scholarly journals Large Deflections in Unmovable Simply Supported Flexible Beam Subjected to Bending Moment.

1994 ◽  
Vol 60 (570) ◽  
pp. 487-493 ◽  
Author(s):  
Atsumi Ohtsuki ◽  
Tsuyoshi Yasui
Keyword(s):  
Bending Moment ◽  
Flexible Beam ◽  
Large Deflections ◽  
Simply Supported

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.

scholarly journals Influence of stirrup spacing on shear resistance and deformation of reinforced concrete beams

2018 ◽  
Vol 7 (1) ◽  
pp. 126
Author(s):  
Latha M S ◽  
Revanasiddappa M ◽  
Naveen Kumar B M
Keyword(s):  
Concrete Beam ◽  
Concrete Beams ◽  
Bending Moment ◽  
Maximum Load ◽  
Reinforced Concrete Beams ◽  
Test Results ◽  
Cement Concrete ◽  
Simply Supported ◽  
Reinforced Cement ◽  
Flexural Reinforcement

An experimental investigation was carried out to study shear carrying capacity and ultimate flexural moment of reinforced cement concrete beam. Two series of simply supported beams were prepared by varying diameter and spacing of shear and flexural reinforcement. Beams of cross section 230 mm X 300 mm and length of 2000 mm. During testing, maximum load, first crack load, deflection of beams were recorded. Test results indicated that decreasing shear spacing and decreasing its diameter resulted in decrease in deflection of beam and increase in bending moment and shear force of beam.

Bending of a Uniformly Loaded Rectangular Plate With Two Adjacent Edges Clamped and the Others Either Simply Supported or Free

1952 ◽  
Vol 19 (4) ◽  
pp. 451-460
Author(s):  
M. K. Huang ◽  
H. D. Conway
Keyword(s):  
Rectangular Plate ◽  
Bending Moment ◽  
Simply Supported

Abstract The distribution of deflection and bending moment in a uniformly loaded rectangular plate having two adjacent edges clamped and the others either simply supported or free, are obtained by a method of superposition. Numerical values are given for square plates and, in one case, the results are compared with those obtained by another method.

Studies on Codimension-3 Degenerate Bifurcations of the Flexible Beam

2001 ◽  
Author(s):  
Wei Zhang ◽  
Feng-Xia Wang ◽  
Hong-Bo Wen
Keyword(s):  
Normal Form ◽  
Flexible Beam ◽  
Main Attention ◽  
Double Zero ◽  
Normal Form Theory ◽  
Simply Supported ◽  
Axial Excitation ◽  
Averaged Equations ◽  
Homoclinic Bifurcations ◽  
Form Theory

Abstract We present the analysis of codimension-3 degenerate bifurcations of a simply supported flexible beam subjected to harmonic axial excitation. The equation of motion with quintic nonlinear terms and the parametrical excitation for the simply supported flexible beam is derived. The main attention is focused on the dynamical properties of the global bifurcations including homoclinic bifurcations. With the aid of normal form theory, the explicit expressions of normal form associated with a double zero eigenvalues and Z2-symmetry for the averaged equations are obtained. Based on the normal form, it has been shown that a simply supported flexible beam subjected to the harmonic axial excitation can exhibit homoclinic bifurcations, multiple limit cycles, and jumping phenomena in amplitude modulated oscillations. Numerical simulations are also given to verify the good analytical predictions.

Impacting of Pipes on Elastic Supports

1986 ◽  
Vol 108 (4) ◽  
pp. 542-546 ◽  
Author(s):  
R. Kumar
Keyword(s):  
Simple Model ◽  
Thermal Stresses ◽  
Impact Force ◽  
Bending Moment ◽  
Elastic Supports ◽  
Simply Supported ◽  
Impact Location ◽  
Piping Systems ◽  
Effect Of Support ◽  
The Impact

Piping systems are often provided with supports and restraints with gaps to reduce the thermal stresses and to limit the motion caused by other loads, e.g., due to pipe rupture or seismic effects. However, the presence of the gap causes the pipe to impact on the support under dynamic loading. In this paper the impacting effects have been studied using a simple model. The effect of support rigidity on the impact force, bending moment and deflection of the pipe has been evaluated. The bending moment at the impact loading is found to decrease up to a certain value of the support stiffness beyond which it increases. However, the impact force increases and the overall deflection at the impact location decreases continuously as the support stiffness is increased. The results are presented in nondimensional form as ratios of the appropriate quantities for the simply supported pipe with no elastic restraint. Thus, they provide useful information for design considering impact effects.

Chained Beam-Constraint-Model (CBCM): A Powerful Tool for Modeling Large and Complicated Deflections of Flexible Beams in Compliant Mechanisms

2014 ◽  
Author(s):  
Fulei Ma ◽  
Guimin Chen
Keyword(s):  
Large Deflection ◽  
Compliant Mechanisms ◽  
Research Community ◽  
The Other ◽  
New Method ◽  
Flexible Beam ◽  
Large Deflections ◽  
Flexible Beams ◽  
Constraint Model

Modeling large deflections has been one of the most fundamental problems in the research community of compliant mechanisms. Although many methods are available, there still exists a need for a method that is simple, accurate, and can be applied to a vast variety of large deflection problems. Based on the beam constraint model (BCM), we propose a new method for modeling large deflections called chained BCM (CBCM), which divides a flexible beam into a few elements and models each element by BCM. It is demonstrated that CBCM is capable of modeling various large and complicated deflections of flexible beams in compliant mechanisms. In general, CBCM obtains accurate results with no more than 6 BCM elements, thus is more efficient than most of the other discretization-based methods.

scholarly journals Dynamic Large Deflection Response of RC Beams under Low-Speed Impact Loading

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Lu Guo ◽  
Renwei Mao ◽  
Zhifang Liu ◽  
Shiqiang Li ◽  
Guiying Wu ◽  
...  
Keyword(s):  
Impact Energy ◽  
Impact Loading ◽  
Large Deflection ◽  
Bending Moment ◽  
Theoretical Models ◽  
Rc Beams ◽  
Low Speed ◽  
Simply Supported ◽  
Analytical Formulas ◽  
Clamped Beams

The dynamic large deflection response of RC beams under low-speed impact loading at their midspan is investigated in this paper. Two simple methods such as extended Hamilton’s principle and equivalent static hypothesis are used to establish the theoretical models for both simply supported and fully clamped RC beams; analytical formulas for the maximum midspan deflection-input impact energy are obtained. The “equal area” method based on the deflection history of beams is only used during these derivations to determine the plastic bending moment and the stress distribution of the structure. Then, finite element simulations are carried out to verify the validity of the proposed predictions. It is shown that the maximum deflections for both simply supported and fully clamped beams are almost proportional with respect to the input impact energy, which agrees well with both simulations and other experimental results. Also, the boundary condition has more effect on the deflection response of the RC beams which is relatively longer.

Large Deflections of Circular Plates

1952 ◽  
Vol 19 (3) ◽  
pp. 287-292
Author(s):  
M. Stippes ◽  
A. H. Hausrath
Keyword(s):  
Circular Plate ◽  
Critical Values ◽  
Graphical Form ◽  
Series Expansions ◽  
Large Deflections ◽  
Circular Plates ◽  
Simply Supported ◽  
Perturbation Procedure

Abstract This paper contains a solution of von Kármán’s equations for a uniformly loaded, simply supported circular plate. The method used to obtain the solution is the perturbation procedure. Series expansions for the deflection and stresses in the plate are obtained. The legitimacy of these expansions is demonstrated in the Appendix. Critical values of stress and deflection are presented in graphical form. Furthermore, tables of coefficients for the afore-mentioned series are presented if anyone desires to extend the results which are presented here.

Forced Vibrations of Thin, Elastic, Rectangular Plates with Edges Elastically Restrained Against Rotation

1977 ◽  
Vol 21 (01) ◽  
pp. 24-29
Author(s):  
E. A. Susemihl ◽  
P. A. A. Laura
Keyword(s):  
Bending Moment ◽  
Forced Vibrations ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Edge Conditions ◽  
Approach Infinity ◽  
Square Plate ◽  
Elastic Rectangular Plate ◽  
Elastically Restrained ◽  
The Galerkin Method

Polynomial coordinate functions and the Galerkin method are used to determine the response of a thin, elastic, rectangular plate with edges elastically restrained against rotation and subjected to sinusoidal excitation. It is shown that when the flexibility coefficients approach infinity (simply supported edge conditions) the calculated results practically coincide with the exact solution in the case of a square plate when four terms of the expansion are used. Dynamic displacement and bending moment amplitudes are tabulated for different length-to-width ratios, flexibility coefficients, and frequency values.

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