The Computation of Flexural–Torsional Buckling Loads

1952 ◽  
Vol 19 (2) ◽  
pp. 214-219
Author(s):  
H. F. Michielsen
Keyword(s):  
Buckling Load ◽  
Trial And Error ◽  
Torsional Buckling ◽  
Buckling Loads ◽  
Cubic Equation ◽  
Flexural Torsional Buckling ◽  
Ordinary Means

Abstract Solution by ordinary means of the cubic equation for the torsional buckling load, first derived by Kappus, often leads to insufficiently accurate results. A method is presented which avoids the loss of accuracy involved. The procedure is straightforward and no graphical means are involved. However, one formula is to be solved by trial and error.

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.

Elastic Flexural-Torsional Buckling of Beam-Column with Equal-Leg Angle Cross-Section

2013 ◽  
Vol 353-356 ◽  
pp. 3151-3154
Author(s):  
Jian Qin ◽  
Yong Jun Xia ◽  
Jin Miao Zhang ◽  
Chun Hua Hu
Keyword(s):  
Numerical Methods ◽  
Engineering Design ◽  
Cross Section ◽  
Computational Efficiency ◽  
Slenderness Ratio ◽  
Governing Equations ◽  
Torsional Buckling ◽  
Buckling Loads ◽  
Beam Columns ◽  
Flexural Torsional Buckling

The flexural-torsional buckling of equal-leg angle member under compression is analyzed and calculated. Based on General bending theory and the section properties of angle, the governing equations of the spatial buckling are presented and the formula of Wagner effect coefficient is deduced. The method can also be used for beam-columns with any type section, and the computational efficiency is much higher than numerical methods. The critical buckling loads of equal-leg angle members with different sizes are calculated and the column curves of critical load and slenderness ratio are plotted which will guide efficiently the actual engineering design.

Study on Calculation Theory of Elastic Flexural-Torsional Buckling Bearing Capacity for Castellated Beams

2015 ◽  
Vol 744-746 ◽  
pp. 1635-1639
Author(s):  
Xiang Rong Chen ◽  
Hai Long Yuan ◽  
Xing Chen ◽  
Zhen Wen Liu
Keyword(s):  
Finite Element Analysis ◽  
Calculation Methods ◽  
Height Ratio ◽  
Torsional Buckling ◽  
Element Analysis ◽  
Buckling Loads ◽  
Buckling Strength ◽  
The Finite Element Analysis ◽  
Flexural Torsional Buckling ◽  
Abaqus Software

The structure of castellated beams is complex, using the computation theory of elastic flexural-torsional buckling of H-shaped beams to study the elastic flexural-torsional buckling strength of castellated beams under different loads, based on simplifying the section's eigenvalues. In addition to the theoretical investigation, the finite element analysis of the accurate critical loads of the beams had been done by the ABAQUS software, a comparison has been made between the calculated loads and analyzed results, error is smaller. Analyzing the effects that divergence ratio, depth-span ratio and distance-height ratio has on the elastic flexural-torsional buckling loads of castellated beams and draw out some reduced calculation methods for the section's eigenvalues and elastic flexural-torsional buckling critical load of castellated beams.

Torsional Buckling of Columns by the Lyapunov Method

1985 ◽  
Vol 29 (03) ◽  
pp. 189-193
Author(s):  
T. A. I. Akeju
Keyword(s):  
Metric Space ◽  
Lyapunov Functional ◽  
Lyapunov Method ◽  
Direct Method ◽  
Stability Theorem ◽  
Torsional Buckling ◽  
Buckling Loads ◽  
Relative Ease ◽  
Flexural Buckling ◽  
Cubic Equation

The paper presents an application of Lyapunov's direct method to torsional and torsional-flexural buckling of columns. A metric space and a Lyapunov functional are proposed for each of the problems. Making use of Zubov's stability theorem and appropriate eigenvalue inequalities, the functionals yield the expressions for the buckling loads for simple and fixed supports. Of particular interest is the relative ease with which the expressions are derived, especially in the torsional-flexural buckling case, where it has not been necessary to seek the roots of the traditional cubic equation which governs the critical loads of the member.

scholarly journals The effect of flexural–torsional buckling on the stability of timber members: a case study

2021 ◽  
Vol 3 (6) ◽  
Author(s):  
Osama A. B. Hassan
Keyword(s):  
Axial Compression ◽  
Bending Moment ◽  
List Type ◽  
Torsional Buckling ◽  
Solution Methods ◽  
Simplified Solution ◽  
The Stability ◽  
Flexural Torsional Buckling ◽  
Building Engineering

Abstract This study investigates the stability of timber members subjected to simultaneously acting axial compression and bending moment, with possible risk for torsional and flexural–torsional buckling. This situation can occur in laterally supported members where one side of the member is braced but the other side is unbraced. In this case, the free side will buckle out of plane while the braced side will be prevented from torsional and flexural–torsional buckling. This problem can be evident for long members in timber-frame structures, which are subjected to high axial compression combined with bending moments in which the member is not sufficiently braced at both sides. This study is based on the design requirement stated in Eurocode 5. Solution methods discussed in this paper can be of interest within the framework of structural and building Engineering practices and education in which the stability of structural elements is investigated. Article Highlights This case study investigates some design situations where the timber member is not sufficiently braced. In this case, a stability problem associated with combined torsional buckling and flexural buckling can arise. The study shows that the torsional and/or flexural–torsional buckling of timber members can be important to control in order to fulfil the criteria of the stability of the member according to Eurocode 5 and help the structural engineer to achieve safer designs. The study investigates also a simplified solution to check the effect of flexural torsional buckling of laterally braced timber members.

scholarly journals CFRP Origami Metamaterial with Tunable Buckling Loads: A Numerical Study

Materials ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 917
Author(s):  
Houyao Zhu ◽  
Shouyan Chen ◽  
Teng Shen ◽  
Ruikun Wang ◽  
Jie Liu
Keyword(s):  
Numerical Study ◽  
Buckling Load ◽  
Fe Modelling ◽  
Buckling Loads ◽  
Folding Angle ◽  
Mechanical Responses ◽  
Reinforced Plastic ◽  
Rate Of Increase ◽  
Practical Engineering ◽  
Identical Rate

Origami has played an increasingly central role in designing a broad range of novel structures due to its simple concept and its lightweight and extraordinary mechanical properties. Nonetheless, most of the research focuses on mechanical responses by using homogeneous materials and limited studies involving buckling loads. In this study, we have designed a carbon fiber reinforced plastic (CFRP) origami metamaterial based on the classical Miura sheet and composite material. The finite element (FE) modelling process’s accuracy is first proved by utilizing a CFRP plate that has an analytical solution of the buckling load. Based on the validated FE modelling process, we then thoroughly study the buckling resistance ability of the proposed CFRP origami metamaterial numerically by varying the folding angle, layer order, and material properties, finding that the buckling loads can be tuned to as large as approximately 2.5 times for mode 5 by altering the folding angle from 10° to 130°. With the identical rate of increase, the shear modulus has a more significant influence on the buckling load than Young’s modulus. Outcomes reported reveal that tunable buckling loads can be achieved in two ways, i.e., origami technique and the CFRP material with fruitful design freedoms. This study provides an easy way of merely adjusting and controlling the buckling load of lightweight structures for practical engineering.

Study of flexural–torsional buckling behaviour of 6061-T6 aluminium alloy unequal-leg angle columns

2021 ◽  
Vol 164 ◽  
pp. 107821
Author(s):  
Ying Zhang ◽  
Yidu Bu ◽  
Yuanqing Wang ◽  
Zhongxing Wang ◽  
Yuanwen Ouyang
Keyword(s):  
Aluminium Alloy ◽  
Torsional Buckling ◽  
Flexural Torsional Buckling
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