Y.Fang  
1 Department of Civil Engineering, Hangzhou City University, Hangzhou 310015, China; [EMAIL_ADDRESS] (Y.F.F)  
Y.Fang  
1 Department of Civil Engineering, Hangzhou City University, Hangzhou 310015, China; [EMAIL_ADDRESS] (Y.F.F)  
Y.Fang  
1 Department of Civil Engineering, Hangzhou City University, Hangzhou 310015, China; [EMAIL_ADDRESS] (Y.F.F)  
Y.Fang  
1 Department of Civil Engineering, Hangzhou City University, Hangzhou 310015, China; [EMAIL_ADDRESS] (Y.F.F)  
Y.Fang  
1 Department of Civil Engineering, Hangzhou City University, Hangzhou 310015, China; [EMAIL_ADDRESS] (Y.F.F)  
Y.Fang  
1 Department of Civil Engineering, Hangzhou City University, Hangzhou 310015, China; [EMAIL_ADDRESS] (Y.F.F)  
Y.Fang  
1 Department of Civil Engineering, Hangzhou City University, Hangzhou 310015, China; [EMAIL_ADDRESS] (Y.F.F)  
Y.Fang  
1 Department of Civil Engineering, Hangzhou City University, Hangzhou 310015, China; [EMAIL_ADDRESS] (Y.F.F)  
Y.Fang  
1 Department of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310015, China; [EMAIL_ADDRESS] (Y.F.F)  
Y.Fang  
1 Department of Civil Engineering, Hangzhou City University, Hangzhou 310015, China; zhangru@hzcuat the early damage stage. Consequently, several nondestructive testing techniques have been investigated and applied for detecting bolt looseness, including the impedance-based method, the magnetic field measurement-based method, the acoustic emission method, the machine vision method, and the guided wave method [4; 5; 6; 7; 8]. Among these methods, the ultrasonic guided wave is particularly well-suited for practical applications due to its low cost, extensive sensing range, and high efficiency [9; 10; 11]. Guided waves have shown great promise in identifying bolt looseness. [PERSON] et al. [12] presented a method to measure the axial force of bolts by extracting the time shifts during the tightening process using noncontact laser ultrasonic guided waves. However, these time shifts were very small within the range of bolt preload and could be affected by measurement noise. [PERSON] et al. [13] proposed detecting bolt looseness by analyzing the Lamb waves passed through the bolt joint. A power transmission coefficient was developed to relate bolt torque to wave transmission. [PERSON] et al. [14] found that the changes in the received wave energy are much influenced by the roughness of the plates. Considering the severe dispersion properties of Lamb waves, [PERSON] et al. [10] presented a SH-typed guided wave-based method with the assistance of magnetostrictive transducers. In addition, [PERSON] et al. [15] introduced a time reversal signal (TRS)-based method, where peak amplitudes in reconstructed signals linearly increased with bolt torque. [PERSON] et al. [16] improved detection efficiency with a modified TRS method, using the TRS from the undamaged case as the excitation. The detection accuracy was not satisfactory for minor bolt looseness. To address this, vibration-acoustic and coda wave-based methods were also presented [17; 18]. The above studies have all focused on simple joints, where two plates are connected by single or multiple bolts. However, wave propagation in beam-column joints will be more complex, and space limitations can restrict transducer installation for capturing transmitted waves. What is more, reflections from the edges and ends of the I-shaped beam complicate the separation of necessary wave packets from the received signals. The dispersion properties of the I-shaped steel beam in the beam column joint should be analyzed to understand the wave propagation characteristics, which is crucial for choosing the proper wave mode and excitation signal. Analytical solutions for simple plates can be easily obtained by solving the motion equations of guided waves, while this approach is not feasible for waveguides with complex cross sections [19]. Numerical simulation methods based on finite element (FE) models are excessively demanding in terms of computational resources [20].