Optimal Design of Triangular Arches against Buckling

Wang, C. M.; Pan, Wenhao; Zhang, J. Q.

doi:10.1061/(asce)em.1943-7889.0001797

Cited by 10 publications

(5 citation statements)

References 16 publications

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“…Although a number of computer programs such as Abaqus, OpenSees, Ansys, and MSC.Marc are readily available for the structural analysis of thin-walled nanostructural members, approaches to obtain the exact solutions [ 4 , 5 , 6 , 7 , 8 , 9 , 10 ] in closed form are helpful in many situations. The matrix stiffness method (MSM) has been found to be a suitable and systematic method for such purposes [ 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 ]. The basic idea of the matrix stiffness method is to establish the equilibrium relationship between the element-end displacements

and the element-end forces

of a beam-column element (where u i , d i , and q i are element-end axial displacement, translational displacement, and rotation angle, respectively; F i , V i , and M i are element-end axial load, shear force, and bending moment, respectively, as shown in Figure 1 ) as

where [ K e ] is the element stiffness matrix for flexural-axial problems.…”

Section: Introductionmentioning

confidence: 99%

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Exact Solutions for Torsion and Warping of Axial-Loaded Beam-Columns Based on Matrix Stiffness Method

et al. 2022

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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.

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and the element-end forces

where [ K e ] is the element stiffness matrix for flexural-axial problems.…”

Section: Introductionmentioning

confidence: 99%

“…Using the element stiffness matrix, many different types of analyses can be conducted, including the traditional analysis for the element deformations and internal forces (e.g., [ 21 , 22 ]), as well as elastic buckling and second-order stability analyses (e.g., [ 15 , 16 , 17 , 18 ]).…”

Section: Introductionmentioning

confidence: 99%

Exact Solutions for Torsion and Warping of Axial-Loaded Beam-Columns Based on Matrix Stiffness Method

et al. 2022

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“…For the first issue, new analytical methods are essential for conducting detailed research on bridge towers by considering the axial force effect. Widely-used methods, such as the finite element method [16][17][18] and the Hencky bar-chain model [3,[19][20][21], may be suitable for solving the problem. In this paper, an effective and easy-to-use method, the matrix stiffness method (MSM), is used for analyzing the exact lateral load-carrying capacity of bridge towers.…”

Section: Guymentioning

confidence: 99%

Optimal Design of Crossbeam Stiffness Factor in Bridge Towers Using a Reliability-Based Approach

Pan,

Zhu,

Zhao

et al. 2023

Buildings

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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.

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“…They come in various forms to cater to diverse requirements, which have ignited extensive research efforts among numerous scholars into this structural system 2–5 . The buckling of steel structures is a key issue, and many scholars have conducted several research on buckling and structural optimization 6,7 . One such improvement is the use of corrugated steel plates in shear walls.…”

Section: Introductionmentioning

confidence: 99%

Seismic experiments and shear resistance prediction of multi‐celled corrugated‐plate CFST walls

Tong,

Zhang,

et al. 2024

Earthq Engng Struct Dyn

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Multi‐celled corrugated‐plate CFST walls (MC‐CFST walls) are innovative composite members for load bearing and energy dissipation. The corrugated steel plates effectively enhance the confinement capacity of the infilled concrete and reduce steel consumption. In this study, the seismic behavior of MC‐CFST walls was investigated through experimental, numerical, and theoretical analyses. Eight specimens were designed considering different key parameters, including the width and depth of the corrugated cell, the amplitude of the corrugated steel plate, and the type of boundary columns. These specimens were tested under axial compression and horizontal cyclic loading. The test results indicated that MC‐CFST walls exhibited excellent energy dissipation capacity and ductility. Specimens with boundary columns exhibited shear failure modes, while those without boundary columns exhibited flexural failure modes. Increasing the width of the corrugated cell or reducing the effective depth of the composite wall had a significant negative impact on its seismic performance. Subsequently, the finite element (FE) model was established and verified against experimental results. Finally, based on the full‐sectional plasticity assumption and the superposition principle, theoretical formulas for predicting the compression‐bending and shear capacities of MC‐CFST walls were proposed and validated against experimental data. The results showed that both theoretical formulas could effectively and accurately predict the shear resistance of MC‐CFST walls, providing valuable references for practical designs.

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Optimal Design of Triangular Arches against Buckling

Cited by 10 publications

References 16 publications

Exact Solutions for Torsion and Warping of Axial-Loaded Beam-Columns Based on Matrix Stiffness Method

Exact Solutions for Torsion and Warping of Axial-Loaded Beam-Columns Based on Matrix Stiffness Method

Optimal Design of Crossbeam Stiffness Factor in Bridge Towers Using a Reliability-Based Approach

Seismic experiments and shear resistance prediction of multi‐celled corrugated‐plate CFST walls

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