73 votes

Why are two wires used in railway overhead equipment?

Overhead line worker here. It's about speed. To answer your question, the purpose of the catenary wire is to get the contact wire to lay flat, so it isn't catenary itself. In your second photo, there ...
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18 votes
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Why does a jumping rope have no bending stiffness and compression stiffness?

TL;DR: The bending and compression (buckling) stiffness is so small because the second moment of area of the fibres is small. Bending stiffness It does have a bending stiffness however it is really ...
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12 votes

Why are two wires used in railway overhead equipment?

It isn't to do with current-carrying capacity; it is to maintain good contact between the current-carrying wire and the pantograph pickup on the locomotive, as it allows the contact wire to be ...
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  • 381
6 votes

Why are two wires used in railway overhead equipment?

Why two wires: A wire hanged at two points sags (it forms a "catenary curve"). The pantograph can only handle a certain sag before losing contact and arcing. The acceptable sag depends on ...
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  • 231
5 votes

Why does concentrated shear force on a beam influence the whole beam?

So, we apply a point load to the end of the cantilever beam and can see that for external equilibrium, there must be shear reaction at the support. (Leaving aside for now the moment reaction that also ...
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5 votes
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Moments of Fixed-Fixed Beam

When trying to figure out whether or not a given reaction will exist at a given support, it's worth remembering what a reaction actually is. A reaction is the means by which the support resists the ...
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5 votes
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What is the significance of hinge in the internal structure of the beam?

A hinge is a point where there is no restriction on rotation. For other points on a beam, the rotation to the left of a point must be equal to the rotation to the right of that same point; that is, ...
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5 votes

Why do we always need to calculate the 'Moment of Inertia' about neutral axis for bending?

The derivation for bending stress is depended on the assumption that the strain distribution across the thickness is linear. i.e. $$\epsilon(z) = a_1 z + a_0$$ where: $a_0$ $a_1$ are coefficients of ...
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5 votes

torque for a machine shaft

$P$ is power. $P = \tau \omega$ $\tau = Torque$ $\omega = Angular Velocity (rad/s)$ https://byjus.com/physics/relation-between-torque-and-power/
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5 votes
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Does lead screw's thread have to be trapezoidal?

It's not exactly clear to me what you mean by trapezoidal thread rod. Like you noticed Metric threads are also trapezoidal (just like ACME with slightly difference face angels). Figure : Common types ...
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4 votes

Does same stress always produce same strain?

Since the bending moment is constant across any section, by the bending equation, the beam will deform as a pure circular arc, i.e. with constant radius of curvature across any small element length, ...
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  • 41
4 votes

Moments of Fixed-Fixed Beam

This is a statically indeterminate problem. I don't know what exactly you mean by moments develop at the fixed supports But I guess you mean if there exist any non-zero components of moment at the ...
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4 votes
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Solving for stiffness matrix numerically by a set of measurements

This is feasible and can be used to modify a theoretical stiffness matrix calculated by the Finite Element method to match experimental results more accurately. The FE model can then be used to ...
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4 votes
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Stretch in Infinitesimal strain theory

Taylor is straightforward: $$ \sqrt{1+2x} =\left.\sqrt{1+2x}\right|_0 +\left.{d \over dx}\sqrt{1+2x}\right|_0x +O(x^2) \\ =1 +\left.{d \over dx}{1 \over \sqrt{1+2x}}\right|_0x +O(x^2) \\ =1 +x +...
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4 votes

Why do we always need to calculate the 'Moment of Inertia' about neutral axis for bending?

Because we're not interested in the moment of inertia or the "c" ordinate of a particular area element of the beam for their own sake - we're interested in them as intermediate steps on the ...
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4 votes

Does lead screw's thread have to be trapezoidal?

You can use regular threaded rod as a lead screw. The size and pitch (and grade) of the thread will determine your precision but 0.5 mm seems overkill for furniture positioning. The smaller the screw ...
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4 votes

Why shouldn't we use Bernoulli beam theory if deformations and rotations are large?

Shear deformation causes the cross-section to twist, thus the plane no longer remains plane, which is one of the cornerstones of the Bernoulli Beam Theory. Also, the large deflection invalidates the ...
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4 votes
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Why shouldn't we use Bernoulli beam theory if deformations and rotations are large?

Apart from the other answers another reason why the Bernoulli-Euler beam theory falls apart at large deformation is due to the approximation about the radius of curvature. The Bernoulli-Euler beam ...
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4 votes

Why does a jumping rope have no bending stiffness and compression stiffness?

Having low stiffness is part of the specification of a rope. It would be far cheaper to obtain the same tensile strength with a solid rod. Creating and manipulating multiple strands is expensive. It ...
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4 votes
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How many more degrees of tilt can the Millennium Tower in San Francisco withstand before it becomes structurally unsound?

Modern building failure due to tipping is rare but did occur, usually under strong earthquakes and loss of foundation (soil and structure), as the tilt will shift the gravity center of the building ...
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3 votes

When calculating a force, why do I get different result when I try to calculate via torque vs via sum of forces at an axis?

Essentially, the problem is poorly conditioned. As drawn, it cannot be in static equilibrium, which is why the equations of equilibrium are returning inconsistent solutions. We can confirm this by ...
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3 votes

Is a beam is subject to axial load, does it mean that deformation is the same in each point?

You seem to be mixing up strain and deformation. The strain, $\epsilon$ or change in length per length, is clearly uniform throughout the beam, and therefore the deformation is not. You get the ...
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  • 1,278
3 votes

Why does concentrated shear force on a beam influence the whole beam?

If we cut a section at any point of the beam, an equal and opposite force will be there (shear reaction) to maintain the equilibrium. So if we think it as a differential section, it will be easy to ...
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3 votes
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Why is the thin-walled cylinder more likely to experience failure along its axis than along its hoop/circumference?

Actually, the pressure inside the vessel is uniform and constant everywhere. What happens is that geometry results in reduced stresses in one direction and not in the other. There may be some ...
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3 votes

How to plot bending moment diagram from shear force diagram

First of all the bending moment, according to the usual convention (and the one you are presenting here) is positive. However, the problem originates when you add the area of the shear force. (...
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3 votes
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What should be the relation between flange length and web thickness for an optimum I - beam?

The answer is "Yes", and the direct source to find such relationship is from the technical publishing, that offer steel design tables/charts showing the most optimum beam/column sections for ...
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3 votes
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Do all structures deform if put a load on them?

TL;DR: Yes, any structure deforms if you put a load on it. Even adding an ant on top of a granite mountain will change (lower) the height of the mountain - imperceptibly so but it will still change it....
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3 votes

Boundary condition at supported end of a rod

None of the three would occur if the material of the element holding the rod is "rigid", or is much stiffer than the rod. For such cases, my assessment is as shown below. For the case that ...
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  • 7,491
3 votes

What is stress stiffening in Finite Element Analysis?

My undestanding is that stress stiffening is the additional stiffness in structures when there is an applied prestressed state. The most common example, -I know of- is how the guitar string (or a beam)...
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3 votes

What is stress stiffening in Finite Element Analysis?

Stress stiffening is the work done to displace the structure that is caused by its internal stress. The simplest formulation of FEA (and classical theories like Euler-Timoshenko beam theory) assume ...
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