The Singular Function Method Based on the Moving Load Deformation of Suspension Bridge

2011 ◽  
Vol 403-408 ◽  
pp. 3059-3062
Author(s):  
Bang Sheng Xing ◽  
Xue Feng Wang
Keyword(s):  
Function Method ◽  
Moving Load ◽  
Bending Moment ◽  
Suspension Bridge ◽  
Simplified Model ◽  
Singular Function ◽  
Concentrated Load ◽  
Influence Line ◽  
Mathematical Equations ◽  
The Moment

This paper uses singular function method to analyze the deformation of simplified model of suspension bridge in the moving load, deduces the mathematical equations of the deflection and bending moment, analyzes the simplified model changes of mechanical deformation at different moving load position by using numerical analysis software mathcad,studies the most unfavorable load position and maximum absolute bending moment in a group of concentrated load, gets the results that the maximum absolute bending moment of suspension bridge section depends on the size of the load, mobile location and its distribution in a moving load. The moment influence line used by singular function is smooth segmentation functions. Researching findings provide theoretical basis for the design of suspension bridge.

Dynamic analysis of a composite beam subjected to a moving load

2009 ◽  
Vol 223 (7) ◽  
pp. 1543-1554 ◽  
Author(s):  
M J Rezvani ◽  
Karami M Khorramabadi
Keyword(s):  
Dynamic Analysis ◽  
Composite Beam ◽  
Moving Load ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Bending Moment ◽  
Axial Direction ◽  
Transformation Method ◽  
Concentrated Load

In this article, the dynamic analysis of an infinite Timoshenko beam made of a laminated composite located on a generalized Pasternak viscoelastic foundation is studied. The beam is subjected to a moving concentrated load. It is assumed that the mechanical properties of the beam change in the direction of the beam thickness but remain constant in the axial direction. Closed-form steady-state solutions, based on the first-order shear deformation theory, are developed. By selection of an appropriate displacement field for the composite beam, and using the principle of total minimum potential energy, the governing partial differential equations of motion are obtained and solved through a complex infinite Fourier transformation method. The results are introduced in terms of deflection, bending moment, shear force, and stress. In addition, the effects of stiffness, shear layer viscosity coefficients of foundation, velocity of the moving load, number of layers, and various angles of layers over the beam response are studied. For some specific cases, the results are compared with those presented in some other published papers, with which good agreements are observed.

Experimental study of moment carrying behavior of typical Tibetan timber beam-column joints

2021 ◽  
pp. 136943322110015
Author(s):  
Ting Guo ◽  
Na Yang ◽  
Huichun Yan ◽  
Fan Bai
Keyword(s):  
Bending Moment ◽  
Structural Performance ◽  
Test Results ◽  
Timber Beam ◽  
Rotational Stiffness ◽  
Trilinear Model ◽  
Column Joint ◽  
Loading Tests ◽  
The Moment ◽  
Relationship Of

This study aimed to investigate the moment carrying behavior of typical Tibetan timber beam-column joints under monotonic vertical static load and also evaluate the influence of length ratio of Gongmu to beam (LRGB) and dowels layout on the structural performance of the joint. Six full-scale specimens were fabricated with same construction but different Gongmu length and dowels position. The moment carrying performance of beam-column joints in terms of failure mode, moment resistance, and rotational stiffness of joints were obtained via monotonic loading tests. Test results indicated that all joints are characterized by compressive failure perpendicular to grain of Ludou. Additionally, it was found that greater LRGB leads to greater initial rotational stiffness and maximum moment of the joint by an increase of restraint length for beam end; however, offsetting dowels toward column resulted smaller stiffness and ultimate bending moment of joints, particularly, offsetting Beam-Gongmu dowels toward column changed the moment-rotation curve pattern of the beam-column joint, accompanied by a hardening stiffness at last phase. Furthermore, a simplified trilinear model was proposed to represent the moment-rotation relationship of the typical Tibetan timber beam-column joint.

Bending of an Infinite Beam on an Elastic Foundation

1937 ◽  
Vol 4 (1) ◽  
pp. A1-A7 ◽  
Author(s):  
M. A. Biot
Keyword(s):  
Elastic Foundation ◽  
Poisson Ratio ◽  
Elementary Theory ◽  
Three Dimensional ◽  
Bending Moment ◽  
Two Dimensional ◽  
Concentrated Load ◽  
Elastic Continuum ◽  
Infinite Beam ◽  
A Value

Abstract The elementary theory of the bending of a beam on an elastic foundation is based on the assumption that the beam is resting on a continuously distributed set of springs the stiffness of which is defined by a “modulus of the foundation” k. Very seldom, however, does it happen that the foundation is actually constituted this way. Generally, the foundation is an elastic continuum characterized by two elastic constants, a modulus of elasticity E, and a Poisson ratio ν. The problem of the bending of a beam resting on such a foundation has been approached already by various authors. The author attempts to give in this paper a more exact solution of one aspect of this problem, i.e., the case of an infinite beam under a concentrated load. A notable difference exists between the results obtained from the assumptions of a two-dimensional foundation and of a three-dimensional foundation. Bending-moment and deflection curves for the two-dimensional case are shown in Figs. 4 and 5. A value of the modulus k is given for both cases by which the elementary theory can be used and leads to results which are fairly acceptable. These values depend on the stiffness of the beam and on the elasticity of the foundation.

scholarly journals Application of Laplace Transform to the Free Vibration of Continuous Beams

2017 ◽  
Vol 63 (1) ◽  
pp. 163-180 ◽  
Author(s):  
H.B. Wen ◽  
T. Zeng ◽  
G.Z. Hu
Keyword(s):  
Free Vibration ◽  
Laplace Transform ◽  
Reaction Force ◽  
Bending Moment ◽  
Frequency Equation ◽  
Simplified Model ◽  
Continuous Beam ◽  
Transform Method ◽  
Continuous Beams ◽  
Vibration Problems

AbstractLaplace Transform is often used in solving the free vibration problems of structural beams. In existing research, there are two types of simplified models of continuous beam placement. The first is to regard the continuous beam as a single-span beam, the middle bearing of which is replaced by the bearing reaction force; the second is to divide the continuous beam into several simply supported beams, with the bending moment of the continuous beam at the middle bearing considered as the external force. Research shows that the second simplified model is incorrect, and the frequency equation derived from the first simplified model contains multiple expressions which might not be equivalent to each other. This paper specifies the application method of Laplace Transform in solving the free vibration problems of continuous beams, having great significance in the proper use of the transform method.

Experimental Evaluation of the Ultimate Bending Moment of a Slender Thin-Walled Box Girder

2015 ◽  
Vol 137 (2) ◽  
Author(s):  
José Manuel Gordo ◽  
C. Guedes Soares
Keyword(s):  
Residual Stresses ◽  
Progressive Collapse ◽  
Bending Moment ◽  
Bending Test ◽  
Postbuckling Behavior ◽  
Box Girder ◽  
Collapse Mode ◽  
Collapse Analysis ◽  
The Moment ◽  
Progressive Collapse Analysis

The results of a four points bending test on a box girder are presented. The experiment is part of series of tests with similar configuration but with different thickness and span between frames. The present work refers to the slenderest plate box girder with a plate's thickness of 2 mm but with a short span between frames. The experiment includes initial loading cycles allowing for partial relief of residual stresses. The moment curvature relationship is established for a large range of curvature. The ultimate bending moment (UM) of the box is evaluated and compared with the first yield moment and the plastic moment allowing the evaluation of the efficiency of the structure. The postbuckling behavior and collapse mode are characterized. Comparison of the experiment with a progressive collapse analysis method is made taking into consideration the effect of residual stresses on envelop of the moment curvature curve of the structure.

Study on Prediction Deflection of at the Girder Midspan of Large Tonnage Gantry Crane Rigid Legs

2014 ◽  
Vol 628 ◽  
pp. 214-218
Author(s):  
Da Peng Zhang ◽  
Wen Ming Cheng ◽  
Kun Cai
Keyword(s):  
Bending Moment ◽  
Moment Of Inertia ◽  
Load Test ◽  
Test Method ◽  
Gantry Crane ◽  
Deflection Curve ◽  
Concentrated Load ◽  
Small Load ◽  
Curve Equation

It is the most important inspection index of the deflection value for the girder of gantry crane under rated load in the overall test. In the overall test for large tonnage gantry crane which prepared for experimental weight is very difficult at the site, or even impossible perform test. In the text, it is deduced the girder deflection curve equation where considering the effects of the leg bending moment to the girder deflection When the concentrated load is applied to the position of L/2,L/3 and 2L/3 of the girder. The girder deflection value can be obtained under small load at the position of L/2,L/3 and 2L/3 of the girder and the actual moment of inertia of the girder and two side leg can be obtained. In this way, the deflection of the large tonnage gantry crane are predicted through the data of the three-position method in the small load test. Three-position small load test method provides a practical and effective method for the prediction of the girder deflection of large tonnage gantry structure.

Explicit Expressions for Buckling Analysis of Thin-Walled Beams Under Combined Loads with Laterally-Fixed Ends and Application to Stability Analysis of Saw Blades

2020 ◽  
pp. 2150032
Author(s):  
Van Binh Phung ◽  
Ngoc Doan Tran ◽  
Viet Duc Nguyen ◽  
V. S. Prokopov ◽  
Hoang Minh Dang
Keyword(s):  
Critical State ◽  
Bending Moment ◽  
Critical Issue ◽  
Eccentric Load ◽  
Concentrated Load ◽  
Combined Loads ◽  
Distributed Load ◽  
Thin Walled ◽  
The Stability ◽  
2D And 3D

This paper studies the critical issue of thin-walled beams with laterally fixed ends. The method for defining the formulae of twist moment for the beams subjected to combined loads was elucidated. Based on this, the governing differential equations of the beam were developed. The procedure for determining the critical state of the beam by the energy method was presented. With this procedure, the critical state of the beam concerned under three types of loadings such as axial force [Formula: see text], bending moment [Formula: see text] and distributed load [Formula: see text] (or concentrated load [Formula: see text]) was examined deliberately. The outcomes were presented in explicit closed-form, which can be illustrated in 2D and 3D graphs. Also, the analytical solution obtained was in agreement with the numerical one obtained by the commercial software NX Nastran. Furthermore, the analytical solutions were applied straightforwardly to explore the stability and design optimization of the tooth-blade for the new frame-type saw machine under an eccentric load. The result can also be promisingly used to study problems of thin-walled beams with laterally fixed ends subjected to other types of loads.

Hydroelastic Analysis for Extended-Column of Extended Draft Semi-Submersible

2014 ◽  
Author(s):  
Zhi Yung Tay ◽  
Petyo Rumenov Popov ◽  
Vasil Zhivkov Yordanov ◽  
Hoang Dat Nguyen
Keyword(s):  
Wave Spectrum ◽  
Bending Moment ◽  
Wave Theory ◽  
Complex Model ◽  
Simplified Model ◽  
Inertia Force ◽  
Natural Period ◽  
Strength Performance ◽  
Hydroelastic Analysis ◽  
Current Loading

This paper presents a simplified model for assessing the hydroelasticity of the extended-column (e-column) for an extended-draft semi-submersible (E-SEMI) by using commercially available software. The E-SEMI comprises a second tier pontoon (STP) connected to a conventional semi-submersible by using extended-column (e-column). The purpose of attaching the STP is to increase the heave added mass, and as a result, could reduce the heaving motion and shift the natural period further away from the wave spectrum by increasing the natural period. One of the challenges of the E-SEMI is to obtain the hydroelastic response of the e-column when subjected to wave and current loadings. The simplified model models the e-column and STP using beam-column theory that has similar vibration frequencies and modes shapes of the complex model. The potential wave theory is used to model the waves and the Morrison equation is use to obtain the drag and inertia force acting on the e-column due to current loading. Hydroelasticity shall be performed on this simplified model to assess the strength performance as well as the deflection of the e-column. The bending moment obtained from the hydroelastic analysis is also significant in the connector design that keeps the e-column in place.

EFFECTS OF THE INITIAL DEFLECTION SHAPE ON THE MOMENT AMPLIFICATION FACTOR OF BEAM-COLUMNS

2018 ◽  
Vol 5 (2) ◽  
Author(s):  
Haruna Utsunomiya ◽  
Masayuki Haraguchi ◽  
Masae Kido ◽  
Keigo Tsuda
Keyword(s):  
Amplification Factor ◽  
Slenderness Ratio ◽  
Compressive Force ◽  
Bending Moment ◽  
Load Ratio ◽  
Longitudinal Direction ◽  
Initial Deflection ◽  
Axial Compressive Force ◽  
Beam Columns ◽  
The Moment

In the design of slender steel beam-columns, the moment amplification factor is used to estimate the maximum moment along with the longitudinal direction. While formulas for evaluating the factor have been presented on the basis of elastic or elastic-plastic analysis, the initial deflection of the column is not considered. The effect that the initial deflection on the strength and behavior of the column has been shown only when the initial deflection shape is half sine wave. This paper discusses the effect of the initial deflection shape on the value of the moment amplification factor by performing the analytical work. The analytical model is the hinged-end beam-column subjected to constant axial compressive force and end moments. First of all, the equilibrium differential equation which governs the problem is solved and the formula for calculating the bending moment is presented. In the parametric study, magnitude of initial deflection, initial deflection shape, axial load ratio, slenderness ratio and end moment ratio are selected as the parameters. In this paper, we discuss the effects of the amount of the initial deflection and the initial deflection shape.

Sign in / Sign up

Export Citation Format

Share Document