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

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Producing a collimated beam from a point source

I have an optical fibre of numerical aperture $NA$, of very small core radius, located at the focal point ,$f$, of a lens. I should produce a collimated beam of initial radius $f\cdot NA$. But what ...
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1answer
53 views

How to model analytical expression for spring constant $k$ for certain structure?

In the deflection of beam, I learned that $$ \delta y=\frac{FL^3}{3EI} $$ where $$ I=\frac{h^3w}{12} $$ Together they comprise $$ F=\frac{Eh^3w}{4L^3}\delta y $$ How do I apply to four beams? ...
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1answer
28 views

determining the stress of a beam

I have a question regarding a beam. I first consider a force applied to both ends of a rectangular beam which is perpendicular to its cross section with dimensions w (width) and h (height). The length ...
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2answers
60 views

Force distribution on corner supported plane [closed]

This question has been annoying me for a while. If you have a completely ridged rectangular plate of width and height x and y that is supported on each corner (A,B,C,D) and has force (F) directly in ...
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1answer
52 views

3D beam deflection

How can you get formula for 3-dimensional beam deflection at the free end of horizontal cantilever due to the cantilever's own gravitational load? I assumed E= 160GPa, $\nu=0$, $\rho=2330kg/m^3$, ...
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61 views

Eigenfrequencies of a truss

I want to calculate the eigenfrequencies of a 3D truss using the finite element method. The beams should be modelled as Timoshenko beams and I want to use arbitrary shape functions. I know how ...
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0answers
20 views

Design a beam that is straightened with force on one end [closed]

From here, I read that if you have a straight beam, bend it with force at one end, and then create a beam with the resulting curvature, the equal and opposite force won't make a straight beam. What ...
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25 views

Bending moment in composite beam with internal “active” stress

I am looking at a problem of a bending composite beam with a symmetric cross -section, $A(s)$. Above the neutral axis $s$ is material $U$ and below the neutral axis is material $L$. $U$ has an ...
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1answer
30 views

Effect of radioactive decay on the structure

In case of electricity, the understanding is that conductivity occurs only on the surface of the element.Is it true for radio-active decay as well ? If not and the decay occurs within the element, ...
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1answer
120 views

9/11 attack: How can a whole building fall even though impact only on the top of building? [closed]

The airplane hit the top of the building. After a few time the whole building collapsed. How is this physically possible?
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1answer
473 views

How to calculate Young's modulus from a set of data?

The set of data are force vs deflection. Is Young's modulus constant for a material? If the beam is fixed by one fixed support and one vertical support $E = \frac {F}{δ}\frac{3.5L^3}{384I}$
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1answer
26 views

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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1answer
50 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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1answer
213 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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1answer
657 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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77 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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1answer
144 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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1answer
259 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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2answers
166 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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1answer
165 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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1answer
148 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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2answers
311 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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1answer
144 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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1answer
149 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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505 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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4answers
2k views

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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1answer
385 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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3answers
403 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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1answer
120 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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0answers
148 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 ...
2
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2answers
4k views

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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0answers
423 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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1answer
386 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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1answer
430 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 ...
3
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2answers
597 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 ...