ORCID Profile
0000-0002-0280-4550
Current Organisation
Zhejiang University
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Publisher: Elsevier BV
Date: 04-2023
Publisher: Elsevier BV
Date: 02-2020
Publisher: Elsevier BV
Date: 05-2020
Publisher: World Scientific Pub Co Pte Ltd
Date: 10-08-2022
DOI: 10.1142/S0219455423500104
Abstract: The out-of-plane buckling behavior of arches is closely related to the element torsional behavior. The traditional 12-degree-of-freedom second-order element stiffness matrix which uses a simplified element torsional stiffness GJ/[Formula: see text] (where [Formula: see text] is the shear modulus, [Formula: see text] the St. Venant torsion constant, [Formula: see text] the element length) may significantly underestimate the out-of-plane buckling loads of funicular arches. This paper presents a simple and effective exact matrix stiffness method (MSM) for the out-of-plane buckling analysis of funicular arches. The developed MSM uses a 14-degree-of-freedom second-order element stiffness matrix of three-dimensional beam-columns considering both torsion and warping deformations. The out-of-plane buckling analysis of funicular arches is performed by using the global structural stability stiffness matrix, which combines the transformed second-order element stiffness matrices. The proposed MSM with the exact 14-degree-of-freedom second-order element stiffness matrix for the out-of-plane buckling analysis is verified by comparing with some classical solutions of funicular circular and parabolic arches with box sections and I-sections. Further discussions show that the 14-degree-of-freedom second-order element stiffness matrix may be reduced to a simplified 12-degree-of-freedom form only by deriving the exact element torsional stiffnesses, which could be significantly larger than GJ/[Formula: see text] for members with large cross-sectional torsional stiffness parameters (especially open cross-sections).
Publisher: MDPI AG
Date: 17-08-2023
DOI: 10.3390/BUILDINGS13082095
Abstract: Optimal design of the crossbeam is essential for the economical design of bridge towers as the crossbeam could considerably enhance the lateral stiffnesses of these towers by providing a special bracing for the tower columns. By using a reliability-based approach, this paper studies the optimal design of the crossbeam stiffness factor in bridge towers this is defined as a dimensionless crossbeam stiffness relative to the tower column stiffness. A novel second-order matrix stiffness method (MSM) is applied to obtain a closed-form solution of the lateral stiffness of the bridge tower. The structural second-order stiffness matrix consists of combinations of the second-order element stiffness matrices and coordinate transformations. Subsequently, a reliability analysis to study the optimal design of the bridge tower is performed by considering the uncertainties arising from the design and construction of the bridge tower. The lateral stiffness of the bridge tower is set as an objective function while the total usage of materials is set as a constraint condition. Then, the influence of the crossbeam stiffness factor on the lateral stiffness of the bridge tower, including the fragility curve and the probabilistic behavior, is examined. Based on the reliability analysis, optimal design recommendations on the crossbeam stiffness of the bridge tower are presented.
Publisher: Elsevier BV
Date: 08-2020
Publisher: Elsevier BV
Date: 02-2020
Publisher: American Society of Civil Engineers (ASCE)
Date: 08-2018
Publisher: MDPI AG
Date: 04-02-2022
DOI: 10.3390/NANO12030538
Abstract: The typically-used element torsional stiffness GJ/L (where G is the shear modulus, J the St. Venant torsion constant, and L the element length) may severely underestimate the torsional stiffness of thin-walled nanostructural members, due to neglecting element warping deformations. In order to investigate the exact element torsional stiffness considering warping deformations, this paper presents a matrix stiffness method for the torsion and warping analysis of beam-columns. The equilibrium analysis of an axial-loaded torsion member is conducted, and the torsion-warping problem is solved based on a general solution of the established governing differential equation for the angle of twist. A dimensionless factor is defined to consider the effect of axial force and St. Venant torsion. The exact element stiffness matrix governing the relationship between the element-end torsion/warping deformations (angle and rate of twist) and the corresponding stress resultants (torque and bimoment) is derived based on a matrix formulation. Based on the matrix stiffness method, the exact element torsional stiffness considering the interaction of torsion and warping is derived for three typical element-end warping conditions. Then, the exact element second-order stiffness matrix of three-dimensional beam-columns is further assembled. Some classical torsion-warping problems are analyzed to demonstrate the established matrix stiffness method.
Publisher: MDPI AG
Date: 11-09-2019
DOI: 10.3390/APP9183814
Abstract: Shear deformable beams have been widely used in engineering applications. Based on the matrix structural analysis (MSA), this paper presents a method for the buckling and second-order solutions of shear deformable beams, which allows the use of one element per member for the exact solution. To develop the second-order MSA method, this paper develops the element stability stiffness matrix of axial-loaded Timoshenko beam–columns, which relates the element-end deformations (translation and rotation angle) and corresponding forces (shear force and bending moment). First, an equilibrium analysis of an axial-loaded Timoshenko beam–column is conducted, and the element flexural deformations and forces are solved exactly from the governing differential equation. The element stability stiffness matrix is derived with a focus on the element-end deformations and the corresponding forces. Then, a matrix structural analysis approach for the elastic buckling analysis of Timoshenko beam–columns is established and demonstrated using classical application ex les. Discussions on the errors of a previous simplified expression of the stability stiffness matrix is presented by comparing with the derived exact expression. In addition, the asymptotic behavior of the stability stiffness matrix to the first-order stiffness matrix is noted.
Publisher: Springer Science and Business Media LLC
Date: 13-12-2020
Publisher: Elsevier BV
Date: 04-2023
Publisher: WORLD SCIENTIFIC (EUROPE)
Date: 05-2020
DOI: 10.1142/Q0237
Publisher: Wiley
Date: 11-06-2021
Publisher: American Society of Civil Engineers (ASCE)
Date: 10-2018
Publisher: Elsevier BV
Date: 06-2019
Publisher: World Scientific Pub Co Pte Ltd
Date: 13-10-2020
DOI: 10.1142/S021945542041014X
Abstract: Buckling loads of arches could be significantly affected by the assumptions made on the load behavior during buckling. For a funicular arch whose centerline coincides with the compression line, we may consider two types of load behaviors based on how the line of load action shifts during buckling. This paper presents the governing differential equations for the elastic in-plane buckling problem of funicular circular arches under uniform radial pressure based on the two different load behavior assumptions, as well as analytical and numerical methods for analysis. For the analytical method, buckling criteria of rotationally-restrained ended circular arches with an internal rotational spring are formulated by using the general solution of the governing differential equation. For the numerical method, the Hencky bar-chain model (HBM) and its simple matrix formulations for general funicular arches are established. The buckling loads and mode shapes of funicular circular arches are solved by using HBM and verified against exact solutions obtained from the analytical method. For funicular catenary arches and parabolic arches, the buckling load solutions by HBM with various number of segments are also obtained and compared with the solutions presented by the previous researchers.
Publisher: American Society of Civil Engineers (ASCE)
Date: 07-2017
Publisher: Elsevier BV
Date: 03-2020
Publisher: American Society of Civil Engineers (ASCE)
Date: 12-2019
Publisher: American Society of Civil Engineers (ASCE)
Date: 09-2017
Publisher: World Scientific Pub Co Pte Lt
Date: 08-2019
DOI: 10.1142/S0219455419500937
Abstract: Presented herein is a matrix method for buckling analysis of general frames based on the Hencky bar-chain model comprising of rigid segments connected by hinges with elastic rotational springs. Unlike the conventional matrix method of structural analysis based on the Euler–Bernoulli beam theory, the Hencky bar-chain model (HBM) matrix method allows one to readily handle the localized changes in end restraint conditions or localized structural changes (such as local damage or local stiffening) by simply tweaking the spring stiffnesses. The developed HBM matrix method was applied to solve some illustrative ex le problems to demonstrate its versatility in solving the buckling problem of beams and frames with various boundary conditions and local changes. It is hoped that this easy-to-code HBM matrix method will be useful to engineers in solving frame buckling problems.
Publisher: MDPI AG
Date: 30-07-2023
DOI: 10.3390/BUILDINGS13081940
Abstract: A comparative study of composite floor systems with I-beams and corrugated web beams is performed based on non-linear programming (NLP) algorithm. The optimization is conducted to find the most economical design with minimum steel consumption considering variables associated with the cross-sectional dimensions and multiple constraints from standards, specifications and engineering practices. Various parameters of live loads ranging from 2 to 10 kN/m2 and spans ranging from 20 to 100 m are considered. The optimization results reveal that composite floors with corrugated web beams have reasonable and economical cross-sections with less steel consumption, owing to the high performance of the corrugated web in shear resistance and stability. Further comparative studies show that composite floors with corrugated web beams are economically competitive for spans larger than 30 m with a steel saving of 20–60%, and composite floors with welded I-beams can be applicable for spans less than 30 m considering the simpler configuration and construction. In addition, a spatially structured cable-supported steel–concrete composite floor system is proposed and recommended for super-large-span floor structures considering the cost-effectiveness of the analyzed floor systems reduces as the span further increases.
Publisher: Elsevier BV
Date: 02-2022
Publisher: SAGE Publications
Date: 04-12-2020
Abstract: This paper proposes a new stiffness-strength-relationship-based design approach that can pinpoint the target design solution for steel buckling-restrained braces (BRB). First, a stiffness–strength requirement interaction curve (the design criterion) with a very simple and easy-to-use form is derived based on a second-order analysis. This interaction curve clearly illustrates the opposing stiffness and strength requirements of the restraining system. Second, based on the geometrical parameters and material properties, a stiffness–strength relationship curve of the BRB restraining system is established. This second relationship curve is expressed by a linear function for a uniform steel BRB. By using the two analytical curves, the point of intersection defines the target design point. A straightforward design procedure for steel BRBs is then developed. A design ex le of steel BRBs is considered to demonstrate this easy-to-use design procedure for obtaining economical BRB designs. The design is verified and discussed by a rigorous finite element analysis.
Publisher: American Society of Civil Engineers (ASCE)
Date: 10-2016
Publisher: Springer Science and Business Media LLC
Date: 22-08-2016
Publisher: American Society of Civil Engineers (ASCE)
Date: 10-2018
Publisher: American Society of Civil Engineers (ASCE)
Date: 07-2020
Publisher: Elsevier BV
Date: 03-2019
Publisher: Elsevier BV
Date: 02-2020
Publisher: World Scientific Pub Co Pte Ltd
Date: 31-03-2023
DOI: 10.1142/S0219455423400059
Abstract: This paper presents the optimal designs of pinned supported funicular arches under equally spaced point loads for maximum in-plane buckling load. Under such loading conditions, the funicular arch shapes comprise straight arch members between the point loads, that is, following the shape of the bending moment diagram of an equivalent simply supported beam under the same loading condition. Two classes of funicular arch optimization problems are considered herein. The first class of funicular arches imposes a constraint on the cross-sectional area to be uniform throughout the entire arch length. The second class of funicular arches allows the cross-sectional area to be different from one straight arch member to another member. To facilitate the buckling analysis, the Hencky bar-chain model (HBM) is adopted. This discrete structural model simplifies the optimization process as the decision variables are the HBM rotational spring stiffnesses that define the cross-sectional areas and the horizontal force that controls the arch shape. Presented herein are new optimal funicular arch shapes under various numbers of equally spaced point loads. By increasing the number of point loads, the optimal solution approaches the solution of a parabolic arch under a uniformly distributed load.
Publisher: Springer Science and Business Media LLC
Date: 19-02-2019
Location: Australia
No related grants have been discovered for W.H. Pan.