scholarly journals Analysis of simply supported wood beams at ambient and high temperatures

2018 ◽  
Vol 7 (2.23) ◽  
pp. 180 ◽  
Author(s):  
Elza M M Fonseca ◽  
Pedro J V Gouveia
Keyword(s):  
High Temperatures ◽  
Cross Sections ◽  
Beam Theory ◽  
Sufficient Accuracy ◽  
Load Bearing Capacity ◽  
Concentrated Load ◽  
Standard Methods ◽  
Simply Supported ◽  
Wood Beams ◽  
Safe Load

The main objective of this work is to present a methodology for safety analysis of simply supported wood beams at ambient and high temperatures with a concentrated load at mid-span. Sixteen different beam configurations will be studied. All calculations were conducted according the Eurocode 5, part 1-1 and part 1-2. During this study will be analyzed the safe load bearing capacity according standards and compared with the elastic and plastic load from beam theory. The beam theory can provide sufficient accuracy up to the point of instability. The standard methods are generally conservative and they are suitable to be used for design purposes with safety. The studied beam cross sections will be in glued laminated wood, as yellow birch, with characteristics equals to a Glulam GL28H. 

Solution for the Shear Lag Problem of U-Shaped Beam by Three Bar Stimulation Method

2013 ◽  
Vol 405-408 ◽  
pp. 1161-1165
Author(s):  
Ya Wen An ◽  
Qi Zhen Zheng ◽  
Ya Min Bao
Keyword(s):  
Differential Equation ◽  
Beam Theory ◽  
Shear Lag ◽  
Uniform Load ◽  
Concentrated Load ◽  
Simply Supported ◽  
Shaped Beam ◽  
Relative Stress ◽  
Stimulation Method ◽  
Theoretical Results

three bar stimulation method was adopted to build a differential equation about shear stress for U-shaped beam slab. Relative stress formula for simply supported beam which is subject to uniform load and concentrated load was obtained by solving and deducing differential equation.In order to compare with general beam theory simply,this paper introduced a concept of shear lag coefficient. Finally,combined with a actual example,after compared with measured value and other theoretical results,final result was satisfactory.

Interaction Curves for Shear and Bending of Plastic Beams

1957 ◽  
Vol 24 (3) ◽  
pp. 453-456
Author(s):  
P. G. Hodge
Keyword(s):  
General Formula ◽  
Plane Stress ◽  
Elementary Theory ◽  
Beam Theory ◽  
Present Theory ◽  
Concentrated Load ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
Interaction Curves

Abstract Interaction curves are presented for plastic beams subject to combined shear and bending. A general formula is obtained and specific curves are drawn for rectangular and I-sections. A simply supported beam with a concentrated load is considered as an example. The results are compared with those of simple beam theory and with available plane-stress solutions. It is concluded that the elementary theory is adequate for height-to-length ratios of less than 0.1, while the present theory is useful in the range from 0.1 to 1.0.

Vibration of Beams and Plate Strips With Three-Dimensional Flexibility

1989 ◽  
Vol 56 (1) ◽  
pp. 228-231 ◽  
Author(s):  
Manuel Stein
Keyword(s):  
Cross Sections ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Beam Theory ◽  
Vibration Modes ◽  
Natural Vibrations ◽  
Accurate Representation ◽  
Simply Supported

Studies making use of higher vibration modes and frequencies have indicated a need for a more accurate beam theory. Equations of motion are developed here that give a more accurate representation of the dynamic behaivor of a beam than conventional beam theory. Results are obtained using these equations for the natural vibrations of simply-supported aluminum beams of rectangular cross-sections. These results are compared to results from conventional beam theory, and they are examined to identify where various effects are important.

Analysis of Rigidity of a Shaft With a Crack Diagonal

2007 ◽  
Author(s):  
Homero J. Rabiela ◽  
Isai´as H. Cruz ◽  
Gilberto A. Miranda ◽  
Mario G. Villeda ◽  
Victor C. Sua´rez ◽  
...  
Keyword(s):  
Cross Sections ◽  
Functional Relationship ◽  
Concentrated Load ◽  
Second Moment ◽  
Simply Supported ◽  
Elastic Range ◽  
Static Conditions ◽  
Diagonal Crack

In this work the rigidity of a shaft with diagonal crack in its half part in its elastic range under static conditions simply supported in its ends and with concentrated load to the center is determined. The functional relationship for the variation of the second moment of area of their different cross-sections is deduced. For double numeric integration the slope and the deformation of the shaft is calculated. The frequency in which the cracked system would enter in resonance is calculated. The rigidity of the shaft with crack is smaller that the rigidity of the shaft without crack. Based on the results of the study is concluded that the rigidity of the shaft with crack can be evaluated with the procedure described to determine a range of frequencies in which the system would enter in resonance. Therefore the system would be unstable and detectable.

Dynamic Instability Analysis and Design Charts of Curved Panels with Linearly Varying Periodic In-Plane Load

2021 ◽  
pp. 2150130
Author(s):  
G. Patel ◽  
A. N. Nayak ◽  
A. K. L. Srivastava
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Dynamic Instability ◽  
Excitation Frequency ◽  
Instability Region ◽  
Concentrated Load ◽  
Simply Supported ◽  
Finite Element Software ◽  
Design Charts ◽  
Curved Panels

The present paper reports an extensive study on dynamic instability characteristics of curved panels under linearly varying in-plane periodic loading employing finite element formulation with a quadratic isoparametric eight nodded element. At first, the influences of three types of linearly varying in-plane periodic edge loads (triangular, trapezoidal and uniform loads), three types of curved panels (cylindrical, spherical and hyperbolic) and six boundary conditions on excitation frequency and instability region are investigated. Further, the effects of varied parameters, such as shallowness parameter, span to thickness ratio, aspect ratio, and Poisson’s ratio, on the dynamic instability characteristics of curved panels with clamped–clamped–clamped–clamped (CCCC) and simply supported-free-simply supported-free (SFSF) boundary conditions under triangular load are studied. It is found that the above parameters influence significantly on the excitation frequency, at which the dynamic instability initiates, and the width of dynamic instability region (DIR). In addition, a comparative study is also made to find the influences of the various in-plane periodic loads, such as uniform, triangular, parabolic, patch and concentrated load, on the dynamic instability behavior of cylindrical, spherical and hyperbolic panels. Finally, typical design charts showing DIRs in non-dimensional forms are also developed to obtain the excitation frequency and instability region of various frequently used isotropic clamped spherical panels of any dimension, any type of linearly varying in-plane load and any isotropic material directly from these charts without the use of any commercially available finite element software or any developed complex model.

scholarly journals A Kollár and Pluzsik anisotropic composite beam theory for arbitrary multicelled cross sections

2016 ◽  
Vol 35 (23) ◽  
pp. 1696-1711 ◽  
Author(s):  
Danilo S Victorazzo ◽  
Andre De Jesus
Keyword(s):  
Finite Element ◽  
Cross Sections ◽  
Composite Beam ◽  
Linear Equations ◽  
Beam Theory ◽  
Element Formulation ◽  
Compliance Matrix ◽  
Asymmetric System ◽  
Anisotropic Composite ◽  
Stiffness Matrices

In this paper we extend Kollár and Pluzsik’s thin-walled anisotropic composite beam theory to include multiple cells with open branches and booms, and present a finite element formulation utilizing the stiffness matrix obtained from this theory. To recover the 4 × 4 compliance matrix of a beam containing N closed cells, we solve an asymmetric system of 2N + 4 linear equations four times with unitary section loads and extract influence coefficients from the calculated strains. Finally, we compare 4 × 4 stiffness matrices of a multicelled beam using this method against matrices obtained using the finite element method to demonstrate accuracy. Similarly to its originating theory, the effects of shear deformation and restrained warping are assumed negligible.

Designing Compressed Reinforcement Cross-Sections by Curvature and Nominal Stiffness Methods

2015 ◽  
Vol 797 ◽  
pp. 69-78
Author(s):  
Krzysztof Kamiński ◽  
Piotr Nowicki
Keyword(s):  
Reinforced Concrete ◽  
Comparative Analysis ◽  
Cross Sections ◽  
Concrete Columns ◽  
Computer Programs ◽  
Significant Issue ◽  
Reinforced Concrete Columns ◽  
Small Eccentricity ◽  
Standard Methods ◽  
Surface Reinforcement

The paper attempts to discuss the still significant issue of methods of design of the reinforced concrete columns according to PN-EN 1992-1-1:2008/A1:2015-03. Two algorithms of the dimensioning sections were developed according to two standard methods of dimensioning eccentrically compressed sections: the method of nominal stiffness (NS) and the method of nominal curvature (NC). Using both algorithms, computer programs in Excel were created. A comparative analysis of several examples of calculation were performed to compare the results of dimensioning of sections eccentrically compressed. The results obtained by the NC method give about 10% less surface reinforcement when loaded with big eccentricity and over 50% less when small eccentricity is applied.

scholarly journals Flexural Interpretation of Simply Supported Laminated Composite Beam

2020 ◽  
Vol 8 (5) ◽  
pp. 3559-3565
Keyword(s):  
Shear Deformation ◽  
Composite Beam ◽  
Laminated Composite ◽  
Beam Theory ◽  
Composite Beams ◽  
Shear Stresses ◽  
Bending Stress ◽  
Simply Supported ◽  
Laminated Composite Beam ◽  
Laminated Composite Beams

In this Paper, the analysis of simply supported laminated composite beam having uniformly distributed load is performed. The solutions obtained in the form of the displacements and stresses for different layered cross ply laminated composite simply supported beams subjected uniformly distributed to load. Different aspect ratio consider for different results in terms of displacement, bending stress and shear stresses. The shear stresses are calculated with the help of equilibrium equation and constitutive relationship. Using displacement field including trigonometric function of laminated composite beams are derived from virtual displacement principle. There are axial displacement, transverse displacement, bending stress and shear stresses. In addition, Euler-Bernoulli (ETB), First order shear deformation beam theory (FSDT), Higher order shear deformation beam theory (HSDT) and Hyperbolic shear deformation beam theory (HYSDT) solution have been made for comparison and better accuracy of solutions and results of static analyses of laminated composite beams for simply supported laminated composite beam.

Nonlinear Vibration Analysis of Functionally Graded Nanobeam Using Homotopy Perturbation Method

2016 ◽  
Vol 9 (1) ◽  
pp. 144-156 ◽  
Author(s):  
Majid Ghadiri ◽  
Mohsen Safi
Keyword(s):  
Differential Equation ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Nonlinear Partial Differential Equation ◽  
Beam Theory ◽  
Nonlocal Elasticity Theory ◽  
Functionally Graded ◽  
Simply Supported ◽  
Homotopy Perturbation ◽  
Functionally Graded Nanobeam

AbstractIn this paper, He's homotopy perturbation method is utilized to obtain the analytical solution for the nonlinear natural frequency of functionally graded nanobeam. The functionally graded nanobeam is modeled using the Eringen's nonlocal elasticity theory based on Euler-Bernoulli beam theory with von Karman nonlinearity relation. The boundary conditions of problem are considered with both sides simply supported and simply supported-clamped. The Galerkin's method is utilized to decrease the nonlinear partial differential equation to a nonlinear second-order ordinary differential equation. Based on numerical results, homotopy perturbation method convergence is illustrated. According to obtained results, it is seen that the second term of the homotopy perturbation method gives extremely precise solution.

Response of a Simply Supported Timoshenko Beam to a Purely Random Gaussian Process

1958 ◽  
Vol 25 (4) ◽  
pp. 496-500
Author(s):  
J. C. Samuels ◽  
A. C. Eringen
Keyword(s):  
Timoshenko Beam ◽  
Beam Theory ◽  
Beam Equation ◽  
Mean Square ◽  
Bending Stress ◽  
Random Loading ◽  
Simply Supported ◽  
The Mean ◽  
Timoshenko Beam Equation ◽  
Classical Beam Theory

Abstract The generalized Fourier analysis is applied to the damped Timoshenko beam equation to calculate the mean-square values of displacements and bending stress, resulting from purely random loading. Compared with the calculations, based on the classical beam theory, it was found that the displacement correlations of both theories were in excellent agreement. Moreover, the mean square of the bending stress, contrary to the results of the classical beam theory, was found to be convergent. Computations carried out with a digital computer are plotted for both theories.

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