The 2019 World Congress on Advances in Structural Engineering and Mechanics (ASEM19)Jeju Island, Korea, September 17 - 21, 2019

System-based reliability analysis for CFST chord to CHS brace truss bridges

*Silin Chen1), Chao Hou2), and Hao Zhang3)

1), 2), 3)

School of Civil Engineering, The University of Sydney, NSW 2006, Australia 1)silin.chen@sydney.edu.au

ABSTRACT

Concrete-filled steel tubular truss (CFST truss for short) is a type of composite structure consisted of CFST chords and hollow tubular braces, which is now widely used in large-span structures such as towers, bridge girders, piers and arch ribs. In the traditional design of CFST truss, structural members and connections are designed separately according to the limit state of component strength. In this paper, a system-based reliability framework combined with advanced numerical analysis is established to investigate the reliability of CFST truss. A prototype of CFST truss, which is validated against experimental results, is used to demonstrate the procedures. A mass simulation of CFST trusses, which takes into account uncertainties is carried out to obtain the strength distribution, followed by reliability analysis to determine the resistance factors under various loading conditions. Monte-Carlo (MC) simulations combined with advanced finite element analysis are used to generate a distribution of the system resistance, and First-Order Reliability Method (FORM) is used to evaluate the reliability of the CFST truss system. Based on these, the reliabilities and related system resistance factors of CFST truss under flexural loading are proposed. 1 INTRODUCTION Concrete-filled steel tubular (CFST) members, where the chords are filled with concrete while the braces remain hollow, are widely used in large-span structures nowadays. It has advantages of high strength, good ductility and fire resistance, which saves formwork during concrete construction and also saves cost and time (Han et al., 2014; Pi et al., 2012). One application of the CFST truss bridge is the Ganhaizi Bridge (shown in Fig. 1), which consists of three CFST chords and circular hollow section (CHS) braces as a support system for bridge decks. According to previous experiments and finite element analysis (FEA), the compression and flexural behaviour of CFST trusses are largely improved compared to those of the referenced CHS trusses (Han et al., 2015; He, 2012; Hou et al., 2017; Xu et al., 2014). The improvement is credited to the composite material properties and confinement effects on core concrete provided by a steel tube.

1)

PhD Candidate 2)

Lecturer 3)

Associate Professor

The 2019 World Congress on Advances in Structural Engineering and Mechanics (ASEM19)Jeju Island, Korea, September 17 - 21, 2019

Fig. 1 Schematic view and photo of a typical CFST truss bridge

for a large number of circular concrete-filled steel columns. For the CFST truss stru Structural reliability refers to the probability that a structure will not fail to perform its intended function (Nowak & Collins, 2013). It has developed over the past 50 years, and the theoretical framework has been provided to many structural types (Ellingwood & Galambos, 1982; Ellingwood et al., 1980; Ellingwood, 2000; Melchers & Beck, 2018; Zhang et al., 2016). In terms of the reliability analysis of steel-concrete composite structures, Beck et al. (2009) performed reliability analysis cture, the uncertainties are more complicated than that of single material structures or CFST components. In order to determine the reliability behaviour of the entire CFST truss structure, it is necessary to consider the potential risks brought about by all the above uncertainties, and then analyze the reliability of the system. In this paper, the sample CFST truss is provided by the previous investigation (Chen et al., 2019; Han et al., 2015; Hou et al., 2017), and FEA models are validated with reported test data. Relevant dimensions are shown in Table 1, where L0 is the effective length of CFST truss, D is the diameter of the outer steel of chords, ts is the thickness of steel and ξ is cross-sectional confinement factor which is crucial in governing the structural strength and stability of CFST structures

(1)

RC deck

(a) Schematic view (Hou et al., 2017)

CFST

chords

CHS brace

(b) On-site photo

The 2019 World Congress on Advances in Structural Engineering and Mechanics (ASEM19)Jeju Island, Korea, September 17 - 21, 2019

Other dimensions are shown in Fig. 1a. Random variables that affect system resistance, including material and geometric nonlinearity, initial geometric imperfections and model error are considered in each model. Model error is defined as the ratio of the capacity of the FEA model to actual capacity. The structure reliability of CFST trusses is analyzed by introducing FORM, in order to obtain suitable system resistance factors (ϕs) for system-based design.

Table 1 Dimensions of the CFST truss specimen

Label Chord L0 (mm) hi (mm) bi (mm) D ts (mm) ξ Failure mode

T8 CFST 4800 375 432 140 4 1.00 Bending failure

2 Advanced analysis model The numerical model of CFST truss with flexural behaviour is established by using the FEA package in ABAQUS. Geometric data, material properties, element selection, interface and boundary conditions are consistent with previous experiments (Han et al., 2015; He, 2012; Hou et al., 2017; Xu et al., 2014). The truss specimen was transversely loaded under the four-point flexural testing. Different FEA models of CFST truss are validated with those reported tests, and specimens T8-1 and T8-2 are chosen as the FEA model in this study for reliability analysis. This model is firstly developed to verify the load-displacement (P - um) curves (shown in Fig. 2a) and failure mode (shown in Fig. 2b) with previous tests, and reasonable predictions are then used for further analysis. The verified FEA models are then modified with uncertainties include the thickness of steel tubes, material properties of steel and concrete, initial steel imperfections and initial concrete imperfections for reliability analysis. 3 Reliability-based evaluation method Structural reliability theory is used to study the effects of uncertainties in CFST truss structural performance. Uncertainties include material properties, geometric configurations, model errors and load variables, and statistics of which are determined by experimental or construction experiences. 3.1 Limit state equation The limit state equation is related to one (possible) failure model of the CFST truss structure. As mentioned before, the overall bending failure can be observed in both experimental and FEA models, so the limit state equation for reliability analysis is as follows:

(2) where ME is the model error variables (Beck et al., 2009; Han et al., 2011; Han et al., 2005). R represents the resistance model, D is the dead load and L is the live load.

The 2019 World Congress on Advances in Structural Engineering and Mechanics (ASEM19)Jeju Island, Korea, September 17 - 21, 2019

Fig. 2 Comparison of the measured and predicted behaviour of specimen T8

Fig. 3 Initial imperfections in CFST truss

3.2 Resistance variables The uncertainties related to resistance variables include elastic modulus of steel (Es), the yield strength of steel (fy), the thickness of steel (ts), the compression strength of

(a) Compared with measured results

0 40 80 120 1600

200

400

600

u =0.01

um (mm)

P (

kN

)

FEA_T8

FEA &

EXP_T8-1 &

EXP_T8-2 by

Hou et al. (2017)

Overall bending failure

(b2) Predicted (b1) Observed in Hou et al. (2017)

(b) Typical failure mode

χc1: gap existence

Steel tube

(b) Initial concrete imperfection (F. Y. Liao et al.,

Infilled concrete

χs

(a) Initial steel imperfection (Chen et al.,

2019) χc2: gap amplitude

The 2019 World Congress on Advances in Structural Engineering and Mechanics (ASEM19)Jeju Island, Korea, September 17 - 21, 2019

concrete (fc’), initial steel imperfection (χs) and initial concrete imperfection (χc1, χc2). Initial

steel imperfections (shown in Fig. 3a) are because steel components are not completely straight during the manufacturing and installation process, and may affect the load-carrying capacity of a steel structure to a large extent. The initial concrete imperfection (shown in Fig. 3b) that may occur during the construction of core concrete pump into steel chords and the existence may influence material interaction, sectional strength and structural stability according to precious researches (F.-Y. Liao et al., 2013). Detailed calculation of statistics of initial imperfections can be found in Chen et al. (2019). Finally, the FEA models are established with the random resistance variables considered above. Statistics of variables are obtained from the literature in this paper (Chen et al., 2019; Ellingwood et al., 1980; Lundberg & Galambos, 1996). 3.3 Load variables A combination of dead load Dn and live load Ln are considered in order to evaluate the reliability of CFST truss under flexural behaviour. The probability for structural dead load

( ) is assumed to be normally distributed, and the statistics of mean-to-nominal value is 1.03 with a COV of 0.08. The structural live load considering traffic load on the bridge can also be fitted as a normal distribution with the mean-to-nominal value as 1.29 and the COV as 0.18 (Ellingwood et al., 1982; Eom & Nowak, 2001). The design value of the load is given by the factored combination, as follows:

ϕsRn = γDDn + γLLn (3) The load combination obtained from AASHTO (2012) at Strength Ι limit state for normal vehicular bridge design without wind load gives γD = 1.25 and γL = 1.75. Eq. (3) is solved with a fixed load ratio Ln/Dn where six values are considered in this paper: Ln/Dn = {0.5;1.0;1.5;2.0;3.0;5.0}.

4 Reliability analysis results The ultimate strength is obtained by MC simulations combined with advanced analysis, and the system resistance factor ϕs is determined for CFST truss under flexural behaviour. To determine the system resistance factor, reliability analysis, which considered random variables, is carried out after that. It also provides a suitable system resistance factor for the system-based design of CFST truss. The uncertainties applied to FEA models are extracted either from previous studies or on-site measurements. The random combination of the value includes geometric and material nonlinearity, initial imperfections and model error are generated from MATLAB. The FEA models are modified using PYTHON. Reliability analysis and evaluation are also carried out in MATLAB. 60 FEA models for the selected cross-sectional confinement factor ξ are analyzed, and the corresponding

ultimate strength is determined when the strain of the bottom steel chord reaches = 0.01 (Han et al., 2015). The probability models of the ultimate strength factor (defined in Eq. 4) for CFST trusses, the distribution type, the mean and the standard deviation, are shown in Fig. 4.

The 2019 World Congress on Advances in Structural Engineering and Mechanics (ASEM19)Jeju Island, Korea, September 17 - 21, 2019

𝑃𝑢𝑖𝑃𝑢𝑜

(4)

where 𝑃 is the ultimate strength of the CFST truss under flexural loading with random variables considered, and 𝑃 is the ultimate strength of the CFST truss without random variables.

Fig. 4 Statistics of the ultimate strength of CFST trusses with ξ = 1.00

Using the reliability analysis method outlined in section 3, the reliability index of CFST truss under flexural behaviour is calculated. The relationship between the resistance factors ϕs and the reliability index β with different live-to-dead load ratio Ln/Dn = {0.5;1.0;1.5;2.0;3.0;5.0} are shown in Fig. 5. The reliability index β decreases with the increase of resistance factor ϕs. Also, the reliability index β with larger live-to-dead load ratio is smaller under the same resistance factor ϕs, because the traffic live load has more variability than the dead load. Based on Fig. 5, the system resistance factors ϕs for a specific target reliability β is then calculated as the addition of each weighted resistance factor. The average value of ϕs is 1.05 for a target reliability index β = 3.5, and is reduced to 0.93 for β = 4.0 for a selected CFST truss with ξ = 1.0.

Fig. 5 The β – ϕs curves for CFST trusses with ξ = 1.00

0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.200

2

4

6

8

N = 60

f X(x

)

0

5

10

15

20

Co

un

ts

0.6 0.7 0.8 0.9 1.0

2

3

4

5

6

Ln/Dn= 2.0

Ln/Dn= 3.0

Ln/Dn= 5.0

s

Ln/Dn= 0.5

Ln/Dn= 1.0

Ln/Dn= 1.5

The 2019 World Congress on Advances in Structural Engineering and Mechanics (ASEM19)Jeju Island, Korea, September 17 - 21, 2019

5 Conclusion The reliability-based evaluation for concrete-filled steel tubular (CFST) truss with flexural behaviour is presented in this paper. The structural behaviour is analyzed and validated using advanced nonlinear finite element analysis (FEA) method. The uncertainties related to resistance variables include elastic modulus of steel (Es), the yield strength of steel (fy), the thickness of steel (ts), the compression strength of concrete (fc

’), initial steel imperfection (χs) and initial concrete imperfection (χc1, χc2) are discussed. The limit state equation for the overall bending failure is solved with a fixed load ratio Ln/Dn

where six values are considered: Ln/Dn = {0.5;1.0;1.5;2.0;3.0;5.0}.The system reliability analysis is carried out using First-Order Reliability Method (FORM) combined with Monte Carlo (MC) simulation and Latin Hypercube sampling (LHS) technique. The ultimate strength is obtained by advanced analysis, and the system resistance factor ϕs is determined. The average value of ϕs is 1.05 for a target reliability index β = 3.5, and 0.93 for β = 4.0 for a selected CFST truss with confinement ratio ξ = 1.0. REFERENCES AASHTO LRFD Bridge design specifications (2012), Washington, D.C.: American Association of State Highway and Transportation Officials. Beck, A. T., de Oliveira, W. L. A., De Nardim, S., & ElDebs, A. L. H. C. (2009), "Reliability-based evaluation of design code provisions for circular concrete-filled steel columns," Engineering Structures, 31(10), 2299-2308. Chen, S., Hou, C., Zhang, H., & Han, L.-H. (2019), "Structural behaviour and reliability of CFST trusses with random initial imperfections," Thin-Walled Structures, 143(106192). Ellingwood, B., & Galambos, T. V. (1982), "Probability-Based Criteria for Structural Design," Structural Safety, 1(1), 15-26. Ellingwood, B., Galambos, T. V., MacGregor, J. G., & Cornell, C. A. (1980), "Development of a probability based load criterion for American national standard A58," Cambridge, MA: National Bureau of Standards. Ellingwood, B., MacGregor, J. G., Galambos, T. V., & Cornell, C. A. (1982), "Probabuility based load criteria - load factors and load combinations," Journal of the Structural Division, 108(5), 978-997. Ellingwood, B. R. (2000), "LRFD: implementing structural reliability in professional practice," Engineering Structures, 22(2), 106-115. Eom, J., & Nowak, A. S. (2001), "Live load distribution for steel girder bridges," Journal of Bridge Engineering, 6(6). Han, L. H., He, S. H., & Liao, F. Y. (2011), "Performance and calculations of concrete filled steel tubes (CFST) under axial tension," Journal of Constructional Steel Research, 67(11), 1699-1709. Han, L. H., Li, W., & Bjorhovde, R. (2014), "Developments and advanced applications of concrete-filled steel tubular (CFST) structures: Members," Journal of Constructional Steel Research, 100, 211-228.

The 2019 World Congress on Advances in Structural Engineering and Mechanics (ASEM19)Jeju Island, Korea, September 17 - 21, 2019

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