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The results of an experimental and analytical study on the static and fatigue behavior in steel-concrete composite beams under the hogging moment were presented in this paper, and the structural deformation was discussed cautiously and emphatically. Firstly, the static and fatigue tests on three inverted simply supported beams were conducted. The development of cracks under static loading, the load-deformation curves, and the values of residual deformation under fatigue load were recorded and analyzed in detail. Several meaningful conclusions were obtained from the analysis of experimental results. To study the development laws of residual deformation under fatigue load, the analytical methods of residual midspan deflection and residual rebar strain were proposed, respectively. The limitation and accuracy of the presented models were studied according to the comparison between the prediction and measured results. The calculation values of the proposed models showed good agreement with the test results. Finally, the design recommendations of fatigue deformation were proposed according to the experimental and analytical study on steel-concrete composite beams subjected to hogging moment.

In recent years, steel-concrete composite structure was popularly used in varied bridges and public buildings due to the many advantages of concrete and steel [

Concrete cracking is a big problem in steel-concrete bridge hogging areas. Crack control of the concrete plate is therefore one of the most critical problems in hogging moment regions close to the intermediate support of the continuous composite bridges. For the construction of a composite bridge, it is an inexpensive and convenient solution that allows cracks to be created within reasonable width limits. A lot of researchers have now paid attention to this aspect, and significant experimental and theoretical studies have been conducted in previous times on the concrete cracking of the composite beams. Shim and Chang [

Until now, there are still no standard and applicable analytical methods for fatigue deformation in the hogging moment regions of steel-concrete composite beams in present design codes. Few researchers have studied the theoretical methods of fatigue deformation. Song et al. [

Set against the above background, this study aims to investigate the static and fatigue properties of steel-concrete composite beams under the hogging moment. The test program was introduced cautiously, and the test results were observed and analyzed in detail. Based on the existing model for analyzing the residual deformation of composite beams subjected to sagging moment, an analytical formula for evaluating the residual deformation in hogging moment regions was then presented. Meanwhile, based on the calculation method of the nonprestressed rebar under fatigue loading in PPC beams, a calculation model was derived for the evaluation of residual strain in the longitudinal rebar. The accuracy of the presented models was studied through the comparison between the prediction and test results.

To study the static and fatigue properties in negative moment regions, three steel-concrete composite beams numbered SCB1-1, SCB1-2, and SCB1-3 were fabricated and used for the loading test. Specimen SCB1-1 was tested under static loading, and the other two specimens were tested subjected to fatigue loading. Each of the beam models had a span of 3500 mm and was 3900 mm long, as shown in Figure _{u} is the ultimate bearing capacity of the test beam without fatigue load. Based on the results of the ultimate bearing capacity _{u} of specimen SCB1-1 and the laws of crack growth, the maximum fatigue load of the SCB1-2 test beam was set to 25% _{u} (i.e., the median value of the 7% _{u} load and 40% _{u} load at the crack stability stage). The maximum fatigue load for the SCB1-3 test beam is set to 40% _{u} (i.e., the load during the crack stability stage). Loading ratio, loading frequency, and static loading rate were 0.2, 2 Hz, and 10 kN/min, respectively. The loading method was sine wave form.

Construction details of tested beams (unit: mm).

Loading setup of the specimens: (a) static loading device and (b) fatigue loading device.

Mechanical properties of the specimen materials.

Material type | Average value of cube strength (MPa) | Average elastic modulus (MPa) | Material type | Thickness or diameter (mm) | Average yield strength (MPa) | Average ultimate strength (MPa) |
---|---|---|---|---|---|---|

Concrete (C50) | 51.2 | 35400 | Top flange and web (Q345) | 12 | 443 | 608 |

Bottom flange (Q345) | 14 | 391 | 520 | |||

Rebar (HRB400) | 16 | 592 | 718 |

Fatigue loading parameters of the test beam.

Specimen | Load limit | Loading ratio | Frequency (Hz) | Loading method | Static loading rate (kN/min) |
---|---|---|---|---|---|

SCB1-2 | 25%_{u} | 0.1 | 2 | Sine wave | 10 |

SCB1-3 | 40%_{u} | 0.1 | 2 | Sine wave | 10 |

The major experimental results of beam specimen SCB1-1 are characterized in Table

Characteristic experimental results of the beam specimen.

Specimen | Initial cracking (70 kN) | Stabilized cracking (400 kN) | Reinforcement yield (700 kN) | Ultimate load (1033 kN) | ||||
---|---|---|---|---|---|---|---|---|

_{cr} (mm) | _{cr} (mm) | _{cr} (mm) | _{cr} (mm) | |||||

SCB1-1 | 0.03 | / | 0.10 | 105 | 0.20 | 104 | >1 mm | 104 |

Crack formation and distribution of the beam specimen under different loading levels (unit: mm): (a) initial cracking load, (b) stabilized cracking load, and (c) ultimate load.

No fatigue failures occurred after 250 × 104 cycles in SCB1-2 when the fatigue upper limit was equal to 250 kN. As for SCB1-3, the fracture of the rebar occurred after about 152 × 10^{4} cycles. Due to the fatigue failure, specimen SCB1-3 had a lower ultimate load of 477.2 kN, which was only 46.2% of SCB1-1. However, specimen SCB1-3 still had good ductility although the fatigue failure had already occurred. The difference between specimens SCB1-2 and SCB1-3 can also be found in the load-deflection curves as shown in Figures

Load-deformation curves after different load cycle numbers: (a) load-deflection curves of SCB1-2, (b) load-deflection curves of SCB1-3, (c) load-strain curves of SCB1-2, and (d) load-strain curves of SCB1-3.

In the experimental tests, strain gauges for measuring reinforcing bars were arranged on longitudinal bars at the midspan section, where the maximum tensile stress probably occurs for simply supported beams under concentrated load in the span center. The gauge locations are shown in Figure

.Locations and arrangement of rebar strain gauges (unit: mm).

.Residual deformation versus cycle ratio: (a) residual midspan deflection and (b) residual rebar strain.

In this study, the existing method for fatigue life of hogging moment regions presented by Song and Wan [_{f1}, _{f2}, and _{f3} are the number of fatigue test cycles of the three components, i.e., studs, steel, and rebars and

Thus, fatigue life _{f} in hogging moment regions can be given as follows:

According to the existing method for plastic slip in shear studs (_{std,n}) [_{n}) in sagging moment regions can be given by Wang and Nie [_{std,n} can be expressed as follows:_{1} and _{2} can be obtained as follows:

In the aforementioned formulas, _{u,0} is the ultimate bearing capacity of studs; _{max} is the fatigue upper limit of studs; and _{min} is the fatigue lower limit of studs.

When the above analytical method in sagging moment regions is employed, the calculation method for predicting the residual deformation value in hogging moment regions was obtained by fitting the measured data in this study. The following relation gives its analytical formulation:

It can be found that the related coefficient

Comparison between predicted and tested residual deflection values.

Specimen | Fatigue life (×10^{4}) _{f} | Static deflection caused by upper limit _{u} (mm) | Residual values (mm) | Deviation (_{t} − _{p})/_{p} × 100% (%) | Proportion _{t}/_{u} × 100 (%) | ||
---|---|---|---|---|---|---|---|

Test _{t} | Prediction _{p} | ||||||

SCB1-2 | 516 | 3.32 | 0.19 | 0.948 | 0.847 | 11.9 | 28.6 |

0.29 | 0.988 | 0.949 | 4.1 | 29.8 | |||

0.39 | 1.018 | 1.065 | −4.4 | 30.7 | |||

0.48 | 1.028 | 1.170 | −12.2 | 31.0 | |||

SCB1-3 | 152 | 5.50 | 0.33 | 1.577 | 1.441 | 9.5 | 28.7 |

0.66 | 1.607 | 1.750 | −8.2 | 29.2 |

For steel-concrete composite structures, the strength or stiffness degradation phenomenon of studs has been investigated under fatigue loading [_{n} − _{n}) relationships of studs under fatigue loading were given in [_{u,N}) can be estimated at a specified number of load cycles as follows:

Through a series of experiments and analyses, it was found that the load-slip behavior after _{n} ≤ 0.8 _{u,N} [_{max,n} with an equivalent slip of _{max,n}. Thus, the residual stiffness of studs can now be written in the following form:

The slip effect at the beam-slab interface has been proved to have a great influence on the mechanical property in the hogging moment regions of continuous composite beams, and an equation proposed by Fan and Nie [_{s} (_{s} and sectional area of reinforcing _{r} are substituted by _{s,n} in equation (_{s} is Young’s modulus of reinforcement; _{s} is the sectional area of the steel beam; _{s} is the second moment of area of the steel beam; _{r} and _{s} are the distances of the beam-slab interface to the centroid of reinforcing bars and steel beam, respectively; _{n} is the shear connection stiffness at the beam-slab interface, _{n} = _{s}_{s,n}; and _{s} is the number of shear studs per row.

In the fatigue stress evaluation of equation (_{sy} is the tensile strength of the reinforcement bar.

By combining equations (_{s} (

When taking the combination effect of composite beams and fatigue effect of studs into account, an analytical model for estimating the residual strain of nonprestressed reinforcement in PPC beams [_{ct,n}) under fatigue loading can be obtained as follows [_{r} is the number of reinforcement bars in the concrete slab; _{r} is the diameter of the longitudinal reinforcement bar; _{c} is Young’s modulus of concrete; _{s} is Young’s modulus of the rebar; _{0} = _{s}/_{c}; _{ct} is the concrete strength of extension; _{sr,n} = 0.02 mm is for the nonrecoverable deformation after unloading; and _{n} = 1.

To verify the accuracy of the analytical model for estimating the residual strain of longitudinal reinforcement in the hogging moment regions of steel-concrete composite beams under fatigue loading, the predicted curves and experimental results of specimens SCB1-2 and SCB1-3 are shown in Figure

.Comparison between predicted and tested residual strain of the rebar.

For further verification of the proposed model quantitatively, the comparison between experimental and calculated residual strain values in stage II (0.1 <

Comparison between predicted and tested residual strain in stage II (0.1 <

Specimen | Fatigue life (×10^{4}) _{f} | Residual strain (×10^{−6}) | Deviation (%) | ||
---|---|---|---|---|---|

Test results | Prediction | ||||

SCB1-2 | 516 | 0.10 | 178.5 | 192.5 | 7.3 |

0.19 | 175.9 | 195.9 | 10.2 | ||

0.29 | 190.2 | 200.6 | 5.2 | ||

0.39 | 197.1 | 206.0 | 4.3 | ||

0.48 | 202.0 | 212.1 | 4.7 | ||

SCB1-3 | 152 | 0.33 | 230.0 | 214.3 | −7.4 |

0.66 | 239.2 | 248.2 | 3.6 |

The residual deflection and strain gradually increased due to the fatigue loading, as observed and analyzed in the experimental test. The residual deflection accounted for more than 30% of the static deflection caused by the fatigue upper limit under the monotonic loading with the increment of repeated cycles (see Table _{0} is the elastic deflection in the hogging moment regions of steel-concrete composite beams; _{N} is the total residual deflection obtained by the analytical model proposed in this paper; and _{s} (

In this paper, the static and fatigue properties of steel-concrete composite beams under the hogging moment were studied with experimental tests and analytical models. Through the experimental tests, the crack development process, the fatigue deflection at the midspan, and the fatigue stress of longitudinal reinforcement were observed and discussed carefully and in detail. Then, the calculation methods for predicting the residual values were given. Details of this study are summarized as follows:

With the experimental test of an inverted specimen, four stages are defined for the overall process of crack developing according to development laws of the average crack spacing, the number of through cracks, and crack width. The average crack spacing and the number of through cracks remained stationary in stages II and III. The width of the major crack increased at a rather rapid speed in stage IV until the beam specimen failed.

Based on the existing model for predicting the residual deflection of composite girders subjected to sagging moment, a calculation method for evaluating the residual values in hogging moment regions is presented. It was found that the residual deflection accounted for more than 30% of the static deflection caused by the fatigue upper limit under the monotonic loading, and this proportion will be larger with the increment of repeated cycles.

Based on the calculation method of nonprestressed reinforcement in PPC beams, an analytical model is proposed for the prediction of residual strain of longitudinal reinforcement in the hogging moment regions of composite beams, which accounts for the slip effect of composite beams and fatigue properties of stud and reinforcement. In stage II (0.1 <

The data used to support the findings of this study are obtained directly from the tests and included within the article.

The authors declare that they have no conflicts of interest.

This research was sponsored by the National Natural Science Foundation of China under project no. 51878151.