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.

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.

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.

scholarly journals Analytical solution to bending of stiffened and continuous antisymmetric laminates

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
Liecheng Sun ◽  
Issam E. Harik
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Analytical Solution ◽  
Displacement Function ◽  
The Other ◽  
Order Partial Differential Equation ◽  
Eighth Order ◽  
Coupling Problem ◽  
Simply Supported ◽  
General Response

AbstractAnalytical Strip Method is presented for the analysis of the bending-extension coupling problem of stiffened and continuous antisymmetric thin laminates. A system of three equations of equilibrium, governing the general response of antisymmetric laminates, is reduced to a single eighth-order partial differential equation (PDE) in terms of a displacement function. The PDE is then solved in a single series form to determine the displacement response of antisymmetric cross-ply and angle-ply laminates. The solution is applicable to rectangular laminates with two opposite edges simply supported and the other edges being free, clamped, simply supported, isotropic beam supports, or point supports.

Experimental Study on the Dynamic Deformation of Simply Supported Beam in Chinese High-speed Railway

2018 ◽  
Author(s):  
Gonglian Dai ◽  
Meng Wang ◽  
Tianliang Zhao ◽  
Wenshuo Liu
Keyword(s):  
High Speed ◽  
Structure Design ◽  
Dynamic Coefficient ◽  
Bridge Structure ◽  
High Speed Railway ◽  
Simply Supported Beam ◽  
Vertical Stiffness ◽  
Simply Supported ◽  
Speed Up ◽  
Design Speed

<p>At present, Chinese high-speed railway operating mileage has exceeded 20 thousand km, and the proportion of the bridge is nearly 50%. Moreover, high-speed railway design speed is constantly improving. Therefore, controlling the deformation of the bridge structure strictly is particularly important to train speed-up as well as to ensure the smoothness of the line. This paper, based on the field test, shows the vertical and transverse absolute displacements of bridge structure by field collection. What’s more, resonance speed and dynamic coefficient of bridge were studied. The results show that: the horizontal and vertical stiffness of the bridge can meet the requirements of <b>Chinese “high-speed railway design specification” (HRDS)</b>, and the structure design can be optimized. However, the dynamic coefficient may be greater than the specification suggested value. And the simply supported beam with CRTSII ballastless track has second-order vertical resonance velocity 306km/h and third-order transverse resonance velocity 312km/h by test results, which are all coincide with the theoretical resonance velocity.</p>

scholarly journals Determination of reinforcing bars for tests of hollow core slabs with continuity

2013 ◽  
Vol 6 (6) ◽  
pp. 903-932
Author(s):  
A. P. Santos ◽  
M. A. Ferreira ◽  
R. C. Carvalho ◽  
L. M. Pinheiro
Keyword(s):  
Shear Strength ◽  
The Other ◽  
Hollow Core ◽  
Reinforcing Bars ◽  
Simply Supported ◽  
Resistance Moment ◽  
Hollow Core Slab ◽  
Maximum Shear Strength

The structural designs of floors formed by hollow core slabs usually consider these as simply-supported slabs. In recent years there have been project changes and hollow core slabs with continuity are widely used. The objective of this study is to suggest a way to calculate the reinforcement bars to be used in tests with continuity provided by a structural topping. Thus, this paper presents a method based on the maximum positive resistance moment and maximum shear strength of a hollow core slab. The method is applied to a test in hollow core slab specimens which have the following dimensions: 2 m width, 6 m long, and 21 cm high. The results indicated that the method was satisfactory to the performed test, and can therefore be applied to the other test configurations or even designs.

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