Questions tagged [stress-strain]
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764
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Buckling of a timber column
I am wondering how the "buckling number" of a timber column is altered by having a vertical element attached to it. Blue line is a roof, green a concrete wall and black is the timber column ...
2
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4
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888
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Uniaxial stress question
Let's have a rectangular profiled bar. Let us introduce force $\vec{F}$ which pull the bar apart. In the picture below let us make a virtual horizontal cut $A$.
Well, everything is in the picture. ...
2
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2
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Pressure in the stress tensor?
The stress tensor can be written as:
$$\sigma_{ij}=-p \delta_{ij}+\sigma'_{ij}\label{1}\tag{1}$$
where $\sigma_{ij}'$ is called the extra stress tensor.
From what I understand pressure is pressure ...
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What causes tensile stress to decrease after a material/wire reaches its ultimate tensile stress?
I was reading the AQA A Level Physics revision guide by Jim Bretihaupt, and in the Materials chapter in the section to do with plastic deformation, it says:
Beyond the ultimate tensile stress,
the ...
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2
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Electrical analogy for stress and strain
It feels like the relation between stress and strain (and other mechanical properties) is analogous to that of some electrical properties (voltage and current?).
I'm comfortable with electrical ...
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Do all impacts create a wave-like disturbance in the medium through which they travel?
There is a scene in the first Matrix movie, where a helicopter strikes a skyscraper. The most interesting part is the 'slow-motion' bit where, as the helicopter strikes the building, a wave first ...
2
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1
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Difficulty in proof of relationship between $Y$, $B$, $\sigma$
On internet, I was looking for the proof regarding the following relationship between $Y$ young's modulus,$\sigma$ poisson's ratio, and $B$ bulk modulus: $Y=3B(1-2\sigma)$, and I came across the ...
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2
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Stress developed in a Hoop due to rotation
In the given question with constant angular velocity. It asks us to find longitudinal stress at each of the positions. Now I'm not even sure what longitudinal stress is but here is what I tried as A ...
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2
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691
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Why can we assume long structural members to be in plane strain?
In plane strain, the strain in one direction is assumed to be zero. It is taught that if we have a structural member that is very long in one direction compared to the others, the strain in the long ...
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2
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237
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Why stress always flows through the shorter/stiffer path?
Why load has a preference at which way to act? What is the reason behind this preference?
Any link or comment would be welcome
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1
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901
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Extension in a vertically hanging rod [closed]
Consider a vertical rod hanging from a ceiling. Neglect lateral contraction and frictional forces and air resistance and change in value of $g$ with height.
Case 1: In the absence of gravity, a rod ...
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Jaumann deviatoric stress rate
Background about terms in this question:
Hookes law and objective stress rates
From my understading, the Jaumann rate of deviatoric stress is written as:
$$dS/dt = \overset{\bigtriangleup}{{S}} = {\...
2
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1
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Why is elastic modulus greater than shear modulus?
I was looking at data for elastic modulus $E$ and shear modulus $G$, and found that $G$ is always lower than $E$. So I'm wondering what are the underlying principles that may be the cause of this.
$$...
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165
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Can stress be observed directly?
Strain can be directly observed using e.g. a ruler. Can (internal) stress be directly observed?
2
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382
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What is the shape of a clamped bent bar?
How would I figure out the Cartesian graph that describes a bar clamped flat for a length on one end with downward force being applied to the other?
I have an idea that the bar will try to average ...
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228
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Why are stress components on opposite faces identical?
The stress tensor stores information about the stress on each of the faces of an infinitesimal volume of material. But I am confused as to why the stress components on opposite faces should be equal. ...
2
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668
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Deformation of a ball when it falls on a rigid surface
Suppose, we drop a rubber ball on the floor. The ball collides with the floor, comes to rest and often bounces back up to lower height. I'm trying to look at this from the force perspective, not ...
2
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Find elongation of a rod of constant volume given Young's modulus, original length and load without assuming that cross-sectional area is constant
The usual formula for Young's modulus:
$$
Y=\frac{FL}{A\Delta l},
$$
(where $F$, $L$, $A$ and $Δl$ are load, original length, and area over which force is applied respectively) can be rearranged to ...
2
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Can fluids sustain tangential forces? How can surface tension act tangentially?
I've read in places that fluids cannot sustain tangential force acting on them. However when reading about surface tension I read the following paragraph on wikipedia
There are two primary mechanisms ...
2
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1
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536
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How can the equation of force for a spring and damper in series simplify to just the equation for a spring if the damper is set to "zero"?
I have been working extensively on modeling physical objects using the stress/strain relationships of springs and dampers as described here:
https://en.wikipedia.org/wiki/Viscoelasticity#...
2
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1
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Why are eggshells so strong?
The usual explanation that someone can find on internet is that it is shaped like an arch, but it is not exactly an arch.
Does anybody knows something more on this?
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Is stress dependent on strain?
Stress-strain curves are drawn with strain on X-axis and stress on Y-axis. Usually the quantities placed on X-axis are independent quantities whereas the one placed on Y-axis are dependent.
So which ...
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Stress and Strain in a standing wave
Where are stress and strain maximum in a Standing wave?
what about a transverse wave?
My book says "strain is maximum at the nodes in a standing wave". But since Antinodes are the position of maximum ...
2
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4
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Why is torsional shear for a circular cross-section maximum at the biggest radius
Equation: Tao = (T*C)/J
i know the equation but it just seems counter-intuitive that the maximum shear stress is at the biggest radius for 3 reasons that I have(thought of).
1- imagine/assume that ...
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Trouble connecting stress and force in continuum mechanics with my concept of force from point mechanics
I'm not very familiar with continuum mechanics and have a hard time combining my knowledge of forces from simple mechanics with what I read about continuum mechanics.
Let's suppose we have a metal ...
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Which stresses a material more: constant high pressure or alternating between low to high [closed]
Let's say we have a glass container with fluid at 7 MPa and another one with fluid alternating between 3 MPa and 7 MPa (or any arbitrary numbers). The highest pressure in the alternating one is equal ...
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738
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Why is 3D stress tensor acting only on three surfaces?
I'm trying to learn about the stress tensor (in 3D)
The tensors are said to have directions (the first subindex $i$ in $\sigma_{ij}$) and specify the surface upon which they act (the second subindex $...
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What does it mean for shear modulus to be less than bulk modulus?
It is known that Shear Modulus is generally less than Young's modulus for most materials.
What does this mean? Does this mean that it is easier to change shape of a fixed body by applying force than ...
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Efficiency of Bicycle Pedalling
Consider a bicycle with multiple gears. Suppose that you are in a starting position with someone holding your bike upright (so when you start there's no issue with clipping in etc). It's well-known (...
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3
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2k
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Why eigenvector points to principal stress plane?
I can represent a tensor by a matrix. Suppose we are talking about a 2nd order tensor, and the matrix is therefore 3x3. If I find one eigenvector of that matrix; that vector represents normal vector ...
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492
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what is the static pressure in a yield stress fluid?
Suppose I have a tank filled and there is no slip at the walls. If the tank is filled with a Newtonian fluid and is in static equilibrium, we know that the pressure is defined as $p = \rho g z$.
But ...
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790
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Are Normal Stress Differences in Newtonian Fluids Equal?
I was reading about normal stress differences in the context of Non-Newtonian fluids. There was a remark that the normal stress differences in Non-Newtonian fluids are not equal whereas the normal ...
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1
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Poisson effect formula for large deformations
English Wikipedia in the Poisson's ratio article gives an equation for large deformation:
$$
\frac{\Delta d}{d}=-1+\frac{1}{\left(1+\dfrac{\Delta L}{L}\right)^\nu}
$$
I couldn't find any reference ...
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2
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How does restoring shear forces arise (in elastic conditions)? Do they arise from central forces or not?
When you apply a shear force onto a solid piece of material (say a block on a surface or a cantilever
beam with a load) that creates shear stress in the elastic regime, there is a restoring force that ...
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Definition of stress (Mechanical Properties of Solids)
See, it's a simple question.What exactly is stress? Is it the restoring force applied by the body in reaction to deformation force or is it the deformation force itself? I had this doubt because in ...
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509
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Stress in a rigid body
Consider two bars one rigid and the other deformable, acted upon by two equal and opposite point loads P as shown. In either of the cases, if we cut the beam from an imaginary section, then, to bring (...
2
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Is there a generally followed "convention" regarding the signs of the diagonal components of the stress tensor?
The question pure compression or pure traction? is very similar to what I wish to ask. One answer to the referenced question includes the sentence: "It is also matter of convention."
My ...
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How does a materials modulus of elasticity (proportional zone ratio) relate to crystal defects?
I'm studying biomedical engineering and I'm about to take "Biomaterials" (basically materials science applied to medicine) final exam. In one recorded class, the professor mentions the ...
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Sand cone in the attic [closed]
My question is based on Halliday books Tom 2, chapter 13 (exercise 42).
There is a cone of sand laying in the attic. Consider stress of the floor under the sand cone.
Why the biggest stress is in ...
2
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1
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310
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Tensile strain produced on two thin rods of different lengths
Suppose there are two thin rods $Y$ and $Z$ with length $L_1$ and $L_2$ respectively. $L_2$ has larger magnitude than $L_1$. Both rods have same density $p$, cross sectional area $A$, Young's Modulus $...
2
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Can I determine a transformation matrix for a stress tensor with respect to the axes $O x_1 x_2 x_3$ to define new axes of maximum shear stresses?
Is it possible to determine a transformation matrix for a given stress tensor with respect to the axes $O x_1 x_2 x_3$ to define new axes $O x'_1 x'_2 x'_3$ of maximum shear stresses?
To make my ...
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1
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Deformation without stress?
Elastic bodies are submit to stress whenever they are deformed. This eventually lead to break them.
However, let's consider a rope. If i stretch it, it is submit to stress and will eventually reach ...
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2
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741
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Relation between strain and velocity
The strain tensor writes $\epsilon_{ij}=\frac{1}{2}\Big(\frac{\partial u_i}{\partial x_j}+\frac{\partial u_i}{\partial x_j}\Big)$ with $u_i$ the displacement in the $i$ direction.
Then $\frac{\...
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Stress/strain within an object experiencing a single applied force
If I push an object in space, will any strain/stress happen within the object, though there is only 1 force rather than a pair of opposite forces on the object?
Can be any (even if trivial) stress/...
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Why is the force on a cross section of a rigid body equal to the force over the entire body?
If we have a block of mass $m$ (distributed uniformly) and a force $F$ acting on it, the block would begin to accelerate with an acceleration $a$. Obviously, the mass of half of the block is $\frac{m}{...
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1
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Why does a rotating flexible disk have wave shape?
I found a video on which they shatter CD with a high RPM tool. Before the CD shatters it has a wavy shape, so I guess an axial force shatters the CD instead of a radial force, probably some kind of ...
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How to calculate external pressure resistance of cylinders and spheres, [closed]
Although I have seen a lot of literature online about how internal pressure resistance is calculated (i.e the pressure in a gas tank) I haven't found anything about the opposite scenario (i.e the ...
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Young's modulus and geometry of test material
When measuring Young's modulus in a material, does the geometry of the material actually matter? I have seen several references recommend that I use cylindrical pieces. But, wouldn't the tests work ...
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1
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80
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Calculate the applied force associated with uniform distortion of an area
I am exploring Hooke's Law and considering how it might apply to an arbitrary area (perhaps as a slice of some volume).
Since $$ F = -kx $$
Would it be correct to calculate the force, $F$, ...
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Why are the x-components of the stress tensor ($\sigma_{xx}, \sigma_{yx}, \text{and } \sigma_{zx}$) different?
I understand the stress tensor at a specific point $P$ as follows. You draw a cube with its center at $P$ and look at its faces. The face with its normal vector in the positive $x$ direction has a ...