The Finite Beam With a Moving Load

1967 ◽  
Vol 34 (1) ◽  
pp. 111-118 ◽  
Author(s):  
C. R. Steele
Keyword(s):  
Moving Load ◽  
Steady State Solution ◽  
Fourier Integral ◽  
Method Of Images ◽  
Asymptotic Results ◽  
Lateral Velocity ◽  
Concentrated Load ◽  
Simply Supported ◽  
Asymptotic Evaluation ◽  
Limiting Case

A “method of images” series solution is obtained which converges rapidly for a simply supported, long beam with a high-velocity, moving concentrated load. Each term of the series is a Fourier integral solution for an appropriate semi-infinite beam problem. The integrals are evaluated in closed form for the beam without a foundation and have a simple asymptotic evaluation for the beam with an elastic foundation. In particular, the asymptotic results provide a solution for the “critical” load velocity, for which a “steady-state” solution does not exist, and for the limiting case of infinite load velocity, for which the beam is given an initial uniform lateral velocity.

The Timoshenko Beam With a Moving Load

1968 ◽  
Vol 35 (3) ◽  
pp. 481-488 ◽  
Author(s):  
C. R. Steele
Keyword(s):  
Steady State ◽  
Timoshenko Beam ◽  
Moving Load ◽  
Beam Theory ◽  
Steady State Solution ◽  
State Solution ◽  
Asymptotic Results ◽  
Concentrated Load ◽  
Steady State Condition ◽  
Bar Velocity

The problem of a semi-infinite Timoshenko beam of an elastic foundation with a step load moving from the supported end at a constant velocity is discussed. Asymptotic solutions are obtained for all ranges of load speed. The solution is shown to approach the “steady-state” solution, except for three speeds at which the steady state does not exist. Previous investigators have considered only the steady-state solution for the moving concentrated load and have indicated that the three speeds are “critical.” It is shown, however, that only the lowest speed is truly critical in that the response increases with time. For the load speed equal to either the shear or bar velocity, the transients due to the end condition never leave the vicinity of the load discontinuities, so a steady-state condition is never attained. However, the response is shown to be bounded in time for a distributed load. Thus the nonexistence of a steady state does not necessarily indicate a critical condition. Furthermore, the concentrated load solution is shown to have validity at speeds the magnitude of the sonic speeds only for loads of a concentration beyond the limitations of beam theory. Asymptotic results have also been obtained for the beam without a foundation. Since the procedure is similar for beams with, and without, a foundation, only the results are included to show a comparison with the numerical results previously obtained by Florence.

The Significance of the Concentrated Load in the Limit Analysis of Conical Shells

1966 ◽  
Vol 33 (1) ◽  
pp. 93-101 ◽  
Author(s):  
John A. DeRuntz ◽  
P. G. Hodge
Keyword(s):  
Yield Condition ◽  
Point Load ◽  
Concentrated Load ◽  
Shallow Shells ◽  
Conical Shells ◽  
Simply Supported ◽  
Tresca Yield Condition ◽  
Wide Range ◽  
Limiting Case ◽  
Yield Conditions

The yield point load of a simply supported conical sandwich shell loaded at its vertex through a rigid central boss is found for a material obeying the Tresca yield condition. Exact solutions are found for a wide range of shell configurations ranging from thick shallow cones to thin steep ones, including large and small boss sizes. The results are compared with those for the limiting case of zero boss radius corresponding to a complete conical shell loaded with a concentrated load at its vertex. It is found that for thick shallow shells the concentrated-load solution is a good approximation to the solution for realistically small boss sizes, but that for thin and/or steep shells the agreement is so poor as to make the concentrated-load solution meaningless. It is shown that such behavior also can be expected for shells obeying more realistic yield conditions.

Dynamic Instability Analysis and Design Charts of Curved Panels with Linearly Varying Periodic In-Plane Load

2021 ◽  
pp. 2150130
Author(s):  
G. Patel ◽  
A. N. Nayak ◽  
A. K. L. Srivastava
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Dynamic Instability ◽  
Excitation Frequency ◽  
Instability Region ◽  
Concentrated Load ◽  
Simply Supported ◽  
Finite Element Software ◽  
Design Charts ◽  
Curved Panels

The present paper reports an extensive study on dynamic instability characteristics of curved panels under linearly varying in-plane periodic loading employing finite element formulation with a quadratic isoparametric eight nodded element. At first, the influences of three types of linearly varying in-plane periodic edge loads (triangular, trapezoidal and uniform loads), three types of curved panels (cylindrical, spherical and hyperbolic) and six boundary conditions on excitation frequency and instability region are investigated. Further, the effects of varied parameters, such as shallowness parameter, span to thickness ratio, aspect ratio, and Poisson’s ratio, on the dynamic instability characteristics of curved panels with clamped–clamped–clamped–clamped (CCCC) and simply supported-free-simply supported-free (SFSF) boundary conditions under triangular load are studied. It is found that the above parameters influence significantly on the excitation frequency, at which the dynamic instability initiates, and the width of dynamic instability region (DIR). In addition, a comparative study is also made to find the influences of the various in-plane periodic loads, such as uniform, triangular, parabolic, patch and concentrated load, on the dynamic instability behavior of cylindrical, spherical and hyperbolic panels. Finally, typical design charts showing DIRs in non-dimensional forms are also developed to obtain the excitation frequency and instability region of various frequently used isotropic clamped spherical panels of any dimension, any type of linearly varying in-plane load and any isotropic material directly from these charts without the use of any commercially available finite element software or any developed complex model.

Performance of Reinforced Concrete Beams with Multiple Openings

2020 ◽  
Vol 857 ◽  
pp. 162-168
Author(s):  
Haidar Abdul Wahid Khalaf ◽  
Amer Farouk Izzet
Keyword(s):  
Reinforced Concrete ◽  
Ultimate Load ◽  
Concrete Beams ◽  
Load Capacity ◽  
Reinforced Concrete Beams ◽  
Design Parameters ◽  
Ultimate Load Capacity ◽  
Concentrated Load ◽  
Simply Supported ◽  
Group I

The present investigation focuses on the response of simply supported reinforced concrete rectangular-section beams with multiple openings of different sizes, numbers, and geometrical configurations. The advantages of the reinforcement concrete beams with multiple opening are mainly, practical benefit including decreasing the floor heights due to passage of the utilities through the beam rather than the passage beneath it, and constructional benefit that includes the reduction of the self-weight of structure resulting due to the reduction of the dead load that achieves economic design. To optimize beam self-weight with its ultimate resistance capacity, ten reinforced concrete beams having a length, width, and depth of 2700, 100, and 400 mm, respectively were fabricated and tested as simply supported beams under one incremental concentrated load at mid-span until failure. The design parameters were the configuration and size of openings. Three main groups categorized experimental beams comprise the same area of openings and steel reinforcement details but differ in configurations. Three different shapes of openings were considered, mainly, rectangular, parallelogram, and circular. The experimental results indicate that, the beams with circular openings more efficient than the other configurations in ultimate load capacity and beams stiffness whereas, the beams with parallelogram openings were better than the beams with rectangular openings. Commonly, it was observed that the reduction in ultimate load capacity, for beams of group I, II, and III compared to the reference solid beam ranged between (75 to 93%), (65 to 93%), and (70 to 79%) respectively.

scholarly journals Peridynamic Higher-Order Beam Formulation

2020 ◽  
Author(s):  
Zhenghao Yang ◽  
Erkan Oterkus ◽  
Selda Oterkus
Keyword(s):  
Finite Element Method ◽  
Cantilever Beam ◽  
Higher Order ◽  
Point Load ◽  
Transverse Displacement ◽  
Lagrange Equations ◽  
Concentrated Load ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
Good Agreement

Abstract In this study, a novel higher-order peridynamic beam formulation is presented. The formulation is obtained by using Euler-Lagrange equations and Taylor’s expansion. To demonstrate the capability of the presented approach, several different beam configurations are considered including simply supported beam subjected to distributed loading, simply supported beam with concentrated load, clamped-clamped beam subjected to distributed loading, cantilever beam subjected to a point load at its free end and cantilever beam subjected to a moment at its free end. Transverse displacement results along the beam obtained from peridynamics and finite element method are compared with each other and very good agreement is obtained between the two approaches.

Optimal Forms of Shallow Shells With Circular Boundary, Part 2: Maximum Buckling Load

1984 ◽  
Vol 51 (3) ◽  
pp. 531-535 ◽  
Author(s):  
R. H. Plaut ◽  
L. W. Johnson
Keyword(s):  
Critical Load ◽  
Elastic Shell ◽  
Material Surface ◽  
Fundamental Vibration ◽  
Uniform Loading ◽  
Concentrated Load ◽  
Shallow Shells ◽  
Simply Supported ◽  
Circular Boundary ◽  
Boundary Part

In Part 1, optimal forms were determined for maximizing the fundamental vibration frequency of a thin, shallow, axisymmetric, elastic shell with given circular boundary. Our objective in this part is to maximize the critical load for buckling under a uniformly distributed load or a concentrated load at the center. Again, the shell form is varied and the material, surface area, and uniform thickness of the shell are specified. Both clamped and simply supported boundary conditions are considered for the case of uniform loading, while one example is presented involving a concentrated load acting on a clamped shell. The optimality condition leads to forms that have zero slope at the boundary if it is clamped. The maximum critical load is sometimes associated with a limit point and sometimes with a bifurcation point. It is often substantially higher than the critical load for the corresponding spherical shell.

scholarly journals Analysis of simply supported wood beams at ambient and high temperatures

2018 ◽  
Vol 7 (2.23) ◽  
pp. 180 ◽  
Author(s):  
Elza M M Fonseca ◽  
Pedro J V Gouveia
Keyword(s):  
High Temperatures ◽  
Cross Sections ◽  
Beam Theory ◽  
Sufficient Accuracy ◽  
Load Bearing Capacity ◽  
Concentrated Load ◽  
Standard Methods ◽  
Simply Supported ◽  
Wood Beams ◽  
Safe Load

The main objective of this work is to present a methodology for safety analysis of simply supported wood beams at ambient and high temperatures with a concentrated load at mid-span. Sixteen different beam configurations will be studied. All calculations were conducted according the Eurocode 5, part 1-1 and part 1-2. During this study will be analyzed the safe load bearing capacity according standards and compared with the elastic and plastic load from beam theory. The beam theory can provide sufficient accuracy up to the point of instability. The standard methods are generally conservative and they are suitable to be used for design purposes with safety. The studied beam cross sections will be in glued laminated wood, as yellow birch, with characteristics equals to a Glulam GL28H. 

Interfacial stresses in reinforced concrete cantilever members strengthened with fibre-reinforced polymer laminates

2019 ◽  
Vol 23 (2) ◽  
pp. 277-288 ◽  
Author(s):  
Xue-jun He ◽  
Chao-Yang Zhou ◽  
Yi Wang
Keyword(s):  
Reinforced Concrete ◽  
Interfacial Stress ◽  
Design Parameters ◽  
Stress Concentrations ◽  
Concentrated Load ◽  
Interfacial Stresses ◽  
Simply Supported ◽  
Reinforced Polymer ◽  
Fibre Reinforced Polymer ◽  
Polymer Laminates

Fibre-reinforced polymers have been increasingly used to strengthen reinforced concrete structures. However, premature brittle debonding failures may occur at the ends of externally bonded fibre-reinforced polymer laminates due to interfacial stress concentrations caused by stiffness imbalances. Although many studies exist on fibre-reinforced polymer-strengthened simply supported beams and slabs, the interfacial stress distributions in fibre-reinforced polymer-strengthened cantilever members are very different from those in simply supported members. Based on the assumptions of linear elasticity, deformation compatibility and static equilibrium conditions, the interfacial stresses in fibre-reinforced polymer-strengthened reinforced concrete cantilever members under arbitrary linear distributed loads were analysed. In particular, closed-form solutions were obtained to calculate the interfacial stresses under either a uniformly distributed load or a single concentrated load located at the overhanging end of the cantilever member. Existing test results on cantilever slabs strengthened by carbon fibre–reinforced polymer sheets were used to verify the model. According to the parametric analysis, the maximum interfacial stresses can be reduced by decreasing the fibre-reinforced polymer thickness, increasing the fibre-reinforced polymer bonding length and increasing the adhesive layer thickness, and by using less rigid fibre-reinforced polymer laminates with high tensile strengths. These results are useful for engineers seeking to optimize strengthening design parameters and implement reliable debonding prevention measures.

scholarly journals Analysis of sectorial plates normally loaded over circular domains. II

1984 ◽  
Vol 7 (4) ◽  
pp. 739-754
Author(s):  
Wadie A. Bassali
Keyword(s):  
Circular Domain ◽  
Method Of Images ◽  
Normal Loading ◽  
Simply Supported ◽  
Circular Domains ◽  
Elastically Restrained

The method of images is applied to derive exact expressions for the deflections of unlimited wedge-shaped plates the central parts of which are cut, when the plate is simply supported on the radial edges, elastically restrained or free along the circular edge and is acted upon by one of three types of normal loading distributed over the surface of a circular domain. Formulae for the bending and twisting moments along the circular edge are given. Limiting forms of the obtained solutions are considered.

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