Thermodynamic and Fluid Dynamic Analysis of Clamping Force Variability in High-Strength Bolts Across Temperature Extremes in Northern China

HSB connections are pivotal in the assembly of substantial steel infrastructures such as bridges, celebrated for their excellent load-bearing strength, fatigue resistance, and straightforward assembly [1]. The performance and reliability of these connections are critically influenced by environmental temperature fluctuations, necessitating a profound understanding of their thermodynamic and fluid dynamic behaviors.

Firstly, scholars worldwide have focused on the impact of high temperatures on the performance of HSB connections, as HSBs are prone to rapid strength degradation and are among the components most vulnerable to failure under extreme heat. Saglik et al. applied tensile, shear, and combined loads to commonly used grade 8.8 and 10.9 HSBs at temperatures up to 700℃, using numerical simulations to analyze the mechanical performance under these conditions [2]. Mamazizi conducted experimental and simulation-based studies on grade 12.9 and 10.9 HSBs to evaluate their physical properties during fire exposure [3, 4]. Xu et al. [5] investigated the creep relaxation mechanisms in bolt connections without washers under high temperatures. Dai et al. [6] developed a numerical simulation model, defining material constitutive behaviors and contact interactions between assembly components, to analyze bolt forces and deformation at elevated temperatures. Nah et al. [7] proposed methods for estimating bolt clamping force in high-temperature environments. Liu et al. [8] experimentally examined the mechanical properties of HSB connections, focusing on changes in friction coefficient, clamping force, and joint behavior under high temperatures. Additionally, Kumar studied the changes in tensile and shear strength of HSBs after fire exposure and cooling, investigating clamping force loss under different cooling methods and burn conditions [9].

Beyond high-temperature effects, HSBs also experience clamping force loss under ambient conditions. Sakura et al. [10] conducted tests with varying surface pressures and applied forces, developing an equation relating friction coefficient to contact surface pressure. Kong et al. [11, 12] explored the impact of clamping force loss on connection performance at room temperature. Nah and Choi [13] studied clamping force loss across different temperature conditions, focusing on the 10℃-50℃ range and developing a regression model for these variations. Data acquisition technology for clamping force is also essential: Huang et al. employed automated digital image correlation to monitor clamping force in real-time, estimating its loss [14]. Jiang and Zhang conducted experiments on clamping force relaxation by altering bolt grip length and load direction [15, 16]. Yuan et al. [17] measured changes in clamping force using an ultrasonic error compensation model based on solid coupling. Given the typical temperature range of -20℃ to 60℃ in northern China, focused research is needed to understand how these variations impact HSB clamping force.

Given the extreme temperatures ranging from -20℃ to 60℃ typically experienced in northern China, this research aims to integrate a thermodynamic and fluid dynamic framework with mechanical evaluations to thoroughly understand how temperature-induced changes affect the clamping force in HSBs. By combining detailed experimental assessments with advanced thermofluid modeling, this study offers a comprehensive analytical approach that addresses both the thermal expansion and contraction inherent in variable climatic conditions, essential for the design and maintenance of robust steel structure connections.

3.1 Relaxation of clamping force

To explore the relaxation behavior of HSBs under a 24℃ ambient temperature, the specimens underwent initial pre-tensioning at this temperature. Following this, they were placed in a constant temperature chamber maintained at 24℃. Throughout the experiment, strain values of the HSBs and ambient temperature were monitored using static strain gauges and temperature sensors, respectively, for a duration of 48 hours. Figure 4 depicts the observed variation in clamping force relaxation of HSBs simulated under a 24℃ environment over a 48-hour period.

From Figure 4, it is evident that the clamping force relaxation of all specimens follows a consistent pattern over time. Within the initial 5 hours, the clamping force loss peaks, ranging from 1.01% to 3.43%. Subsequently, after 7 hours, the clamping force loss of most specimens stabilizes. After 48 hours, the clamping force loss for all specimens falls within the range of 1.01% to 3.44%. According to the Chinese standard JGJ 82-2011, the final tightening force is prescribed at 1.1 times the design clamping force, with clamping force quality acceptance conducted within 1 hour ≤ t ≤ 48 hours post-final tightening. The experimental findings indicate that the clamping force loss of all specimens is notably below the stipulated 10% in the design. Furthermore, clamping force relaxation is completed within 7 hours. Hence, it is advisable to set the final tightening value at 1.1 times the design clamping force, with clamping force quality acceptance ideally performed within 7 hours ≤ t ≤ 24 hours post-final tightening.

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Figure 4. Variation in clamping force relaxation of HSBs in a 24℃ environment

3.2 Clamping force temperature effect

Figure 5 illustrates the change in clamping force over time for HSBs under various ambient temperatures. In this figure, the red line represents the temperature gradient over a period of 144 hours, with constant temperatures maintained at -20℃, -10℃, 0℃, 20℃, 40℃, and 60℃ for 24 hours each. After the HSB’s relaxation at 24℃, the temperature in the constant temperature chamber was sequentially adjusted to 20℃, 40℃, and 60℃. Following each temperature adjustment, strain values for the HSBs were recorded hourly, beginning two hours after the adjustment, with data collection continuing for 24 hours at each temperature. Similarly, the specimen was placed in a refrigerated environment to simulate conditions of -20℃, -10℃, and 0℃, with identical sampling frequency and duration, which will not be reiterated here.

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Figure 5. Variation of clamping force of HSBs over time at different environmental temperatures

Table 2 provides a detailed account of the hourly clamping force loss rate for HSBs at constant temperatures of -20℃, -10℃, 0℃, 40℃, and 60℃. Upon completing relaxation at 20℃, the clamping force loss for HSBs at this temperature is defined as zero. The figure reveals that clamping force decreases with increasing temperature and stabilizes at each constant temperature. Additionally, variations in clamping force loss across specimens are observed, attributed to differences in the machining and assembly precision of specimen components.

Table 2. Hourly clamping force loss rate of HSBs under constant temperatures

Figure 6 illustrates the regression curve depicting the clamping force loss of HSBs concerning environmental temperature. Within the temperature span of -20℃ to 60℃, specimen Bolt-4 demonstrates the highest clamping force loss at 60℃ environmental temperature, reaching a maximum of -19.02%. At 60℃, the average clamping force loss ratio for all specimens stands at -9.82%. Conversely, at -20℃, the clamping force of all specimens increases, with an average increment of 12.38%. Notably, Bolt-4 exhibits the most substantial increase in clamping force, with a rise of 24.68%. Given that steel bridges in northern China typically undergo temperature fluctuations ranging from -20℃ to 60℃, particularly during hot summers, it is imperative to consider the influence of clamping force loss of HSBs on the joint's slip-bearing capacity.

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Figure 6. Regression curve depicting the clamping force loss of HSBs relative to environmental temperature

Table 3 presents the average clamping force loss of HSBs for all specimens under the temperature gradient ranging from -20℃ to 60℃. Regression analysis was performed on the clamping force loss data from the six HSB specimens relative to environmental temperature, resulting in the derivation of the regression equation:

$\begin{gathered}P^{\prime}=0.0009 T^2-0.3142 T+5.6688 \\ R^2=0.7614\end{gathered}$      (1)

In the given formula, T represents the ambient temperature in degrees Celsius (℃); t represents the duration for which the specimen is maintained at a constant temperature of T ℃ (h); P represents the loss ratio of clamping force, equal to $100 \% \times\left(P_{\mathrm{T}}-P_0\right) / P_0(\%)$. $P_0$ represents the clamping force of HSBs after relaxation at an ambient temperature of 20℃, while $P_T$ represents the clamping force of HSBs at the ambient temperature T.

Table 3. Average clamping force loss of HSBs at various constant temperatures

Figure 7 displays the influence of temperature on the clamping force of HSBs at different measuring points along the rod axis. The graph illustrates that within the temperature range of -20 to 60℃, the clamping force decreases as the temperature increases for all HSB specimens. Compared to specimens Bolt-1 and Bolt-2, the variations in clamping force between specimens Nut-1 and Nut-2 are relatively minor. Regression analysis of the average clamping force loss at the 38mm measuring point concerning environmental temperature resulted in the following regression equation:

$\begin{gathered}P=0.0012 T^2-0.2235 T+5.1630 \\ R^2=0.9750\end{gathered}$        (2)

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Figure 7. Relationship between clamping force at different positions of HSBs and temperature gradient

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Figure 8. Regression curves of clamping force of HSBs at different measuring point locations with respect to environmental temperature

Figure 8 shows regression curves of clamping force of HSBs at different measuring point locations with respect to environmental temperature. From the graph, it can be observed that there is a notable difference in the regression curve equations of clamping force established at the 28mm and 38mm measuring points under the same environmental temperature. Table 4 provides detailed data on the average clamping force loss of HSBs at the 28mm and 38mm measurement points as a function of ambient temperature. The impact of the measuring point location on the clamping force of HSBs varies consistently with the same temperature, correlating with the complexity of stress along the rod axis. Thus, measuring points should be positioned away from areas of complex stress along the rod axis.

Table 4. Average clamping force loss of HSBs at different temperature gradients and measurement points