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Second-order dynamic analysis of semi-rigid steel frames via a novel finite element method with consistent mass matrices
 
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1
Faculty of Civil Engineering, Hanoi Architectural University, Hanoi, Vietnam
 
2
Faculty of Mechanical-Automotive and Civil Engineering, Electric Power University, Hanoi, Vietnam
 
These authors had equal contribution to this work
 
 
Publication date: 2026-03-27
 
 
Corresponding author
Hai Quang Nguyen   

Faculty of Mechanical-Automotive and Civil Engineering, Electric Power University, Hanoi, Vietnam
 
 
Adv. Sci. Technol. Res. J. 2026; 20(7)
 
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ABSTRACT
In practical analysis, steel frames are often idealized with fully rigid or hinged connections, although actual connections exhibit semi-rigid behavior that can be modeled as rotational springs. Existing literature predominantly addresses static performance, whereas comprehensive studies dealing with geometrically nonlinear dynamic behavior of semi-rigid steel frames are still relatively scarce. This paper therefore proposes a new consistent mass matrix and an effective displacement-based finite element formulation for analyzing semi-rigid steel frames under dynamic loads, including P-Delta effects. A new expression for determining the reversal moment under dynamic loading is also introduced. The proposed algorithm fully represents the nonlinear hysteretic response of semi-rigid connections, enabling computation of frame’s nonlinear dynamic response. A MATLAB program was developed and validated against published results. The analyses show that connection hysteresis and geometric nonlinearity significantly affect the transient response of steel frames.
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