Health Assessment of a Multi-Bolted Connection due to Removing Selected Bolts

In the paper, experimental studies of an asymmetric preloaded sevenbolted connection are presented. The tightening process of the connection was carried out with a wrench, monitoring the values of the bolt forces with a calibrated strain gauge measuring system. Two methods of bolt tightening were tested: in one and several passes. After all bolts were tightened, the selected bolts were removed, simulating bolt failure under the loading conditions of the connection. The influence of the method and sequence of bolt tightening on the distribution of bolt forces values after the introduction of failure states of some bolts was investigated. The results were statistically processed and presented in the form of graphs showing the distributions of normalised bolt forces values for all the considered failure cases.


INTRODUCTION
Bolted and multi-bolted connections are among the most commonly used temporary fastenings in both mechanical and structural engineering [1][2][3]. Various experimental studies on these connections are still undertaken by many authors.
Recently, a lot of attention has been paid to research in the field of structural health monitoring of bolts and bolted connections under the influence of the loss of load capacity of the supporting element of the structure. Kozłowski and Kukla [4], and Kukla and Kozlowski [5] described experimental tests of unstiffened two-sided connections with a flush and extended end plate, which consisted in checking the behaviour of the structure due to the loss of one of the columns. Similar tests were performed by Xu et al. [6], and Gao et al. [7]. Experimental investigation of steel moment frames subjected to column loss were carried out by Marginean et al. [8]. In contrast, the progressive collapse mechanism of bolted structures were analysed, among others, by Tang et al. [9], Wang et al. [10], and Chen et al. [11].
On the other hand, less attention has been paid to experimental research in the field of structural health monitoring of bolts and bolted connections due to loss of load capacity of selected fasteners in the connection. Li and Hao [12] monitored the state of bolted connections in a truss bridge model due removing selected bolts. Yan et al. [13] described an experimental validation of a damage detection method on a full-scale highway sign support truss. As one of the simulated failures, they considered the loss of all bolts in one of the flange connection in this truss. Pham and Hancock [14], and Pham et al. [15] investigated deformations of connections of beams with cold-formed C-sections for different number of bolt rows. There are also only a few papers on modelling the phenomena occurring in bolted connections under the influence of fasteners failure [16][17][18][19]. Therefore, this subject has been taken up in the presented paper.
An indispensable part of assessing the structural condition of bolted connections is monitoring of bolt forces and detection of joint loosening. They are implemented in many ways. The change in magnetic flux density as a diagnostic parameter of the bolt tightening torque was used by Mori et al. [20]. The papers by Yasui et al. [21], Kim and Hong [22], Blachowski et al. [23], and Pan et al. [24] were written on the subject of ultrasonic measurement of axial stress in bolts. Monitoring of bolt forces can also be carried out using embedded fiber Bragg gratings (FBG) sensors [25]- [28]. Martinez et al. [29], Zhang et al. [30], and Wang et al. [31] applied acoustic methods to monitor bolt loosening, while for the same purpose Wang et al. [32], Wang et al. [33], Huynh et al. [34], and Na [35] used impedance methods. Nazarko and Ziemianski [36] applied the phenomenon of elastic wave propagation, introduced and measured by piezoelectric transducers, to identify the forces in the bolts in a flange connection. The relationships between the measured signal changes and the variations of the forces in the bolts were assessed in this case using artificial neural networks. Sun et al. [37] proposed a bolt-loosening detection method based on the binocular vision. In addition, vision-based methods for the bolts looseness detection were also presented by Wang et al. [38], and Huynh [39]. Sidorov et al. [40] designed and implemented sensor nodes (named TenSense M20) for continuous remote structural health monitoring of bolted connections.
However, the most common method of measuring bolt forces is the method based on the use of resistance strain gauges. The measurements are made by means of strain gauges glued to the outside of the bolt shank [41]- [46], inserted into the hole inside the bolt shank [47][48][49][50][51] or on the bolt head [52]. In addition to ultrasonic sensing, it is the method with the highest accuracy [36]. Therefore, this method has been also implemented in the presented paper.
Experimental tests of the process of tightening multi-bolted connections are carried out mainly for connections showing geometric symmetry or load symmetry. These studies include tightening in one pass [53][54][55] and in several passes [56][57][58]. In this study, these two types of tightening were also used. However, in order to make the research universal, it was performed for the case of asymmetric multi-bolted connection. The research is an extension of the paper [45] and will be used to validate the modelling method of the tightening process of arbitrary multi-bolted connections presented in [59,60].
The paper is structured as follows: Section 2 describes the research stand and research procedure, including details of tightening methods and scenarios of simulated failure of the tested multi-bolted connection. Section 3 focuses on results of the research as well as a discussion about them. Section 4 gives some additional conclusions from the conducted research.

RESEARCH STAND AND PROCEDURE
The geometry of the tested connection and the assumptions made at the design stage are described in detail in [45]. Only general information on this subject will be presented in this paper. The diagram of the multi-bolted connection is shown in Fig. 1a. It consists of two joined elements (2) and (3), fastened with seven M10x1.25 bolts (4) and nuts (5). The element (2) is welded to the upper plate (1), and the element (3) to the base (6). The connection is tilted relative to the base (6) by 60 deg. All the joined elements are made of 1.0577 steel. The bolts are made in the mechanical property class 8.8, and the nuts in the mechanical property class 8.
The contact surface between the joined elements and the adopted bolt numbering are shown in Fig. 1b.
The force changes in each bolt were measured using four TENMEX TFxy-4/120 strain gauges with two axes of measuring ladders arranged perpendicularly to each other. The strain gauges were glued to the bolt shanks in a full strain gauge bridge configuration (Fig. 2). The view of the bolts prepared for the measurements is shown in Fig. 3. Before the beginning of the study, each of the bolts was calibrated on the Instron 8850 testing machine [46]. As a result of this calibration, a set of regression equations was obtained for the bolts loading and unloading processes in the form: where F ci denotes the calibration axial force of the i-th bolt, a i is the slope of the regression curve, and V i denotes the voltage (for i = 1, 2, …, 7). The above equations were used to determine the forces in the bolts based on the voltmeter indications and through the program written in the MATLAB R2018b Simulink (Fig. 4).    The value of the bolts preload F p was determined as equal to 22 kN based on the PN-EN 1993-1-8 standard [61] and the analysis of the permissible surface pressure values between the nuts and the lower joined element.
The bolts were tightened with a wrench and the force values in the bolts were controlled by the measuring system shown in Fig. 4. The process of tightening the multi-bolted connection was carried out for two assembly methods: in one pass (the bolts were tightened immediately to the full preload value F p ) and in three passes (in the first pass, the bolts were preloaded to the value of 0.2·F p , while in the second and third pass to the value of 0.6·F p , and F p , respectively).
A summary of information on the assembly methods is shown in Table 1. In both assembly methods, the bolts were tightened sequentially according to the paths shown in Table 2.
After tightening all the bolts, the connection failure was simulated by removing selected bolts. Two states of this analysis were introduced, shown in Table 3.
Each experiment was repeated three times. The further part of the paper presents the values of bolt forces understood as the arithmetic mean of the data obtained in these experiments.

RESEARCH RESULTS
The distributions of the mean values of forces F pi in the bolts in relation to the value of the initial force F p0 in the case of failure states of the bolts after tightening the multi-bolted connection in one pass are presented in Fig. 5. Figure 6 shows similar diagrams for the case of tightening the connection in three passes.
Based on the analysis of the graphs in Figs Table 4. Based on its analysis, it can be concluded that the maximum force increments in the bolts caused by the assumed failure states do not depend on the method and sequence of bolt tightening. They are generally in the range of 0.51 to 0.76%. One pass Three passes  The distributions of the mean values of forces F pi in the bolts in relation to the value of the initial force F p0 at the end of State 1 of the multi-bolted connection failure, depending on the method of performing the tightening process are presented in Fig. 7. Figure 8 shows similar diagrams for the case of State 2 of the multi-bolted connection failure.
Based on the analysis of the graphs in Figs The maximum values of the Z 2 index obtained for individual tightening methods and the connection failure states are presented in Table 5. Based on its analysis, it can be concluded that the maximum differences in the values of bolt forces achieved for the compared tightening methods slightly depend on the sequence of bolt tightening. They are generally in the range of 0.43 to 1.72%.

CONCLUDING REMARKS
The paper presents an original laboratory stand intended for testing a selected asymmetric multi-bolted connection under the conditions of initial tightening the connection. The influence of the method and sequence of bolt tightening on the distribution of force values in bolts after the introduction of selected states of bolts failure was demonstrated. The stand can be used for further studies in the field of assessing the influence of removing selected bolts in the connection subjected to external loads on a testing machine.