Stress Definition and 1000 Threads

In books that deal with continuum modelling of materials that include the presence of internal rotations/torques in the microstructure, the torque is defined as follows: $$ \tau = \int ((r \times t + m) dA) + \int ( (r \times f + l) dV )$$ From this definition, the stress tensor and couple...

I've just started learning about tensors from Jeevanjee's highly praised 'An Introduction to Tensors and Group Theory for Physicists'. He defines a tensor as a function, linear in each of its arguments, that takes some vectors (maybe only 2) and produces a number. [The components of the tensor...

The definitions of power and work in continuum mechanics are: $$ W = \int T \cdot u dA + \int b \cdot u dV (1) $$ $$ P = \int T \cdot v dA + \int b \cdot v dV (2) $$ ##u## is the displacement vector, ##v## is the velocity, ##T## is the cauchy stress tensor, ##b## is the body force ##A## is...

In summary Tzz in maxwells stress tensor represents a force per unit area in the z direction acting on an area element that is oriented along the z direction also why it could be non zero eventhough the electric field along z is zero and I'm talking here in electrostatic

TL;DR Summary: I'm comparing the viscoelastic properties of rubber and foam using compression tests. The SLS model predicts exponentially decaying stress for linear displacement, but my results show exponentially increasing stress, especially for rubber. How can I reconcile this? Hello...

'Gummy 1' = Black Line 'Gummy 2' = Orange Line Approach: Using the diameter given and the force measurements on the vertical axis of the graph, I've worked out the cross-sectional area of the mold to be 0.000706858, which I've rounded to 0.00071. Using this data and the equation Stress = F/A...

Is it possible to move Stress-Energy tensor to the left side of EFE? R=T => R-T=0. Relativists move cosmological constant Λ to the right side of EFE. Can we move SE tensor to make a vacuum?

Hi, I've problem thinking about this problem isn't the force acting on "nothing"? how can there be any stress, I'm lost!

I have two concentric thick cylinders in close tolerance (currently 50 micron gap), with a thin layer of glue between them. Internal cylinder is made from steel and external cylinder is made from ceramic (so the thermal expansion coefficient is not the same) The assembly is headed form inside...

Stress = F(restoring)/ Cross sectional area Stress = 2F/A

A load of 100 kg acting in the axial direction is applied to a nut coupled with a standard M10 bolt. The nominal thread diameter is 10 mm; pitch is 1.5 mm. Thus, the stress acting on a single thread in the bolt is: 1000 N / (0.25 * pi * (10 mm - 0.93194 * 1.5 mm)^2) ≈ 17.21 MPa 17 MPa seems...

A bar is 100mm long and has a 20mm by 10mm cross section. It is subject the following complex loading a tensile load of 10,000N along its length a compressive load of 100,000N on its 100mm by 20mm faces a tensile load of 100,000N on its 100mm by 10mm faces Calculate the stress and strain on...

Left side is fixed and right side is held together by a non deformable plate. There are two members with space inbetween. My question is when i want to calculate the stress due to bending moment at point A, which is shown in the crossection, where is the neutral axis? Is it at the middle of the...

The formula for von Mises stress for a plane stress (2d) condition with no shear stress is: So if S1 = 1000, S2 = 0 , then Svm = 1000. If the S2 is now increased from 0 to 500. The von Mises stress will go from 1000 to 866 I understand this is how the equation works, but can someone give me...

First, my ignorance... I know there are classes of equations: Laplace, Poisson, Wave, Diffusion, etc. (I suppose Laplace is a subset of Poisson, but that is not the issue). Into what category of mathematical equations would you place the field equations of elasticity (stress/strain/displacement)?

Question: Solution: I need help with the last part. I think my numerical factors are incorrect, even if I add the last term it will get worse. What have I done wrong, or is there a better way to deal with this?

Im so confused on these solutions here for the shear stresses. Why is Tau_V sometimes negative and sometimes positive? Can someone please explain this and maybe illustrate? Here for example. Heres the solution for problem b): Here Tau_V (talking about F_xQ/(Ir) ) is negative, so how im...

I do private studies on my own for fun and right now I read about relativistic field theory as a preparation for later studies of quantum field theory. I simply do not understand where equation 13.78 in Goldstein's "Classical Mechanics" third edition comes from. Please explain. Please also...

a) I can find the compressive strain on the aluminium column using the formula ##\sigma = E\epsilon## as we know ##\sigma = F/A##. The area of the column is ##A = \pi r^2 = 0.126m^2## and the force on the column is ##F = 300*(9.8)N = 2940N##. The stress therefore is ##\sigma =...

Here is my combined loading: The book solution for normal and shear stresses respectively are: a) ##20.4~\text{MPa}, 14.34 ~\text{MPa} ## - I find both b) ##-21.5~\text{MPa}, \boxed{19.98~\text{MPa}}## - I find the normal stress, but I'm not getting the book answer for the shear stress...

Hi im trying to understand truss bridges. Where would max stress be in single span truss bridge if it was evenly loaded across the bridge? I thought single span truss bridge, max stress would be in the ends of the bridge. it would act like a simple supported beam with max bending motion being...

Hello All, I'm trying to figure out how to strengthen a box beam that's been welded to another box beam. In the photo on the left is 2 beams welded to each other, they are 2x1" Aluminum 6061-T6, with a 1/8" wall thickness. The yellow lines indicate the location of the weld. A force of 216 lbs is...

Hey Im doing FEA and got stuck on question. The diagram go me stuck, because looking through the workbook it says high stresses are in red and low in blue, whereas they included both different kind of stresses on the same diagram and no data. Note: High Compressive strains are noted by blue...

Why do the Cauchy Stress Tensor & the Energy Momentum Tensor have the same SI units? Shouldn't adding time as a dimension changes the Energy Momentum Tensor's units? Did Einstein start with the Cauchy Tensor when he started working on the right hand side of the field equations of GR? If so, What...

I have tried to calculate the safe load with the equation of maximum shear stress, A = 4*6*10^-4, and the given shear stress 5MPa, but I couldn't seem to get the right answer which is 18kN.

Is that correct: in stress sound the glostis is more open and in unstress sound the glostis more narrow?

Hi, good evening/morning/night! I have a problem with this 2 homework problems about curved beams. In both I must calculate the stress at points A and B. My procedure is correct, but for some reason in: First problem - the effort in A is very close to that of the teacher, but the effort in B...

Good Morning! I understand that a vector is a physical object I understand that it is the underlying basis that determines how the components transform. However, I encounter this: https://en.wikipedia.org/wiki/Covariance_and_contravariance_of_vectors The fifth paragraph has this statement A...

I'm wonder how one could calculate the total mega pascals total mega pascals that can be applied to a spinning flywheel before it exceeds its tensile strength example: a cast iron flywheel is spinning at 10,000rpm(Tangential velocity = 104.72) it has a radius of 100mm and a weight of 500g...

Summary: Each angle has a different type of corner, rectangular, circular, and triangular. Which one is the strongest? All three angles are mounted in the ground and made of the same material. The same force ‘w’ towards the ground is acting on all angles, which one is the strongest? Please...

My answer is A but the answer key is B. I don't understand why B. I would think B is the breaking point. Thanks

Hi, I have developed a catenary software that calculates the tension force resulting from the wire and now I am working on suitable fixing methods and including the option for this within the software. Has anyone got any guidance on working out the stresses applied on the attached...

Hi, it's not easy to find formulas for stress in rectangular pressure vessels. However, I've found some in a Polish book titled "Podstawy konstrukcji aparatury chemicznej" (Fundamentals of the design of chemical process equipment) by J. Pikon. The problem is that the book provides equations for...

I have no formal training in any type of engineering, so if my request is confusing, I apologize. I believe I am seeking data on the ultimate internal stress of various silica aerogels in compression mode. I found a paper published by Dylan J. Boday where CVD of cyanoacrylates was used to...

Hi all, I have some detailed design work coming up designing bolted/pinned interfaces, so I’m doing some examples trying to remember what I learned at uni. I would like to calculate the stresses in bolts and pins of a hypothetical mechanical assembly, but I have a question before I get started...

Hi, I'm trying to verify the results of a finite element analysis of a corrugated tube (bellow) subjected to axial load. Here are my analytical calculations based on Roark's Formulas for Stress and Strain (originally the formulas are from the article "On the Theory of Thin Elastic Toroidal...

Summary:: Torsional stress on freely spinning shaft? Hey guys, I’m having some confusion with a certain section of the “Torsion” chapter in my mechanics of materials book: “power transmission”. Please see the problem below. This is very easy to SOLVE (basically plug and chug with the...

Hi guys, this is an exercise I have been tasked to solve for an assignment. First of explaining you what I have done to solve it using the shear equation, in order to find the maximum shear stress and the shear flow in the juncture, one big question: how is it legal to utilize the shear formula...

Greetings, while studying the stress in the rotating thing ring and find out the last equation that says I would like to understand why? Thank you!

I am in a course in applied strength of materials and we often use the 3D stress tensor for stress analysis of materials i.e. Mohr's circles, bending, torsion, etc. Is the stress-energy tensor in relativity basically a 4-d extension to the Cauchy stress tensor commonly used in mechanical...

Hello, I am trying to get some intuition about the direction of the shear stress caused by the Hertz contact pressure. Once I exert some pressure downwards on a spherical object the direction of the Hertz pressure will be upwards. However, this case some shear stress to exist, but I can't see...

If you already kind of understand anti-oxidant effects on inflammation jump past the "background" paragraphs Background anti-oxidant: Mitochondria produce energy in the cell, primarily from Krebs cycle (citric acid cycle is another name). Reactive Oxygen Species (ROS) like H2O2 Hydrogen...

It is a sensor with a fixed surface and a prescribed displacement on the opposite To remove this message error, I have tried to Increase iterations Refined mesh Applied parametric studies And some other ideas from forums However it still cannot be solved It also has a warning of MUMPS out...

Hi all, I am currently trying to prove formula 21 from the attached paper. My work is as follows: If anyone can point out where I went wrong I would greatly appreciate it! Thanks.

Two questions, but one thread will suffice. 1) Feeling very tired/foggy and haven't felt naturally motivated to work much at physics in the last couple of weeks, instead opting for distractions and a fair bit of idling. Is this a sign of burnout, or does this sound normal? 2) Due to some...

Hello brilliant engineers. How to calculate the bending stress of a lattice boom crane design? It’s clear how to calculate a single chord in a lattice box, at least as a cantilevered tube. However, when placed in a box lattice what is the proper approach? I’m constructing this crane in...

For a Prandtl stress function to be valid, it must be zero on the boundary. For a circular bar, both of these work: $$\phi_1 = C\left(\frac{x^2}{r^2}+ \frac{y^2}{r^2} - 1\right)$$ $$\phi_2 = C \left(x^2+ y^2- r^2\right)$$ But performing the integration for the internal torque M gives...

How come in the lewis bending equation for spur gear tooth does the lewis form factor depend on x? x being the vertical distance measured from the triangle that is formed from the base t and fillet a. I know that you can express the height h and width t in terms of x such that x= t^2/4h, but why?