Large Deflections of a Simply Supported Beam Subjected to Moment at One End

1984 ◽  
Vol 51 (3) ◽  
pp. 519-525 ◽  
Author(s):  
P. Seide
Keyword(s):  
Linear Theory ◽  
Bending Moment ◽  
Critical Value ◽  
The Other ◽  
Large Deflections ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
Elastica Theory ◽  
Angle Of Rotation

The large deflections of a simply supported beam, one end of which is free to move horizontally while the other is subjected to a moment, are investigated by means of inextensional elastica theory. The linear theory is found to be valid for relatively large angles of rotation of the loaded end. The beam becomes transitionally unstable, however, at a critical value of the bending moment parameter MIL/EI equal to 5.284. If the angle of rotation is controlled, the beam is found to become unstable when the rotation is 222.65 deg.

The dynamic lateral instability of beams

1954 ◽  
Vol 226 (1164) ◽  
pp. 111-128
Keyword(s):  
Theoretical Analysis ◽  
Reasonable Agreement ◽  
Vertical Plane ◽  
Bending Moment ◽  
Critical Value ◽  
The Other ◽  
Lateral Bending ◽  
Lateral Instability ◽  
Maximum Stiffness ◽  
The Moment

The vibrations of a deep slender beam, bent to uniform curvature by in variant moments acting in a vertical plane, which is also the plane of maximum stiffness, have been studied. It is shown that the moments couple up the lateral bending and torsional modes of the beam, those modes being replaced by two independent modes, each involving torsion and flexure. One of these m odes is associated with a frequency which decreases with increasing bending moment, the frequency becoming zero when the moment reaches the critical value for lateral instability. The other mode is associated with a frequency which increases with bending moment. Experiments were carried out on an I-section cantilever carrying an end mass. Owing to the varying bending moment, the theoretical analysis of this case is more complicated, and an iterative method, originated by Schwarz (1890), has been employed. Results are in reasonable agreement with experiment.

Response of Elastic Bodies to a Uniformly Accelerating Point Force

1970 ◽  
Vol 92 (2) ◽  
pp. 400-403
Author(s):  
T. F. Raske ◽  
Ki Sub Joung
Keyword(s):  
Cylindrical Shell ◽  
Dynamic Response ◽  
Rectangular Plate ◽  
Linear Theory ◽  
Point Force ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
Shallow Cylindrical Shell ◽  
Elastic Bodies ◽  
Constant Magnitude

An analysis based upon linear theory is presented for determining the dynamic response of a simply supported beam, rectangular plate and shallow cylindrical shell to a point force of variable magnitude uniformly accelerating across the surface of these elastic bodies. It is shown that resonant conditions are not associated with problems of this type. Typical deflection profiles are included for a constant magnitude point force accelerating across a beam.

Stability of Rectangular Plates Under Shear and Bending Forces

1936 ◽  
Vol 3 (4) ◽  
pp. A131-A135 ◽  
Author(s):  
Stewart Way
Keyword(s):  
Critical Load ◽  
Rectangular Plate ◽  
Bending Moment ◽  
The Other ◽  
Rectangular Plates ◽  
Bending Stress ◽  
Simply Supported ◽  
Tension And Compression ◽  
The Way

Abstract The author first discusses the problem of a plane, simply supported rectangular plate loaded by shearing forces in the plane of the plate on all four edges. There are two stiffeners attached one third and two thirds of the way along the plate. The critical load is calculated for various stiffener rigidities. Also, the rigidity necessary to keep the stiffeners straight when the plate buckles is found. This stiffener rigidity is found to be slightly larger than that necessary for a plate with one stiffener and the same panel dimensions as the plate with two stiffeners. The second problem discussed by the author is that of a plane, simply supported rectangular plate loaded by uniformly distributed edge shearing forces in the plane of the plate and linearly distributed tension and compression in the plane of the plate at the ends. The end forces vary from tension hσo, at one corner to—hσo, at the other corner, so that their resultant is a bending moment. The presence of the edge shearing forces is found to diminish the critical bending stress in this case. Calculations are made for various magnitudes of bending and shearing forces for plates of various proportions.

DETECTION OF DAMAGE LOCATIONS IN A BEAM USING THE WAVELET ANALYSIS

2001 ◽  
Vol 01 (03) ◽  
pp. 455-465 ◽  
Author(s):  
Y. Y. LEE ◽  
K. M. LIEW
Keyword(s):  
Wavelet Analysis ◽  
Damage Detection ◽  
Case Studies ◽  
Bending Moment ◽  
Eigenvalue Analysis ◽  
Open Crack ◽  
Beam Structures ◽  
Simply Supported Beam ◽  
Simply Supported

This paper presents an effective way in damage detection of beam structures using the wavelet analysis along with the general beam solution. Two case studies are considered: (1) a clamped beam with a damage point of zero bending moment; and (2) a simply supported beam with a transverse open crack. The proposed method is capable of revealing the precise damage locations which is generally difficult to be identified using the standard eigenvalue analysis.

Research on Numerical Computation of Natural Frequency of Transverse Vibration for Simply Supported Beam of Non-Uniform

2011 ◽  
Vol 71-78 ◽  
pp. 3316-3319 ◽  
Author(s):  
Bo Qian
Keyword(s):  
Differential Equation ◽  
Numerical Computation ◽  
Natural Frequency ◽  
Transverse Vibration ◽  
Vertical Direction ◽  
Bending Moment ◽  
Variable Coefficients ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
Computation Step

Recursive and inexplicit differential equation of the second order with variable coefficients is derived from the fourth order linear homogeneous differential equation with variable coefficients of transverse vibration of non-uniform beam, which is about deflection and bending moment according to boundary conditions and order reduction. By finite difference method, numerical computation and accuracy are studied for natural frequency of transverse vibration for simply supported beam of non-uniform. Theoretical analysis and orthogonal computation examples show that numerical computation algorithm is very simple, and accuracy of computation depends on variety rate of gradually changed cross section in vertical direction and numbers of computation step, which is independent of width and length of beam; numerical accuracy of computation is estimable for given length or numbers of computation step; and reasonable length or numbers of computation step is determinable for given accuracy demand.

scholarly journals Effect of Material Characteristics of High Damping Rubber Bearings on Aseismic Behaviors of a Two-Span Simply Supported Beam Bridge

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Yumin Zhang ◽  
Jiawu Li
Keyword(s):  
Time History ◽  
Bending Moment ◽  
Seismic Energy ◽  
Northridge Earthquake ◽  
Horizontal Shear ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
High Damping Rubber ◽  
Rubber Bearings ◽  
Beam Bridge

There are a large number of damping materials in high-damping rubber (HDR) bearings, so the HDR bearings have the characteristics of both common rubber bearings and damping measures and show good aseismic effect. In this paper, the time-history dynamic analysis method is used to study the seismic effects of HDR bearings on the aseismic behaviors of two-span simply supported beam bridge under Northridge earthquake by changing the damping characteristics of the bearings. It is found that, with increasing damping of the bearings, both the horizontal shear and the displacement of the HDR bearings decrease, and the seismic energy dissipates through both the yield deformation and damping of the bearings. Although the girder and bearings have smaller displacement, when the HDR bearings with larger damping, the seismic responses, including displacement of pier top, shear force of pier bottom, and bending moment of pier bottom, are hardly affected by the change of the damping of the bearings. The HDR bearings with higher damping and yield characteristics separate and dissipate the seismic energy transmitted to the superstructure of the bridge and have better seismic effect on the structure in an earthquake.

Solution of Statically Indeterminate Beam with Straight Axis by Section-Conversion Method

2015 ◽  
Vol 744-746 ◽  
pp. 292-297
Author(s):  
Xiao Jin Yu
Keyword(s):  
Compatibility Condition ◽  
Internal Force ◽  
The Other ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
Base Element ◽  
Conversion Method ◽  
Displacement Equation ◽  
Internal Forces

For computation of reaction, internal force and displacement of a beam, the displacement equation from Conversion Method is used in establishing compatibility condition of deformation. In the process of Section-Conversion Method, the joints without sway is set as the coordinate criterion. Cutting the part between two joints as a base element with the method of section, it becomes a simply supported beam in form. The internal forces at the section cut are those which equivalent forces from other side of the beam. According to the axiom of action and reaction, the equivalent forces react to the other part of the beam. The displacement equations are used for all parts one by one. The precision resolutions of reaction, internal force and displacement of a beam are achieved.

Moments and Deflections of a Simply-Supported Beam Grillage

1957 ◽  
Vol 8 (4) ◽  
pp. 360-368 ◽  
Author(s):  
J. P. Ellington ◽  
H. McCallion
Keyword(s):  
Finite Differences ◽  
The Other ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
Sinusoidal Variation

Summary:By using the methods of the Calculus of Finite Differences, expressions are obtained for the nodal moments and deflections of a simply-supported grillage, subjected to a loading constant along one set of beams and having a sinusoidal variation along the other set of beams. A simple example verifies the expressions and illustrates their use.

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