The buckling load of an elastically supported cantilevered column with continuously varying cross section and distributed axial load

1973 ◽  
Vol 42 (6) ◽  
pp. 355-359 ◽  
Author(s):  
J. Gl�ck
Keyword(s):  
Cross Section ◽  
Axial Load ◽  
Buckling Load ◽  
Elastically Supported

scholarly journals SERIES SOLUTION OF LARGE DEFORMATION OF A BEAM WITH ARBITRARY VARIABLE CROSS SECTION UNDER AN AXIAL LOAD

2009 ◽  
Vol 51 (1) ◽  
pp. 10-33 ◽  
Author(s):  
SHIJUN LIAO
Keyword(s):  
Differential Equations ◽  
Cross Section ◽  
Axial Load ◽  
Nonlinear Differential Equations ◽  
Variable Cross Section ◽  
Variable Coefficients ◽  
Buckling Load ◽  
Moment Of Inertia ◽  
Variable Cross ◽  
Critical Buckling Load

AbstractA general analytic approach is proposed for nonlinear eigenvalue problems governed by nonlinear differential equations with variable coefficients. This approach is based on the homotopy analysis method for strongly nonlinear problems. As an example, a beam with arbitrary variable cross section acted on by a compressive axial load is used to show its validity and effectiveness. This approach provides us with great freedom to transfer the original nonlinear buckling equation with variable coefficients into an infinite number of linear differential equations with constant coefficients that are much easier to solve. More importantly, it provides us with a convenient way to guarantee the convergence of solution series. As an example, the beam displacement and the critical buckling load can be obtained for arbitrary variable cross sections. The influence of nonuniformity of moment of inertia is investigated in detail and the optimal distributions of moment of inertia are studied. It is found that the critical buckling load of a beam with the optimal distribution of moment of inertia can be approximately 21–22% larger than that of a uniform beam with the same average moment of inertia. Mathematically, this approach is rather general and thus can be used to solve many other linear/nonlinear differential equations with variable coefficients.

Instability of an Elastically Supported Beam under a Travelling Inertia Load

1970 ◽  
Vol 12 (5) ◽  
pp. 373-376 ◽  
Author(s):  
D. E. Newland
Keyword(s):  
Dynamic Instability ◽  
Buckling Load ◽  
Railway Track ◽  
Axial Buckling ◽  
Elastically Supported ◽  
Bending Wave

It is shown that an unstable bending wave may be excited in an elastically supported beam by a travelling inertia load. Since the occurrence of this dynamic instability reduces the axial buckling load of the beam, the result is relevant to present studies of the temperature buckling of continuous welded railway track.

scholarly journals A Numerical Study of the Effect of Component Dimensions on the Critical Buckling Load of a GFRP Composite Strut under Uniaxial Compression

Materials ◽  
2020 ◽  
Vol 13 (4) ◽  
pp. 931 ◽  
Author(s):  
Quoc Hoan Doan ◽  
Duc-Kien Thai ◽  
Ngoc Long Tran
Keyword(s):  
Uniaxial Compression ◽  
Cross Section ◽  
Numerical Study ◽  
Slenderness Ratio ◽  
Thickness Ratio ◽  
Buckling Load ◽  
Critical Buckling Load ◽  
Channel Section ◽  
Gfrp Composite ◽  
Thin Walled

In the practical design of thin-walled composite columns, component dimensions should be wisely designed to meet the buckling resistance and economic requirements. This paper provides a novel and useful investigation based on a numerical study of the effects of the section dimensions, thickness ratio, and slenderness ratio on the critical buckling load of a thin-walled composite strut under uniaxial compression. The strut was a channel-section-shaped strut and was made of glass fiber-reinforced polymer (GFRP) composite material by stacking symmetrical quasi-isotropic layups using the autoclave technique. For the purpose of this study, a numerical finite element model was developed for the investigation by using ABAQUS software. The linear and post-buckling behavior analysis was performed to verify the results of the numerical model with the obtained buckling load from the experiment. Then, the effects of the cross-section dimensions, thickness ratio, and slenderness ratio on the critical buckling load of the composite strut, which is determined using an eigenvalue buckling analysis, were investigated. The implementation results revealed an insightful interaction between cross-section dimensions and thickness ratio and the buckling load. Based on this result, a cost-effective design was recommended as a useful result of this study. Moreover, a demarcation point between global and local buckling of the composite strut was also determined. Especially, a new design curve for the channel-section GFRP strut, which is governed by the proposed constitutive equations, was introduced to estimate the critical buckling load based on the input component dimension.

scholarly journals Investigation of Parameters Affecting the Equivalent Yield Curvature of Reinforced Concrete Columns

Materials ◽  
2020 ◽  
Vol 13 (7) ◽  
pp. 1594
Author(s):  
Umut Hasgul
Keyword(s):  
Reinforced Concrete ◽  
Cross Section ◽  
Axial Load ◽  
Concrete Columns ◽  
Load Level ◽  
Combined Effects ◽  
Reinforced Concrete Columns ◽  
Independent Effects ◽  
Equivalent Yield ◽  
Section Dimension

In this study, the response quantities affecting the equivalent yield curvature, which is important in the deformation-based seismic design and assessment of structural systems, are investigated for reinforced concrete columns with a square cross-section. In this context, the equivalent yield curvatures were determined by conducting moment–curvature analyses on various column models, in which the axial load level, cross-section dimension, longitudinal reinforcement ratio, and concrete compression strength were changed parametrically, and the independent and/or combined effects of the relevant parameters were discussed. Depending on the axial load levels of P/Agfc′ < 0.3, P/Agfc′ = 0.3, and P/Agfc′ > 0.3 for the considered columns, the yielding of reinforcement, yielding of reinforcement and/or concrete crushing, and concrete crushing governed the yield conditions, respectively. It can be noted that the cross-section dimension and axial load level became the primary parameters. Even though the independent effects with regard to particular parameters remained at minimal levels, the combined effects of them with the axial load became important in terms of the equivalent yield curvature.

NONLINEAR ANALYSIS OF A BARBELL-SHAPED CROSS SECTION WALL USING FIBER SLICE

2014 ◽  
Vol 1 (1) ◽  
Author(s):  
Dae-Han Jun ◽  
Pyeong-Doo Kang
Keyword(s):  
Reinforced Concrete ◽  
Analytical Model ◽  
Cross Section ◽  
Cross Sections ◽  
Axial Load ◽  
Nonlinear Response ◽  
Shear Walls ◽  
Lateral Loads ◽  
Fiber Element ◽  
Shaped Cross Section

Reinforced concrete shear walls are effective for resisting lateral loads imposed by wind or earthquakes. This study investigates the effectiveness of a wall fiber element in predicting the flexural nonlinear response of reinforced concrete shear walls. Model results are compared with experimental results for reinforced concrete shear walls with barbell-shaped cross sections without axial load. The analytical model is calibrated and the test measurements are processed to allow for a direct comparison of the predicted and measured flexural responses. Response results are compared at top displacements on the walls. Results obtained in the analytical model for barbell-shaped cross section wall compared favorably with experimentally responses for flexural capacity, stiffness, and deformability.

Prediction of axial hysteresis in locked coil ropes

1996 ◽  
Vol 31 (5) ◽  
pp. 341-351 ◽  
Author(s):  
M Raoof ◽  
I Kraincanic
Keyword(s):  
Theoretical Model ◽  
Cross Section ◽  
Axial Load ◽  
Dynamic Instability ◽  
Contact Forces ◽  
Damping Capacity ◽  
Outermost Layer ◽  
Parametric Studies ◽  
Load Perturbations ◽  
Practical Implications

In published literature, the strand constructions dealt with have almost invariably involved only wires which are circular in cross-section. There are, however, instances when shaped wires are used in, for example, half-lock and full-lock coil constructions. The paper reports details of a theoretical model which enables an insight to be gained into various characteristics of axially loaded lock coil ropes. The model is based on an extension of a previously reported orthotropic sheet concept and provides a fairly simple means of estimating wire kinematics, interwire/interlayer contact forces, effective axial stiffnesses and axial hysteresis in axially preloaded locked coil ropes experiencing uniform cyclic axial load perturbations. The theory takes interwire contact deformations and friction into account. Final numerical results based on theoretical parametric studies on some substantial cables highlight the substantial role that the outermost layer(s) with shaped wires play as regards the overall axial damping capacity of fully bedded-in (old) locked coil ropes, and it is found that (for the same lay angles and outer diameters) axial hysteresis in locked coil ropes is generally higher than spiral strands which are composed of only round wires. This finding may have significant practical implications in terms of the design against dynamic instability of structures supported by such cables.

Optimal Forms of Shallow Cylindrical Panels With Respect to Vibration and Stability

1986 ◽  
Vol 53 (1) ◽  
pp. 135-140 ◽  
Author(s):  
R. H. Plaut ◽  
L. W. Johnson
Keyword(s):  
Surface Area ◽  
Fundamental Frequency ◽  
Axial Load ◽  
Cylindrical Panel ◽  
Buckling Load ◽  
Material Surface ◽  
Uniform Thickness ◽  
Simply Supported ◽  
Cylindrical Panels

Thin, shallow, elastic, cylindrical panels with rectangular planform are considered. We seek the midsurface form which maximizes the fundamental frequency of vibration, and the form which maximizes the buckling value of a uniform axial load. The material, surface area, and uniform thickness of the panel are specified. The curved edges are simply supported, while the straight edges are either simply supported or clamped. For the clamped case, the optimal panels have zero slope at the edges. In the examples, the maximum fundamental frequency is up to 12 percent higher than that of the corresponding circular cylindrical panel, while the buckling load is increased by as much as 95 percent. Most of the solutions are bimodal, while the rest are either unimodal or trimodal.

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