain versus relative position under a certain load level. Then, the slope of the regressed straight line is taken as the curvature. The obtained curvature of the concrete correlates with that of the steel section very well. Together with the validation of ‘Plane Section Assumption’, it is reliable to assume the curvatures of different materials on a particular section are the same. The column curvature was calculated by normal strain of the steel sections. In addition, it can be observed that the curvature developed more rapidly when the load level was beyond 60%, indicating the reduction of bending stiffness.
Fig. 15. Phase 2: specimen deformation.
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Fig. 16. Phase 2: hysteretic curves a) D10-1(up); b) D10-1(low); c) D15-1(up); d) D15-1(low); e) D10-1/D10-2 envelope; f) D15-1/D15-2 envelope.
2.2. Phase 2 – Quasi-static tests Phase 2 of the experimental campaign consist in four 1/6 scaled specimens with their geometrical configurations presented in Fig. 9 and Table 4. The behaviour, including the capacity, deformation capacity, and hysteretic performance of the specimens under simulated seismic loads, are examined according to different eccentricities. Axial force has been applied with different eccentricities values: 10% - specimens D10-1 and D10-2, and 15% -specimens D15-1 and D15-2, to account for the diversity in materials and fabrication. Horizontal force is applied at the mid-height of the specimens. Transverse load (V) is equal to two times the horizontal end reaction on the top and bottom of the specimens. A bottom hinge is placed on the ground and a top hinge is installed on the top of the specimen, connecting it to the vertical actuator. Both the hinges are fixed by a frame that restricts horizontal displacements, as well as out-of-plane
Fig. 17. Phase 2: Specimens energy consumption.
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Fig. 18. Plastic Simplified Method: a) Interaction curve; b) Equivalent cross-section definition.
displacements Fig. 10c. The defined material characterizations are given in Table 4. The concrete compressive strength was obtained on cubes of 150 mm. The aimed concreted grade was C60, while the steel sections and beams were made of Q460 and S235 steel, the tested values are presented in Table 5. As shown in Fig. 11, axial load slowly increases until it reaches the gravity load. Then, the axial load and the transverse load are increased proportionally. The axial load is increased by 500 kN steps, and the lateral load is applied cyclically, while keeping the axial load constant. Displacement and strain sensor were installed, having the layout presented in Fig. 12. Critical Section 1 was near the conjunction of the column and the beam, located 100 mm from the corner of the column, while critical Section 2 was near the end of the column, 300 mm away from critical Section 1. The sensors were installed on both the upper and lower columns. General behaviours of the quasi-static tests are quite alike, the eccentricity ratios do not differ much. Crack distributions and failure modes indicate that the specimens fail in combined compression and flexure patterns, as shown in Fig. 13. When the first step of the loading is completed, the test specimens do not show significant deformations and cracks. During the second step of the loading, cracks and concrete crush gradually develop, and the cumulative damage at the column corners leads to the failure of the specimen. All four specimens failed in combined compression and bending – the specimen failed because the corners of the concrete were crushed – which met the purpose of the experiment program. The final crack distributions of the specimens are presented in Fig. 13. The specimens held integrity during the whole loading process. Despite the surrounding concrete was damaged due to lack of confinement, the concrete core remains intact due to the confinement effect provided by the steel sections. In turn, the concrete core helped ensure that the steel sections would not buckle when the vertical load was very large. Based on the strain distribution of the steel profile and reinforcement, the “Plane Section Assumption” can be verified, Fig. 14. Test results indicates that specimen D10-1 there is a linearity between the steel profile and the longitudinal reinforcement, while the specimens with higher eccentricity D15-1, the slip effect between the steel- concrete interface is observed after the peak load occurs. The rotation of the beam leads to different loading conditions for the upper and lower column. Therefore, the measured axial load, lateral
load, and lateral displacement must be modified to account for the rotation. Fig. 15 presents the deformation pattern of the upper half of the specimen. Suppose the rotation of the ‘ground beam’ is α – positive in clockwise direction, and negative in counter-clockwise direction. In addition, assume the ‘ground beam’ of the specimen is a rigid body, which does not have any deformation during the test. This assumption is reasonable because no significant deformation was observed within the ‘ground beam’ during the test. N0,V0 and Δ0 are the recorded data of axial load, lateral load, and lateral displacement, where N0 was directly recorded by the system; Δ0 was recorded by a displacement sensor installed in the middle of the specimen; and V0 is one-half of the load applied by the lateral actuator. Nup, Vup, and Δup are the equivalent axial load, lateral load, and lateral displacement of the upper column. ‘h’ is the height of one-half of the specimen, 1200 mm. According to the geometric relationships, the modified test data can be expressed as follows:
{Nup = N0 cos =
0 /cos
+ V0 sin Vup = + h tan
N0 cos
+ V0 sin
up
Nlow = N0 cos + V0 sin Vlow = N0 cos + V0 sin h tan low = 0 /cos (2)
Hysteretic curves of the specimen are presented behaviour Fig. 16. Except for specimen D10-1, other specimens have all been affected by the rotation of the beam. The beam of specimen D15-1, for example, rotated counter-clockwise during the test. When the specimen moved toward right, the rotation made the equivalent lateral displacement of the upper column smaller, and that of the lower column larger. Therefore, the hysteretic curve of specimen D15-1(up) is more spread out in the negative part, while the curve of specimen D15-1(low) is more spread out in the positive part. Although the behaviour of the specimens was affected by the rotation of the beams, the hysteretic curves are still stable. The specimens showed some pinching at the beginning of the test, but the degree of pinching was mitigated as the lateral displacement was increasing. For the last several circles of the loading, the hysteretic curves are round and stable, suggesting a good ability of energy dissipation. The hypothesis of ‘Plane Section Assumption,’ is verified within the 15% eccentricity ratio. Despite the damage to the concrete cover, the concrete core remains intact due to the confinement effect provided by
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Fig. 19. Definition of equivalent plates to rebars.
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Fig. 20. Definition of equivalent plates to steel profile.
the steel sections. The concrete core confinement prevents the steel sections from buckling. Local buckling of longitudinal rebar and breakage of the transverse ties are detected. The ability to dissipate energy is shown by stable and round hysteretic curves, without a large dependence on the eccentricity ratio. When the lateral displacement grows, materials yield and friction between the materials consume energy. Therefore, energy consumption increases, as does the lateral displacement Fig. 17.
partially encased sections and concrete filled rectangular and circular tubes. The first method is a numerical and general method, while the second one is a simplified analytical method, applied only to doubly symmetrical sections and uniform along the height of the element. By using the simplified method, the interaction curve can be approached by a succession of lines joining 4 characteristic points A, B, C, D, as shown in Fig. 18. The following assumptions should also be considered, because are underlying the prescriptions from EN 1994-1-1: there is a complete interaction between steel and concrete, the plane sections remain plane after deformation and the concrete resistance in traction is neglected. The development of a method of calculation of concrete sections with several encased steel sections requires the calculation of section characteristics like the moment of inertia, the plastic moment, the
3. Validation of FEM and adapted code 3.1. Adapted plastic distribution method EN 1994-1-1 - Clause 6.7 [1] provides two design methods in the design of composite compression members with encased sections,
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Fig. 21. Stress block distribution for rectangular column with 4 encased profiles [16].
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Fig. 22. Material constitutive curves: a) concrete; b) steel [16].
Elastic Cap Steel Beam
Concrete
Steel Column
a)
c) Fig. 23. Phase 1: Abaqus FE models: a) concrete mesh; b) steel section mesh, c) boundary conditions.
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Fig. 24. Phase 1: Abaqus FE models: spring connector.
Fig. 25. Phase 1: Axial force vs. vertical deflection.
elastic neutral axis and the plastic neutral axis of huge mega column sections. Such calculation can be made either by means of dedicated software in which all the data are given, each reinforcing bar being defined in position and section. The calculation can also be “handmade”, in which case the calculation becomes tedious due to the high number of longitudinal bars in mega columns. In order to facilitate such calculation, some simplifications are proposed hereafter which replaces lines of rebars by equivalent plates, Fig. 19. The steel profiles are defined as equivalent plates following the suggestions in Fig. 20.
The presented method in accordance to EN 1994-1-1 allows to evaluate the nominal resistance of the composite column, based on the plastic stress distribution of the composite cross-sections [15]. A twostep calculation can be used to determine the flexural resistance of the composite cross-section, as shown in Fig. 21 [7]: Step 1: Determine the position of the neutral axis (N.A.) based on the balance condition of the axial load. Four distinct situations of the position of the N.A are identified. Step 2: Calculate the flexural resistance of the composite cross-
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implemented numerical model of concrete. The numerical model fails to simulate the situation where the concrete smashing occurs. Nevertheless, the model is able to predict the bearing capacity of the column and will be used furthermore in the validation of the N-M interaction curve. The column capacity decreases as the load eccentricity increases and deflection is developing, Fig. 25b) and c). Contrary to pure axial specimens, eccentric specimens did not experienced sudden drop of the applied load, the axial load is decreasing gradually after the peak point. Table 7 presents the numerical values of the axial load vs. vertical displacement curves. The numerical results are under 10% difference from the experimental tests. In conclusion the simplifications made for the numerical model can be used for a further sensitivity study. The FEM and analytical interaction curves, presented in Fig. 26, show results like the capacity of the experimentally tested mega column. The Fiber model represents the classical pivot method developed for the reinforced concrete structural elements, where the strains are considered linear along the cross-section [3,17]. Tests results show good convergence with the numerical simulations. For specimen subjected to axial load, test results are smaller than prediction given by both fiber and the simplified method. The comparison of crack development can be observed in Figs. 27 and 28. For the specimens subjected only to axial load, the formation of vertical cracks can be observed on the face of the concrete side. The crush of the concrete in the compressed zone was limited due to the definition of the concrete material using concrete damage plasticity law. Similar behaviour can be observed for specimens subjected to eccentric loads.
Fig. 26. Phase 1: Interaction curve bending moment - axial force constructed using FEM models.
section based on the position of the N.A. CL represents the neutral axis of the cross-section. 3.2. Validation of test results using FEM models Software Abaqus [16] has been chosen for the FEM analyses only for Phase 1 specimens subjected to axial load. The definition of the concrete behaviour has been made by using a concrete damage plasticity model. The uniaxial constitutive law for concrete material has been obtained using the EN 1992-1-1 [17] material law as show in Fig. 22. The steel material for rebars and steel profile was defined using a bilinear material law with values from the experimental tests. Only half of the ISRC column was built in the program due to the symmetry. An overview of the FE model and the mesh of concrete and steel sections are presented in Fig. 23. An elastic ‘cap’ was positioned above the model to simulate the sand layer. Axial load was applied to the reference point (RP), whose position was the same as the center of the hinge. The load was first transferred to the elastic cap through constrains between the RP and cap top surface, then to the column itself. The concrete and steel sections were simulated by three dimensional eight-node solid elements, and bars are simulated by T3D2 truss elements. To simplify the model, bars and steel beams were TIE connected to the concrete – no relative displacement and strain difference. The interaction of concrete and steel section interface was simulated by nonlinear springs along each dimension, Fig. 24. There were three spring connectors at each node pair, one in the normal direction and two in the tangential direction. The node of concrete and steel of each node pair overlapped in space, the initial length of the spring elements was zero. Before peak point, the simulated axial load vs. vertical displacement' curve follows similar paths to the experimental curve at all three eccentricities values. The reduction of the axial capacity occurred due to the degradation of material strength, cracks in the concrete, spill and damage of the concrete and buckling of the longitudinal bars, Fig. 25a). Small divergencies between the FEM and the experimental test could be noticed especially for 0% eccentricity specimens, due to the
4. Concluding remarks Six 1/4 scaled concrete encased composite columns with multi-separate steel sections were tested to understand better their performance and ductility behaviour. The test results were in accordance with the expected results and the specimens shown sufficient deformation capacity. The specimens are able to maintain the bending moment at the maximum requirement, while the curvature is developed until column failure. The full composite action was observed during the tests, even though the steel sections are not connected to one another. Test results of this test program reveal that the ‘Plane Section Assumption’ is generally valid for specimens with an e/h = 10% and an e/h = 15%, but the interface slip grew with the eccentricity, which suggests that the shear demand is relatively larger for mega columns. The concrete core, surrounded by the steel profiles, is highly confined, thus increasing the ductility of the composite column. Available design standards are providing no information on how to properly design reinforced column sections with more than one embedded steel profile. For this, a new extended method based on Eurocode 4 simplified design method has been developed in order to propose a design guidance for composite columns with several steel profiles embedded. The method is an extension of the Plastic Distribution Method and takes into account all the simplified assumptions that are defined in EN 1994-1-1 - Clause 6.7. The results of the experimental campaign have been validated with FEM methods and compared with simplified code provisions methods. The comparison shows matching results. The simplifications brought to the numerical simulations can be adapted for further parametric studies. The simple adapted method can be used to perform “hand-made” evaluation of the axial force-bending moment interaction curve.
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vertical crack
a)
b)
corner cracks crush of the concrete
corner cracks
c)
d)
Fig. 27. Phase 1: Crack comparison for specimens subjected to axial loads: a) Specimen E00-1 at 70% of failure load; b) Specimen E00-1 at failure load.
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crush of the concrete
a)
horizontal cracks
b)
Fig. 28. Phase 1: Crack comparison for specimens subjected to eccentric loads; a) Specimen E15-1 at failure load – damage evolution; b) Specimen E15-1 at failure load – experimental test;
Acknowledgements
[6] Mirza SA, Tikka TK. Flexural stiffness of composite columns subjected to major axis bending. ACI Struct J 1999;96(1):19–28. [7] Smart Composite Components - Concrete Structures Reinforced by Steel Profiles, Smart CoCo, European Commission. Research Programme of the Research Funds for Coal and Steel, TGS8 2016. RFSR-CT-2012-00031. [8] Morino S. Recent developments in hybrid structures in Japan—research, design and construction. Eng Struct 1998;20(4):336–46. [9] Munoz PR, Hsu CTT. Behavior of biaxially loaded concrete-encased composite columns. J. Struct. Eng. 1997;123(9):1163–71. [10] Chen CC, Li JM, Weng CC. Experimental behaviour and strength of concrete-encased composite beam–columns with T-shaped steel section under cyclic loading. J Constr Steel Res 2005;61(7). [11] Fei D, Tao C, Congzhen X. Performance and capacity of isolated reinforced concrete columns and design approaches. CABR testing report, Beijing, China. 2015. [12] Xiao C, Deng F. Experimental study on concrete encased composite columns with separate steel sections. Steel Compos. Struct. 2017;23(4). [13] Deng F, Chen T, Xiao C. Engineering properties of composite megacolumns with separately encased hot rolled steel profiles. CTBUH research paper. 2016. [14] Plumier A, Bogdan T, Degee H. Design of columns with several encased steel profiles for combined compression and bending. Final report created for ArcelorMittal website. 2012. [15] Gerardy JC, Trabucco D, Xiao C, Davies D. Composite mega columns: Testing multiple, concrete-encased, hot rolled steel sections. CTBUH research report. 2016. [16] SIMULIA User Assistance. Abaqus, © Dassault Systèmes Simulia Corp. RI, USA: Providence; 2017. [17] EN 1992-1-1. Eurocode 2: Design of concrete structures – Part 1–1: General rules and rules for building. 2004.
This project was coordinated by the Council of Tall Buildings and Urban Habitat (CTBUH). The structural engineering firm Magnusson Klemencic Associates (MKA) provided background studies on composite mega columns projects. The China Academy of Building Research (CABR) was engaged to develop the testing program for the subject columns. The authors gratefully acknowledge the support and contributions from these organizations. References [1] EN 1994-1-1. Eurocode 4: Design of composite steel and concrete structures – Part 1–1: General rules and rules for building. 2004. [2] ANSI/AISC 360-16. Specification for structural steel buildings. 2016. [3] Ye L, Ehua F. State-of-the-art of study on the behaviors of steel reinforced concrete structure. China Civil Eng J 2000;33(5):1–11. [4] El-Tawil S, Deierlein GG. Strength and ductility of concrete encased composite columns. J Struct Eng 1999;125(9):1009–19. [5] Dundar C, Tokgoz S, Tanrikulu AK, Baran T. Behaviour of reinforced and concrete-encased composite columns subjected to biaxial bending and axial load. Build Environ 2008;43(6):1109–20.
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Structures journal homepage: www.elsevier.com/locate/structures
Mega columns with several reinforced steel profiles – Experimental and numerical investigations
T
T. Bogdana, , M. Chrzanowskib, C. Odenbreitb ⁎
a b
ArcelorMittal Global R&D, Construction and Infrastructure Application Department, 66, rue de Luxembourg, L-4009 Esch-sur-Alzette, Luxembourg ArcelorMittal Chair of Steel and Façade Engineering, FSTC, RUES, University of Luxembourg, 6, rue Richard Coudenhove-Kalergi, L-1359 Luxembourg, Luxembourg
ARTICLE INFO
ABSTRACT
Keywords: Steel concrete composite mega column Separate steel sections Down-scaled experimental tests Plastic strain distribution method
Steel reinforced concrete (SRC) columns are widely used in super high-rise buildings, since they can provide larger load bearing capacity and better ductility than traditional reinforced concrete (RC) columns. Current design code like EN 1994-1-1 (EN 1994-1-1, 2004 [1]) (limited to one single encased profile), while AISC 360-16 (ANSI/AISC 360-16, 2016 [2]) allows the design of composite sections with two or more encased sections, although the way to perform such design is not detailed. To understand better the structural behaviour of such composite mega columns and provide a easy to use design method, a two-phase experimental campaign was conducted on scaled isolated steel reinforced concrete (ISRC) columns. Phase 1 of the study includes six 1/4scaled ISRC columns under static loads: every two of the specimens are loaded statically with the eccentricity ratio of 0, 10%, and 15%, respectively. Phase 2 of the study includes four 1/6-scaled ISRC columns under quasistatic loads: every two of the specimens were loaded under simulated seismic loads with the equivalent eccentricity ratios of 10% and 15%, respectively. A finite element analysis was conducted as a supplement to the physical tests to provide a deeper insight into the behaviour of SRC columns. It is concluded from these experiments that sufficient composite action exists between the concrete and the steel sections for the tested SRC specimens, and that the current code provisions are applicable for the considered configuration, in predicting the flexural capacity of SRC columns when the eccentricity ratio is less than or equal to 15%. The present paper summarizes the principles and an application method for the design of such columns under combined axial compression and bending. The method is based on simplifications provided in EN 1994–1-1. The validation of the method is made using experimental and numerical results.
1. Introduction Composite columns are frequently used in high rise buildings. Two commonly used types of composite columns for tall buildings are concrete encased composite columns and concrete filled steel tube columns. The concrete-encased composite column contains a structural steel with or without shear connectors and the surrounding concrete which is further reinforced by longitudinal bars and transverse bars. By utilizing the composite action between the concrete and the steel section, the capacity of the composite column is higher than the summation of the capacities of the concrete and the steel section [3]. A substantial number of experimental tests have been conducted to observe the behaviour of concrete encased composite columns subjected to axial and eccentric loads [4–10].
⁎
The current design codes, [1,2] consider composite structural elements but they do not offer specific provisions on the design of composite sections with two or more encased steel sections. The lack of knowledge on the axial, bending and shear behaviour of composite mega columns, along with the resulting lack of clarity in the codes, leads to the need for experimental performance tests. These tests provide a base for the simplified design approach and are used to calibrate numerical models to describe the designs and to validate the results. The experimental campaign took place within CABR Laboratories and the Laboratories of Tsinghua University, Beijing [11,12]. Experimental results are validated by finite element models (FEM) in accordance with the experimental values. FEM allow also for a deeper insight on steel-concrete interaction forces and stress distribution.
Corresponding author. E-mail address: [email protected] (T. Bogdan).
https://doi.org/10.1016/j.istruc.2019.06.024 Received 30 November 2018; Received in revised form 28 June 2019; Accepted 28 June 2019 Available online 10 July 2019 2352-0124/ © 2019 Institution of Structural Engineers. Published by Elsevier Ltd. All rights reserved.
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Polystyrene t=10mm
25
450 180
630
80
Endplate
130
220
900
1000
225
Lateral Plate t=8mm Q235
225
a)
10
25.5
53
55
(4)HEM100(H120X106X12X20)
53
25.5
450
3.25mm @ 80mm Yield strength = 500Mpa
450
60
b)
60
c)
Fig. 1. Details of the static tests: a) steel layout – longitudinal view; b) Cross-section details; c) Shear studs layout (Units: mm).
Finally, simplified design methods based on European, Chinese, and US codes are suggested and the results are compared to the numerical and experimental values. Then, through three examples of application to selected mega column cross-sections, the given simplified design methods are proven to be an effective and handy design tool.
2. Experimental program The column specimens' overall layout and geometry have been based on suggested sections of representative full-scale composite columns used for high-rise buildings, from Magnusson Klemencic
Fig. 2. Phase 1: Specimens fabrication: a) overview; b) longitudinal bar details; d) concrete mold.
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Fig. 3. Phase 1: Test setup: a) static setup in laboratory b) boundary conditions; c) load application.
concentrated load, using a 200-tons servo system at Tsinghua University [11]. The experimental setup consists in two hinges, as shown in Fig. 3. One hinge is placed on the ground and fixed by blocks to avoid any horizontal displacements. The other one is placed on the top of the test specimen, connected to a transition beam that serves as a connector between the hinge, the horizontal actuator and the vertical actuator. Sand layers are placed between the test specimen and the hinge, and polytetrafluoroethylene (PTFE) plates are placed under the end plates of the steel sections, to make sure that the steel – concrete interface slip can be developed near the test specimen ends to simulate real boundary conditions. In real structures, relative slip may occur along the composite column at any point. If the sand layers and PTFE plates are not provided, the rigid surface of the hinge will force the test specimen end to stay in the same plane. Consequently, relative displacement between the concrete and the steel sections near the test specimen ends will be limited. Fig. 2 shows different stages of specimens' fabrication. The loading rate is slow enough to avoid dynamic effects. Loads are increased to peak value until the specimens failed. Each two of specimens were loaded under the same eccentricity ratio e/h: 0% (E00-1, E00-2), 10% (E10-1, E10-2), and 15% (E15-1, E15-2), where: “h” is the cross section height and “e” is the distance between the neutral axis and the load application (Fig. 3). Due to second order effects, the actual eccentricity ratios got larger. The exact values of these eccentricities are presented in Table 2. During the test, the lateral displacement of the transition beam is strictly controlled by the horizontal actuators to
Table 1 Phase 1: Selected materials for the tests. Concrete Hot rolled jumbo sections Longitudinal reinforcement Stirrups Shear studs
C60 (fck = 60 MPa) according to Chinese Code, with 5 mm aggregate maximum size HEM100 (120x106x12x20) ASTM A572 Gr.50/S355 (fyk = 355 MPa = 50ksi) 8 mm dia HRB400 (ASTM A615), (fyk = 400 MPa) 3.25 mm dia @ 80 mm HRB500 (fyk = 500 MPa) 6 mm DIA × 25 mm Nelson headed Studs; ASTM A108 @ 144 mm O·C. 5 mm DIA × 20 mm Nelson headed Studs; ASTM A108 @ 144 mm O.C. Grade 4.8
Associates, Seattle (MKA). Overall dimensions of the columns are 1800 × 1800 mm, with a height of 9 m at the lobby level (base of the tower) and 4.5 m at the typical floor. The experimental campaign is divided in 2 phases: 6 static tests and 4 quasi-static tests [13]. 2.1. Phase 1 – static tests Phase 1 contains 6 specimens with the same geometry configuration, detailed in Fig. 1. The specimens are tested to failure by applying Table 2 Phase 1: Obtained material strengths (Units: MPa). Specimen ID
Actual eccentricities e/h [%]
Concrete cubic strength
Yield strength of steel section flange
Yield strength of steel section web
Yield strength of longitudinal bar
Yield strength of transverse bar
E00-1 E00-2 E10-1 E10-2 E15-1 E15-2
0.0 0.0 12.4 12.9 19.9 17.9
61.17 56.62 59.75 68.40 67.50 75.17
408 398 423 383 377 389
523 411 435 415 404 405
438
597
5
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Fig. 4. Phase 1: Configuration of strain and displacement gauges.
corner cracks
corner cracks crush of the concrete
vertical crack
vertical crack
new crack
corner cracks
a)
corner cracks
b)
c)
Fig. 5. Phase 1: Fig. 4. Crack development of specimens subjected to eccentric loads.
ensure that the lateral displacement of the top end has zero value. The selected materials for the static tests are presented in Table 1. Since the concrete strength is sensitive to its age, concrete cubes were tested or each specimen before and after the tests. Table 2 presents the
actual material strengths. The data in this test program include measuring the strain on the profiles, longitudinal bars, ties and concrete surface. The strain sensors are placed on four sections for each specimen, as shown in Fig. 4. The
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vertical cracks
initial cracks
crush of the concrete
horizontal cracks
a)
b)
Fig. 6. Phase 1: Crack development of specimens subjected to eccentric loads: a) 70% of the maximum load; b) failure load.
Table 3 Phase 1: Specimen capacities (Units: kN,m). Spec.
Nmax
Mmax
Ecc Ratio
efailure/einitial
E00-1 E00-2 E10-1 E10-2 E15-1 E15-2
17,082 15,325 14,360 13,231 12,041 12,759
143 52 803 767 1076 1026
1.9% 0.8% 12.4% 12.9% 19.9% 17.9%
– – 1.24 1.29 1.33 1.19
Fig. 7. Phase 1: a) Moment vs. rotation at mid-section; b) bending moment – axial force interaction curves.
Fig. 8. Phase 1: Curvature development at mid-height of specimens. a) Specimen E10-1; b) Specimen E15-1.
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7
130 140 30 300
3.25@36
300
200
2.95@55
(4)HEM80(H80X70X12X12)
300
292
b)
300
292
300
35
20
25
20
Lateral Plate t=8mm Q235 Polystyrene t=5mm
35
300
30
300
100
Steel Endplate
40
a)
40
c)
Fig. 9. Phase 2: Quasi-static tests: a) steel layout – longitudinal; b) steel layout – cross-section; c) shear studs layout.
Table 4 Phase 2: Selected materials for the tests (Units: MPa). Concrete Hot rolled jumbo sections
C60 (fck = 60 MPa), with 5 mm aggregate maximum size Horizontal: 140x73x4.7 × 6.9 mm Vertical: HEM80 (80 × 60 × 12 × 12 mm) S235 (fyk = 235 MPa) 6/8 mm dia - HRB400 (ASTM A615), (fyk = 400 MPa) 3.25 mm dia @ 36 mm HRB500 (fyk = 500 MPa) 5 mm DIA × 25 mm Nelson headed Studs; ASTM A108 @ 150 mm O.C. 5 mm DIA × 15 mm Nelson headed Studs; ASTM A108 @ 150 mm O.C Grade 4.8
Longitudinal reinforcement Stirrups Shear studs
N-Axial Force
100
300
600
900
V-Shear Force
Critical Section
2V-Shear Force 100
1900
(3.25mmDIA@36mm (Yield strength = 500Mpa)
150
3.25@36
Critical Section
V-Shear Force
a)
b)
N-Axial Force
Fig. 10. Phase 2: Quasi-static tests: a) laboratory setup; b) boundary conditions; c) test setup.
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c)
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Table 5 Phase 2: Obtained material strengths (Units: MPa). Specimen ID
Eccentricities e/h [%]
D10-1 D10-2 D15-1 D15-2
Concrete cubic strength
10.0 10.0 15.0 15.0
Steel section Ultimate strength
Yield strength
Ultimate strength
Yield strength
Ultimate strength
457
603
459
689
572
638
70.3 70.6 76.3 67.3
Spec.
Design values
Experimental values
Ratio (%)
E00-1 E00-2 E10-1 E10-2 E15-1 E15-2
17,392
17,082 15,325 14,360 13,231 12,041 12,759
102% 114% 99% 108% 99% 94%
11,924
The static test results confirm the composite mega column expected behaviour, and provide additional evidence of vertical and lateral displacements, curvature and ductility, axial and bending stiffness, and relative displacements between steel sections and concrete. As the axial load increases, cracks develop – at first vertically, where the concrete cover is limited, and then horizontally, when the specimen is reaching failure. When the deflections are large, the axial load decreases in value and the test stops. On purely axial specimens, the axial load starts decreasing after reaching the peak value due to an increased vertical deflection. The second load drop occurs when the column fails, when sudden, significant deflections and damage occurs, Fig. 25a). Eccentric specimens do not experience a sudden drop of applied load, as the axial load gradually decreases after the peak point. Meanwhile, the horizontal deflection and concrete damage continuously develop, especially on areas of the concrete under tension. On purely axial specimens, buckling of the longitudinal rebar and breakage of ties are observed. Figs. 5 and 6 present the crack development during the loading phase. Steel profiles yield, but do not buckle. No significant deformations of the profiles are registered. Fig. 7a) present the bending moment vs. rotation at the mid-section of the specimens. It can be observed that the bending moment of the mid-section remains constant as the curvature develops. The slopes of the curves become smaller with the increase of rotation, suggesting that the bending stiffness decreases as the load increases. The area under the curve can be expressed in absorbed energy by the specimen, since the energy can be expressed as the moment times the angle. Thus, for columns with an eccentricity ratio less than 15%, the ductility of the column in terms of ‘moment vs. rotation’ is satisfactory. The N-M interaction points from Fig. 7b) were evaluated using the Plumier et al. method [14]. Average material strengths of the 6 tests specimens were used., creating divergences between the design curves and recorded data points. For specimens subjected to eccentric loads,
Table 7 Axial force capacity – comparisons (Units: kN, mm). Spec.
E00-1 E00-2 E10-1 E10-2 E15-1 E15-2
Experimental values
Transverse rebar
Yield strength
Table 6 Phase 1: Axial force capacity – comparisons (Units: kN).
14,227
Longitudinal rebar
Design values
Nexp
Δexp
Ndesign
Δdesign
17,082 15,325 14,360 13,231 12,041 12,759
4.17 3.43 3.55 3.46 2.79 2.70
17,006 15,879 14,500 14,031 12,521 13,012
3.98 4.25 3.60 3.34 3.35 3.43
displacement sensor consists in two parts: a slide rheostat and a steel box. The slide rheostat is stuck on the surface of the steel section, surrounded by the steel box and the steel box is surrounded by concrete. During the test, the slide rheostat will move with the steel section and the box will move with the concrete, so the relative displacement can be detected.
Fig. 11. Phase 2: Load introduction: a) axial load history; b) horizontal load history.
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Fig. 12. Phase 2: Load introduction: a) strain sensor on concrete; b) strain sensor on critical Section 1; c) strain sensor on critical Section 2.
test results show good correlation with the curves. For specimens subjected to axial loads, test results are smaller than predictions since the concrete strengths of E00-1 and E00-2 specimens are lower than the average value of the six, and the calculated results have not considered
yet the buckling and P-Δ effects. Comparisons between the design values and experimental ones are given in Table 6. Table 3 lists the capacities and the corresponding bending moments on the mid-height cross-section of the columns. The bending moment
Fig. 13. Phase 2: Crack distribution and failure modes of specimens: a) Specimen D10-1; b) Specimen D15-1.
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Fig. 14. Phase 2: Strain distribution: a) Specimen D10-1; b) Specimen D15-1.
was determined by Eq. (1):
M = N (ei + )
(1)
where ei is the initial eccentricity of the specimen, and δ is the horizontal deflection of the mid-height cross-section due to the second order effect. Although the initial eccentricity of specimen E00-1 and E00-2 was zero, horizontal deflections of these two columns were recorded during the test. Nevertheless, the eccentricities were very small under the maximum load level, so that the axial resistances of these two specimens were not significantly influenced. For specimens subjected to eccentric loads, the eccentricities under the maximum load level were 19%~33% larger than the initial eccentricities due to the second order effect. Since this paper deals with short columns, the second order effect will not be discussed in detail. Fig. 8 represents the curvature development for specimens E10-1 and E15-1. Similar behaviour was observed for specimens E10-2 and E15-2. A linear regression is created using points of normal stain versus relative position under a certain load level. Then, the slope of the regressed straight line is taken as the curvature. The obtained curvature of the concrete correlates with that of the steel section very well. Together with the validation of ‘Plane Section Assumption’, it is reliable to assume the curvatures of different materials on a particular section are the same. The column curvature was calculated by normal strain of the steel sections. In addition, it can be observed that the curvature developed more rapidly when the load level was beyond 60%, indicating the reduction of bending stiffness.
Fig. 15. Phase 2: specimen deformation.
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Fig. 16. Phase 2: hysteretic curves a) D10-1(up); b) D10-1(low); c) D15-1(up); d) D15-1(low); e) D10-1/D10-2 envelope; f) D15-1/D15-2 envelope.
2.2. Phase 2 – Quasi-static tests Phase 2 of the experimental campaign consist in four 1/6 scaled specimens with their geometrical configurations presented in Fig. 9 and Table 4. The behaviour, including the capacity, deformation capacity, and hysteretic performance of the specimens under simulated seismic loads, are examined according to different eccentricities. Axial force has been applied with different eccentricities values: 10% - specimens D10-1 and D10-2, and 15% -specimens D15-1 and D15-2, to account for the diversity in materials and fabrication. Horizontal force is applied at the mid-height of the specimens. Transverse load (V) is equal to two times the horizontal end reaction on the top and bottom of the specimens. A bottom hinge is placed on the ground and a top hinge is installed on the top of the specimen, connecting it to the vertical actuator. Both the hinges are fixed by a frame that restricts horizontal displacements, as well as out-of-plane
Fig. 17. Phase 2: Specimens energy consumption.
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Fig. 18. Plastic Simplified Method: a) Interaction curve; b) Equivalent cross-section definition.
displacements Fig. 10c. The defined material characterizations are given in Table 4. The concrete compressive strength was obtained on cubes of 150 mm. The aimed concreted grade was C60, while the steel sections and beams were made of Q460 and S235 steel, the tested values are presented in Table 5. As shown in Fig. 11, axial load slowly increases until it reaches the gravity load. Then, the axial load and the transverse load are increased proportionally. The axial load is increased by 500 kN steps, and the lateral load is applied cyclically, while keeping the axial load constant. Displacement and strain sensor were installed, having the layout presented in Fig. 12. Critical Section 1 was near the conjunction of the column and the beam, located 100 mm from the corner of the column, while critical Section 2 was near the end of the column, 300 mm away from critical Section 1. The sensors were installed on both the upper and lower columns. General behaviours of the quasi-static tests are quite alike, the eccentricity ratios do not differ much. Crack distributions and failure modes indicate that the specimens fail in combined compression and flexure patterns, as shown in Fig. 13. When the first step of the loading is completed, the test specimens do not show significant deformations and cracks. During the second step of the loading, cracks and concrete crush gradually develop, and the cumulative damage at the column corners leads to the failure of the specimen. All four specimens failed in combined compression and bending – the specimen failed because the corners of the concrete were crushed – which met the purpose of the experiment program. The final crack distributions of the specimens are presented in Fig. 13. The specimens held integrity during the whole loading process. Despite the surrounding concrete was damaged due to lack of confinement, the concrete core remains intact due to the confinement effect provided by the steel sections. In turn, the concrete core helped ensure that the steel sections would not buckle when the vertical load was very large. Based on the strain distribution of the steel profile and reinforcement, the “Plane Section Assumption” can be verified, Fig. 14. Test results indicates that specimen D10-1 there is a linearity between the steel profile and the longitudinal reinforcement, while the specimens with higher eccentricity D15-1, the slip effect between the steel- concrete interface is observed after the peak load occurs. The rotation of the beam leads to different loading conditions for the upper and lower column. Therefore, the measured axial load, lateral
load, and lateral displacement must be modified to account for the rotation. Fig. 15 presents the deformation pattern of the upper half of the specimen. Suppose the rotation of the ‘ground beam’ is α – positive in clockwise direction, and negative in counter-clockwise direction. In addition, assume the ‘ground beam’ of the specimen is a rigid body, which does not have any deformation during the test. This assumption is reasonable because no significant deformation was observed within the ‘ground beam’ during the test. N0,V0 and Δ0 are the recorded data of axial load, lateral load, and lateral displacement, where N0 was directly recorded by the system; Δ0 was recorded by a displacement sensor installed in the middle of the specimen; and V0 is one-half of the load applied by the lateral actuator. Nup, Vup, and Δup are the equivalent axial load, lateral load, and lateral displacement of the upper column. ‘h’ is the height of one-half of the specimen, 1200 mm. According to the geometric relationships, the modified test data can be expressed as follows:
{Nup = N0 cos =
0 /cos
+ V0 sin Vup = + h tan
N0 cos
+ V0 sin
up
Nlow = N0 cos + V0 sin Vlow = N0 cos + V0 sin h tan low = 0 /cos (2)
Hysteretic curves of the specimen are presented behaviour Fig. 16. Except for specimen D10-1, other specimens have all been affected by the rotation of the beam. The beam of specimen D15-1, for example, rotated counter-clockwise during the test. When the specimen moved toward right, the rotation made the equivalent lateral displacement of the upper column smaller, and that of the lower column larger. Therefore, the hysteretic curve of specimen D15-1(up) is more spread out in the negative part, while the curve of specimen D15-1(low) is more spread out in the positive part. Although the behaviour of the specimens was affected by the rotation of the beams, the hysteretic curves are still stable. The specimens showed some pinching at the beginning of the test, but the degree of pinching was mitigated as the lateral displacement was increasing. For the last several circles of the loading, the hysteretic curves are round and stable, suggesting a good ability of energy dissipation. The hypothesis of ‘Plane Section Assumption,’ is verified within the 15% eccentricity ratio. Despite the damage to the concrete cover, the concrete core remains intact due to the confinement effect provided by
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Fig. 19. Definition of equivalent plates to rebars.
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Fig. 20. Definition of equivalent plates to steel profile.
the steel sections. The concrete core confinement prevents the steel sections from buckling. Local buckling of longitudinal rebar and breakage of the transverse ties are detected. The ability to dissipate energy is shown by stable and round hysteretic curves, without a large dependence on the eccentricity ratio. When the lateral displacement grows, materials yield and friction between the materials consume energy. Therefore, energy consumption increases, as does the lateral displacement Fig. 17.
partially encased sections and concrete filled rectangular and circular tubes. The first method is a numerical and general method, while the second one is a simplified analytical method, applied only to doubly symmetrical sections and uniform along the height of the element. By using the simplified method, the interaction curve can be approached by a succession of lines joining 4 characteristic points A, B, C, D, as shown in Fig. 18. The following assumptions should also be considered, because are underlying the prescriptions from EN 1994-1-1: there is a complete interaction between steel and concrete, the plane sections remain plane after deformation and the concrete resistance in traction is neglected. The development of a method of calculation of concrete sections with several encased steel sections requires the calculation of section characteristics like the moment of inertia, the plastic moment, the
3. Validation of FEM and adapted code 3.1. Adapted plastic distribution method EN 1994-1-1 - Clause 6.7 [1] provides two design methods in the design of composite compression members with encased sections,
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Fig. 21. Stress block distribution for rectangular column with 4 encased profiles [16].
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Fig. 22. Material constitutive curves: a) concrete; b) steel [16].
Elastic Cap Steel Beam
Concrete
Steel Column
a)
c) Fig. 23. Phase 1: Abaqus FE models: a) concrete mesh; b) steel section mesh, c) boundary conditions.
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Fig. 24. Phase 1: Abaqus FE models: spring connector.
Fig. 25. Phase 1: Axial force vs. vertical deflection.
elastic neutral axis and the plastic neutral axis of huge mega column sections. Such calculation can be made either by means of dedicated software in which all the data are given, each reinforcing bar being defined in position and section. The calculation can also be “handmade”, in which case the calculation becomes tedious due to the high number of longitudinal bars in mega columns. In order to facilitate such calculation, some simplifications are proposed hereafter which replaces lines of rebars by equivalent plates, Fig. 19. The steel profiles are defined as equivalent plates following the suggestions in Fig. 20.
The presented method in accordance to EN 1994-1-1 allows to evaluate the nominal resistance of the composite column, based on the plastic stress distribution of the composite cross-sections [15]. A twostep calculation can be used to determine the flexural resistance of the composite cross-section, as shown in Fig. 21 [7]: Step 1: Determine the position of the neutral axis (N.A.) based on the balance condition of the axial load. Four distinct situations of the position of the N.A are identified. Step 2: Calculate the flexural resistance of the composite cross-
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implemented numerical model of concrete. The numerical model fails to simulate the situation where the concrete smashing occurs. Nevertheless, the model is able to predict the bearing capacity of the column and will be used furthermore in the validation of the N-M interaction curve. The column capacity decreases as the load eccentricity increases and deflection is developing, Fig. 25b) and c). Contrary to pure axial specimens, eccentric specimens did not experienced sudden drop of the applied load, the axial load is decreasing gradually after the peak point. Table 7 presents the numerical values of the axial load vs. vertical displacement curves. The numerical results are under 10% difference from the experimental tests. In conclusion the simplifications made for the numerical model can be used for a further sensitivity study. The FEM and analytical interaction curves, presented in Fig. 26, show results like the capacity of the experimentally tested mega column. The Fiber model represents the classical pivot method developed for the reinforced concrete structural elements, where the strains are considered linear along the cross-section [3,17]. Tests results show good convergence with the numerical simulations. For specimen subjected to axial load, test results are smaller than prediction given by both fiber and the simplified method. The comparison of crack development can be observed in Figs. 27 and 28. For the specimens subjected only to axial load, the formation of vertical cracks can be observed on the face of the concrete side. The crush of the concrete in the compressed zone was limited due to the definition of the concrete material using concrete damage plasticity law. Similar behaviour can be observed for specimens subjected to eccentric loads.
Fig. 26. Phase 1: Interaction curve bending moment - axial force constructed using FEM models.
section based on the position of the N.A. CL represents the neutral axis of the cross-section. 3.2. Validation of test results using FEM models Software Abaqus [16] has been chosen for the FEM analyses only for Phase 1 specimens subjected to axial load. The definition of the concrete behaviour has been made by using a concrete damage plasticity model. The uniaxial constitutive law for concrete material has been obtained using the EN 1992-1-1 [17] material law as show in Fig. 22. The steel material for rebars and steel profile was defined using a bilinear material law with values from the experimental tests. Only half of the ISRC column was built in the program due to the symmetry. An overview of the FE model and the mesh of concrete and steel sections are presented in Fig. 23. An elastic ‘cap’ was positioned above the model to simulate the sand layer. Axial load was applied to the reference point (RP), whose position was the same as the center of the hinge. The load was first transferred to the elastic cap through constrains between the RP and cap top surface, then to the column itself. The concrete and steel sections were simulated by three dimensional eight-node solid elements, and bars are simulated by T3D2 truss elements. To simplify the model, bars and steel beams were TIE connected to the concrete – no relative displacement and strain difference. The interaction of concrete and steel section interface was simulated by nonlinear springs along each dimension, Fig. 24. There were three spring connectors at each node pair, one in the normal direction and two in the tangential direction. The node of concrete and steel of each node pair overlapped in space, the initial length of the spring elements was zero. Before peak point, the simulated axial load vs. vertical displacement' curve follows similar paths to the experimental curve at all three eccentricities values. The reduction of the axial capacity occurred due to the degradation of material strength, cracks in the concrete, spill and damage of the concrete and buckling of the longitudinal bars, Fig. 25a). Small divergencies between the FEM and the experimental test could be noticed especially for 0% eccentricity specimens, due to the
4. Concluding remarks Six 1/4 scaled concrete encased composite columns with multi-separate steel sections were tested to understand better their performance and ductility behaviour. The test results were in accordance with the expected results and the specimens shown sufficient deformation capacity. The specimens are able to maintain the bending moment at the maximum requirement, while the curvature is developed until column failure. The full composite action was observed during the tests, even though the steel sections are not connected to one another. Test results of this test program reveal that the ‘Plane Section Assumption’ is generally valid for specimens with an e/h = 10% and an e/h = 15%, but the interface slip grew with the eccentricity, which suggests that the shear demand is relatively larger for mega columns. The concrete core, surrounded by the steel profiles, is highly confined, thus increasing the ductility of the composite column. Available design standards are providing no information on how to properly design reinforced column sections with more than one embedded steel profile. For this, a new extended method based on Eurocode 4 simplified design method has been developed in order to propose a design guidance for composite columns with several steel profiles embedded. The method is an extension of the Plastic Distribution Method and takes into account all the simplified assumptions that are defined in EN 1994-1-1 - Clause 6.7. The results of the experimental campaign have been validated with FEM methods and compared with simplified code provisions methods. The comparison shows matching results. The simplifications brought to the numerical simulations can be adapted for further parametric studies. The simple adapted method can be used to perform “hand-made” evaluation of the axial force-bending moment interaction curve.
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vertical crack
a)
b)
corner cracks crush of the concrete
corner cracks
c)
d)
Fig. 27. Phase 1: Crack comparison for specimens subjected to axial loads: a) Specimen E00-1 at 70% of failure load; b) Specimen E00-1 at failure load.
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crush of the concrete
a)
horizontal cracks
b)
Fig. 28. Phase 1: Crack comparison for specimens subjected to eccentric loads; a) Specimen E15-1 at failure load – damage evolution; b) Specimen E15-1 at failure load – experimental test;
Acknowledgements
[6] Mirza SA, Tikka TK. Flexural stiffness of composite columns subjected to major axis bending. ACI Struct J 1999;96(1):19–28. [7] Smart Composite Components - Concrete Structures Reinforced by Steel Profiles, Smart CoCo, European Commission. Research Programme of the Research Funds for Coal and Steel, TGS8 2016. RFSR-CT-2012-00031. [8] Morino S. Recent developments in hybrid structures in Japan—research, design and construction. Eng Struct 1998;20(4):336–46. [9] Munoz PR, Hsu CTT. Behavior of biaxially loaded concrete-encased composite columns. J. Struct. Eng. 1997;123(9):1163–71. [10] Chen CC, Li JM, Weng CC. Experimental behaviour and strength of concrete-encased composite beam–columns with T-shaped steel section under cyclic loading. J Constr Steel Res 2005;61(7). [11] Fei D, Tao C, Congzhen X. Performance and capacity of isolated reinforced concrete columns and design approaches. CABR testing report, Beijing, China. 2015. [12] Xiao C, Deng F. Experimental study on concrete encased composite columns with separate steel sections. Steel Compos. Struct. 2017;23(4). [13] Deng F, Chen T, Xiao C. Engineering properties of composite megacolumns with separately encased hot rolled steel profiles. CTBUH research paper. 2016. [14] Plumier A, Bogdan T, Degee H. Design of columns with several encased steel profiles for combined compression and bending. Final report created for ArcelorMittal website. 2012. [15] Gerardy JC, Trabucco D, Xiao C, Davies D. Composite mega columns: Testing multiple, concrete-encased, hot rolled steel sections. CTBUH research report. 2016. [16] SIMULIA User Assistance. Abaqus, © Dassault Systèmes Simulia Corp. RI, USA: Providence; 2017. [17] EN 1992-1-1. Eurocode 2: Design of concrete structures – Part 1–1: General rules and rules for building. 2004.
This project was coordinated by the Council of Tall Buildings and Urban Habitat (CTBUH). The structural engineering firm Magnusson Klemencic Associates (MKA) provided background studies on composite mega columns projects. The China Academy of Building Research (CABR) was engaged to develop the testing program for the subject columns. The authors gratefully acknowledge the support and contributions from these organizations. References [1] EN 1994-1-1. Eurocode 4: Design of composite steel and concrete structures – Part 1–1: General rules and rules for building. 2004. [2] ANSI/AISC 360-16. Specification for structural steel buildings. 2016. [3] Ye L, Ehua F. State-of-the-art of study on the behaviors of steel reinforced concrete structure. China Civil Eng J 2000;33(5):1–11. [4] El-Tawil S, Deierlein GG. Strength and ductility of concrete encased composite columns. J Struct Eng 1999;125(9):1009–19. [5] Dundar C, Tokgoz S, Tanrikulu AK, Baran T. Behaviour of reinforced and concrete-encased composite columns subjected to biaxial bending and axial load. Build Environ 2008;43(6):1109–20.
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