DIAGRAMS FOR STRESS AND DEFLECTION PREDICTION IN CROSS-LAMINATED TIMBER (CLT) PANELS WITH NON-CLASSICAL BOUNDARY CONDITIONS

Invention of cross-laminated timber (CLT) was a big milestone for building with wood. Due tonovelty of CLT and timber’s complex mechanical behavior, the existing design codes cover onlyrectangular CLT panels, simply supported along 2 parallel or all 4 edges, making numerical methodsnecessary in other cases. This paper presents a practical engineering tool for stress and deflectionprediction of CLT panels with non-classical boundary conditions, based on the software for thecomputational analysis of laminar composites, previously developed by the authors. Diagramsapplicable in engineering practice are developed for some common cases. The presentedmethodology could be a basis for more detailed design handbooks and guidelines for various layoutsof CLT panels and different types of loadings.

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Buckling of Composite and Homogeneous Isotropic Cylindrical Shells Under Axial and Radial Loading

Journal of Applied Mechanics ◽

10.1115/1.3564772 ◽

1969 ◽

Vol 36 (4) ◽

pp. 791-798 ◽

Cited By ~ 20

Author(s):

M. M. Lei ◽

Shun Cheng

Keyword(s):

Boundary Conditions ◽

Axial Compression ◽

Circular Cylindrical Shell ◽

Radial Pressure ◽

Buckling Load ◽

Simply Supported ◽

Classical Boundary ◽

Axial Compressive Stress ◽

Radial Loading ◽

Geometrical Dimensions

A theoretical analysis of the buckling of a multilayered thin orthotropic composite circular cylindrical shell of finite length, subjected to (a) uniform axial compression, and (b) axial compression combined with radial pressure, is presented. At each end of the shell, four boundary conditions are satisfied. Four combinations of boundary conditions for simply supported shells, and four combinations of boundary conditions for clamped shells, are treated. These boundary conditions are reduced to the vanishing of a fourth-order determinant. Buckling loads for boron-epoxy composite shells are determined and the results are shown in a series of diagrams. The effect of boundary conditions on the buckling load for various geometrical dimensions of composite cylinders is investigated. Details of the boundary conditions are shown to have strong influence on the buckling load of the shell. The minimum critical axial compression for a simply supported shell with boundary conditions SS1 is as low as 79 percent of the minimum critical axial compression for a shell with classical boundary conditions SS3. As a special case of a composite shell, the minimum critical axial compressive stress for a homogeneous, isotropic, simply supported shell with end conditions SS1 is found to be 43.7 percent of the classical critical stress.

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Frequency Equations and Modes of Free Vibrations of Rectangular Plates with Various Edge Conditions

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1243/pime_proc_1994_208_133_02 ◽

1994 ◽

Vol 208 (5) ◽

pp. 307-319 ◽

Cited By ~ 15

Author(s):

C W Bert ◽

M Malik

Keyword(s):

Boundary Conditions ◽

Exact Solutions ◽

Free Vibrations ◽

Edge Condition ◽

Rectangular Plates ◽

Simply Supported ◽

Aspect Ratios ◽

Edge Conditions ◽

Classical Boundary ◽

Free Edges

This paper considers linear free vibrations of thin isotropic rectangular plates with combinations of the classical boundary conditions of simply supported, clamped and free edges and the mathematically possible condition of guided edges. The total number of plate configurations with the classical boundary conditions are known to be twenty-one. The inclusion of the guided edge condition gives rise to an additional thirty-four plate configurations. Of these additional cases, twenty-one cases have exact solutions for which frequency equations in explicit or transcendental form may be obtained. The frequency equations of these cases are given and, for each case, results of the first nine mode frequencies are tabulated for a range of the plate aspect ratios.

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Exact Elasticity Solution for the Density Functionally Gradient Beam by Using Airy Stress Function

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.110-116.4669 ◽

2011 ◽

Vol 110-116 ◽

pp. 4669-4676 ◽

Cited By ~ 2

Author(s):

Alireza R. Daneshmehr ◽

Saeed Momeni ◽

Mahdi Reza Akhloumadi

Keyword(s):

Boundary Conditions ◽

Stress Function ◽

Rectangular Cross Section ◽

Airy Stress Function ◽

Uniform Load ◽

Functionally Gradient ◽

Different Types ◽

Classical Boundary ◽

Clamped Beams ◽

Fixed End

In this paper the problem of a density-functionally gradient beam subjected to uniform load is studied. Airy stress function methodology is used to obtain a set of analytical solutions for simply supported and clamped beams subjected to uniform load. A stress function in the form of polynomial is proposed and determined. The treatment for fixed-end boundary conditions is the same as that presented by Timoshenko and Goodier (1970). By this method all of the analytical plane-stress solutions can be obtained for a uniformly loaded isotropic beam with rectangular cross section under different types of classical boundary conditions.

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Experimental Modal Analysis of Appropriate Boundary Conditions for the Evaluation of Cross-Laminated Timber Panels for an In-Line Approach

Forest Products Journal ◽

10.13073/fpj-d-20-00062 ◽

2021 ◽

Vol 71 (2) ◽

pp. 161-170

Author(s):

Adam Faircloth ◽

Loic Brancheriau ◽

Hassan Karampour ◽

Stephen So ◽

Henri Bailleres ◽

...

Keyword(s):

Finite Element Analysis ◽

Finite Element ◽

Boundary Conditions ◽

Modal Analysis ◽

Experimental Testing ◽

Critical Role ◽

Element Analysis ◽

Cross Laminated Timber ◽

Simply Supported ◽

The Finite Element Analysis

Abstract Transverse modal analysis of timber panels is a proven effective alternative method for approximating a material's elastic constants. Specific testing configurations, such as boundary conditions (BC) and location of sensor and impact, play a critical role in the accuracy of the results obtained from the experimental assessment. This article investigates signal-specific details, such as the signal quality factor, that directly relate to the damping properties and internal friction as well as frequency shifting obtained from six different BCs. A freely supported (FFFF), opposing minor sides (shorter length) simply supported, and major sides (longest length) free (SFSF), as well as the reverse of the SFSF configuration with minor sides free and major lengths simply supported (FSFS) and all sides simply supported (SSSS) setup, are investigated. Variations into the proposed methods used to achieve an FFFF supported system are also considered. A combination of experimental testing in parallel with finite element analysis was conducted to re-create the setup that would be used within a manufacturing facility for nondestructive assessment of full-size cross-laminated timber panels. The differences between all BC configurations for their resonance frequency quality and location indicate that a freely supported system provides higher-resolution results, good comparison of less than 10 percent error with the finite element analysis and experimental results, and advantages in a simple experimental setup for the intended application.

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Withdrawal Properties of Self-Tapping Screws in Japanese larch (Larix kaempferi (Lamb.) Carr.) Cross Laminated Timber

Forests ◽

10.3390/f12050524 ◽

2021 ◽

Vol 12 (5) ◽

pp. 524

Author(s):

Junhua Xu ◽

Shuangbao Zhang ◽

Guofang Wu ◽

Yingchun Gong ◽

Haiqing Ren

Keyword(s):

Regression Model ◽

Engineering Design ◽

Wood Species ◽

Japanese Larch ◽

Effective Length ◽

Larix Kaempferi ◽

Cross Laminated Timber ◽

The World ◽

Different Types ◽

Length Increment

With the increasing popularity of cross-laminated timber (CLT) constructions around the world, there have been attempts to produce CLT using local wood species in different countries, such as Japanese larch (Larix kaempferi (Lamb.) Carr.) in China. Thus, the need to investigate the connection performance also increases to support the design and construction of CLT buildings using local wood species. In this study, the withdrawal properties of three different types of self-tapping screws (STS), with a diameter of 6 mm, 8 mm, and 11 mm, were tested with Japanese larch CLT. The results revealed that the withdrawal strength of STS increased with increasing density and effective length, but decreased with an increasing diameter. With a density increment of 0.05 g/cm3, the withdrawal strength increased by an average of 9.4%. With an effective length increment of 24 mm, the withdrawal strength increased by an average of 1.4%. An empirical regression model was adopted to predict the withdrawal strength of Japanese larch CLT based on the results, which can be used for potential engineering design of CLT connections using STS.

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The Bending, Buckling, and Flexural Vibration of Simply Supported Polygonal Plates by Point-Matching

Journal of Applied Mechanics ◽

10.1115/1.3641670 ◽

1961 ◽

Vol 28 (2) ◽

pp. 288-291 ◽

Cited By ~ 51

Author(s):

H. D. Conway

Keyword(s):

Hydrostatic Pressure ◽

Boundary Conditions ◽

Flexural Vibration ◽

Frequency Equation ◽

Numerical Results ◽

Special Technique ◽

Point Matching ◽

Buckling Loads ◽

Simply Supported ◽

Flexural Vibrations

The bending by uniform lateral loading, buckling by two-dimensional hydrostatic pressure, and the flexural vibrations of simply supported polygonal plates are investigated. The method of meeting the boundary conditions at discrete points, together with the Marcus membrane analog [1], is found to be very advantageous. Numerical examples include the calculation of the deflections and moments, and buckling loads of triangular square, and hexagonal plates. A special technique is then given, whereby the boundary conditions are exactly satisfied along one edge, and an example of the buckling of an isosceles, right-angled triangle plate is analyzed. Finally, the frequency equation for the flexural vibrations of simply supported polygonal plates is shown to be the same as that for buckling under hydrostatic pressure, and numerical results can be written by analogy. All numerical results agree well with the exact solutions, where the latter are known.

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A semi-analytical three-dimensional free vibration analysis of functionally graded curved panels integrated with piezoelectric layers

Science and Engineering of Composite Materials ◽

10.1515/secm-2013-0225 ◽

2014 ◽

Vol 21 (4) ◽

pp. 571-587 ◽

Cited By ~ 5

Author(s):

Hamid Reza Saeidi Marzangoo ◽

Mostafa Jalal

Keyword(s):

Boundary Conditions ◽

Vibration Analysis ◽

Natural Frequencies ◽

Differential Quadrature Method ◽

Three Dimensional ◽

Free Vibration Analysis ◽

Functionally Graded ◽

Simply Supported ◽

Piezoelectric Layers ◽

Curved Panels

AbstractFree vibration analysis of functionally graded (FG) curved panels integrated with piezoelectric layers under various boundary conditions is studied. A panel with two opposite edges is simply supported, and arbitrary boundary conditions at the other edges are considered. Two different models of material property variations based on the power law distribution in terms of the volume fractions of the constituents and the exponential law distribution of the material properties through the thickness are considered. Based on the three-dimensional theory of elasticity, an approach combining the state space method and the differential quadrature method (DQM) is used. For the simply supported boundary conditions, closed-form solution is given by making use of the Fourier series expansion, and applying the differential quadrature method to the state space formulations along the axial direction, new state equations about state variables at discrete points are obtained for the other cases such as clamped or free-end conditions. Natural frequencies of the hybrid curved panels are presented by solving the eigenfrequency equation, which can be obtained by using edges boundary conditions in this state equation. The results obtained for only FGM shell is verified by comparing the natural frequencies with the results obtained in the literature.

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Vibrational Analysis of a Single-Layered Nanoporous Graphene Membrane

NANO ◽

10.1142/s1793292016500430 ◽

2016 ◽

Vol 11 (04) ◽

pp. 1650043 ◽

Cited By ~ 4

Author(s):

Haw-Long Lee ◽

Win-Jin Chang

Keyword(s):

Boundary Conditions ◽

Vibrational Analysis ◽

Atomic Scale ◽

Good Correspondence ◽

Graphene Layers ◽

Simply Supported ◽

Vibrational Behavior ◽

Fundamental Frequencies ◽

Nanoporous Graphene ◽

New Applications

In this study, we use the atomic-scale finite element method to investigate the vibrational behavior of the armchair- and zigzag-structured nanoporous graphene layers with simply supported-free-simply supported-free (SFSF) and clamped-free-free-free (CFFF) boundary conditions. The fundamental frequencies computed for the graphene layers without pores are compared with the results of previous studies. We observe very good correspondence of our results with that of the other studies in all the considered cases. For the armchair- and zigzag-structured nanoporous graphenes with SFSF and CFFF boundary conditions, the frequencies decrease with increasing porosity. When the positions of the pores are symmetric with respect to the center of the graphene, the frequency of the zigzag nanoporous graphene is higher than that of the armchair one. To the best of our knowledge, this is first study investigating the relation between the vibrational behavior and porosity of nanoporous graphene layers, which is essential for tuning the material/structural design and exploring new applications for nanoporous graphenes.

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Natural Frequencies of Parallelogrammic Plates Using Characteristic Orthogonal Polynomials in Rayleigh-Ritz Method

ASME 1992 International Computers in Engineering Conference: Volume 2 — Finite Element Techniques; Computers in Education; Robotics and Controls ◽

10.1115/cie1992-0083 ◽

1992 ◽

Author(s):

L. T. Lee ◽

W. F. Pon

Keyword(s):

Boundary Conditions ◽

Coordinate System ◽

Orthogonal Polynomials ◽

Natural Frequencies ◽

Ritz Method ◽

Energy Functional ◽

Comprehensive Treatment ◽

Energy Functionals ◽

Simply Supported ◽

Cartesian Coordinate

Abstract Natural frequencies of parallelogrammic plates are obtained by employing a set of beam characteristic orthogonal polynomials in the Rayleigh-Ritz method. The orthogonal polynomials are generalted by using a Gram-Schmidt process, after the first member is constructed so as to satisfy all the boundary conditions of the corresponding beam problems accompanying the plate problems. The strain energy functional and kinetic energy functionals are transformed from Cartesian coordinate system to a skew coordinate system. The natural frequencies obtained by using the orthogonal polynomial functions are compared with those obtained by other methods with all four edges clamped boundary conditions and greet agreements are found between them. The natural frequencies for parallelogrammic plates with other boundary conditions, such as four edges simply supported, clamped-free and simply supported-free, are also obtained. This method is considered as a better and accurate comprehensive treatment for this type of problems.

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Standardization of Three Efficient Footbridges: Von Mises, Monocontentio and Bicontentio Prototypes.

10.24904/footbridge2022.106 ◽

2021 ◽

Author(s):

Mario Guisasola

Keyword(s):

Boundary Conditions ◽

Structural Characteristics ◽

Structural Behavior ◽

Bending Moments ◽

Variable Depth ◽

Constant Depth ◽

Simply Supported ◽

Vertical Walls ◽

Basic Concepts ◽

Von Mises

The Von Mises, Monocontentio and Bicontentio footbridges are three parameterized metal bridge whose main structural characteristics are their variable depth depending on the applied stress and the embedding of abutments. Its use is considered suitable for symmetrical or asymmetrical topographies with slopes or vertical walls on one or both edges. The footbridges include spans spaced apart by 20 to 66 meters, and are between 2 to 4.5 meters wide.Its design is based on five basic concepts: integration in the geometry of the environment; continuous search for simplicity; design based on a geometry that emanates from structural behavior; unitary and round forms; and long- lasting details.The structural behavior of these prototypes has been compared with three types of constant-depth metal beams: the bridge simply supported, and the bridge embedded on one or both sides.The embedding of abutments, and the adoption of a variation of depth adapted to the bending moments diagrams, allow for more efficient and elegant forms which are well-adapted to the boundary conditions.

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