scholarly journals Analytical method comparison on critical force of the stepped column model of telescopic crane

2018 ◽  
Vol 10 (10) ◽  
pp. 168781401880869 ◽  
Author(s):  
Fenglin Yao ◽  
Wenjun Meng ◽  
Jie Zhao ◽  
Zhanjiao She ◽  
Guoshan Shi
Keyword(s):  
Ritz Method ◽  
Method Comparison ◽  
Recursive Formula ◽  
Transcendental Equation ◽  
Critical Force ◽  
Effective Length ◽  
Deflection Curve ◽  
Stability Calculation ◽  
Column Model ◽  
The Ideal

The calculation of the critical force of the stepped column model of telescopic boom crane is the key to stability calculation of all-terrain crane. In slightly bending theory, differential equation can be built up, and then the deflection curve of ideal column can be obtained. Using this curve and the Rayleigh–Ritz method, the Euler force of the ideal column can be obtained. For n-stepped columns, Euler forces and the effective length coefficients can be acquired using the deflection curve of the ideal column and parabolic curve, respectively, combined with the Rayleigh–Ritz method. Differential equations of the n-stepped telescopic boom are established based on the vertical and horizontal buckling theory. The recursive formula of the stability of the n-stepped telescopic boom is deduced by the mathematical induction method. For the transcendental equation in the recursive formula, combined with the structural force characteristics and supplementary formulas, the Levenberg–Marquardt numerical optimization algorithm is used to solve the equations with n unknowns. Length coefficients obtained by the three methods are compared using GB3811-2008 and ANSYS 17.0. The results show that the accuracy of the numerical algorithm is the highest, and the first two algorithms will produce large errors when the stepped columns have more steps.

Steel Rod Stability and Inelastic Buckling Study

2013 ◽  
Vol 357-360 ◽  
pp. 626-630
Author(s):  
Yao Zheng ◽  
Hong Zheng
Keyword(s):  
Residual Stress ◽  
Eighteenth Century ◽  
Stability Problem ◽  
Critical Force ◽  
Axial Pressure ◽  
Inelastic Buckling ◽  
Accidental Eccentricity ◽  
Pressure Bar ◽  
Straight Rod ◽  
The Ideal

Research on stability problem, has put forward the famous bar under axial pressure formula from the middle of the eighteenth Century Euler critical force, more than 200 years, the elastic range but recognize that Euler's formula is only suitable for the material, but it took more than a hundred years. Study on the inelastic critical load of column, double modulus theory and the tangent modulus theory. These theories are starting from the ideal straight rod, and practical bar called " defects exist various accidental eccentricity " ( such as physical and geometrical aspects of the initial deflection rod, pressure asymmetry in aspects of material unevenness, residual stress) is not consistent. Thus the utility pressure bar, should according to the eccentric pressing rod is considered more practical.

Nomograms for Determination of Effective Length of the Unregular Frames Based on Mechanics and Steel Structure

2014 ◽  
Vol 886 ◽  
pp. 402-407
Author(s):  
Da Tian Zhang ◽  
Dong Hua Zhou
Keyword(s):  
Steel Structure ◽  
Effective Length ◽  
Structure Stability ◽  
Displacement Method ◽  
Complex Situation ◽  
Stability Calculation ◽  
Effective Length Factor ◽  
Practical Engineering ◽  
Relevant Calculation

Determining the frame column effective length is a key part of the structure stability calculation in practical engineering. This specification for design of steel structure and specification for design of concrete are given in some relevant calculation formula and forms, but these formulas and tables can only be applied to the simple situation. In the complex situation, such as the frame column axial force and height is large, the formula is not applicable, may leads to unsafe results. In this paper. the formulas are deduced by using second-order displacement method in order to solve these problems,and the chart for determining the effective length is also obtained. The chart can be used to calculate the effective length factor quickly and concisely.

scholarly journals COMPARATIVE ANALYSIS OF THE BUCKLING FACTOR OF THE STEEL ARCH BRIDGES

2019 ◽  
Vol 11 (1) ◽  
pp. 11-16
Author(s):  
Sigutė Žilėnaitė
Keyword(s):  
Comparative Analysis ◽  
20Th Century ◽  
Compressive Force ◽  
Critical Force ◽  
Effective Length ◽  
Initial Stresses ◽  
Axial Compressive Force ◽  
Late 20Th Century ◽  
Arch Bridges ◽  
The Stability

The dominant axial compressive force makes the arches become extremely sensitive to the loss of stability. Their stability analysis was first initiated in the late 20th century. The first stability research of single arches was carried out inplane at the elastic stage of the arches. Later the behaviour of arches in the elastic-plastic stage, the initial stresses and geometric imperfections before the arch buckles were also assessed, the effective length of the arches and the out-of-the-plane arch strength conditions were being identified as well as the effect of the temperature on the stability of the arch. The expression of the critical force of the arches connected by vertical hangers with a chord and its dependant elements were defined by Petersen in the late 20th century. The design methodology for the formal design of arches connected by vertical hangers with a stiffening girder is presented in Annex D of the Eurocode 1993-2. Nevertheless, the area of application and the main assumptions are not defined. The first part of the comparative analysis identifies the assumptions for arch bridge modelling under which the buckling factor β dependence curves in Figure D.4 of Annex D to Eurocode 1993-2 can be applied. In the second part a comparison of the the normative βEC factor value and the one established by the numerical experiment with the increase in the number of hangers and change in the hanger network form is presented.

The Chart Method of Multi-Columns Effective Length with Difference Axial Force

2014 ◽  
Vol 610 ◽  
pp. 12-16
Author(s):  
Jing Lin Zhu ◽  
Dong Hua Zhou ◽  
Yao Zheng ◽  
Zhi Lun Ouyang ◽  
Chun Xiu Han
Keyword(s):  
Axial Force ◽  
Steel Structures ◽  
Effective Length ◽  
Stability Calculation ◽  
Practical Engineering

In practical engineering, multi-columns stability calculation is very common and very important. Determining the multi-columns effective length is the most important in stability calculation. So there are some nomo-graphs and formulas in Chinese Code for design of steel structures .The structures are very varied and calculation is too difficult. The nomo-graph and formulas in chinese standards are not fully applicable to a variety of situations. For example, in the multi-frame, the axial force is large difference between stories. If we determine the effective length with the nomo-graph and formulas in chinese standards, it will be unsafe in sometimes. This paper gives some nomo-graphs and formulas to determined the effective length. According to the method, we can determined the effective length quickly, and visually see the trend in the curves of effective length when the parameters change. The nomo-graph and formulas in this can be said to be a supplement to the chinese standards.

A Calculation Method of High-Pier's Effective Length Factor Considering the Dead Weight

2013 ◽  
Vol 361-363 ◽  
pp. 1278-1283
Author(s):  
Peng Liu ◽  
Rui Zhi Wang ◽  
Fei Zheng ◽  
Qiong He
Keyword(s):  
Boundary Conditions ◽  
Calculation Method ◽  
Critical Force ◽  
Effective Length ◽  
Ideal Boundary ◽  
Dead Weight ◽  
Numerical Examples ◽  
First Order ◽  
Effective Length Factor ◽  
High Pier

Nowadays, uncertainty regarding the calculation method of effective length factor of high-pier has brought many inconveniences to the design of bridge. To solve the problem, this paper demonstrates the calculation method of effective length factor on the basis of Eulers formula considering both the influence of high-pier s dead weight and non-ideal boundary conditions on the critical force of first-order buckling. The influence of piers dead weight on effective length factor in the construction and finished stage are evaluated by numerical examples. Results show that: the effective length factor becomes smaller considering dead weight both in construction and finished stage. Moreover, high-piers dead weight causes more influence in the construction stage than finished stage which should be considered seriously in the design and construction.

scholarly journals An Accurate Measurement Method for Tension Force of Short Cable by Additional Mass Block

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Shuichang Li ◽  
Longlin Wang ◽  
Hua Wang ◽  
Peihua Shi ◽  
Riyan Lan ◽  
...  
Keyword(s):  
Natural Frequency ◽  
Force Measurement ◽  
Ritz Method ◽  
Added Mass ◽  
Short Length ◽  
Effective Length ◽  
Tension Force ◽  
Analytical Relationship ◽  
Test Accuracy ◽  
Additional Mass

The equivalent effective length parameter is introduced into the vibration equation of short cable; that is, the boundary condition that affects the test accuracy of short cable force is equivalent to the calculated length of cable. By attaching an additional mass block to the cable, new parameters are introduced to identify the tension force. Vibration differential equations are established for cable with and without addition mass block, taking new parameters into account, such as equivalent effective length and added mass. By solving the equations using the RITZ method, the analytical relationship between the natural frequency of cable and equivalent effective length before and after a mass block is added can be developed. It can also develop an analytical method to identify the equivalent effective length depending on whether the added mass block is attached. Then, tension force of short length cable can be evaluated by measuring its natural frequency based on equivalent effective length. The method is verified by field tests. The tests results indicate the new method mentioned in this paper is going to largely improve the accuracy of tension force measurement of short length cable.

The Overall Stability Calculation Method for Sway Frame

2012 ◽  
Vol 594-597 ◽  
pp. 686-690
Author(s):  
Wei Feng Tian ◽  
Ji Ping Hao ◽  
Chun Lei Fan
Keyword(s):  
Calculation Method ◽  
Theoretical Calculations ◽  
Simple Calculation ◽  
Elastic Stability ◽  
Negative Stiffness ◽  
Effective Length ◽  
Good Precision ◽  
Stiffness Ratio ◽  
Stability Calculation ◽  
Effective Length Method

There are three levels in stability calculating for sway frame. The first level is the traditional effective length method. The second level is the effective length method considering interaction of columns in one story and the third level is the effective length method considering inter-story interaction. The traditional effective length method may lead to unsafe design. Using the concept of equivalent negative stiffness, story stiffness to negative stiffness ratio factor and story support factor were proposed. Through the story stiffness to negative stiffness ratio factor, the weak-story and the inter-story support relationship can be found. Then, a formula for calculating the elastic stability capacity of sway frame is proposed, by which the inter-column interaction and inter-story interaction can be considered, and the finite element buckling analysis for stability capacity can be avoided. Through the stability capacity, the column effective length can be calculated. The results show that this simple calculation method has good precision and accuracy, can be used for engineering design and theoretical calculations.

scholarly journals CROSS-PLY BENDING EQUATION AND APPLICATION FOR COMPRESSED ROD WITH CRACK

Aviation ◽  
2004 ◽  
Vol 8 (4) ◽  
pp. 27-31
Author(s):  
Igor Pavelko ◽  
Vitaly Pavelko
Keyword(s):  
Mechanical Properties ◽  
Transcendental Equation ◽  
Critical Force ◽  
Theoretical Base ◽  
Common Solution ◽  
Linear Fracture ◽  
Main Equation ◽  
The Common ◽  
The Relationship ◽  
Power Concept

The aim of this paper is the analysis of rod cross‐ply bending and stability of rod systems in the presence of cracks. The power concept (its theoretical base is Maxwell's theorem about the reciprocity of displacements) and linear fracture mechanics methods for research of mechanical properties of rod systems in the presence of cracks nave been used. The main equation of the rod cross‐ply bending and the common solution of this equation were obtained. The expression of the relationship between rod deflection and the disturbing cross‐force was obtained. Some transcendental equation allows defining the inferior boundary of critical force of rod with a crack.

scholarly journals THE APPROXIMATE SOLUTION FOR PLATES USING MODIFIED RAYLEIGH-RITZ METHOD

2017 ◽  
Vol 13 (4) ◽  
pp. 121-127
Author(s):  
Gaik A. Manuylov
Keyword(s):  
Special Functions ◽  
Ritz Method ◽  
Critical Force ◽  
Elastic Plates ◽  
Concentrated Force ◽  
Uniform Compression ◽  
Level Lines ◽  
Distributed Load ◽  
Geometric Estimates ◽  
Good Agreement

For thin elastic plates of arbitrary shape with a smooth pinched or hinged contour based on the modified Rayleigh-Ritz method, explicit expressions are obtained for the approximate values of the maximum deflection from a uniformly distributed load, the deflection at the point of application of the concentrated force, the critical force of uniform compression, and the first eigenfrequency. The lateral movements were approximated by special functions having level lines similar to the plate contour. The results of calculating the plate in the form of a pear-shaped oval are presented, which are in good agreement with the two-sided geometric estimates of the corresponding solutions

scholarly journals Solution of the Grazing Goat Problem: A Conflict between Beauty and Pragmatism

2021 ◽  
Vol 3 (2) ◽  
pp. 23-27
Author(s):  
Robert J Marks II
Keyword(s):  
Closed Form ◽  
Numerical Evaluation ◽  
Closed Form Solution ◽  
Transcendental Equation ◽  
Form Solution ◽  
Closed Form Solutions ◽  
Contour Integrals ◽  
Applied Mathematician ◽  
Pure Mathematician ◽  
The Ideal

What is the ideal solution of a problem in mathematics? It depends on your nerd ideology. Pure mathematicians worship the beauty of a mathematics result. Closed form solutions are particularly beautiful. Engineers and applied mathematicians, on the other hand, focus on the result independent of its beauty. If a solution exists and can be calculated, that's enough. The job is done. An example is solution of the grazing goat problem. A recent closed form solution in the form of a ratio of two contour integrals has been found for the grazing goat problem and its beauty has been admired by pure mathematicians. For the engineer and applied mathematician, numerical solution of the grazing goat problem comes from an easily derived transcendental equation. The transcendental equation, known for some time, was not considered a beautiful enough solution for the pure mathematician so they kept on looking until they found a closed form solution. The numerical evaluation of the transcendental equation is not as beautiful. It is not in closed form. But the accuracy of the solution can straightforwardly be evaluated to within any accuracy desired. To illustrate, we derive and solve the transcendental equation for a generalization of the grazing goat problem.

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