Shear in Structural Stability: On the Engesser–Haringx Discord

2010 ◽  
Vol 77 (3) ◽  
Author(s):  
Johan Blaauwendraad
Keyword(s):  
Structural Engineering ◽  
Flexural Rigidity ◽  
Thought Experiment ◽  
Quantitative Information ◽  
Buckling Load ◽  
Structural Members ◽  
Buckling Loads ◽  
Critical Buckling Load ◽  
Helical Springs ◽  
Wide Range

Since Haringx introduced his stability hypothesis for the buckling prediction of helical springs over 60 years ago, discussion is on whether or not the older hypothesis of Engesser should be replaced in structural engineering for stability studies of shear-weak members. The accuracy and applicability of both theories for structures has been subject of study in the past by others, but quantitative information about the accuracy for structural members is not provided. This is the main subject of this paper. The second goal is to explain the experimental evidence that the critical buckling load of a sandwich beam-column surpasses the shear buckling load GAs, which is commonly not expected on basis of the Engesser hypothesis. The key difference between the two theories regards the relationship, which is adopted in the deformed state between the shear force in the beam and the compressive load. It is shown for a wide range of the ratio of shear and flexural rigidity to which extent the two theories agree and/or conflict with each other. The Haringx theory predicts critical buckling loads which are exceeding the value GAs, which is not possible in the Engesser approach. That sandwich columns have critical buckling loads larger than GAs does, however, not imply the preference of the Haringx hypothesis. This is illustrated by the introduction of the thought experiment of a compressed cable along the central axis of a beam-column in deriving governing differential equations and finding a solution for three different cases of increasing complexity: (i) a compressed member of either flexural or shear deformation, (ii) a compressed member of both flexural and shear deformations, and (iii) a compressed sandwich column. It appears that the Engesser hypothesis leads to a critical buckling load larger than GAs for layered cross section shapes and predicts the sandwich behavior very satisfactory, whereas the Haringx hypothesis then seriously overestimates the critical buckling load. The fact that the latter hypothesis is perfectly confirmed for helical springs (and elastomeric bearings) has no meaning for shear-weak members in structural engineering. Then, the Haringx hypothesis should be avoided. It is strongly recommended to investigate the stability of the structural members on the basis of the Engesser hypothesis.

Critical Buckling Load of Triple-Walled Carbon Nanotube Based on Nonlocal Elasticity Theory

2020 ◽  
Vol 62 ◽  
pp. 108-119
Author(s):  
Tayeb Bensattalah ◽  
Ahmed Hamidi ◽  
Khaled Bouakkaz ◽  
Mohamed Zidour ◽  
Tahar Hassaine Daouadji
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Axial Compression ◽  
Buckling Load ◽  
Small Scale ◽  
Beam Model ◽  
Buckling Loads ◽  
Critical Buckling Load ◽  
Nonlocal Continuum Theory ◽  
Walled Carbon Nanotubes

The present paper investigates the nonlocal buckling of Zigzag Triple-walled carbon nanotubes (TWCNTs) under axial compression with both chirality and small scale effects. Based on the nonlocal continuum theory and the Timoshenko beam model, the governing equations are derived and the critical buckling loads under axial compression are obtained. The TWCNTs are considered as three nanotube shells coupled through the van der Waals interaction between them. The results show that the critical buckling load can be overestimated by the local beam model if the small-scale effect is overlooked for long nanotubes. In addition, a significant dependence of the critical buckling loads on the chirality of zigzag carbon nanotube is confirmed, and these are then compared with: A single-walled carbon nanotubes (SWCNTs); and Double-walled carbon nanotubes (DWCNTs). These findings are important in mechanical design considerations and reinforcement of devices that use carbon nanotubes.

scholarly journals Buckling of nanobeams and nanorods with cracks

2019 ◽  
Author(s):  
Hina Arif ◽  
Jaan Lellep
Keyword(s):  
Cross Sections ◽  
Nonlocal Theory ◽  
Theory Of Elasticity ◽  
Buckling Load ◽  
Buckling Loads ◽  
Critical Buckling Load ◽  
Piecewise Constant ◽  
Cracklike Defects ◽  
General Method

Buckling of nanobeams and nanorods is treated with the help of the nonlocal theory of elasticity. The nanobeams under consideration have piecewise constant dimensions of cross sections and are weakened with cracks or cracklike defects emanating at the re-entrant corners of steps. A general method for determination of critical buckling loads of stepped nanobeams with cracks is developed. The influence of defects on the critical buckling load is evaluated numerically and compared with similar results of other researchers.

scholarly journals DETERMINATION OF THE CRITICAL BUCKLING LOADS OF EULER COLUMNS USING STODOLA-VIANELLO ITERATION METHOD

2018 ◽  
Vol 30 (3) ◽  
Author(s):  
Ofondu I.O. ◽  
Ikwueze E.U. ◽  
Ike C.C.
Keyword(s):  
Iteration Method ◽  
Longitudinal Axis ◽  
Rayleigh Quotient ◽  
Buckling Load ◽  
Buckling Loads ◽  
Critical Buckling Load ◽  
Relative Errors ◽  
Fixed End

The Stodola-Vianello iteration method was implemented in this work to determine the critical buckling load of an Euler column of length l with fixed end (x = 0) and pinned end (x = l), where the longitudinal axis is the x-direction.The critical buckling loads were found to be variable, depending on the x-coordinate. Integration and the Rayleigh quotients were used to find average buckling coefficients. First iteration gave relative errors of 4% using integration and 2.5% using Rayleigh quotient.Second iteration gave average relative errorsless than 1% for both the integration and the Rayleigh quotients. Better estimates of the critical buckling loads were obtained using the Rayleigh quotient in the Stodola-Vianello’s iteration.

scholarly journals Using ANN to Estimate the Critical Buckling Load of Y Shaped Cross-Section Steel Columns

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Thuy-Anh Nguyen ◽  
Hai-Bang Ly ◽  
Hai-Van Thi Mai ◽  
Van Quan Tran
Keyword(s):  
Correlation Coefficient ◽  
Cross Section ◽  
Structural Engineering ◽  
Buckling Load ◽  
Model Assessment ◽  
Ann Model ◽  
Critical Buckling Load ◽  
Steel Columns ◽  
Marquardt Algorithm ◽  
Shaped Cross Section

Accurate measurement of the critical buckling stress is crucial in the entire field of structural engineering. In this paper, the critical buckling load of Y-shaped cross-section steel columns was predicted by the Artificial Neural Network (ANN) using the Levenberg-Marquardt algorithm. The results of 57 buckling tests were used to generate the training and testing datasets. Seven input variables were considered, including the column length, column width, steel equal angles thickness, the width and thickness of the welded steel plate, and the total deviations following the Ox and Oy directions. The output was the critical buckling load of the columns. The accuracy assessment criteria used to evaluate the model were the correlation coefficient (R), root mean square error (RMSE), and mean absolute error (MAE). The selection of an appropriate structure of ANN was first addressed, followed by two investigations on the highest accuracy models. The first one consisted of the ANN model that gave the lowest values of MAE = 40.0835 and RMSE = 30.6669, whereas the second one gave the highest value of R = 0.98488. The results revealed that taking MAE and RMSE for model assessment was more accurate and reasonable than taking the R criterion. The RMSE and MAE criteria should be used in priority, compared with the correlation coefficient.

Buckling analysis of orthotropic smart laminated nanoplates based on the nonlocal continuum mechanics using third-order shear and normal deformation theory

2018 ◽  
Vol 32 (5) ◽  
pp. 593-618
Author(s):  
Morteza Ghasemi ◽  
Abdolrahman Jaamialahmadi
Keyword(s):  
Boundary Condition ◽  
Deformation Theory ◽  
Open Circuit ◽  
Buckling Load ◽  
Closed Circuit ◽  
Third Order ◽  
Buckling Loads ◽  
Critical Buckling Load ◽  
Normal Deformation ◽  
Piezoelectric Layers

In this article, the nonlocal buckling behavior of biaxially loaded graphene sheet with piezoelectric layers based on an orthotropic intelligent laminated nanoplate model is studied. The nonlocal elasticity theory is used in the buckling analysis to show the size scale effects on the critical buckling loads. The electric potential in piezoelectric layers satisfies Maxwell’s equation for either open- or closed-circuit boundary conditions. Based on the third-order shear and normal deformation theory, the nonlinear equilibrium equations are obtained. In order to obtain the linear nonlocal stability equations, the adjacent equilibrium criterion is used. The linear nonlocal governing stability equations are solved analytically, assuming simply supported boundary condition along all edges. To validate the results, the critical buckling loads are compared with those of molecular dynamics simulations. Finally, the effects of different parameters on the critical buckling loads are studied in detail. The results show that by increasing the nonlocal parameter, the critical buckling load decreases. The piezoelectric effect increases the critical buckling load for both open- and closed-circuit boundary conditions. For open-circuit boundary condition, the variation in the critical buckling load is due to the stiffness and piezoelectric effects, but for closed circuit, it is due to the stiffness effect only. Also, the critical buckling load for open circuit is bigger than that of closed one.

scholarly journals Hybrid Artificial Intelligence Approaches for Predicting Critical Buckling Load of Structural Members under Compression Considering the Influence of Initial Geometric Imperfections

2019 ◽  
Vol 9 (11) ◽  
pp. 2258 ◽  
Author(s):  
Hai-Bang Ly ◽  
Lu Minh Le ◽  
Huan Thanh Duong ◽  
Thong Chung Nguyen ◽  
Tuan Anh Pham ◽  
...  
Keyword(s):  
Artificial Intelligence ◽  
Mean Squared Error ◽  
Optimization Technique ◽  
Buckling Load ◽  
Structural Members ◽  
Geometric Imperfections ◽  
Inference System ◽  
Critical Buckling Load ◽  
Initial Geometric Imperfections ◽  
Hybrid Artificial Intelligence

The main aim of this study is to develop different hybrid artificial intelligence (AI) approaches, such as an adaptive neuro-fuzzy inference system (ANFIS) and two ANFISs optimized by metaheuristic techniques, namely simulated annealing (SA) and biogeography-based optimization (BBO) for predicting the critical buckling load of structural members under compression, taking into account the influence of initial geometric imperfections. With this aim, the existing results of compression tests on steel columns were collected and used as a dataset. Eleven input parameters, representing the slenderness ratios and initial geometric imperfections, were considered. The predicted target was the critical buckling load of columns. Statistical criteria, namely the correlation coefficient (R), the root mean squared error (RMSE), and the mean absolute error (MAE) were used to evaluate and validate the three proposed AI models. The results showed that SA and BBO were able to improve the prediction performance of the original ANFIS. Excellent results using the BBO optimization technique were achieved (i.e., an increase in R by 7.15%, RMSE by 40.48%, and MAE by 38.45%), and those using the SA technique were not much different (i.e., an increase in R by 5.03%, RMSE by 26.68%, and MAE by 20.40%). Finally, sensitivity analysis was performed, and the most important imperfections affecting column buckling capacity was found to be the initial in-plane loading eccentricity at the top and bottom ends of the columns. The methodology and the developed AI models herein could pave the way to establishing an advanced approach to forecasting damages of columns under compression.

Finite element studies on buckling of laminated cylindrical skew panels

2014 ◽  
Vol 21 (4) ◽  
pp. 551-558 ◽  
Author(s):  
Chikkol Venkateshappa Srinivasa ◽  
Yalaburgi Jayadevappa Suresh ◽  
Wooday Puttiah Prema Kumar
Keyword(s):  
Finite Element ◽  
Fiber Orientation ◽  
Orientation Angle ◽  
Laminated Composite ◽  
Buckling Load ◽  
Stacking Sequence ◽  
Skew Angle ◽  
Buckling Loads ◽  
Critical Buckling Load ◽  
Fiber Orientation Angle

AbstractThe present paper presents the finite element studies made on critical buckling load of isotropic and laminated composite cylindrical skew panels. Analysis is performed using CQUAD4 and CQUAD8 elements of MSC/NASTRAN. It is found that the CQUAD8 element yields better results compared to the CQUAD4 element in terms of accuracy and convergence. Using the CQUAD8 element, the effects of the panel angle, skew angle, aspect ratio, and length-to-thickness ratio on the critical buckling load of isotropic cylindrical skew panels have been studied. The effects of additional parameters such as fiber orientation angle, numbers of layers (NL), and stacking sequence on the critical buckling load of laminated composite cylindrical skew panels have also been studied. The critical buckling loads are found to increase with the increase in panel angle and skew angle. When the NL in the laminate is large, the variation of the critical buckling load with the NL is not appreciable. The boundary conditions are found to have significant influence on the critical buckling load.

Effects of Delamination on the Critical Buckling Load of Glass Fiber Reinforced Epoxy Composite Plates

2018 ◽  
Vol 10 (4) ◽  
Author(s):  
S. Venkatesh ◽  
S. Prakash ◽  
S. Raja ◽  
S. Manigandan ◽  
P. Sivashankari
Keyword(s):  
Composite Laminates ◽  
Epoxy Composite ◽  
Composite Plates ◽  
Vertical Displacement ◽  
Buckling Load ◽  
Buckling Loads ◽  
Critical Buckling Load ◽  
Finite Element Software ◽  
Aspect Ratios ◽  
Glass Fiber Reinforced

The effects of the delamination in the critical buckling load failure of E-Glass /epoxy composite laminates are analysed. The buckling load of rectangular composite plates is determined by carrying out the experimental work for different aspect ratios of range 2 to 3. The specimens are made with unidirectional fibres of orientation (90/45/-45/0)s. The width of long 100 mm and 50 mm at the centre of the plate, a single substantial delamination is made at the mid layer produced by Teflon film using hand lay-up technique. The buckling loads of plates were found by using simply supported boundary condition and kept the other side edges free. The experimental buckling loads were found from the graph drawn for vertical displacement vs load. By drawing the graph for the vertical displacement vs. load, the experimental buckling load can be calculated. Using finite element software of ANSYS 10, the experimental results were validated.

scholarly journals Best Level of Parameters for a Critical Buckling Load for Circular Thin- Walled Structure Subjected to Bending

2019 ◽  
Vol 13 (4) ◽  
pp. 12-21
Author(s):  
Hussein M. H. Al-Khafaji
Keyword(s):  
Buckling Load ◽  
Effective Parameter ◽  
Element Analysis ◽  
Critical Buckling Load ◽  
Thin Walled Structures ◽  
Load Combination ◽  
Wide Range ◽  
Different Types ◽  
Analysis Of Results ◽  
Thin Walled

Circular thin walled structures have wide range of applications. This type of structure is generally exposed to different types of loads, but one of the most important types is a buckling. In this work, the phenomena of buckling was studied by using finite element analysis. The circular thin walled structure in this study is constructed from; cylindrical thin shell strengthen by longitudinal stringers, subjected to pure bending in one plane. In addition, Taguchi method was used to identify the optimum combination set of parameters for enhancement of the critical buckling load value, as well as to investigate the most effective parameter. The parameters that have been analyzed were; cylinder shell thickness, shape of stiffeners section and the number of stiffeners. Furthermore, to verify the contribution of parameters on buckling response, the analysis of variance technique (ANOVA) method was implemented, which gave the contribution weight as percentages. The analysis of results by these two methods showed that the more effective parameter on the critical buckling load was the thickness of cylinder’s shell and the lowest effective was the number of stiffeners The values of parameters that gave the best critical buckling load combination were: 1) the ratio of cylinder’s diameter to thickness of its shell was 133, 2) the ratio of the depth to thickness of stiffeners was1.6, and 3) the number of stiffeners was 12.

Flexural-Torsional Buckling of Pultruded Fiber-Reinforced Polymer Angle Beams under Eccentric Loading

2020 ◽  
Vol 982 ◽  
pp. 201-206
Author(s):  
Jaksada Thumrongvut ◽  
Natthawat Pakwan ◽  
Samaporn Krathumklang
Keyword(s):  
Buckling Load ◽  
Fiber Reinforced Polymer ◽  
Width Ratio ◽  
Fiber Reinforced ◽  
Torsional Buckling ◽  
Eccentric Load ◽  
Buckling Loads ◽  
Reinforced Polymer ◽  
Cross Sectional Dimension ◽  
Flexural Torsional Buckling

In this paper, the experimental study on the pultruded fiber-reinforced polymer (pultruded FRP) angle beams subjected to transversely eccentric load are presented. A summary of critical buckling load and buckling behavior for full-scale flexure tests with various span-to-width ratios (L/b) and eccentricities are investigated, and typical failure mode are identified. Three-point flexure tests of 50 pultruded FRP angle beams are performed. The E-glass fibre/polyester resin angle specimens are tested to examine the effect of span-to-width ratio of the beams on the buckling responses and critical buckling loads. The angle specimens have the cross-sectional dimension of 76x6.4 mm with span-to-width ratios, ranging from 20 to 40. Also, four different eccentricities are investigated, ranging from 0 to ±2e. Eccentric loads are applied below the horizontal flange in increments until beam buckling occurred. Based upon the results of this study, it is found that the load and mid-span vertical deflection relationships of the angle beams are linear up to the failure. In contrast, the load and mid-span lateral deflection relationships are geometrically nonlinear. The general mode of failure is the flexural-torsional buckling. The eccentrically loaded specimens are failed at critical buckling loads lower than their concentric counterparts. Also, the quantity of eccentricity increases as buckling load decreases. In addition, it is noticed that span-to-width ratio increases, the buckling load is decreased. The eccentric location proved to have considerable influence over the buckling load of the pultruded FRP angle beams.

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