A structural element whose length greatly exceeds both its width and height, which are of the same order of magnitude.

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I'm looking for a formal definition of 'scintillations' in laser beam propagation

I'm trying to make a scintillometer, based on Rytov's method. I've understood the whole phenomenon, and gone through some of the research papers in the field. But, I haven't encountered any definition ...
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22 views

Dimensional scaling of structural stiffness

Consider a beam of some material with Young modulus $E$, the axial stiffness of the beam is given by the expression $$k = \frac{A E}{L}$$ where $A$ is cross-sectional area of the beam, and L is the ...
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33 views

Simple Beam Worst Case Scenario

Part 1 If I have a simple beam with two supports and a static load, does placing the load in the center push the beam closest to breaking (catastrophic failure)? Will this be more likely to break ...
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83 views

Bending moment of a cantilever beam

The following procedure is here. Consider a cantilever fixed at one end and loaded at the other one. In cartesian coordinates (if $y$ is horizontal and $x$ vertical, meaning that the load acts ...
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27 views

How to specify boundary conditions as function of curvature in dynamic elastic beam pde?

In this article (already mentioned in this question) the dynamics of a planar elastic beam with "cantilever constrains" (one clamped end and one free end) is modeled. Using the Euler-Bernoulli Beam ...
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34 views

Neutral axis location in a beam with axial load

Assume that we have a beam that is axially loaded. Is the position of the neutral axis in this beam is dependent to the magnitude or position of the load?
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53 views

Is the moment-curvature relation for an elastic beam general?

The relationship between the moment and the curvature for an elastic beam is $$M = -EI\kappa$$ Previously, I have only used this with small deflections in static calculations. I am currently working ...
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98 views

How does the net torque have to be 0 at all points for static equilibrium? [duplicate]

I know that for a mass to be in static equilibrium two things have to be satisfied: $\sum F=0$ and $\sum T=0$, where $T$ represents torque. However, I am not sure how the latter can apply in a ...
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85 views

How to have an I-Beam bend as little as possible

I have an I-Beam cantilever beam and apply a force to the free end. If I want the displacement in the vertical axis of the end being forced to be as small as possible from that when no force is ...
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121 views

Theoretical limits to specific strength with hierarchical structures

Specific strength (measured in units of pressure/density or speed$^2$ which in MKS there is a proposal for labelling it as the Yuri (meter/second)$^2$) is defined as tensile strength divided by ...
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109 views

Large rotation Euler-Bernoulli beam boundary condition

Is given in Wikipedia as $$EI\frac{d^4u}{dx^4}-\frac{3}{2}EA\left(\frac{du}{dx}\right)^2\frac{d^2u}{dx^2} = q(x) ,$$ where $q(x)$ is the transverse load (assuming uniform cross-section and no axial ...
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138 views

Why is deflection at the boundary 0 for the given statically indeterminate beam problem?

I have been trying really hard to understand the boundary condition applied to the indeterminate beam problems.. although i am citing a particular problem, i have been finding the same approach in ...
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What are some structures which minimize surface stress upon expansion

Intro I am currently researching into a problem involving the cyclical expansion and contraction of a 3 layered structure comprised of an internal metal encased by another metal encased in an outer ...
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40 views

Why do we consider the application of force as well as bending moment in finding the moments of a beam?

In the standard techniques of beam related problems, solving for moment at any cross section includes counting the torque due to shear force as well as some extra moment, which according to me ...
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94 views

buckling of tube - shell thickness vs. momentum of inertia optimum

is there any simple formula (perhabs semi emperical, or aproximatively derived model) for buckling of tube under axial compression load given its crossection and wall thickness? ( and naturraly ...
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99 views

What is the difference between a linear and non-linear solution in the bending of beams?

I have been working on a simulator for bending of beams and came now to a tricky doubt: What should be the difference between a linear and non linear solution in this case (graphic at bottom)? The ...
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284 views

Can somebody explain the graphical integration method in a better way?

After hours of research all what I can find is this: http://www.public.iastate.edu/~fanous/ce332/virtualwork/homepage.html can somebody explain this method in a better way. If the moment diagram ...
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Why does diamond have lower tensile strength than Iron?

Let me first give you the tensile strength of both substance: Diamond: 16000 MPa Steel : 2617 MPa As you guys should know, tensile strength is how much a ...
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324 views

Large deflection of cantilever beam

How can I find the amount of point force at the end of a cantilever plastic beam that produces e.g. 45° slope at the end of the beam? Is this the right equation: $$F=\frac{2EI\theta ^2}{L^2 ...
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214 views

What do tensile strength values mean and why are they reported in units of pressure?

How does one interpret the numbers when reading data about tensile strength, yield strength, and the likes? Say for example reinforcing bars. Grade 40 Rebars are rated at 70,000 PSI for its ultimate ...
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111 views

What is the $n$ in the formula in Solid Mechanics? [closed]

The formula is about the critical force for the elastic beam that is supported by its joints: $$ P_{cr} ~=~ n^2 \pi^2 \frac{EI}{ L^2} $$ It should be based on the book Parnes - Solid ...
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95 views

Deriving the curve of a cantilever

Essentially, there is a beam of length L and negligible mass sticking out of a wall with a mass Mg hanging at the end of it. We are given an equation for elastic energy (which I don't think needs to ...
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Stress in a thick-walled pressure vessel

I can find many references that give the stress in the walls of a pressure vessel for spheres and tubes, but they all seem to be limited to a thin-wall approximation. I'll limit my writing here to ...
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359 views

Stress analysis of a cantilever beam using FDM

I am a CSE researcher with a not so in depth background of physics. As a part of my research in object modelling, I am trying to computationally figure out the stress for various objects by using ...
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300 views

Solving the differential equation of a beam under moving load using green functions

i started working on this paper and i didnt understand one part of it , the problem is : Solve this equation using green functions : $$ EI {\partial^4 y(x,t)\over\partial x^4}+\mu ...
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378 views

Euler's buckling formula applicable for impact calculations?

$$F = \frac{\pi^2 EI}{(KL)^2}$$ Is Euler's buckling formula applicable for impact calculations, considering speeds relevant for a car or aircraft crash? If there is a level where the formula ...
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544 views

What is the mathematical formulation for buckling?

Argument: Buckling is an engineering concept that can only be applied to thin columns with compressive loading. (Is it possible to) Prove the above sentence right or wrong with mathematical ...