- Email: [email protected]
Evaluation of embedded concrete-filled tube (CFT) column-to-foundation connections
Engineering Structures 56 (2013) 22–35
Contents lists available at SciVerse ScienceDirect
Engineering Structures journal homepage: www.elsevier.com/locate/engstruct
Evaluation of embedded concrete-filled tube (CFT) column-to-foundation connections Jiho Moon a, Dawn E. Lehman b,⇑, Charles W. Roeder b, Hak-Eun Lee a a b
School of Civil, Environmental & Architectural Engineering, Korea University, 5-1, Anam-dong, Sungbuk-gu, Seoul 136-701, South Korea Department of Civil & Environmental Engineering, University of Washington, Seattle, WA 98195-2700, USA
a r t i c l e
i n f o
Article history: Received 12 April 2012 Revised 15 April 2013 Accepted 16 April 2013 Available online 21 May 2013 Keywords: Concrete-filled tubes (CFTs) Embedded connection Composite structure Minimum embedment depth Non-linear finite element analysis
a b s t r a c t Concrete-filled tubes (CFTs) are effective structural components. Relative to conventional reinforced concrete components, they have higher strength-to-size efficiency and facilitate rapid construction. Yet they are not used frequently in US construction. The component response is well understood from extensive experimental and analytical studies that have been conducted on CFT components themselves. There remains a fundamental challenge of implementing these components in structural systems, which is caused by the uncertainty of the connection design and performance. Relative to component research, limited research has focused on the connections of CFT columns. A recent research effort has resulted in a new embedded connection for a CFT column anchored into a reinforced concrete foundation. The connection is fully capable of transferring combined bending and axial loads and has sufficient deformability to sustain multiple inelastic deformation cycles under extreme loading. In addition, the connection has unique features that facilitate constructability and rapid construction. However, the connection design to date is solely based on experimental study, which evaluated a very limited range of design parameters. A coordinated analytical study, using high-resolution continuum models, was undertaken to investigate the unstudied parameters and develop appropriate design expressions, which is the subject of this paper. An analytical model was developed and verified using the test results. The verified model was then used to conduct a parametric study to enhance the understanding of the experimental behavior and extend the test databases. Parameters studied included the embedment depth, diameter-to-thickness (D/t) ratio, shear reinforcement ratio, strength ratio of the concrete in the footing and concrete infill, and the axial load ratio. From the analysis results, the failure mechanisms were evaluated with respect to the individual parameters. The results showed that an increase in embedment depth, D/t ratio, shear reinforcement ratio, the axial load ratio, or the ratio of the concrete strength in the footing relative to the concrete infill of CFT column increased the connection strength and could result in ductile yielding of the CFT column, which is the desired response mode. Finally, the analysis and test results were combined to develop a refined design equation for the required embedment depth. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Concrete-filled tubes (CFTs) are composite members, which consist of a steel tube and concrete infill. CFTs used as building columns and bridge piers have several advantages over conventional structural components, including their strength-to-size efficiency and facilitation of rapid construction. The previous researches are heavily focused on the CFT component response. Extensive experimental studies on CFT component subjected to pure axial, pure bending, or combined axial-bending loading have been conducted and the results are summarized by Roeder et al. [1]. Other researchers have studied CFTs analytically
⇑ Corresponding author. Tel.: +1 206 715 2108. E-mail address: [email protected] (D.E. Lehman). 0141-0296/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.engstruct.2013.04.011
and developed models appropriate for simulating the CFT component response [2–5]. However, only limited studies have focused on the connection of the CFT component to adjacent components, such as the foundation [6,7]. This limitation in the research has resulted in limiting the use of CFT components in US construction. The connections must be practical and economical. They must develop full composite flexural strength to achieve the benefits of CFT members as columns or piers. Further, good ductility or inelastic deformation capacity is required of these connections in moderate to high seismic zones. A recent testing effort has resulted in an efficient CFT column to foundation connection, appropriate for both bridge and building construction [6]. This connection is capable of transferring the full composite resistance of the CFT column to the footing, while
J. Moon et al. / Engineering Structures 56 (2013) 22–35
sustaining inelastic deformation demands resulting from extreme loading. The proposed connection is shown in Fig. 1a. Typically, embedded CFT connections use a full base plate. Here, a steel annular ring is welded to the base of the steel tube to provide anchorage of the column into the footing and to transfer the column forces and moments into the foundation. Two types of construction methods were explored: (1) monolithic and (2) isolated. For the monolithic connection, the tube is temporarily supported while the footing is cast around it to embed the steel tube and its annular ring. The isolated connection casts the footing concrete prior to the column concrete, thereby separating the reinforcing cage construction and the structural steel placement. The isolated connection is fabricated using the following construction sequence: (1) cast the footing with a void or recess formed by a corrugated steel tube at the column location, (2) lower the CFT column into place, (3) grout the column into place with fiber reinforced grout, and (4) fill the column with self-consolidating low-shrinkage concrete. Extensive experimental studies were conducted for these connections [8–11]. The results show that the connections have two different possible failure modes depending on the embedment depth, as shown in Fig. 1b. Pullout failure may occur when the embedment depth is not sufficient, while punching shear failure might occur with shallow base depth below the CFT column. With sufficient connection strength, both of these failure modes can be suppressed thereby resulting in ductile yielding of the column, which is the desired response mode. Therefore, it is critical to identify all parameters that influence the failure modes of the connection (Brittle pull-out failure or ductile failure of CFT pier or column). The experimental research alone did not provide sufficient study of all pertinent variables. Thus, a companion analytical study was undertaken. This paper presents non-linear finite element analysis of the monolithic embedded connection for the CFT column to enhance the understanding of the experimental results by demonstrating the failure modes of the connection and by extending the existing test database through analysis of the parameters that have not been tested such as large D/t ratio and high axial load ratio. The analysis model was successfully verified. The verified model
23
was used to investigate the effects of embedment depth, D/t ratio, shear reinforcement, concrete strength ratio between the footing and concrete infill of CFT column, and axial load ratio. Finally, a design equation for minimum embedment depth to ensure ultimate strength of the embedded connection was evaluated. 2. Finite element model of embedded CFT connection The analytical study was conducted using the general-purpose finite element analysis program ABAQUS [12]. Fig. 2 shows an example of finite element model of the CFT connection, column and foundation. Because of symmetry, a half model of the specimen was used, which saved modeling and computing time. The 8-node solid (C3D8R), 4-node shell (S4R), and 2-node truss element (T3D2) were used to model concrete, steel tube, and steel reinforcement, respectively. The interface between concrete and steel tube was separately modeled explicitly using the GAP element that is provided by ABAQUS [12] to simulate the contact behavior between the concrete and the steel tube. GAP elements allow relative movement between the steel and concrete while restricting penetration of one node into an adjacent one. The normal stresses generated in the GAP element result in shear stress transfer between the steel and the concrete fill through friction. Relative movement (slip) between the internal reinforcing bar and the concrete was not modeled; the reinforcement was assumed to be perfectly bonded, which was modeled using the EMBEDED option in ABAQUS [12]. Fig. 3a shows the uniaxial stress–strain relationship of concrete used in this study. The compressive stress–strain relationship proposed by Saenz [13] was employed where it is assumed that the stress–stain relationship is linear up to a stress of 0.5fc0 and the maximum compressive strength, fc0 , is achieved when compressive strain is 0.003. For the tensile stress–strain relationship of concrete, the curve proposed by Hsu and Mo [14] was adopted. Tensile stress–strain relationship is linear uppto ffiffiffiffi stress at cracking of concrete, fcr, where fcr is defined as 0.31 fc0 MPa [14] and the softening relationship is given by Eq. (1):
Fig. 1. Proposed connection and failure modes of footing: (a) monolithic and isolated connections; and (b) possible failure modes of footing.
24
J. Moon et al. / Engineering Structures 56 (2013) 22–35
Fig. 2. Components of the finite element model: (a) concrete infill and footing; (b) steel tube; (c) interface between infill and tube; and (d) reinforcing bar.
Fig. 3. Material models: (a) concrete; and (b) bare and embedded reinforcing bar.
ecr 0:4 Þ when ec 6 ecr : ec
fc ¼ fcr ð
ð1Þ
In Eq. (1), ecr is strain at cracking of concrete. Inelastic behavior of concrete was modeled using the concrete damaged plasticity model proposed by Lee and Fenves [15] available in ABAQUS [12]. This constitutive model uses a non-associated flow rule and is suitable for simulation of the stress triaxially-dependent plastic hardening. The dilation angle of the concrete, w, which is the measured angle plane where p are the hydrostatic stress tensor q and q in the p and Von-Mises equivalent effective stress tensor respectively, is an important model parameter in the concrete damaged plasticity model. The dilation angle, w, was approximated as 20° and 31° for the concrete infill in the tube and the concrete in the footing, respectively, based on the results of the previous research and parametric studies [4,15] A tri-linear stress–strain relationship was used for the steel in the tube. Young’s modulus, Es, was approximated as 200,000 MPa; and Poisson’s ratio, ts, was set as 0.3. The plastic plateau terminates when strain of the steel, es, is equal to 10 times the yield strain of the steel (10esy) and stress increases up to ultimate strength of the steel, fu, which is achieved when the ultimate strain of the steel, esu, is 0.1. The measured properties of the steel and concrete were used to establish the material models when available. The average stress–strain relationship of reinforcing bar embedded in concrete depends on the effective reinforcement ratio, and can differ from the properties of bare reinforcing bar for low reinforcement ratios as shown in Fig. 3b [14]. The primary difference is the lower effective yield stress below the yield stress of reinforcing bar, fyr. In this study, the average stress–strain relationship of
embedded reinforcing bar proposed by Hus and Mo [14] was adopted, and it is given by
fr ¼ Er er when f r 6 fyr0
ðaÞ
ð2Þ
fr ¼ ð0:91 2BÞfyr þ ð0:02 þ 0:25BÞEr er when f r > fyr0
ðbÞ
where
fyr0 ¼ ð0:93 2BÞfyr ;
and B ¼
1:5 1 fcr : q fyr
ð3Þ
In Eq. (2), Er is young’s modulus of the reinforcing bar, fr and er are the stress and strain in the reinforcing bar, respectively, and f’yr is the reduced yield stress of embedded reinforcing bars. Eqs. (2) and (3) are applicable for reinforcement ratios, q, larger than 0.15% [14]. Eqs. (2) and (3) were derived assuming the tensile stress–stain relationship of the concrete can be expressed as Eq. (1). The choice of the tensile stress–stain relationship of the concrete can affect the behavior of the concrete structure, and the parametric study was performed for various types of the tensile stress–strain relationship of the concrete in this study. From the results, combination of Eq. (1) with Eqs. (2) and (3) was adopted. The details of the results of parametric study are shown in Section 3.4. 3. Verification of finite element model 3.1. Test overview The model described above was verified using the test results. Specifically, the results of the monolithically embedded connection tests were compared with analytical results. Fig. 4 shows the
J. Moon et al. / Engineering Structures 56 (2013) 22–35
dimensions and reinforcement layout for the test specimens. A spiral weld steel tube with a nominal yield strength of 480 MPa was used in Specimens K1–K3. Specimens K1 and K2 are nominally identical, in which Specimen K2 has shear reinforcement and Specimen K1 does not. Specimen K3 has a deeper embedment depth. In contrast to the K-series, the two remaining specimens used a tube with a nominal steel strength of 345 MPa where spiral weld tube was used for Specimen 1–50 and straight-seam weld tube was used for Specimen 4–50. The height of column above the footing was 1828.8 mm (72 in), and the footing was 1930.4 mm (76 in.) in the direction of loading by 1727.2 mm (68 in.) wide for these specimens. The depth of the footing was 609.6 mm (24 in.). The diameter of tube was 508 mm (20 in.) and the D/t ratio was 80 for all specimens, where D is external diameter of CFT and t is the thickness of steel tube, respectively. The size of the footing was determined through preliminary analysis conducted by Kingsley [8]. Kingsley [8] conducted the finite element analysis with footing depths from 1.2D to 1.8D and showed very little effect on the performance of the connection. The 1.2D footing depth develops adequate shear and flexural resistance and is proportional to footings used in practice. The flexural reinforcing bar in the direction of loading consisted of No. 6 bars spaced at 101.6 mm (4 in.) for all specimens, as shown in Fig. 4. The flexural reinforcing bar in the direction perpendicular to loading consisted of No. 4 bars spaced at 228.6 mm (9 in.) for Specimens K1 and K2, while No. 6 bars spaced 101.6 mm (4 in.) for Specimens K3, 1–50, and 4–50. The nominal area of No. 4 and 6 bars are 129 and 284 mm2 (0.20 and 0.44 in.2), respectively. Specimen K1 had no shear reinforcement in the footing, while No. 3 ties were uniformly used for Specimens K2, K3, 1–50, and 4–50 resulting in a 0.27% shear reinforcement ratio, qv, where the nominal area of No. 3 bar is 71 mm2 (0.11 in.2). The material properties and embedment depth of each specimen are summarized in Table. 1. In Table 1, le represents the embedment depth. The applied axial load was 0.1Po, where Po is the squash load and is defined as 0.95fc0 Ac + fyAs where fy is yield stress of steel tube, Ac and As are the areas of concrete infill and steel tube, respectively [16]. 3.2. Mesh convergence study including determination of friction coefficient Fig. 5a and b shows boundary condition and mesh geometries that were used for the mesh convergence study, respectively. The
25
nodes at the base of the footing were fully restrained, and the x direction of the symmetric section was restrained as shown in Fig. 5a. The distributed axial load was applied at the top of the CFT on the concrete section using the pressure load option in ABAQUS [12]. Then, the distributed lateral displacement was applied on the 1/4 perimeter of steel tube at the top of the CFT as shown in Fig. 5a. A mesh convergence study was conducted using three different mesh types as shown in Fig. 5b for K1, K2, and K3 specimens where the friction coefficient was set as 0.35. The results of the mesh convergence study are summarized in Table 2. In Table 2, Mu,FEM and Mu,test represent the maximum flexural capacity of the CFT column obtained from finite element analysis and test, respectively. The solutions vary a little for Mesh 1–3, as shown in Table 2 (the maximum difference is 4% for K3 specimen). The differences of Mu,FEM/Mu,test between Mesh 2 and Mesh 3 were approximately less than 1% for all analysis models. Thus, Mesh 3 was adopted for analysis in this study. The friction coefficient between steel and concrete can range from 0.3 to 0.6 [17]. To determine reasonable value of the friction coefficient for the analysis, a parametric study was conducted for K1, K2, and K3 specimen by varying the friction coefficient. The results of parametric study are summarized in Table 2. Three different values of friction coefficient (0.25, 0.35, and 0.47) were studied. The analysis results with a friction coefficient of 0.35 provided the best results, as shown in Table 2 with an average discrepancy of 4.39%. This value was adopted for the analyses.
3.3. Model validation through comparison with previous test results Fig. 6 compares the moment-drift relationships obtained from tests with those obtained from finite element analysis. Table 3 also compares analytical results with test results for the five specimens. The dashed line in Fig. 6 represents the flexural strength of the CFT column calculated from the plastic stress distribution method (PSDM), Mu,PSDM [16]. Drift is defined as the lateral displacement at the top of specimen divided by the column length above the footing. It can be seen that the analysis results accurately predict stiffness and strength. On average, the model simulated the experimental results well. It should be noted that monotonic loading was applied in this study, and post-peak behavior might not be accurate, since post-peak strength loss is frequently caused by initiation of tearing of the steel tube, which are not included in the model. However, the post-peak behavior has little effect the max-
Fig. 4. Dimensions of test specimens.
26
J. Moon et al. / Engineering Structures 56 (2013) 22–35
Table 1 Properties of verification models. Test specimen
Study parameter
le/D
fc0 ,CFT (MPa/ksi)
fc0 ,FT (MPa/ksi)
fy (MPa/ksi)
fu (MPa/ksi)
K1 K2 K3 1–50 4–50
No shear reinforcement Shear reinforcement Embedment depth Straight welded tube Spiral welded tube
0.6 0.6 0.9 0.8 0.8
75.8/11 75.8/11 71/10.3 59.9/8.7 59.3/8.6
75.8/11 75.8/11 71/10.3 75.8/11 74.4/10.8
525.7/76.3 525.7/76.3 525.7/76.3 337.6/49 351.4/51
602.2/87.4 602.2/87.4 602.2/87.4 413.4/60 537.4/78
Fig. 5. Boundary condition and mesh for analysis model: (a) loading and boundary condition; (b) mesh for analysis model.
Table 2 Results of mesh convergence study and effect of friction coefficient. Test specimen
K1 K2 K3
Mesh convergence study (F.C. = 0.35)
Effect of friction coefficient
Mu,FEM/Mu,test (Mesh#1)
Mu,FEM/Mu,test (Mesh#2)
Mu,FEM/Mu,test (Mesh#3)
Mu,FEM/Mu,test (F.C.=0.25)
Mu,FEM/Mu,test (F.C.=0.35)
Mu,FEM/Mu,test (F.C.=0.47)
0.98 1.07 0.93
0.97 1.05 0.97
0.96 1.06 0.97 Average discrepancy (%)
0.86 0.95 0.93 8.67
0.96 1.06 0.97 4.39
1.05 1.11 0.98 6.01
imum resistance estimate, which is the primary issue for evaluating strength of the CFT column-to-footing connection. Specimens K1 and K2 exhibited pullout failure of the CFT column from the footing [8]. For Specimen K1 (le/D = 0.6, and qv = 0%), tension yielding and local buckling of the tube above the footing was not detected during the test. The theoretical predictions also showed that yielding was not developed and Mu,test/ Mu,PSDM is less than 1. The difference between the maximum resistance obtained in the test and finite element analysis was 4% for K1 as shown in Table 3. Fig. 7 compares the crack formation of the footing, which eventually led to pullout failure, in the experiment and the analysis. In both the experiment and the analysis, cracks radiating diagonally from the column are observed. The analysis assumed that cracking initiated where the tensile equivalent plastic strain is greater than zero, and the maximum principal plastic
strain is positive. The direction of the vector normal to the crack plane is assumed to be parallel to the direction of the maximum principal plastic strain [12]. Specimen K2 exhibited similar damage pattern with larger strength than Specimen K1, as a result of the additional vertical reinforcement that was placed in the footing. The strength predicted by the finite element analysis was 6% larger than the resistance measured in the test. The full flexural capacity of the CFT column was developed for specimen K3 (le/D = 0.9, and qv = 0.27%), 1–50 and 4–50(le/D = 0.8, and qv = 0.27%). Furthermore, large deformation demands were sustained without significant strength deterioration for these specimens. For all three specimens, local buckling of the tube occurred near the column base. Very little damage to the footing was observed in either the test or the analysis. Local buckling eventually led to tearing of the tube, which limited the strength and deformability. Fig. 7
27
J. Moon et al. / Engineering Structures 56 (2013) 22–35
Fig. 6. Comparison of predicted and measured base moment vs. drift: (a) Specimen K1 (b) Specimen K2 (c) Specimen K3 (d) Specimen 1–50 and (e) Specimen 4–50.
Table 3 Comparison of analysis results with test results (verification model). Test specimen
Mu,PSDM (kN m)
Mu,test (kN m)
Mu,FEM (kN m)
Mu,test/Mu,PSDM
Mu,test/Mu,FEM
Failure mode (test)
Failure mode (FEM)
K1 K2 K3 1–50 4–50
1300.74 1300.74 1288.20 890.52 913.23
1135.42 1187.74 1451.37 1074.40 996.32
1091.44 1257.58 1401.98 989.33 1013.49
0.87 0.91 1.13 1.21 1.09
1.04 0.94 1.04 1.09 0.98
Footing failure Footing failure Local buckling Local buckling Local buckling
Footing failure Footing failure Local buckling Local buckling Local buckling
Fig. 7. Simulated and observed damage patterns.
compared the shape of the local buckling observed in the test with that predicted in the analysis for K3, and significant similarity is noted. The difference between the test and the finite element analysis was 4% for K3 specimen. The discrepancy between the test and
finite element analysis were 9 and 2% for 1–50 and 4–50 specimens, respectively. Taken as a whole, comparison of the simulation and experimental results including the predicted response and damage modes
28
J. Moon et al. / Engineering Structures 56 (2013) 22–35
such as cracking in the footing and local buckling of the tube indicates that the finite element modeling approach provides an accurate simulation. 3.4. Effect of reinforcing ratio on the tensile stress–strain relationship of concrete An accurate simulation of the tensile stress–strain response is critical to an accurate analysis of some categories of reinforced concrete components. In particular, sections with low levels of reinforcement and low or no axial load exhibit stronger influences from the tensile response. Generally, it is assumed that the tensile strength of concrete is approximately between 8% and 10% of the concrete compressive strength. The tensile response is modeled linearly to the maximum tensile strength of the concrete; the post-peak response is modeled with the tensile stresses decreasing linearly to zero at a strain equal to 10 times the peak strain, that is the strain corresponding to the maximum tensile strength of the concrete [12]. In this conventional model, stress–strain curve of bare rebar is often used. This conventional approach was compared with the modeling approach used in this study, which includes the impact of embedded reinforcing bars (Eqs. (1)–(3)) [14]. Fig. 8 shows the effects of tensile stress–strain relationship of the concrete and stress–stain curve of the reinforcing bar on the analysis results. The cracking stress, fcr, is assumed to be 9% of fc0 for the conventional method. It was found that both conventional method and embedded-bar modeling approach used in this study provided good results for Specimen K3 where minimal to modest footing cracks occurred. However, the results were improved using the embedded-rebar model for Specimen K2, which exhibited more significant cracking. For this specimen, conventional method overestimated the strength, as shown in Fig. 8b; the embedded modeling approach resulted in predictions that agreed well with test results. The results of embedding low levels of reinforcement in concrete changes the overall curve of the bar, as shown in Fig. 3b, and results in a larger strain corresponding to the yield stress, which becomes more significant with decreases in the reinforcement ratio. As a result, combination of Eq. (1) with Eqs. (2), (3) provided good results regardless of the failure modes of the CFT column-to-foundation connection. 4. Parametric study 4.1. Variables for parametric study A series of parametric studies were performed to investigate the behavior of the embedded CFT foundation connection. Table 4 provides values for the key variables evaluated. A total of 56 models
were analyzed to study the impact of D/t ratio, embedment length, le, shear reinforcement ratio, qv, the concrete compressive strength ratio between the footing and infill of the CFT, fc0 ,FT/fc0 ,CFT, and axial load ratio, P/Po. Specimen K3 shown in Fig. 4 served as the reference model. Nominal material strengths were used. As a result, the concrete compressive strength of footing, fc0 ,FT, the concrete compressive strength of the infill of CFT column, fc0 ,CFT, yield stress of steel tube, fy, ultimate stress of the steel tube, fu, and yield stress of the rebar, fyr, were 34.5, 34.5, 344.8, 482.7, and 413.7 MPa (5, 5, 50, 70, and 60 ksi), respectively. The embedment length ratio le/D was selected based on the results of the results of previous studies [8–11]. Previous results show that the full flexural strength was observed for most test specimens when embedment depth is larger than 80% of diameter of CFT column. Thus, to evaluate the impact of the embedment length ratio, le/D was varied from 0.6 to 0.9. For the base models in Table 4, the following values of the key parameters were studied:
D/t ratios of 60, 80, 100, and 120. Concrete strength ratios, fc0 ,FT/fc0 ,CFT of 0.7, 1, 1.5, and 2. Shear reinforcement ratios, qv, of 0%, 0.15%, 0.27% and 0.5%. Axial load ratios, P/Po, of 0.1, 0.2, and 0.3. Column diameters, D, of 508, 762, and 1524 mm (20, 30, and 60 in.).
It should be noted that the footing dimension and total amount of reinforcement were proportioned to D.
4.2. Evaluation of different failure mechanisms Fig. 9 shows base moment-drift relationship for two different failure modes. The x and y axes in Fig. 9(a) denote drift and normalized flexural strength of the embedded connection, Mu,FEM/Mu,PSDM, respectively. The value of Mu,PSDM is the theoretical flexural strength of the CFT column calculated from plastic stress distribution method [16]. The model-naming scheme denotes the key variables studied. Results of two models are shown in Fig. 9, where Model CFT60-0.6-0-1 had a D/t ratio of 60, embedment depth ratio (le/D) of 0.6, shear reinforcing ratio of 0%, and a concrete strength ratio of 1. In contrast, Model CFT80-0.9-0.27-1 has a D/t ratio of 80, embedment depth ratio (le/D) of 0.9, shear reinforcement (qv) of 0.27%, and a concrete strength ratio of 1. The results shown in Fig. 9 indicate two different failure modes of the CFT connection. Model CFT60-0.6-0-1 has relatively larger normalized flexural strength of CFT column than that of CFT800.9-0.27-1. For Model CFT60-0.6-0-1, Mu,FEM/Mu,PSDM is 0.75 indicating that the full flexural capacity of the CFT was not developed while Mu,FEM was 13% larger than the theoretical flexural strength
Fig. 8. Effects of tensile stress–strain relationship of the concrete and stress–stain curve of the reinforcing bar on the analysis results: (a) K3 specimen; (b) K2 specimen.
J. Moon et al. / Engineering Structures 56 (2013) 22–35 Table 4 Base models for parametric study. Model
D (mm/in)
D/t
le/D
qv (%)
fc0 ,FT (Mpa/ksi)
P/Po
CFT60-0.6-0.27-1 CFT60-0.7-0.27-1 CFT60-0.8-0.27-1 CFT60-0.9-0.27-1
508/20 508/20 508/20 508/20
60 60 60 60
0.6 0.7 0.8 0.9
0.27 0.27 0.27 0.27
34.5/5 34.5/5 34.5/5 34.5/5
0.1 0.1 0.1 0.1
Note: fy = 344.8 MPa (50 ksi); fu = 482.7 MPa (70 ksi); fyr = 413.7 MPa (60 ksi); and fc0 ,CFT = 34.5 MPa (5 ksi) for all analysis models.
29
cracking initiates but is limited, resulting in ductile response. The initial crack formed at the tip of the annular ring with an angle of approximately 45°. However, the cracking was much more limited than Models CFT60-0.6-0-1, and the deformability of the system came from the extensive yielding of the steel tube in tension and compression, as shown in Fig. 10b. The results show that the shear capacity of the footing must be considered in the design to achieve full plastic action in the column resulting in maximum drift capacity. 4.3. Evaluation of parameter impact
Mu,PSDM for Model CFT80-0.9-0.27-1, indicating that the model achieved the desired response mode of column yielding. The key difference in these two models is the location of the initiation and progression of damage. For Model CFT60-0.6-0-1, the footing is severely damaged and pullout failure occurs, as illustrated in Fig. 9b. For Model CFT80-0.9-0.27-1, inelastic action is sustained by the steel tube with yielding, and local buckling of steel tube controls the strength of the specimen while mitigating footing damage because of the increased embedment depth. These differences are studied in more depth in Fig. 10. The distribution of stresses and crack pattern of footing (middle section) at 4% drift are shown in Fig. 10a and b for Models CFT60-0.6-0-1 and CFT80-0.9-0.27-1, respectively. When the embedment depth was shallow without shear reinforcement (Model CFT60-0.6-0-1), significant cracking was noted on the tension side of column in the footing; this cracking was severe and resulted in lost tensile resistance. Significant cracking permitted separation of the concrete infill and footing and resulted in increased compression stresses at the bottom of the annular ring and interface between the CFT and footing in compression side, as shown in Fig. 10a. As a result, a portion of the steel tube that was in compression had locally yielded. In contrast, Model CFT80-0.9-0.27-1, which had adequate embedment depth and shear reinforcement, the footing
The impact of each of the study parameters was assessed through a series of parametric study. Fig. 11 shows the effect of D/t ratio, where D/t ratio is plotted on the x-axis. Three different parameters are used to assess the parameter impact and these parameters are plotted on the y-axis. The parameters were the normalized strength ratio (Mu,FEM/Mu,PSDM) (Fig. 11a), the normalized uplift of the footing where the uplift is normalized to H, the height of the footing (Fig. 11b), and normalized out-of-plane deformation (OPD) of the steel tube, where the OPD is normalized to the column diameter (Fig. 11c). Uplift and out-of-plane deformation of the steel tube were measured at the interface between the CFT column and the footing in tension side, and at a height of 76.2 mm (3 in.) above the footing on the compression side, respectively (see Fig. 9b for illustration of these key points). The following observations are made: (1) The flexural strength ratio, Mu,FEM/Mu,PSDM, is not impacted by the D/t ratio for well-anchored connections (e.g., le/D = 0.9), (2) The uplift is similarly constant for well-anchored connections (e.g., le/D = 0.9), (3) The out-of-plane displacement increases significantly with D/t ratio, regardless of the anchorage depth. These figures also illustrate the impact of normalized embedment depth on the response. Each connected line represents one le/D ratio, as indicated by the symbols and the legends. In contrast
Fig. 9. Simulation results for models CFT60-0.6-0-1 and CFT80-0.9-0.27-1: (a) moment–drift relationships; and (b) damage modes.
30
J. Moon et al. / Engineering Structures 56 (2013) 22–35
Fig. 10. Stress distributions and crack patterns for analysis models: (a) CFT60-0.6-0-1; and (b) CFT80-0.9-0.27-1 (Note: 1 ksi = 6.89 MPa).
Fig. 11. Effect of D/t ratio: (a) Mu,FEM/Mu,PSDM vs. D/t; (b) uplift/H vs. D/t; and (c) O.P.D/D vs. D/t.
to the D/t ratio, the embedment depth has a much more significant impact on the response. The flexural strength of the system reduces for lower le/D, while the uplift increases. The OPD decreases
with increasing le/D, but this is expected since, for lower le/D ratios, the response of the system is controlled by damage in the footing and therefore tube buckling is limited.
J. Moon et al. / Engineering Structures 56 (2013) 22–35
Fig. 12 shows the effect of concrete compressive strength ratio of the footing and CFT column infill, fc0 ,FT/fc0 ,CFT. Larger fc0 ,FT/fc0 ,CFT ratio results in a stronger concrete strength of the footing. Although this is contrary to practice, the results show that a ratio of 1 is required to achieve the flexural strength. Furthermore, Fig. 12 suggests that an increase in fc0 ,FT/fc0 ,CFT ratio reduces the damage of the footing and is helpful to increase Mu,FEM/Mu,PSDM. This is a similar trend to that identified with increasing D/t ratio. Larger compressive capacity of the footing concrete also reduced the uplift (Fig 12b). The OPD increased with increasing the strength ratio, since the larger footing strength encourages yielding and buckling of the steel tube. The impact of the shear reinforcement on the response is shown in Fig. 13. In all cases, models without shear reinforcement failed to achieve their flexural strength. For lower values of le/D, the impact of the shear reinforcement in the footing was more significant. For example, the models with an le/D = 0.6 showed an increase in strength with additional shear reinforcement; for models with larger le/D ratio, the increase was less significant. The effects of axial load ratio are summarized in Fig. 14. In general, Mu,FEM/Mu,PSDM was increased with increasing P/Po when Mu,FEM/Mu,PSDM is less than one (lower anchorage lengths with significant impact of the footing response). For well-anchored models, increasing P/Po beyond 0.2 does not increase the strength ratio. However, in all cases increasing P/Po reduced the uplift deformation of the footing. In most cases, increasing P/Po increased the OPD. In contrast to the expected response, for well-anchored models (le/D = 0.9), the OPD decreased with increasing values of P/Po. This trend is explored further by comparing two models with two different axial load ratios of 0.1 and 0.2 at 4% drift, as shown in Fig. 15. The figure plots the maximum principle plastic strain gradients that represent the cracking in the concrete infill and footing. The figure shows that the compressive region of the concrete infill increases with an increase in the axial load ratio, suggesting that an increased amount of concrete is engaged to sustain the combined demands from tension and axial compressive loading (P). In addition, the arc of the tube engaged in sustaining the compressive force is also increased. The combination of these responses results in decreasing the simulated OPD. However, additional displacement demand that may result in significant damage to the concrete infill accelerates buckling of the steel tube. This latter behavior has been observed by others [18]. It is also noted that the tensile strains in some cracked region are very high in Fig. 15. This is because that the slope of the tensile stress–strain curve is almost zero when the tensile strain is large [approximately 0.01 from Eq. (1)]. Thus, tensile strain could be dramatically increased even if the decrease in tensile stress is very small. Finally, the impact of the column diameter (D) was investigated by studying CFT columns with diameters of 508, 762, and 1524 mm (20, 30, and 60 in.). There was no impact on the response.
31
5. Design of embedded CFT connection An empirically-derived design equation to estimate the minimum embedment depth, le, was proposed based on a series of test results [8–11]. The expression was derived using geometry and equilibrium of the connection corresponding to pullout failure, as depicted in Fig. 16. The tube is embedded a length le. The annular ring has an outer diameter of Do. For the derivation of the design equation, shear stress angle b1 in the concrete footing is approximated as 45°. (Note, this angle has been verified by the finite element analysis, for which the crack that initiates on the tension side of the column forms at an angle of approximately 45°.) Equilibrium in vertical direction is given by the following equation:
T s ¼ V c sin b1 :
ð4Þ
In the expression, Ts and Vc are the tensile force in the steel and shear force in the concrete, respectively. For an incremental angle of Dc, Ts and Vc are given by
T s ¼ Dc
D le fs t and V c ¼ sc Dc ðD0 þ le cot b1 Þ: 2 2 sin b1
ð5Þ
Substituting Eq. (5) into Eq. (4) with b1 = 45°, shear stress of the footing, sc, that is needed to develop stress of fs in steel tube can be computed using Eq. (6).
sc ¼
Dtfs 2
ðle þ D0 le Þ
:
ð6Þ
It is noted that shear stress of the footing, sc, is the same with the shear stress of the concrete in the footing since the shear reinforcing bar is ignored in Eq. (6). To achieve full flexural strength of the CFT column, the steel tube must fully yield, ideally reaching its ultimate strength, fu. Thus, the shear stress capacity, sc, was computed by substituting fu for fs in Eq. (6). Significant variability exists in the shear stress capacity of the concrete. For this qffiffiffiffiffiffiffi ffi reason, Lee [11] provided that sc should be smal0 ler than a fc;FT to achieve full flexural capacity of the CFT column, and a varies from 0.42 to 0.57 (MPa unit). However, that proposal was based on limited experimental data. In this study, this shear stress range was reexamined and calibrated by using results of parametric study as well as the experimental results. Fig. 17 shows the evaluation of design equation to estimate the minimum embedment depth. In Fig. 17, the x-axis is the normalized shear qffiffiffiffiffiffiffi ffi 0 stress, sc/ fc;FT , where sc is calculated from Eq. (6) with fs equal to fu. As expected, the results show that Mu,FEM/Mu,PSDM decreases and uplift increases (equivalent to increased damage sustained qffiffiffiffiffiffiffi ffi 0 by the footing) with increasing sc/ fc;FT . Also, out-of-plane deforqffiffiffiffiffiffiffi ffi 0 mation of the steel tube increases with decreasing sc/ fc;FT as shown in Fig. 17c, which also indicates that higher shear stress
Fig. 12. Effect of fc0 ,FT/fc0 ,CFT: (a) Mu,FEM/Mu,PSDM vs. fc0 ,FT/fc0 ,CFT; (b) Uplift/H vs. fc0 ,FT/fc0 ,CFT; and (c) O.P.D/D vs. fc0 ,FT/fc0 ,CFT.
32
J. Moon et al. / Engineering Structures 56 (2013) 22–35
Fig. 13. Effect of qv: (a) Mu,FEM/Mu,PSDM vs. qv; (b) Uplift/H vs. qv; and (c) O.P.D/D vs. qv.
Fig. 14. Effect of P/Po: (a) Mu,FEM/Mu,PSDM vs. P/Po; (b) Uplift/H vs. P/Po; and (c) O.P.D/D vs. P/Po.
Fig. 15. Variation of crack patterns for different axial load ratio (4% drift).
in the footing limits the inelastic action in the tube, and potentially changes the response mode from ductile yielding of the column to brittle response of the connection. From the comparative study, test results of monolithically embedded connection and analysis results without shear reinforcing bar provide a lower bound on the embedment depth. A linear regression was performed using these data (Linear Regression_1 in Fig. 17a). The value of Mu,FEM/Mu,PSDM was larger than 1 when Eq. (7a) is satisfied. These results are applicable to foundation designs for which ductility in the tube is not a design requirement,
including regions of low and moderate seismicity, as indicated below. For regions of low and moderate seismicity
Dtfu 2 ðle
þ D 0 le Þ
qffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffi 0 0 ¼ 0:6 fc;FT MPa ð7:2 for psi unitÞ ðaÞ 6 a fc;FT
For regions of high seismicity
Dtfu 2 ðle
þ D 0 le Þ
qffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffi 0 0 6 a fc;FT ¼ 0:55 fc;FT MPa ð6:6 for psi unitÞ ðbÞ
ð7Þ
33
J. Moon et al. / Engineering Structures 56 (2013) 22–35
Fig. 16. Schematic view of footing resistance to cone pullout failure.
Fig. 17. Evaluation of design equation: (a) Mu,FEM/Mu,PSDM vs. sc/(fc0 ,FT)0.5; (b) Uplift/H vs. sc/(fc0 ,FT)0.5; and (c) O.P.D/D vs. sc/(fc0 ,FT)0.5.
Satisfaction of this minimum does not guarantee significant plastic action in the CFT column, since CFT column-to-foundation connection must be fully yielded and provide the significant inelastic deformation capacity. From the observation of the test and finite element analysis results, it was found that the full strength of the CFT column was usually 10–20% larger than theoretical value. Full plastic action occurred when Mu,test/Mu,PSDM is larger than 1.15. Table 5 shows the summary of drift ductility, l, for the test results conducted [9–11], where drift ductility is defined as the ratio of maximum amount of deflection (drift) divided by the amount of deflection (drift) at yield. The yield point of these specimens was defined as the point where the steel strain equals the yield strain of the material. The maximum deformation was defined as the point prior to 20% loss in lateral strength. On average, the drift ductility of the CFT column was 8.8. Thus, target strength ratio of CFT column-to-foundation connection was selected as 1.15Mu,PSDM for more extreme loading. Then, an alternative linear regression was conducted using analysis results with shear reinforcing bar and isolated embedded connection test data (Linear Regression_2 in Fig. 17a), because the scatter was considerably reduced when these data were used for regression. ffiffiffiffiffiffiffiffi The ratio of Mu,FEM/Mu,PSDM was larger than 1.15 when sc/ q 0 fc;FT 6 0.55 (MPa unit). This value is recommended for high seismic regions as described in Eq. (7b). It should be noted that target strength ratio of CFT column-to-foundation connection was adopted as 1.15Mu,PSDM for high seismic region based on the test results shown in Table 5 since they show appropriate ductility level that show the plastic action. However, these tests have the clear limit about the details and material properties of tested specimens. For example, D/t ratio and qv were limited to 80% and 0.27%,
respectively. Thus, this target strength ratio for high seismic region may not be appropriate for the CFT column-to-foundation connection that deviates from the profiles of test specimens used in this study, and the care should be taken to apply the proposed equation for high seismic region. Scatter is observed in the data presented in Fig. 17. The simulations suggest that the shear reinforcement ratio and axial load ratio can reduce the required embedment depth. However, these factors were neglected in the derivation of Eq. (6). Eq. (8) was derived by conducting a regression analysis of the results of parametric study.
ð1 þ qv Þ0:46 ð1 þ P=Po Þ0:51 sc;m ¼
Dtfu 2
ðle þ D0 le Þ
:
ð8Þ
In Eq. (8), sc,m is the modified shear stress of the concrete in the footing that is needed to develop stress of fu in steel tube, and qv is the shear reinforcement ratio in percent (%). In Eq. (8), the value of qv never exceeds 0.3%, and the value of P/Po cannot exceed 0.2 since little benefit of these parameters were observed for a well-anchored CFT-footing connection from the analysis. The shear stress range of embedded CFT connection was evaluated by using Eq. (8) and the results are shown in Fig. 18. The variability in the prediction was reduced by using Eq. (8). Similar with Eq. (7), the shear stress range was evaluated and the results are given by For regions of low and moderate seismicity
Dtfu 2 ðle
þ D 0 le Þ
qffiffiffiffiffiffiffiffi 0 6 a fc;FT ¼ 0:55ð1 þ qv Þ0:46 ð1 þ P=Po Þ0:51 qffiffiffiffiffiffiffiffi 0 fc;FT MPa ð6:6 for psi unitÞ
ð9aÞ
34
J. Moon et al. / Engineering Structures 56 (2013) 22–35
Table 5 Drift ductility of the test specimens where Mu,test/Mu,PSDM P 1.15. Test specimen
D (mm/in.)
le/D
D/t
fy (MPa/ksi)
fc0 ,CFT (MPa/ksi)
fc0 ,CFT/fc0 ,FT
qv (%)
P/Po
Mu,test/Mu,PSDM
l
W5 [9] W6 [9] C1 [10] C2 [10] C4 [10] 1–50 [11] 2–50 [11] 5–50 [11] 6–50 [11]
508/20 508/20 508/20 508/20 508/20 508/20 508/20 508/20 508/20
0.9 0.75 0.9 0.9 0.9 0.8 0.775 0.7 0.6
80 80 80 80 80 80 80 80 80
520.9/75.6 520.9/75.6 520.9/75.6 520.9/75.6 520.9/75.6 337.6/49 337.6/49 351.4/51 351.4/51
77.2/11.2 81.3/11.8 67.5/9.8 66.8/9.7 68.2/9.9 59.9/8.7 64.1/9.3 67.5/9.8 69.6/10.1
1 1 1 1 1 0.79 0.82 0.84 0.86
0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27
0.1 0.1 0.1 0.1 0.2 0.1 0.1 0.1 0.1
1.15 1.22 1.27 1.30 1.23 1.17 1.17 1.31 1.22
7.1 8.3 6.3 7.3 7.8 13.5 11.6 9.2 8.2
Fig. 18. Evaluation of modified design equation: (a) Mu,FEM/Mu,PSDM vs. sc,m/(fc0 ,FT)0.5; (b) Uplift/H vs. sc,m/(fc0 ,FT)0.5; and (c) O.P.D/D vs. sc,m/(fc0 ,FT)0.5.
For regions of high seismicity
Dtfu 2 ðle
þ D0 le Þ
qffiffiffiffiffiffiffiffi 0 6 a fc;FT ¼ 0:47ð1 þ qv Þ0:46 ð1 þ P=Po Þ0:51 qffiffiffiffiffiffiffiffi 0 fc;FT MPa ð5:7 for psi unitÞ:
ð9bÞ
Thus, the minimum embedment depth of the CFT connection can be obtained by solving Eq. (9) to include the benefits of shear reinforcement and axial load. a in Eq. (9a) is amplified up to 0.68 (MPa unit) by introducing the shear reinforcement ratio of 0.3% and axial load ratio of 0.2. In the case of a in Eq. (9b), a varies from 0.47 to 0.58 (MPa unit). Lee [11] suggested a is between 0.42 and 0.57 (MPa unit) and his proposed range for a is similar with that from this study. ACI 318 code [19] provides the critical failure shear force in Section 11.2.1. Similarly with thus study, theq critical ffiffiffiffiffiffiffiffi shear stress spec0 ified in ACI [19] can be expressed as sc/ fc;FT = Ck where C varies from 2 to 4 (in psi unit) and k is 1 for normal concrete. This dimensionless critical shear stress range was also plotted with analysis results and test results, as shown in Figs 17 and 18. From the comparative study, it was found that ACI318 [19] give a conservative value for pullout failure of the CFT column-to-foundation connection. 6. Summary and conclusions Concrete filled tubes offer substantial benefits over conventional construction methods because of their inherent strength, stiffness, stability all of which contribute to reduced labor and material requirements. However, CFT components are seldom used in part because there are few validated constructible connections. Prior experimental studies have developed a feasible CFT-to-foundation connection. However, the data were limited and the full range of design parameters could not be evaluated.
This research extended those studies by conducting non-linear finite element analyses to investigate the impact of salient design parameters on the embedded foundation connection for the CFT columns. The finite element model was verified using measured response and observed damage of prior test results, including cracking of the footing and local buckling of the steel tube. The analytical study revealed two different failure modes, both of which were observed in the testing. For models with shallow embedment depths and insufficient shear reinforcement in the footing, heavy cracking was observed adjacent to the tension side of the CFT column in the footing and this cracking led to loss of strength prior to development of the theoretical flexural strength. In contrast, when the embedment depth was sufficiently deep and shear reinforcement were provided, the steel tube fully yielded in tension and compression; in that case the CFT column controlled the response of the system with local buckling and yielding of the tube. With a validated model in hand, a parametric study was performed to study the effects of D/t ratio, embedment length, shear reinforcement ratio, concrete compressive strength ratio of the footing and infill in the CFT, and axial load ratio. The analysis results showed that: (1) The embedment depth had the most dramatic impact on the response of the CFT column-to-footing subassemblies, (2) The flexural strength ratio, Mu,FEM/Mu,PSDM, was not impacted by the D/t ratio for well-anchored connections (e.g., le/D = 0.9) while D/t ratio had significant effect on the Mu,FEM/Mu,PSDM for shallow embedment depth (e.g., le/D = 0.6), (3) For models with lower embedment depths, the impact of the shear reinforcing bar was more significant, (4) An increase in fc0 ,FT/fc0 ,CFT ratio reduced the damage of the footing and was helpful to increase Mu,FEM/Mu,PSDM, and (5) In general, Mu,FEM/Mu,PSDM was increased with increasing P/Po when Mu,FEM/Mu,PSDM was less than one. However, for well-anchored models, increasing P/Po beyond 0.2 did not increase the strength ratio. Two design equations to estimate the minimum embedment depth were derived using the analytical results and previous test
J. Moon et al. / Engineering Structures 56 (2013) 22–35
data. From the results, the minimum embedment depth that guarantees full flexural strength of CFT column from plastic stress distribution method can be obtained by solving Eq. (7a). For regions of high seismicity, Eq. (7b) is recommended. A modified design equation was proposed to include benefits of shear reinforcement and axial load ratio as Eq. (9) and the scatter of analysis and test results was reduced.
[6] [7] [8]
[9]
Acknowledgements [10]
This work was completed partially with funding provided by the Washington State Department of Transportation (WSDOT) through the project entitled, ‘‘Design of Bridge Foundations with Steel Casings’’. Mr. Bijan Khaleghi is the WSDOT Bridge Design Engineer and the coordinator of this project. The advice and financial support of the WSDOT is gratefully acknowledged. References [1] Roeder CW, Lehman DE, Bishop E. Strength and stiffness of circular concrete filled tubes. J Struct Eng ASCE 2010;136(12):1545–53. [2] Hu HT, Huang CS, Wu MH, Wu YM. Nonlinear analysis of axial loaded concretefilled tube columns with confinement effect. J Struct Eng ASCE 2003;129(10):1322–9. [3] Lu H, Han LH, Zhao XL. Analytical behavior of circular concrete-filled thinwalled steel tubes subjected to bending. Thin-Walled Struct 2009;47:346–58. [4] Moon J, Lehman DE, Roeder CW, Lee H-E. Analytical modeling of bending of circular concrete-filled steel tubes. Eng Struct 2012;42:349–61. [5] Moon J, Lehman DE, Roeder CW, Lee H-E. Strength of circular concrete-filled tubes (CFT) with and without internal reinforcement under combined loading.
[11]
[12] [13] [14] [15] [16] [17] [18] [19]
35
J Struct Eng ASCE; in press. http://dx.doi.org/10.1061/(ASCE)ST.1943541X.0000788. Lehman DE, Roeder CW. Foundation connections for circular concrete-filled tubes. J Construct Steel Res 2012;78:212–25. Pecce M, Rossi F. The non-linear model of embedded steel-concrete composite column bases. Eng Struct 2013;46:247–63. Kingsley A. Experimental and analytical investigation of embedded column base connections for concrete filled high strength steel tubes. MS thesis. Seattle, WA: Univ. of Washington; 2005. Williams TS. Experimental investigation of high strength concrete filled steel tubes in embedded column base foundation connections. Seattle, WA: Univ. of Washington; 2006. Chronister A. Experimental investigation of high strength concrete filled steel tubes in embedded column base foundation connections. MS thesis. Seattle, WA: Univ. of Washington; 2007. Lee JR. Experimental investigation of embedded connections for concretefilled steel tube columns subjected to combined axial-flexural loading. MS thesis. Seattle, WA: Univ. of Washington; 2011. ABAQUS. ABAQUS analysis user’s manual version 6.9-2 2009. Providence, RI, USA: Dassault Systemes Simulia Corp. Saenz LP. Discussion of ‘equation for the stress-strain curve of concrete’ by P. Desayi, and S. Krishnan. ACI J 1964;61:1229–35. Hsu TTC, Mo Y-L. Unified theory of concrete structures. 2nd ed. John Wiley & Sons, Inc.; 2010. Lee J, Fenves GL. Plastic-damage model for cyclic loading of concrete structures. J Eng Mech ASCE 1998;124(8):892–900. AISC. Specifications for structural steel buildings, Chicago, IL; 2008. Baltay P, Gjelsvik A. Coefficient of friction for steel on concrete at high normal stress. J Mater Civ Eng ASCE 1990;2(1):46–9. Marson J, Bruneau M. Cyclic testing of concrete-filled circular steel bridge piers having encased fixed-base detail. J Bridge Eng ASCE 2004;9(1):14–23. ACI. Building code requirements for structural concrete and commentary, ACI318-11 2011, Farmington Hills, MI.
Contents lists available at SciVerse ScienceDirect
Engineering Structures journal homepage: www.elsevier.com/locate/engstruct
Evaluation of embedded concrete-filled tube (CFT) column-to-foundation connections Jiho Moon a, Dawn E. Lehman b,⇑, Charles W. Roeder b, Hak-Eun Lee a a b
School of Civil, Environmental & Architectural Engineering, Korea University, 5-1, Anam-dong, Sungbuk-gu, Seoul 136-701, South Korea Department of Civil & Environmental Engineering, University of Washington, Seattle, WA 98195-2700, USA
a r t i c l e
i n f o
Article history: Received 12 April 2012 Revised 15 April 2013 Accepted 16 April 2013 Available online 21 May 2013 Keywords: Concrete-filled tubes (CFTs) Embedded connection Composite structure Minimum embedment depth Non-linear finite element analysis
a b s t r a c t Concrete-filled tubes (CFTs) are effective structural components. Relative to conventional reinforced concrete components, they have higher strength-to-size efficiency and facilitate rapid construction. Yet they are not used frequently in US construction. The component response is well understood from extensive experimental and analytical studies that have been conducted on CFT components themselves. There remains a fundamental challenge of implementing these components in structural systems, which is caused by the uncertainty of the connection design and performance. Relative to component research, limited research has focused on the connections of CFT columns. A recent research effort has resulted in a new embedded connection for a CFT column anchored into a reinforced concrete foundation. The connection is fully capable of transferring combined bending and axial loads and has sufficient deformability to sustain multiple inelastic deformation cycles under extreme loading. In addition, the connection has unique features that facilitate constructability and rapid construction. However, the connection design to date is solely based on experimental study, which evaluated a very limited range of design parameters. A coordinated analytical study, using high-resolution continuum models, was undertaken to investigate the unstudied parameters and develop appropriate design expressions, which is the subject of this paper. An analytical model was developed and verified using the test results. The verified model was then used to conduct a parametric study to enhance the understanding of the experimental behavior and extend the test databases. Parameters studied included the embedment depth, diameter-to-thickness (D/t) ratio, shear reinforcement ratio, strength ratio of the concrete in the footing and concrete infill, and the axial load ratio. From the analysis results, the failure mechanisms were evaluated with respect to the individual parameters. The results showed that an increase in embedment depth, D/t ratio, shear reinforcement ratio, the axial load ratio, or the ratio of the concrete strength in the footing relative to the concrete infill of CFT column increased the connection strength and could result in ductile yielding of the CFT column, which is the desired response mode. Finally, the analysis and test results were combined to develop a refined design equation for the required embedment depth. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Concrete-filled tubes (CFTs) are composite members, which consist of a steel tube and concrete infill. CFTs used as building columns and bridge piers have several advantages over conventional structural components, including their strength-to-size efficiency and facilitation of rapid construction. The previous researches are heavily focused on the CFT component response. Extensive experimental studies on CFT component subjected to pure axial, pure bending, or combined axial-bending loading have been conducted and the results are summarized by Roeder et al. [1]. Other researchers have studied CFTs analytically
⇑ Corresponding author. Tel.: +1 206 715 2108. E-mail address: [email protected] (D.E. Lehman). 0141-0296/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.engstruct.2013.04.011
and developed models appropriate for simulating the CFT component response [2–5]. However, only limited studies have focused on the connection of the CFT component to adjacent components, such as the foundation [6,7]. This limitation in the research has resulted in limiting the use of CFT components in US construction. The connections must be practical and economical. They must develop full composite flexural strength to achieve the benefits of CFT members as columns or piers. Further, good ductility or inelastic deformation capacity is required of these connections in moderate to high seismic zones. A recent testing effort has resulted in an efficient CFT column to foundation connection, appropriate for both bridge and building construction [6]. This connection is capable of transferring the full composite resistance of the CFT column to the footing, while
J. Moon et al. / Engineering Structures 56 (2013) 22–35
sustaining inelastic deformation demands resulting from extreme loading. The proposed connection is shown in Fig. 1a. Typically, embedded CFT connections use a full base plate. Here, a steel annular ring is welded to the base of the steel tube to provide anchorage of the column into the footing and to transfer the column forces and moments into the foundation. Two types of construction methods were explored: (1) monolithic and (2) isolated. For the monolithic connection, the tube is temporarily supported while the footing is cast around it to embed the steel tube and its annular ring. The isolated connection casts the footing concrete prior to the column concrete, thereby separating the reinforcing cage construction and the structural steel placement. The isolated connection is fabricated using the following construction sequence: (1) cast the footing with a void or recess formed by a corrugated steel tube at the column location, (2) lower the CFT column into place, (3) grout the column into place with fiber reinforced grout, and (4) fill the column with self-consolidating low-shrinkage concrete. Extensive experimental studies were conducted for these connections [8–11]. The results show that the connections have two different possible failure modes depending on the embedment depth, as shown in Fig. 1b. Pullout failure may occur when the embedment depth is not sufficient, while punching shear failure might occur with shallow base depth below the CFT column. With sufficient connection strength, both of these failure modes can be suppressed thereby resulting in ductile yielding of the column, which is the desired response mode. Therefore, it is critical to identify all parameters that influence the failure modes of the connection (Brittle pull-out failure or ductile failure of CFT pier or column). The experimental research alone did not provide sufficient study of all pertinent variables. Thus, a companion analytical study was undertaken. This paper presents non-linear finite element analysis of the monolithic embedded connection for the CFT column to enhance the understanding of the experimental results by demonstrating the failure modes of the connection and by extending the existing test database through analysis of the parameters that have not been tested such as large D/t ratio and high axial load ratio. The analysis model was successfully verified. The verified model
23
was used to investigate the effects of embedment depth, D/t ratio, shear reinforcement, concrete strength ratio between the footing and concrete infill of CFT column, and axial load ratio. Finally, a design equation for minimum embedment depth to ensure ultimate strength of the embedded connection was evaluated. 2. Finite element model of embedded CFT connection The analytical study was conducted using the general-purpose finite element analysis program ABAQUS [12]. Fig. 2 shows an example of finite element model of the CFT connection, column and foundation. Because of symmetry, a half model of the specimen was used, which saved modeling and computing time. The 8-node solid (C3D8R), 4-node shell (S4R), and 2-node truss element (T3D2) were used to model concrete, steel tube, and steel reinforcement, respectively. The interface between concrete and steel tube was separately modeled explicitly using the GAP element that is provided by ABAQUS [12] to simulate the contact behavior between the concrete and the steel tube. GAP elements allow relative movement between the steel and concrete while restricting penetration of one node into an adjacent one. The normal stresses generated in the GAP element result in shear stress transfer between the steel and the concrete fill through friction. Relative movement (slip) between the internal reinforcing bar and the concrete was not modeled; the reinforcement was assumed to be perfectly bonded, which was modeled using the EMBEDED option in ABAQUS [12]. Fig. 3a shows the uniaxial stress–strain relationship of concrete used in this study. The compressive stress–strain relationship proposed by Saenz [13] was employed where it is assumed that the stress–stain relationship is linear up to a stress of 0.5fc0 and the maximum compressive strength, fc0 , is achieved when compressive strain is 0.003. For the tensile stress–strain relationship of concrete, the curve proposed by Hsu and Mo [14] was adopted. Tensile stress–strain relationship is linear uppto ffiffiffiffi stress at cracking of concrete, fcr, where fcr is defined as 0.31 fc0 MPa [14] and the softening relationship is given by Eq. (1):
Fig. 1. Proposed connection and failure modes of footing: (a) monolithic and isolated connections; and (b) possible failure modes of footing.
24
J. Moon et al. / Engineering Structures 56 (2013) 22–35
Fig. 2. Components of the finite element model: (a) concrete infill and footing; (b) steel tube; (c) interface between infill and tube; and (d) reinforcing bar.
Fig. 3. Material models: (a) concrete; and (b) bare and embedded reinforcing bar.
ecr 0:4 Þ when ec 6 ecr : ec
fc ¼ fcr ð
ð1Þ
In Eq. (1), ecr is strain at cracking of concrete. Inelastic behavior of concrete was modeled using the concrete damaged plasticity model proposed by Lee and Fenves [15] available in ABAQUS [12]. This constitutive model uses a non-associated flow rule and is suitable for simulation of the stress triaxially-dependent plastic hardening. The dilation angle of the concrete, w, which is the measured angle plane where p are the hydrostatic stress tensor q and q in the p and Von-Mises equivalent effective stress tensor respectively, is an important model parameter in the concrete damaged plasticity model. The dilation angle, w, was approximated as 20° and 31° for the concrete infill in the tube and the concrete in the footing, respectively, based on the results of the previous research and parametric studies [4,15] A tri-linear stress–strain relationship was used for the steel in the tube. Young’s modulus, Es, was approximated as 200,000 MPa; and Poisson’s ratio, ts, was set as 0.3. The plastic plateau terminates when strain of the steel, es, is equal to 10 times the yield strain of the steel (10esy) and stress increases up to ultimate strength of the steel, fu, which is achieved when the ultimate strain of the steel, esu, is 0.1. The measured properties of the steel and concrete were used to establish the material models when available. The average stress–strain relationship of reinforcing bar embedded in concrete depends on the effective reinforcement ratio, and can differ from the properties of bare reinforcing bar for low reinforcement ratios as shown in Fig. 3b [14]. The primary difference is the lower effective yield stress below the yield stress of reinforcing bar, fyr. In this study, the average stress–strain relationship of
embedded reinforcing bar proposed by Hus and Mo [14] was adopted, and it is given by
fr ¼ Er er when f r 6 fyr0
ðaÞ
ð2Þ
fr ¼ ð0:91 2BÞfyr þ ð0:02 þ 0:25BÞEr er when f r > fyr0
ðbÞ
where
fyr0 ¼ ð0:93 2BÞfyr ;
and B ¼
1:5 1 fcr : q fyr
ð3Þ
In Eq. (2), Er is young’s modulus of the reinforcing bar, fr and er are the stress and strain in the reinforcing bar, respectively, and f’yr is the reduced yield stress of embedded reinforcing bars. Eqs. (2) and (3) are applicable for reinforcement ratios, q, larger than 0.15% [14]. Eqs. (2) and (3) were derived assuming the tensile stress–stain relationship of the concrete can be expressed as Eq. (1). The choice of the tensile stress–stain relationship of the concrete can affect the behavior of the concrete structure, and the parametric study was performed for various types of the tensile stress–strain relationship of the concrete in this study. From the results, combination of Eq. (1) with Eqs. (2) and (3) was adopted. The details of the results of parametric study are shown in Section 3.4. 3. Verification of finite element model 3.1. Test overview The model described above was verified using the test results. Specifically, the results of the monolithically embedded connection tests were compared with analytical results. Fig. 4 shows the
J. Moon et al. / Engineering Structures 56 (2013) 22–35
dimensions and reinforcement layout for the test specimens. A spiral weld steel tube with a nominal yield strength of 480 MPa was used in Specimens K1–K3. Specimens K1 and K2 are nominally identical, in which Specimen K2 has shear reinforcement and Specimen K1 does not. Specimen K3 has a deeper embedment depth. In contrast to the K-series, the two remaining specimens used a tube with a nominal steel strength of 345 MPa where spiral weld tube was used for Specimen 1–50 and straight-seam weld tube was used for Specimen 4–50. The height of column above the footing was 1828.8 mm (72 in), and the footing was 1930.4 mm (76 in.) in the direction of loading by 1727.2 mm (68 in.) wide for these specimens. The depth of the footing was 609.6 mm (24 in.). The diameter of tube was 508 mm (20 in.) and the D/t ratio was 80 for all specimens, where D is external diameter of CFT and t is the thickness of steel tube, respectively. The size of the footing was determined through preliminary analysis conducted by Kingsley [8]. Kingsley [8] conducted the finite element analysis with footing depths from 1.2D to 1.8D and showed very little effect on the performance of the connection. The 1.2D footing depth develops adequate shear and flexural resistance and is proportional to footings used in practice. The flexural reinforcing bar in the direction of loading consisted of No. 6 bars spaced at 101.6 mm (4 in.) for all specimens, as shown in Fig. 4. The flexural reinforcing bar in the direction perpendicular to loading consisted of No. 4 bars spaced at 228.6 mm (9 in.) for Specimens K1 and K2, while No. 6 bars spaced 101.6 mm (4 in.) for Specimens K3, 1–50, and 4–50. The nominal area of No. 4 and 6 bars are 129 and 284 mm2 (0.20 and 0.44 in.2), respectively. Specimen K1 had no shear reinforcement in the footing, while No. 3 ties were uniformly used for Specimens K2, K3, 1–50, and 4–50 resulting in a 0.27% shear reinforcement ratio, qv, where the nominal area of No. 3 bar is 71 mm2 (0.11 in.2). The material properties and embedment depth of each specimen are summarized in Table. 1. In Table 1, le represents the embedment depth. The applied axial load was 0.1Po, where Po is the squash load and is defined as 0.95fc0 Ac + fyAs where fy is yield stress of steel tube, Ac and As are the areas of concrete infill and steel tube, respectively [16]. 3.2. Mesh convergence study including determination of friction coefficient Fig. 5a and b shows boundary condition and mesh geometries that were used for the mesh convergence study, respectively. The
25
nodes at the base of the footing were fully restrained, and the x direction of the symmetric section was restrained as shown in Fig. 5a. The distributed axial load was applied at the top of the CFT on the concrete section using the pressure load option in ABAQUS [12]. Then, the distributed lateral displacement was applied on the 1/4 perimeter of steel tube at the top of the CFT as shown in Fig. 5a. A mesh convergence study was conducted using three different mesh types as shown in Fig. 5b for K1, K2, and K3 specimens where the friction coefficient was set as 0.35. The results of the mesh convergence study are summarized in Table 2. In Table 2, Mu,FEM and Mu,test represent the maximum flexural capacity of the CFT column obtained from finite element analysis and test, respectively. The solutions vary a little for Mesh 1–3, as shown in Table 2 (the maximum difference is 4% for K3 specimen). The differences of Mu,FEM/Mu,test between Mesh 2 and Mesh 3 were approximately less than 1% for all analysis models. Thus, Mesh 3 was adopted for analysis in this study. The friction coefficient between steel and concrete can range from 0.3 to 0.6 [17]. To determine reasonable value of the friction coefficient for the analysis, a parametric study was conducted for K1, K2, and K3 specimen by varying the friction coefficient. The results of parametric study are summarized in Table 2. Three different values of friction coefficient (0.25, 0.35, and 0.47) were studied. The analysis results with a friction coefficient of 0.35 provided the best results, as shown in Table 2 with an average discrepancy of 4.39%. This value was adopted for the analyses.
3.3. Model validation through comparison with previous test results Fig. 6 compares the moment-drift relationships obtained from tests with those obtained from finite element analysis. Table 3 also compares analytical results with test results for the five specimens. The dashed line in Fig. 6 represents the flexural strength of the CFT column calculated from the plastic stress distribution method (PSDM), Mu,PSDM [16]. Drift is defined as the lateral displacement at the top of specimen divided by the column length above the footing. It can be seen that the analysis results accurately predict stiffness and strength. On average, the model simulated the experimental results well. It should be noted that monotonic loading was applied in this study, and post-peak behavior might not be accurate, since post-peak strength loss is frequently caused by initiation of tearing of the steel tube, which are not included in the model. However, the post-peak behavior has little effect the max-
Fig. 4. Dimensions of test specimens.
26
J. Moon et al. / Engineering Structures 56 (2013) 22–35
Table 1 Properties of verification models. Test specimen
Study parameter
le/D
fc0 ,CFT (MPa/ksi)
fc0 ,FT (MPa/ksi)
fy (MPa/ksi)
fu (MPa/ksi)
K1 K2 K3 1–50 4–50
No shear reinforcement Shear reinforcement Embedment depth Straight welded tube Spiral welded tube
0.6 0.6 0.9 0.8 0.8
75.8/11 75.8/11 71/10.3 59.9/8.7 59.3/8.6
75.8/11 75.8/11 71/10.3 75.8/11 74.4/10.8
525.7/76.3 525.7/76.3 525.7/76.3 337.6/49 351.4/51
602.2/87.4 602.2/87.4 602.2/87.4 413.4/60 537.4/78
Fig. 5. Boundary condition and mesh for analysis model: (a) loading and boundary condition; (b) mesh for analysis model.
Table 2 Results of mesh convergence study and effect of friction coefficient. Test specimen
K1 K2 K3
Mesh convergence study (F.C. = 0.35)
Effect of friction coefficient
Mu,FEM/Mu,test (Mesh#1)
Mu,FEM/Mu,test (Mesh#2)
Mu,FEM/Mu,test (Mesh#3)
Mu,FEM/Mu,test (F.C.=0.25)
Mu,FEM/Mu,test (F.C.=0.35)
Mu,FEM/Mu,test (F.C.=0.47)
0.98 1.07 0.93
0.97 1.05 0.97
0.96 1.06 0.97 Average discrepancy (%)
0.86 0.95 0.93 8.67
0.96 1.06 0.97 4.39
1.05 1.11 0.98 6.01
imum resistance estimate, which is the primary issue for evaluating strength of the CFT column-to-footing connection. Specimens K1 and K2 exhibited pullout failure of the CFT column from the footing [8]. For Specimen K1 (le/D = 0.6, and qv = 0%), tension yielding and local buckling of the tube above the footing was not detected during the test. The theoretical predictions also showed that yielding was not developed and Mu,test/ Mu,PSDM is less than 1. The difference between the maximum resistance obtained in the test and finite element analysis was 4% for K1 as shown in Table 3. Fig. 7 compares the crack formation of the footing, which eventually led to pullout failure, in the experiment and the analysis. In both the experiment and the analysis, cracks radiating diagonally from the column are observed. The analysis assumed that cracking initiated where the tensile equivalent plastic strain is greater than zero, and the maximum principal plastic
strain is positive. The direction of the vector normal to the crack plane is assumed to be parallel to the direction of the maximum principal plastic strain [12]. Specimen K2 exhibited similar damage pattern with larger strength than Specimen K1, as a result of the additional vertical reinforcement that was placed in the footing. The strength predicted by the finite element analysis was 6% larger than the resistance measured in the test. The full flexural capacity of the CFT column was developed for specimen K3 (le/D = 0.9, and qv = 0.27%), 1–50 and 4–50(le/D = 0.8, and qv = 0.27%). Furthermore, large deformation demands were sustained without significant strength deterioration for these specimens. For all three specimens, local buckling of the tube occurred near the column base. Very little damage to the footing was observed in either the test or the analysis. Local buckling eventually led to tearing of the tube, which limited the strength and deformability. Fig. 7
27
J. Moon et al. / Engineering Structures 56 (2013) 22–35
Fig. 6. Comparison of predicted and measured base moment vs. drift: (a) Specimen K1 (b) Specimen K2 (c) Specimen K3 (d) Specimen 1–50 and (e) Specimen 4–50.
Table 3 Comparison of analysis results with test results (verification model). Test specimen
Mu,PSDM (kN m)
Mu,test (kN m)
Mu,FEM (kN m)
Mu,test/Mu,PSDM
Mu,test/Mu,FEM
Failure mode (test)
Failure mode (FEM)
K1 K2 K3 1–50 4–50
1300.74 1300.74 1288.20 890.52 913.23
1135.42 1187.74 1451.37 1074.40 996.32
1091.44 1257.58 1401.98 989.33 1013.49
0.87 0.91 1.13 1.21 1.09
1.04 0.94 1.04 1.09 0.98
Footing failure Footing failure Local buckling Local buckling Local buckling
Footing failure Footing failure Local buckling Local buckling Local buckling
Fig. 7. Simulated and observed damage patterns.
compared the shape of the local buckling observed in the test with that predicted in the analysis for K3, and significant similarity is noted. The difference between the test and the finite element analysis was 4% for K3 specimen. The discrepancy between the test and
finite element analysis were 9 and 2% for 1–50 and 4–50 specimens, respectively. Taken as a whole, comparison of the simulation and experimental results including the predicted response and damage modes
28
J. Moon et al. / Engineering Structures 56 (2013) 22–35
such as cracking in the footing and local buckling of the tube indicates that the finite element modeling approach provides an accurate simulation. 3.4. Effect of reinforcing ratio on the tensile stress–strain relationship of concrete An accurate simulation of the tensile stress–strain response is critical to an accurate analysis of some categories of reinforced concrete components. In particular, sections with low levels of reinforcement and low or no axial load exhibit stronger influences from the tensile response. Generally, it is assumed that the tensile strength of concrete is approximately between 8% and 10% of the concrete compressive strength. The tensile response is modeled linearly to the maximum tensile strength of the concrete; the post-peak response is modeled with the tensile stresses decreasing linearly to zero at a strain equal to 10 times the peak strain, that is the strain corresponding to the maximum tensile strength of the concrete [12]. In this conventional model, stress–strain curve of bare rebar is often used. This conventional approach was compared with the modeling approach used in this study, which includes the impact of embedded reinforcing bars (Eqs. (1)–(3)) [14]. Fig. 8 shows the effects of tensile stress–strain relationship of the concrete and stress–stain curve of the reinforcing bar on the analysis results. The cracking stress, fcr, is assumed to be 9% of fc0 for the conventional method. It was found that both conventional method and embedded-bar modeling approach used in this study provided good results for Specimen K3 where minimal to modest footing cracks occurred. However, the results were improved using the embedded-rebar model for Specimen K2, which exhibited more significant cracking. For this specimen, conventional method overestimated the strength, as shown in Fig. 8b; the embedded modeling approach resulted in predictions that agreed well with test results. The results of embedding low levels of reinforcement in concrete changes the overall curve of the bar, as shown in Fig. 3b, and results in a larger strain corresponding to the yield stress, which becomes more significant with decreases in the reinforcement ratio. As a result, combination of Eq. (1) with Eqs. (2), (3) provided good results regardless of the failure modes of the CFT column-to-foundation connection. 4. Parametric study 4.1. Variables for parametric study A series of parametric studies were performed to investigate the behavior of the embedded CFT foundation connection. Table 4 provides values for the key variables evaluated. A total of 56 models
were analyzed to study the impact of D/t ratio, embedment length, le, shear reinforcement ratio, qv, the concrete compressive strength ratio between the footing and infill of the CFT, fc0 ,FT/fc0 ,CFT, and axial load ratio, P/Po. Specimen K3 shown in Fig. 4 served as the reference model. Nominal material strengths were used. As a result, the concrete compressive strength of footing, fc0 ,FT, the concrete compressive strength of the infill of CFT column, fc0 ,CFT, yield stress of steel tube, fy, ultimate stress of the steel tube, fu, and yield stress of the rebar, fyr, were 34.5, 34.5, 344.8, 482.7, and 413.7 MPa (5, 5, 50, 70, and 60 ksi), respectively. The embedment length ratio le/D was selected based on the results of the results of previous studies [8–11]. Previous results show that the full flexural strength was observed for most test specimens when embedment depth is larger than 80% of diameter of CFT column. Thus, to evaluate the impact of the embedment length ratio, le/D was varied from 0.6 to 0.9. For the base models in Table 4, the following values of the key parameters were studied:
D/t ratios of 60, 80, 100, and 120. Concrete strength ratios, fc0 ,FT/fc0 ,CFT of 0.7, 1, 1.5, and 2. Shear reinforcement ratios, qv, of 0%, 0.15%, 0.27% and 0.5%. Axial load ratios, P/Po, of 0.1, 0.2, and 0.3. Column diameters, D, of 508, 762, and 1524 mm (20, 30, and 60 in.).
It should be noted that the footing dimension and total amount of reinforcement were proportioned to D.
4.2. Evaluation of different failure mechanisms Fig. 9 shows base moment-drift relationship for two different failure modes. The x and y axes in Fig. 9(a) denote drift and normalized flexural strength of the embedded connection, Mu,FEM/Mu,PSDM, respectively. The value of Mu,PSDM is the theoretical flexural strength of the CFT column calculated from plastic stress distribution method [16]. The model-naming scheme denotes the key variables studied. Results of two models are shown in Fig. 9, where Model CFT60-0.6-0-1 had a D/t ratio of 60, embedment depth ratio (le/D) of 0.6, shear reinforcing ratio of 0%, and a concrete strength ratio of 1. In contrast, Model CFT80-0.9-0.27-1 has a D/t ratio of 80, embedment depth ratio (le/D) of 0.9, shear reinforcement (qv) of 0.27%, and a concrete strength ratio of 1. The results shown in Fig. 9 indicate two different failure modes of the CFT connection. Model CFT60-0.6-0-1 has relatively larger normalized flexural strength of CFT column than that of CFT800.9-0.27-1. For Model CFT60-0.6-0-1, Mu,FEM/Mu,PSDM is 0.75 indicating that the full flexural capacity of the CFT was not developed while Mu,FEM was 13% larger than the theoretical flexural strength
Fig. 8. Effects of tensile stress–strain relationship of the concrete and stress–stain curve of the reinforcing bar on the analysis results: (a) K3 specimen; (b) K2 specimen.
J. Moon et al. / Engineering Structures 56 (2013) 22–35 Table 4 Base models for parametric study. Model
D (mm/in)
D/t
le/D
qv (%)
fc0 ,FT (Mpa/ksi)
P/Po
CFT60-0.6-0.27-1 CFT60-0.7-0.27-1 CFT60-0.8-0.27-1 CFT60-0.9-0.27-1
508/20 508/20 508/20 508/20
60 60 60 60
0.6 0.7 0.8 0.9
0.27 0.27 0.27 0.27
34.5/5 34.5/5 34.5/5 34.5/5
0.1 0.1 0.1 0.1
Note: fy = 344.8 MPa (50 ksi); fu = 482.7 MPa (70 ksi); fyr = 413.7 MPa (60 ksi); and fc0 ,CFT = 34.5 MPa (5 ksi) for all analysis models.
29
cracking initiates but is limited, resulting in ductile response. The initial crack formed at the tip of the annular ring with an angle of approximately 45°. However, the cracking was much more limited than Models CFT60-0.6-0-1, and the deformability of the system came from the extensive yielding of the steel tube in tension and compression, as shown in Fig. 10b. The results show that the shear capacity of the footing must be considered in the design to achieve full plastic action in the column resulting in maximum drift capacity. 4.3. Evaluation of parameter impact
Mu,PSDM for Model CFT80-0.9-0.27-1, indicating that the model achieved the desired response mode of column yielding. The key difference in these two models is the location of the initiation and progression of damage. For Model CFT60-0.6-0-1, the footing is severely damaged and pullout failure occurs, as illustrated in Fig. 9b. For Model CFT80-0.9-0.27-1, inelastic action is sustained by the steel tube with yielding, and local buckling of steel tube controls the strength of the specimen while mitigating footing damage because of the increased embedment depth. These differences are studied in more depth in Fig. 10. The distribution of stresses and crack pattern of footing (middle section) at 4% drift are shown in Fig. 10a and b for Models CFT60-0.6-0-1 and CFT80-0.9-0.27-1, respectively. When the embedment depth was shallow without shear reinforcement (Model CFT60-0.6-0-1), significant cracking was noted on the tension side of column in the footing; this cracking was severe and resulted in lost tensile resistance. Significant cracking permitted separation of the concrete infill and footing and resulted in increased compression stresses at the bottom of the annular ring and interface between the CFT and footing in compression side, as shown in Fig. 10a. As a result, a portion of the steel tube that was in compression had locally yielded. In contrast, Model CFT80-0.9-0.27-1, which had adequate embedment depth and shear reinforcement, the footing
The impact of each of the study parameters was assessed through a series of parametric study. Fig. 11 shows the effect of D/t ratio, where D/t ratio is plotted on the x-axis. Three different parameters are used to assess the parameter impact and these parameters are plotted on the y-axis. The parameters were the normalized strength ratio (Mu,FEM/Mu,PSDM) (Fig. 11a), the normalized uplift of the footing where the uplift is normalized to H, the height of the footing (Fig. 11b), and normalized out-of-plane deformation (OPD) of the steel tube, where the OPD is normalized to the column diameter (Fig. 11c). Uplift and out-of-plane deformation of the steel tube were measured at the interface between the CFT column and the footing in tension side, and at a height of 76.2 mm (3 in.) above the footing on the compression side, respectively (see Fig. 9b for illustration of these key points). The following observations are made: (1) The flexural strength ratio, Mu,FEM/Mu,PSDM, is not impacted by the D/t ratio for well-anchored connections (e.g., le/D = 0.9), (2) The uplift is similarly constant for well-anchored connections (e.g., le/D = 0.9), (3) The out-of-plane displacement increases significantly with D/t ratio, regardless of the anchorage depth. These figures also illustrate the impact of normalized embedment depth on the response. Each connected line represents one le/D ratio, as indicated by the symbols and the legends. In contrast
Fig. 9. Simulation results for models CFT60-0.6-0-1 and CFT80-0.9-0.27-1: (a) moment–drift relationships; and (b) damage modes.
30
J. Moon et al. / Engineering Structures 56 (2013) 22–35
Fig. 10. Stress distributions and crack patterns for analysis models: (a) CFT60-0.6-0-1; and (b) CFT80-0.9-0.27-1 (Note: 1 ksi = 6.89 MPa).
Fig. 11. Effect of D/t ratio: (a) Mu,FEM/Mu,PSDM vs. D/t; (b) uplift/H vs. D/t; and (c) O.P.D/D vs. D/t.
to the D/t ratio, the embedment depth has a much more significant impact on the response. The flexural strength of the system reduces for lower le/D, while the uplift increases. The OPD decreases
with increasing le/D, but this is expected since, for lower le/D ratios, the response of the system is controlled by damage in the footing and therefore tube buckling is limited.
J. Moon et al. / Engineering Structures 56 (2013) 22–35
Fig. 12 shows the effect of concrete compressive strength ratio of the footing and CFT column infill, fc0 ,FT/fc0 ,CFT. Larger fc0 ,FT/fc0 ,CFT ratio results in a stronger concrete strength of the footing. Although this is contrary to practice, the results show that a ratio of 1 is required to achieve the flexural strength. Furthermore, Fig. 12 suggests that an increase in fc0 ,FT/fc0 ,CFT ratio reduces the damage of the footing and is helpful to increase Mu,FEM/Mu,PSDM. This is a similar trend to that identified with increasing D/t ratio. Larger compressive capacity of the footing concrete also reduced the uplift (Fig 12b). The OPD increased with increasing the strength ratio, since the larger footing strength encourages yielding and buckling of the steel tube. The impact of the shear reinforcement on the response is shown in Fig. 13. In all cases, models without shear reinforcement failed to achieve their flexural strength. For lower values of le/D, the impact of the shear reinforcement in the footing was more significant. For example, the models with an le/D = 0.6 showed an increase in strength with additional shear reinforcement; for models with larger le/D ratio, the increase was less significant. The effects of axial load ratio are summarized in Fig. 14. In general, Mu,FEM/Mu,PSDM was increased with increasing P/Po when Mu,FEM/Mu,PSDM is less than one (lower anchorage lengths with significant impact of the footing response). For well-anchored models, increasing P/Po beyond 0.2 does not increase the strength ratio. However, in all cases increasing P/Po reduced the uplift deformation of the footing. In most cases, increasing P/Po increased the OPD. In contrast to the expected response, for well-anchored models (le/D = 0.9), the OPD decreased with increasing values of P/Po. This trend is explored further by comparing two models with two different axial load ratios of 0.1 and 0.2 at 4% drift, as shown in Fig. 15. The figure plots the maximum principle plastic strain gradients that represent the cracking in the concrete infill and footing. The figure shows that the compressive region of the concrete infill increases with an increase in the axial load ratio, suggesting that an increased amount of concrete is engaged to sustain the combined demands from tension and axial compressive loading (P). In addition, the arc of the tube engaged in sustaining the compressive force is also increased. The combination of these responses results in decreasing the simulated OPD. However, additional displacement demand that may result in significant damage to the concrete infill accelerates buckling of the steel tube. This latter behavior has been observed by others [18]. It is also noted that the tensile strains in some cracked region are very high in Fig. 15. This is because that the slope of the tensile stress–strain curve is almost zero when the tensile strain is large [approximately 0.01 from Eq. (1)]. Thus, tensile strain could be dramatically increased even if the decrease in tensile stress is very small. Finally, the impact of the column diameter (D) was investigated by studying CFT columns with diameters of 508, 762, and 1524 mm (20, 30, and 60 in.). There was no impact on the response.
31
5. Design of embedded CFT connection An empirically-derived design equation to estimate the minimum embedment depth, le, was proposed based on a series of test results [8–11]. The expression was derived using geometry and equilibrium of the connection corresponding to pullout failure, as depicted in Fig. 16. The tube is embedded a length le. The annular ring has an outer diameter of Do. For the derivation of the design equation, shear stress angle b1 in the concrete footing is approximated as 45°. (Note, this angle has been verified by the finite element analysis, for which the crack that initiates on the tension side of the column forms at an angle of approximately 45°.) Equilibrium in vertical direction is given by the following equation:
T s ¼ V c sin b1 :
ð4Þ
In the expression, Ts and Vc are the tensile force in the steel and shear force in the concrete, respectively. For an incremental angle of Dc, Ts and Vc are given by
T s ¼ Dc
D le fs t and V c ¼ sc Dc ðD0 þ le cot b1 Þ: 2 2 sin b1
ð5Þ
Substituting Eq. (5) into Eq. (4) with b1 = 45°, shear stress of the footing, sc, that is needed to develop stress of fs in steel tube can be computed using Eq. (6).
sc ¼
Dtfs 2
ðle þ D0 le Þ
:
ð6Þ
It is noted that shear stress of the footing, sc, is the same with the shear stress of the concrete in the footing since the shear reinforcing bar is ignored in Eq. (6). To achieve full flexural strength of the CFT column, the steel tube must fully yield, ideally reaching its ultimate strength, fu. Thus, the shear stress capacity, sc, was computed by substituting fu for fs in Eq. (6). Significant variability exists in the shear stress capacity of the concrete. For this qffiffiffiffiffiffiffi ffi reason, Lee [11] provided that sc should be smal0 ler than a fc;FT to achieve full flexural capacity of the CFT column, and a varies from 0.42 to 0.57 (MPa unit). However, that proposal was based on limited experimental data. In this study, this shear stress range was reexamined and calibrated by using results of parametric study as well as the experimental results. Fig. 17 shows the evaluation of design equation to estimate the minimum embedment depth. In Fig. 17, the x-axis is the normalized shear qffiffiffiffiffiffiffi ffi 0 stress, sc/ fc;FT , where sc is calculated from Eq. (6) with fs equal to fu. As expected, the results show that Mu,FEM/Mu,PSDM decreases and uplift increases (equivalent to increased damage sustained qffiffiffiffiffiffiffi ffi 0 by the footing) with increasing sc/ fc;FT . Also, out-of-plane deforqffiffiffiffiffiffiffi ffi 0 mation of the steel tube increases with decreasing sc/ fc;FT as shown in Fig. 17c, which also indicates that higher shear stress
Fig. 12. Effect of fc0 ,FT/fc0 ,CFT: (a) Mu,FEM/Mu,PSDM vs. fc0 ,FT/fc0 ,CFT; (b) Uplift/H vs. fc0 ,FT/fc0 ,CFT; and (c) O.P.D/D vs. fc0 ,FT/fc0 ,CFT.
32
J. Moon et al. / Engineering Structures 56 (2013) 22–35
Fig. 13. Effect of qv: (a) Mu,FEM/Mu,PSDM vs. qv; (b) Uplift/H vs. qv; and (c) O.P.D/D vs. qv.
Fig. 14. Effect of P/Po: (a) Mu,FEM/Mu,PSDM vs. P/Po; (b) Uplift/H vs. P/Po; and (c) O.P.D/D vs. P/Po.
Fig. 15. Variation of crack patterns for different axial load ratio (4% drift).
in the footing limits the inelastic action in the tube, and potentially changes the response mode from ductile yielding of the column to brittle response of the connection. From the comparative study, test results of monolithically embedded connection and analysis results without shear reinforcing bar provide a lower bound on the embedment depth. A linear regression was performed using these data (Linear Regression_1 in Fig. 17a). The value of Mu,FEM/Mu,PSDM was larger than 1 when Eq. (7a) is satisfied. These results are applicable to foundation designs for which ductility in the tube is not a design requirement,
including regions of low and moderate seismicity, as indicated below. For regions of low and moderate seismicity
Dtfu 2 ðle
þ D 0 le Þ
qffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffi 0 0 ¼ 0:6 fc;FT MPa ð7:2 for psi unitÞ ðaÞ 6 a fc;FT
For regions of high seismicity
Dtfu 2 ðle
þ D 0 le Þ
qffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffi 0 0 6 a fc;FT ¼ 0:55 fc;FT MPa ð6:6 for psi unitÞ ðbÞ
ð7Þ
33
J. Moon et al. / Engineering Structures 56 (2013) 22–35
Fig. 16. Schematic view of footing resistance to cone pullout failure.
Fig. 17. Evaluation of design equation: (a) Mu,FEM/Mu,PSDM vs. sc/(fc0 ,FT)0.5; (b) Uplift/H vs. sc/(fc0 ,FT)0.5; and (c) O.P.D/D vs. sc/(fc0 ,FT)0.5.
Satisfaction of this minimum does not guarantee significant plastic action in the CFT column, since CFT column-to-foundation connection must be fully yielded and provide the significant inelastic deformation capacity. From the observation of the test and finite element analysis results, it was found that the full strength of the CFT column was usually 10–20% larger than theoretical value. Full plastic action occurred when Mu,test/Mu,PSDM is larger than 1.15. Table 5 shows the summary of drift ductility, l, for the test results conducted [9–11], where drift ductility is defined as the ratio of maximum amount of deflection (drift) divided by the amount of deflection (drift) at yield. The yield point of these specimens was defined as the point where the steel strain equals the yield strain of the material. The maximum deformation was defined as the point prior to 20% loss in lateral strength. On average, the drift ductility of the CFT column was 8.8. Thus, target strength ratio of CFT column-to-foundation connection was selected as 1.15Mu,PSDM for more extreme loading. Then, an alternative linear regression was conducted using analysis results with shear reinforcing bar and isolated embedded connection test data (Linear Regression_2 in Fig. 17a), because the scatter was considerably reduced when these data were used for regression. ffiffiffiffiffiffiffiffi The ratio of Mu,FEM/Mu,PSDM was larger than 1.15 when sc/ q 0 fc;FT 6 0.55 (MPa unit). This value is recommended for high seismic regions as described in Eq. (7b). It should be noted that target strength ratio of CFT column-to-foundation connection was adopted as 1.15Mu,PSDM for high seismic region based on the test results shown in Table 5 since they show appropriate ductility level that show the plastic action. However, these tests have the clear limit about the details and material properties of tested specimens. For example, D/t ratio and qv were limited to 80% and 0.27%,
respectively. Thus, this target strength ratio for high seismic region may not be appropriate for the CFT column-to-foundation connection that deviates from the profiles of test specimens used in this study, and the care should be taken to apply the proposed equation for high seismic region. Scatter is observed in the data presented in Fig. 17. The simulations suggest that the shear reinforcement ratio and axial load ratio can reduce the required embedment depth. However, these factors were neglected in the derivation of Eq. (6). Eq. (8) was derived by conducting a regression analysis of the results of parametric study.
ð1 þ qv Þ0:46 ð1 þ P=Po Þ0:51 sc;m ¼
Dtfu 2
ðle þ D0 le Þ
:
ð8Þ
In Eq. (8), sc,m is the modified shear stress of the concrete in the footing that is needed to develop stress of fu in steel tube, and qv is the shear reinforcement ratio in percent (%). In Eq. (8), the value of qv never exceeds 0.3%, and the value of P/Po cannot exceed 0.2 since little benefit of these parameters were observed for a well-anchored CFT-footing connection from the analysis. The shear stress range of embedded CFT connection was evaluated by using Eq. (8) and the results are shown in Fig. 18. The variability in the prediction was reduced by using Eq. (8). Similar with Eq. (7), the shear stress range was evaluated and the results are given by For regions of low and moderate seismicity
Dtfu 2 ðle
þ D 0 le Þ
qffiffiffiffiffiffiffiffi 0 6 a fc;FT ¼ 0:55ð1 þ qv Þ0:46 ð1 þ P=Po Þ0:51 qffiffiffiffiffiffiffiffi 0 fc;FT MPa ð6:6 for psi unitÞ
ð9aÞ
34
J. Moon et al. / Engineering Structures 56 (2013) 22–35
Table 5 Drift ductility of the test specimens where Mu,test/Mu,PSDM P 1.15. Test specimen
D (mm/in.)
le/D
D/t
fy (MPa/ksi)
fc0 ,CFT (MPa/ksi)
fc0 ,CFT/fc0 ,FT
qv (%)
P/Po
Mu,test/Mu,PSDM
l
W5 [9] W6 [9] C1 [10] C2 [10] C4 [10] 1–50 [11] 2–50 [11] 5–50 [11] 6–50 [11]
508/20 508/20 508/20 508/20 508/20 508/20 508/20 508/20 508/20
0.9 0.75 0.9 0.9 0.9 0.8 0.775 0.7 0.6
80 80 80 80 80 80 80 80 80
520.9/75.6 520.9/75.6 520.9/75.6 520.9/75.6 520.9/75.6 337.6/49 337.6/49 351.4/51 351.4/51
77.2/11.2 81.3/11.8 67.5/9.8 66.8/9.7 68.2/9.9 59.9/8.7 64.1/9.3 67.5/9.8 69.6/10.1
1 1 1 1 1 0.79 0.82 0.84 0.86
0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27
0.1 0.1 0.1 0.1 0.2 0.1 0.1 0.1 0.1
1.15 1.22 1.27 1.30 1.23 1.17 1.17 1.31 1.22
7.1 8.3 6.3 7.3 7.8 13.5 11.6 9.2 8.2
Fig. 18. Evaluation of modified design equation: (a) Mu,FEM/Mu,PSDM vs. sc,m/(fc0 ,FT)0.5; (b) Uplift/H vs. sc,m/(fc0 ,FT)0.5; and (c) O.P.D/D vs. sc,m/(fc0 ,FT)0.5.
For regions of high seismicity
Dtfu 2 ðle
þ D0 le Þ
qffiffiffiffiffiffiffiffi 0 6 a fc;FT ¼ 0:47ð1 þ qv Þ0:46 ð1 þ P=Po Þ0:51 qffiffiffiffiffiffiffiffi 0 fc;FT MPa ð5:7 for psi unitÞ:
ð9bÞ
Thus, the minimum embedment depth of the CFT connection can be obtained by solving Eq. (9) to include the benefits of shear reinforcement and axial load. a in Eq. (9a) is amplified up to 0.68 (MPa unit) by introducing the shear reinforcement ratio of 0.3% and axial load ratio of 0.2. In the case of a in Eq. (9b), a varies from 0.47 to 0.58 (MPa unit). Lee [11] suggested a is between 0.42 and 0.57 (MPa unit) and his proposed range for a is similar with that from this study. ACI 318 code [19] provides the critical failure shear force in Section 11.2.1. Similarly with thus study, theq critical ffiffiffiffiffiffiffiffi shear stress spec0 ified in ACI [19] can be expressed as sc/ fc;FT = Ck where C varies from 2 to 4 (in psi unit) and k is 1 for normal concrete. This dimensionless critical shear stress range was also plotted with analysis results and test results, as shown in Figs 17 and 18. From the comparative study, it was found that ACI318 [19] give a conservative value for pullout failure of the CFT column-to-foundation connection. 6. Summary and conclusions Concrete filled tubes offer substantial benefits over conventional construction methods because of their inherent strength, stiffness, stability all of which contribute to reduced labor and material requirements. However, CFT components are seldom used in part because there are few validated constructible connections. Prior experimental studies have developed a feasible CFT-to-foundation connection. However, the data were limited and the full range of design parameters could not be evaluated.
This research extended those studies by conducting non-linear finite element analyses to investigate the impact of salient design parameters on the embedded foundation connection for the CFT columns. The finite element model was verified using measured response and observed damage of prior test results, including cracking of the footing and local buckling of the steel tube. The analytical study revealed two different failure modes, both of which were observed in the testing. For models with shallow embedment depths and insufficient shear reinforcement in the footing, heavy cracking was observed adjacent to the tension side of the CFT column in the footing and this cracking led to loss of strength prior to development of the theoretical flexural strength. In contrast, when the embedment depth was sufficiently deep and shear reinforcement were provided, the steel tube fully yielded in tension and compression; in that case the CFT column controlled the response of the system with local buckling and yielding of the tube. With a validated model in hand, a parametric study was performed to study the effects of D/t ratio, embedment length, shear reinforcement ratio, concrete compressive strength ratio of the footing and infill in the CFT, and axial load ratio. The analysis results showed that: (1) The embedment depth had the most dramatic impact on the response of the CFT column-to-footing subassemblies, (2) The flexural strength ratio, Mu,FEM/Mu,PSDM, was not impacted by the D/t ratio for well-anchored connections (e.g., le/D = 0.9) while D/t ratio had significant effect on the Mu,FEM/Mu,PSDM for shallow embedment depth (e.g., le/D = 0.6), (3) For models with lower embedment depths, the impact of the shear reinforcing bar was more significant, (4) An increase in fc0 ,FT/fc0 ,CFT ratio reduced the damage of the footing and was helpful to increase Mu,FEM/Mu,PSDM, and (5) In general, Mu,FEM/Mu,PSDM was increased with increasing P/Po when Mu,FEM/Mu,PSDM was less than one. However, for well-anchored models, increasing P/Po beyond 0.2 did not increase the strength ratio. Two design equations to estimate the minimum embedment depth were derived using the analytical results and previous test
J. Moon et al. / Engineering Structures 56 (2013) 22–35
data. From the results, the minimum embedment depth that guarantees full flexural strength of CFT column from plastic stress distribution method can be obtained by solving Eq. (7a). For regions of high seismicity, Eq. (7b) is recommended. A modified design equation was proposed to include benefits of shear reinforcement and axial load ratio as Eq. (9) and the scatter of analysis and test results was reduced.
[6] [7] [8]
[9]
Acknowledgements [10]
This work was completed partially with funding provided by the Washington State Department of Transportation (WSDOT) through the project entitled, ‘‘Design of Bridge Foundations with Steel Casings’’. Mr. Bijan Khaleghi is the WSDOT Bridge Design Engineer and the coordinator of this project. The advice and financial support of the WSDOT is gratefully acknowledged. References [1] Roeder CW, Lehman DE, Bishop E. Strength and stiffness of circular concrete filled tubes. J Struct Eng ASCE 2010;136(12):1545–53. [2] Hu HT, Huang CS, Wu MH, Wu YM. Nonlinear analysis of axial loaded concretefilled tube columns with confinement effect. J Struct Eng ASCE 2003;129(10):1322–9. [3] Lu H, Han LH, Zhao XL. Analytical behavior of circular concrete-filled thinwalled steel tubes subjected to bending. Thin-Walled Struct 2009;47:346–58. [4] Moon J, Lehman DE, Roeder CW, Lee H-E. Analytical modeling of bending of circular concrete-filled steel tubes. Eng Struct 2012;42:349–61. [5] Moon J, Lehman DE, Roeder CW, Lee H-E. Strength of circular concrete-filled tubes (CFT) with and without internal reinforcement under combined loading.
[11]
[12] [13] [14] [15] [16] [17] [18] [19]
35
J Struct Eng ASCE; in press. http://dx.doi.org/10.1061/(ASCE)ST.1943541X.0000788. Lehman DE, Roeder CW. Foundation connections for circular concrete-filled tubes. J Construct Steel Res 2012;78:212–25. Pecce M, Rossi F. The non-linear model of embedded steel-concrete composite column bases. Eng Struct 2013;46:247–63. Kingsley A. Experimental and analytical investigation of embedded column base connections for concrete filled high strength steel tubes. MS thesis. Seattle, WA: Univ. of Washington; 2005. Williams TS. Experimental investigation of high strength concrete filled steel tubes in embedded column base foundation connections. Seattle, WA: Univ. of Washington; 2006. Chronister A. Experimental investigation of high strength concrete filled steel tubes in embedded column base foundation connections. MS thesis. Seattle, WA: Univ. of Washington; 2007. Lee JR. Experimental investigation of embedded connections for concretefilled steel tube columns subjected to combined axial-flexural loading. MS thesis. Seattle, WA: Univ. of Washington; 2011. ABAQUS. ABAQUS analysis user’s manual version 6.9-2 2009. Providence, RI, USA: Dassault Systemes Simulia Corp. Saenz LP. Discussion of ‘equation for the stress-strain curve of concrete’ by P. Desayi, and S. Krishnan. ACI J 1964;61:1229–35. Hsu TTC, Mo Y-L. Unified theory of concrete structures. 2nd ed. John Wiley & Sons, Inc.; 2010. Lee J, Fenves GL. Plastic-damage model for cyclic loading of concrete structures. J Eng Mech ASCE 1998;124(8):892–900. AISC. Specifications for structural steel buildings, Chicago, IL; 2008. Baltay P, Gjelsvik A. Coefficient of friction for steel on concrete at high normal stress. J Mater Civ Eng ASCE 1990;2(1):46–9. Marson J, Bruneau M. Cyclic testing of concrete-filled circular steel bridge piers having encased fixed-base detail. J Bridge Eng ASCE 2004;9(1):14–23. ACI. Building code requirements for structural concrete and commentary, ACI318-11 2011, Farmington Hills, MI.