In organic chemistry, ring strain is a type of instability that exists when bonds in a molecule form angles that are abnormal. Strain is most commonly discussed for small rings such as cyclopropanes and cyclobutanes, whose internal angles are substantially smaller than the idealized value of approximately 109°. Because of their high strain, the heat of combustion for these small rings is elevated.Ring strain results from a combination of angle strain, conformational strain or Pitzer strain (torsional eclipsing interactions), and transannular strain, also known as van der Waals strain or Prelog strain. The simplest examples of angle strain are small cycloalkanes such as cyclopropane and cyclobutane.
'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...
The annulus (“rim”) clamping the circular membrane over its cylindrical shell has a number of bolts ‘n’ positioned equidistantly around its perimeter. I’m guessing that the amount of transverse strain at those bolts would be where we might reasonably assume to be zero.
When I was first trying...
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...
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)?
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 =...
Earlier today, I posted a question about the strain energy function.
I am happy with the answer (I love this group).
But the answer opened up a deeper question.
Many elasticity textbook posit the existence of a strain energy function:
And they make an additional assumption about its...
(If this is in the wrong forum, please move it)
Here is the potential energy of a spring
Here is the strain energy function in elasticity
The look alike -- I like that.
If we want the force in the spring, we take the derivative of V with respect to the displacement and make the result...
This is from my notes:
Point D is called ultimate tensile strength and defined as highest possible within this material.
So it means that point D should be at the highest point of the graph (more like absolute maximum in math)? Because it seems that from the graph point D is not at maximum...
In every book I checked, the energy (per unit mass) of elastic deformation is derived as follows:
## \int \sigma_1 d \epsilon_1 = \frac{\sigma_1 \epsilon_1}{2} ##
and then, authors (e.g. Timoshenko & Goodier) sum up such terms and substitute ##\epsilon ## from generalised Hooke's law i.e.
##...
Summary:: Can anyone help me with this 3d Volumetric Strain and Volume Change. The is question is attached as a document below with the question and my attempt at the answer
All questions and attempted answers are in the attached file below
While introducing tensile stress, we're shown a bar fixed at a support being subjected to a force in the axial direction at the opposite end. Then, since the bar is in translational equilibrium, we say that internal forces must balance it out, and this internal resistance per unit area is known...
Hi, I ran into problems using the poisson ratio.
For a FE simulation I created a simple 2D 1mm x 1mm block, and prescribed a 0.1 mm displacement at the top edge.
Furthermore, the bottom edge is constraint in the y-dir, and the left edge in the x-dir.
The material parameters are E = 100, and v...
Hi. I'm a physician trying to understand the micromechanics of lung injury due to overdistension. The basic idea is that overstretching of the plasma membrane of the lung epithelial cell causes "stress failure" --> i.e. plasma membrane rupture --> cell death. The concepts of stress, strain, and...
Hi,
in mechanics of materials books one may easily find fomulas for stress and strain in thin- and thick-walled cylindrical pressure vessels subjected to internal pressure. However, it is assumed that they are open. So what are the formulas for stress and strain in capped vessels (with flat or...
I would assume that because the samples are made of the same material they would fail at the same stress and so the same strain. However, the data shows that the sample with a greater cross-sectional area fails at a greater strain, and the two are roughly proportional. Does anyone know what...
My guess is that the deformation immediately before would be the sum of elastic and plastic deformation, and the deformation after would be just the plastic deformation, and it therefore would decrease. Is this correct?
This is a quick multiple choice question in which I need to interpret the graph and see which statement is true
This is what I have found from looking at the graph
I know that strength is determined by the maximum stress a material can withstand in its elastic region.
And toughness is the...
Hello,
My question is simple. I have read that isotropic biaxial strain does not lower C2 symmetry, but no proof whatsoever was provided. I would like to know if it is actually true and have a solid proof. If someone can provide it, that would be wonderful. But also explaining me how to start...
As all attempts to get it right but without success this is one of the problems with my workout . Where i did wrong calculations ?
The questions got the answers in brackets.
I would like to know some guidelines regarding this topic. The characteristics of wave propagation depend highly on the orientation of fibre (unidirectional and warp & weft arrangement), fibre volumetric fraction, relative fibre modulli etc. What is the relation of wave propagation and these...
Imagine a bubble vibrating in air. Because it vibrates, it's interfacial area increases, thus new molecules are added and removed from the surface as it vibrates.
Consider a molecule is initially at position X_0 at the interface, and over a certain amount of time molecules squeeze and disappear...
Summary: In terms of stress, strain & deformation, what is better for a given component. 1) low stress or high stress 2) less strain or large strain 3) less deformation or large deformation?
Some dimensional changes were made in an existing component to study how these changes effect the...
Hi everyone.
I'm studying Mechanics of Materials and I got some question about 'nominal/true strain'.
First of all, I agree that in tensile test, nominal stress is always smaller than true stress
σt > σn
cause when the material specimen is being stretched, then the actual area of the...
If I can determine the weight of that heavy object placed on the plank, I will be able to determine the stretch of that wire. But, when using the second condition for static equilibrium (torques of the system equal to 0), I always end up with two unknowns, no matter what point of rotation I...
Hello,
I am a civil engineer and have been working on concrete creep phenomenon for several years now. After reviewing a large amount of literature on related topics throughout this time, some interesting observations have emerged, and they have formed the idea that the material creep mechanism...
So I got a is elongation.
For part b and d, I am unsure where to start.
For c, i got compression
and for e, I put that the dotted line is the red block
The answer says B, it does makes sense, but why D is regarded as incorrect. If the Elastic Potential energy when loading is the area under the loading curve, so why not with the unloading?
Homework Statement
Hi all, this isn't exactly homework, but it is nonetheless a problem I would like to solve, so here goes.
Consider a thin-walled ring/hoop with diameter "d" and thickness "t". I want to know the change of diameter "Δd" due to the stress caused by pressure "p" being applied...
I disassembled an electronic scale. I removed a piece from the corner. I think it is an strain gauge. When I Press on it a reading appears on The liquid crystal display. It might Say 9.6 or 10.8 or 11.5. I used a multimeter to measure it resistance. It 992 ohms. Unless I press on it. Then its...
Homework Statement .[/B]
For a certain type of steel, stress is always proportional to strain with Young's modulus 20 x 10^10 N/m^2. The steel has density 7.86 x 10^3 kg/m^3. A rod 80.0 cm long, made of this steel, is fired at 12.0 m/s straight at a very hard wall.
a) The speed of a...
Hello,
I am working on a project for an EE class and am brushing back up on the basics of strain and stress. My question was to do with how strain works in a material and if it is constant throughout. Say for example you had a setup like this
The change in resistance the strain gauge...
Homework Statement
Homework Equations
ΔL=LαΔT
σ=EΔL/L
The Attempt at a Solution
For part a, I used the coefficient of linear expansion for copper and the change in temperature to find the change in length (0.068%). I thought part b had the same answer. The two are attached, and I would...
I'm trying to understand the following derivation. Starting with the one-dimensional equation for a traveling wave ##u = u_0 \exp{[j(\omega t - \beta z)]}## the goal is to derive the phase relation between strain and velocity. The author first derives the relationship between strain and particle...
Hello,
I am a 3rd year EEE student and am working on a project that will go on to form my 3rd year dissertation. I am having trouble formulating a project idea from the guidelines. I was told I should use a strain sensor to form some kind of self sensing smart material that could be used to...
Hey all,
I am using a Wheatstone bridge with 4 strain gauges as resistors. I have a formula for the output voltage (Vout). My questions is how do I make it so instead of voltage I measure force?
Do I simply apply a set max. force (let's say 140N), see what voltage I get (Vout,max) and then use...
Hi all
I was hoping someone could shed some light on the following:-
I am trying to understand what Yield strength is and understand the exact limit of where elastic and plastic deformation occurs on a stress strain curve.
Correct me if I am wrong but I define:-
Yield strength as the amount...
Homework Statement
A sample is put in tension and a strain rosette gives the following results:
i) Calculate principal strains and poissons ratio using Mohrs strain circle.
ii) Calculate principal stresses from principal strains and poissons ratio.
Homework Equations
Mohr's strain circle
γ =...
Hello.
I am finding out how many normal force between ring and cylinder. I try to find around for many hours but get noting. there are 8.2 mm inner diameters than put in 8.6 mm cylinder. The hardness of sealing element is 55 ShA. Contact area is 48.63 mm^2. I have data and drawing in attachment...
Homework Statement
I am following a textbook "Seismic Wave Propagation in Stratiﬁed Media" by Kennet, I was greeted by the fact that he decided to use cylindrical coordinates to compute the Stress and Strain tensor, so given these two relations, that I believed to be constitutive given an...
I’m studying large strain and deformation solid mechanics and I have a (seemingly) basic question on solution approaches. Is my interpretation below correct?
The governing equation of momentum for solid mechanics can be solved using a total or updated Lagrangian approach. The updated...
I am trying to figure out if there is a way to measure muscle strain.
If I apply a force F to compress a hand grip to the maximum distance x
The work done to compress the hand grip is F*x
Work done = Fx
Since work done = energy used, I can change the equation to:
Energy used = Fx
When...
Homework Statement
A rod of length ##L_o## is kept on a friction-less surface. The coefficient of linear expansion for the material of the rod is ##\alpha##. The the temperature of the rod is increased by ##\Delta T## the strain developed in the rod will be?
Homework Equations
$$ \Delta L=...
Hi all,
I have some doubts regarding the strain tensors Abaqus uses for the case of Geometrical non linear analysis.
In the case of geometrically linear analysis, all the strain tensors will be equal to engineering strain, So it doesn't matter which strain tensor Abaqus uses.
But for...