Study on Deformation and Stress of CRCP under Concentrated Vertical Load with Hollow Foundation

2011 ◽  
Vol 250-253 ◽  
pp. 3415-3420
Author(s):  
Xiao Bing Chen ◽  
Xiao Ming Huang ◽  
Jin Hu Tong
Keyword(s):  
Equivalence Principle ◽  
Transverse Crack ◽  
Torsion Theory ◽  
Slab Thickness ◽  
Vertical Load ◽  
Effective Measure ◽  
Small Deflection ◽  
Half Wave ◽  
Elastic Thin Plate ◽  
Deflection Theory

Based on the equivalence principle, the concentrated vertical load which acts on the Continuously Reinforced Concrete Pavement(CRCP) transverse crack is translated into the equivalent half-wave sine load by Fourier transform. According to the translation principle of the force, the half-wave sine vertical load acting on the CRCP transverse crack is decomposed to the half-wave sine vertical load and the torsion force acting on the center of CRCP. Lastly, the deflection, torsional displacement and stress formulas of CRCP under the concentrated vertical load with hollow foundation are put forward, which is on the basis of the small deflection theory of elastic thin plate and torsion theory. The results show that increasing the slab thickness is the most effective measure to reduce maximal deflection, distortion displacement and stress of CRCP concentrated vertical load with hollow foundation.

Research on Deflection and Stress of CRCP under Concentrated Vehicle Load over Hollow Base

2011 ◽  
Vol 255-260 ◽  
pp. 1800-1805 ◽  
Author(s):  
Xiao Bing Chen ◽  
Xiao Ming Huang ◽  
Jin Hu Tong
Keyword(s):  
Slab Thickness ◽  
Lateral Bending ◽  
Slab Width ◽  
Preferential Choice ◽  
Vehicle Load ◽  
Small Deflection ◽  
Half Wave ◽  
Maximal Stress ◽  
Elastic Thin Plate ◽  
Deflection Theory

Based on the small deflection theory of elastic thin plate and the equivalence principle of deflection and stress, the concentrated vehicle load which acts on the CRCP is translated into the equivalent half-wave sine load by Fourier transform. On the basis of this transform, the deflection and stress formulas are put forward when CRCP is subjected to a concentrated vehicle load with hollow foundation. The following results are obtained from the analysis. The maximal deflection is proportional to the concentrated vehicle load and slab width, and inversely proportional to the lateral bending stiffness and slab thickness. The slab width and thickness have a significant influence on the maximal deflection. The maximal stress is proportional to the concentrated vehicle load and slab width as well as inversely proportional to the slab thickness. The influence of slab thickness is significant to the maximal stress. In conclusion, increasing the slab thickness is the preferential choice to reduce the maximal deflection and stress.

Research on Load Transfer of Continuously Reinforced Concrete Pavement with Hollow Foundation

2011 ◽  
Vol 97-98 ◽  
pp. 60-68
Author(s):  
Xiao Bing Chen ◽  
Xiao Ming Huang ◽  
Jin Hu Tong
Keyword(s):  
Finite Element ◽  
Fourier Transform ◽  
Reinforced Concrete ◽  
Equivalence Principle ◽  
Load Transfer ◽  
Concrete Pavement ◽  
Vertical Load ◽  
Small Deflection ◽  
Half Wave ◽  
Deflection Theory

Based on the equivalence principle of bending deflection and torsional displacement, the concentrated vertical load which acts on the center of a continuously reinforced concrete pavement (CRCP) is translated into an equivalent half-wave sine load by Fourier transform. On the basis of this transform and deformation harmony condition of crack, the equations of load transfer are established. According to the translation principle of the force, the equations of load transfer of adjacent slabs are worked out. With the small deflection theory of elastic thin slabs, the bending deflection and torsional displacement formulas of CRCP under the concentrated vertical load with hollow foundation are deduced, which is verified by the results of finite element(FE). The results show that the characteristic of CRCP after cracking is related to the rigidity factor which is proportional to the spacing of adjacent cracks and the width of CRCP.

The Mixed-Body Model: A Method for Predicting Large Deflections in Stepped Cantilever Beams

2021 ◽  
pp. 1-18
Author(s):  
Brandon Sargent ◽  
Collin Ynchausti ◽  
Todd G Nelson ◽  
Larry L Howell
Keyword(s):  
Large Deflections ◽  
Cantilever Beams ◽  
Element Analysis ◽  
Body Model ◽  
Minimal Error ◽  
Small Deflection ◽  
Rigid Body Model ◽  
Expected Values ◽  
Deflection Theory ◽  
Sample Set

Abstract This paper presents a method for predicting endpoint coordinates, stress, and force to deflect stepped cantilever beams under large deflections. This method, the Mixed-Body Model or MBM, combines small deflection theory and the Pseudo-Rigid-Body Model for large deflections. To analyze the efficacy of the model, the MBM is compared to a model that assumes the first step in the beam to be rigid, to finite element analysis, and to the numerical boundary value solution over a large sample set of loading conditions, geometries, and material properties. The model was also compared to physical prototypes. In all cases, the MBM agrees well with expected values. Optimization of the MBM parameters yielded increased agreement, leading to average errors of <0.01 to 3%. The model provides a simple, quick solution with minimal error that can be particularly helpful in design.

Bending of a Cylindrically Aeolotropic Circular Plate With Eccentric Load

1952 ◽  
Vol 19 (1) ◽  
pp. 9-12
Author(s):  
A. M. Sen Gupta
Keyword(s):  
Boundary Conditions ◽  
Circular Plate ◽  
Uniform Thickness ◽  
Eccentric Load ◽  
Concentrated Load ◽  
Different Boundary Conditions ◽  
Small Deflection ◽  
Deflection Theory ◽  
Clamped Edge

Abstract The problem of small-deflection theory applicable to plates of cylindrically aeolotropic material has been developed, and expressions for moments and deflections produced have been found by Carrier in some symmetrical cases under uniform lateral loadings and with different boundary conditions. The author has also found the moments and deflection in the case of an unsymmetrical bending of a plate loaded by a distribution of pressure of the form p = p0r cos θ, with clamped edge. The object of the present paper is to investigate the problem of the bending of a cylindrically aeolotropic circular plate of uniform thickness under a concentrated load P applied at a point A at a distance b from the center, the edge being clamped.

On Free Vibrations of a Thin Spinning Disk Stiffened With an Outer Reinforcing Ring

1988 ◽  
Vol 110 (4) ◽  
pp. 507-514 ◽  
Author(s):  
S. K. Sinha
Keyword(s):  
Data Storage ◽  
Free Vibrations ◽  
Circular Ring ◽  
Outer Edge ◽  
Design Parameters ◽  
Computer Data ◽  
Storage Devices ◽  
Small Deflection ◽  
Deflection Theory ◽  
Annular Disks

Thin spinning annular disks, which have widely varying applications ranging from inertial wheels in spacecraft to computer data storage devices, experience some inherent vibration problems during operation. One of the techniques to control the vibrations of the disk, being analyzed in this paper, is to stiffen it by attaching a reinforcing ring at its outer edge. The present work considers the effect of adding such a ring and discusses the changes in the natural frequencies for a large range of design parameters. The classical plate bending equation based upon small deflection theory which includes the contribution of rotational membrane stresses has been used in the eigenvalue formulation. Numerical results presented in a nondimensional form should be useful in predicting the dynamic response of such a disk stiffened with a circular ring under the spinning conditions.

Bending of Sandwich Plates of Variable Thickness

1988 ◽  
Vol 55 (2) ◽  
pp. 419-424 ◽  
Author(s):  
N. Paydar ◽  
C. Libove
Keyword(s):  
Potential Energy ◽  
Variable Thickness ◽  
Middle Surface ◽  
Total Potential Energy ◽  
Sandwich Plates ◽  
Energy Principle ◽  
Total Potential ◽  
Small Deflection ◽  
The Face ◽  
Deflection Theory

A small deflection theory, consisting of differential equations and a total potential energy expression, is presented for determining the stresses and deformations in variable thickness elastic sandwich plates symmetric about a middle surface. The theory takes into account the contribution of the face-sheet membrane forces (by virtue of their slopes) to the transverse shear. A finite-difference formulation of the stationary total potential energy principle is presented along with an illustrative application.

Stress Concentrations in Thin Spherical Shells

1966 ◽  
Vol 88 (2) ◽  
pp. 231-236 ◽  
Author(s):  
Egor P. Popov ◽  
Joseph Penzien ◽  
Mandayam K. S. Rajan
Keyword(s):  
Axial Load ◽  
Shear Load ◽  
Stress Distributions ◽  
Stress Concentrations ◽  
Spherical Shells ◽  
Practical Applications ◽  
Small Deflection ◽  
External Moment ◽  
Rigid Insert ◽  
Deflection Theory

Stress distributions occurring in the proximity of rigid circular inserts attached to thin spherical shells are reported in this paper. The solutions are achieved by employing conical coordinates tangent to the sphere at its intersection with the insert. A small-deflection theory is used and results are stated in terms of readily available functions. For convenience in practical applications, solutions for several loading conditions are carried through to completion. Specifically, the paper gives formulas for stress distributions occurring in a spherical shell when provided with a rigid insert and when subjected to (a) internal pressurization in the shell; (b) axial load on the insert; (c) external moment on the insert; and (d) tangential shear load on the insert. The necessary constants of integration are given in tables and the procedure developed is illustrated by a comprehensive example.

scholarly journals Nonlinear Free Vibration Analysis of Axisymmetric Polar Orthotropic Circular Membranes under the Fixed Boundary Condition

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Zhoulian Zheng ◽  
Jianjun Guo ◽  
Weiju Song ◽  
Xiaoting He ◽  
Faming Lu ◽  
...  
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Circular Membrane ◽  
Nonlinear Free Vibration ◽  
Frequency Method ◽  
Initial Displacement ◽  
Small Deflection ◽  
Deflection Theory ◽  
Polar Orthotropic

This paper presents the nonlinear free vibration analysis of axisymmetric polar orthotropic circular membrane, based on the large deflection theory of membrane and the principle of virtual displacement. We have derived the governing equations of nonlinear free vibration of circular membrane and solved them by the Galerkin method and the Bessel function to obtain the generally exact formula of nonlinear vibration frequency of circular membrane with outer edges fixed. The formula could be degraded into the solution from small deflection vibration; thus, its correctness has been verified. Finally, the paper gives the computational examples and comparative analysis with the other solution. The frequency is enlarged with the increase of the initial displacement, and the larger the initial displacement is, the larger the effect on the frequency is, and vice versa. When the initial displacement approaches zero, the result is consistent with that obtained on the basis of the small deflection theory. Results obtained from this paper provide the accurate theory for the measurement of the pretension of polar orthotropic composite materials by frequency method and some theoretical basis for the research of the dynamic response of membrane structure.

Rectangular Pressure Vessels of Finite Length

1990 ◽  
Vol 112 (1) ◽  
pp. 50-56 ◽  
Author(s):  
A. E. Blach ◽  
V. S. Hoa ◽  
C. K. Kwok ◽  
A. K. W. Ahmed
Keyword(s):  
Finite Length ◽  
Design Method ◽  
Circular Cross Section ◽  
Pressure Vessels ◽  
Small Deflection ◽  
Asme Code ◽  
Test Pressure ◽  
Section Viii ◽  
Deflection Theory ◽  
Large Deflection Theory

Design Rules in the ASME Code, Section VIII, Division 1, cover the design of unreinforced and reinforced rectangular pressure vessels. These rules are based on “infinitely long” vessels of non-circular cross section and stresses calculated are based on a linearized “small deflection” theory of plate bending. In actual practice, many pressure vessels can be found which are of finite length, often operating successfully under pressures two to three times as high as those permitted under the Code rules cited. This paper investigates the effects of finite length on the design formulae given by the ASME Code, and also a design method based on “large deflection” theory coefficients for short rectangular pressure vessels. Results based on analysis are compared with values obtained from finite element computations, and with experimental data from strain gage measurements on a test pressure vessel.

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