Dynamic Analysis of Frames With Material and Geometric Nonlinearities Based on the Semirigid Technique

Au, Ftk; Yan, ZH

doi:10.1142/s0219455408002727

Cited by 15 publications

(6 citation statements)

References 15 publications

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“…The calculation of plastic rotation is only necessary when a potential plastic-hinge section becomes active by moving into the plastic region. The process is similar to that adopted by Au and Yan (2008), except that the effect of distributed load on the elastic rotation ai e should also be included. There are two ways to calculate the plastic rotation, depending on the nature of plastic hinge.…”

Section: Plastic Rotationmentioning

confidence: 99%

Nonlinear dynamic analysis of frames with plastic hinges at arbitrary locations

Yan¹,

Au²

2009

Structural Design Tall Build

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This paper presents a method for nonlinear dynamic analysis of frames subjected to distributed loads, which is based on the semi-rigid technique and moving node strategy. The plastic hinge is modelled as a pseudo-semi-rigid connection with nonlinear hysteretic moment-curvature characteristics at element ends. The stiffness matrix with material and geometric nonlinearities is expressed as a sum of products of the standard and geometric stiffness matrices with their corresponding correction matrices based on the plasticity-factors developed from the section fl exural stiffness at the plastic hinge locations. Each beam member is modelled by two elements. The moving node strategy is applied to the intermediate node to track the exact location of any intermediate plastic hinge that may be formed. Equilibrium iterations and geometry updating are carried out in every time step. Stiffness degradation is adopted to describe the deterioration of plastic hinges, and the effects of various parameters in the degradation model are evaluated. Examples are used to illustrate the applicability and excellent performance of the proposed method. practical design, nonlinear dynamic analysis is still essential, especially to those structures that are irregular and those of which the higher mode effects cannot be ignored. Besides, the strong-motion peculiarity is also a problem that the pushover analysis needs to overcome (Elnashai, 2002). Therefore, dynamic analysis is still important to frames with nonlinearities.Under lateral loading, the frame members subjected to distributed load may have plastic hinges formed at intermediate locations besides the member ends. To capture the behaviour of the intermediate plastic hinges, an effi cient method for elasto-plastic large defl ection analysis of steel frames using an element with plastic hinges at mid-span and two ends was proposed (Chen and Chan, 1995). As the intermediate plastic hinges can only be formed at mid-span, the results obtained are subject to certain errors. Later, the moving node strategy was presented for the elasto-plastic analysis of frames subjected to loads including linearly varying distributed load (Wong, 1996). In addition, certain applications of the moving node method in the second-order inelastic analysis of two-and three-dimensional steel frames were reported (Kim et al., 2004;Kim and Choi, 2005). However, the above research on the intermediate plastic hinge was only for the static analysis of frames. Such plastic hinges are often formed when the frame is subjected to strong seismic excitations, and therefore, the corresponding dynamic problem warrants further study.The material and geometric nonlinearities in beam-column elements may be simulated by either the plastic hinge element or the fi bre element. Although the fi bre element model can handle the residual stresses and better simulate the yielding process, it is rather computation intensive. On the other hand, the plastic hinge element model can simulate nonlinearities well and it is computationally effi c...

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Section: Plastic Rotationmentioning

confidence: 99%

Nonlinear dynamic analysis of frames with plastic hinges at arbitrary locations

Yan¹,

Au²

2009

Structural Design Tall Build

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“…Recent works on secondary analysis include several references. [11][12][13][14][15][16][17][18][19][20] Brazil and Mazzilli 11 have presented a general FEM formulation of planar frames with a geometrically nonlinear behavior, constituted by a linear elastic material. A nonlinear steady-state vibration analysis of plane structures, using the finite element and harmonic balance method, has been carried out by Chen et al 12 A nonlinear dynamic analysis of frames, considering geometric and material nonlinearities, has also been conducted by Au and Yun.…”

Section: Introductionmentioning

confidence: 99%

“…Brazil and Mazzilli 11 have presented a general FEM formulation of planar frames with a geometrically nonlinear behavior, constituted by a linear elastic material. A nonlinear steady‐state vibration analysis of plane structures, using the finite element and harmonic balance method, has been carried out by Chen et al 12 A nonlinear dynamic analysis of frames, considering geometric and material nonlinearities, has also been conducted by Au and Yun 13 . Furthermore, Mamouri et al 14 have studied the geometric nonlinear instability of frame structures considering large motions.…”

Section: Introductionmentioning

confidence: 99%

“…A nonlinear steady-state vibration analysis of plane structures, using the finite element and harmonic balance method, has been carried out by Chen et al 12 A nonlinear dynamic analysis of frames, considering geometric and material nonlinearities, has also been conducted by Au and Yun. 13 Furthermore, Mamouri et al 14 have studied the geometric nonlinear instability of frame structures considering large motions. Moghadam and Aziminejad 15 have evaluated the interaction between in-plane torsion of an asymmetric tall building and P-delta effects in elastic and inelastic ranges.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear dynamic P‐delta interaction between TMD and the frame structure under proportional internal resonances

Afshar

2022

Structural Contr & Hlth

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The effect of axial loads on the dynamic interaction of a shear frame and tuned mass dampers (TMDs) is evaluated under harmonic and seismic lateral loads.Taking into account the nonlinear geometric stiffness created by the small and large TMD gravity load on the frame columns, the nonlinear differential equations of motion of coupled TMD and frame are derived. Then, the interaction between the small and large TMD and the frame is studied, and the equations of motion are investigated. Nonlinear P-delta effects couple the TMD and frame responses. By using the method of multiple scales, the asymptotic solution of the nonlinear differential equations is derived, and the effect of two-toone internal resonance, called proportional resonance, is examined. System stability under near-internal resonance is investigated by plotting the modal amplitude responses vs. variations of excitation frequency and amplitude. The jump and saturation phenomena can be observed in the plots. A parametric study is conducted on the effect of variations of the quantities, e.g., damping ratios of the structure and TMD, the mass ratio, and the axial load ratio, on the response amplitude of the structure and TMD. The time and frequency responses of two linear and nonlinear dynamics for the TMD-structure interaction under harmonic and seismic excitation are also studied and compared.

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“…One simplified technique commonly accepted in the analysis of nonlinear structures is updating the stiffness matrix (e.g., Liu 2003and 2005, Au and Yan 2008, Yan and Au 2010, and this updating concept has been fully adopted in all commercial software packages, including Perform-3D (2008). However, significant computational effort is often required to update the stiffness matrix associated with nonlinear dynamic analysis of moment-resisting framed structures with rigid-end offsets, which generally causes software developers to create numerically-based rather than theoretically-based solution algorithms.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Modal Analysis of Structures with Rigid-End Offsets

Wong¹

2012

20th Analysis and Computation Specialty Conference

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The nonlinear modal analysis (NMA) methodology for analyzing moment-resisting framed structures is here extended to include frame elements with rigid-end offsets.Four key components of the NMA methodology for conducting dynamic analysis of nonlinear framed structures include: (1) the force analogy method for material nonlinearity; (2) stability functions for geometric nonlinearity; (3) the state space method for dynamic analysis; and (4) modal superposition for computational efficiency. Under this NMA methodology, the nonlinear stiffness matrices capturing full panel zone rigidities and centroidal locations of plastic hinges in moment-resisting frames are completely derived in conjunction with satisfying global equilibrium, joint compatibility, and element force-displacement relationship. Nonlinear dynamic analysis of a 10-story steel frame with rigid-end offsets is then performed and results are compared with those obtained using Perform-3D (P3D) commercial software. Good agreement between NMA and P3D results indicate accuracy of the proposed methodology even though it is based on different assumptions.

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Dynamic Analysis of Frames With Material and Geometric Nonlinearities Based on the Semirigid Technique

Cited by 15 publications

References 15 publications

Nonlinear dynamic analysis of frames with plastic hinges at arbitrary locations

Nonlinear dynamic analysis of frames with plastic hinges at arbitrary locations

Nonlinear dynamic P‐delta interaction between TMD and the frame structure under proportional internal resonances

Nonlinear Modal Analysis of Structures with Rigid-End Offsets

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