Stress and strain Definition and 77 Threads

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...

I am looking for clarification of some terms found in Roark's Formulas for Stress and Strain 9E. Table 13.4 pg 543 as well as preceding tables frequently reference R_A as the radius of common circumference. I take this to mean that this value could include any radius that both cylinders share...

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 =...

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...

What I do not get is why should a stress much lower than yield point cause deformation in a material? If temperature is high intermolecular attraction is reduced and thus even low stress can deform things. But if it is low Then a force lower than yield point should be less than intermolecular...

I don't attempt solving a problem until I fully understand it, conceptually. After the hit (when maximum velocity is reached) the person starts losing momentum, having a constant upwards acceleration. The forces acting on the person are gravity and the normal to the ground. $$N - mg = ma$$...

[Mentor Note -- Thread moved to the ME forum to get better views] Let's consider an incompressible block of Neo-Hookean material. Let the initial reference geometry be described by ##B=[0,b] \times [0,b] \times [0,h]##. The professor gave me the following task: Of course there can be many...

Hi everyone, I'm trying to understand the rationale behind the boundary condition for the problem "Finite bending of an incompressible elastic block". (See here from page 180).Here we have as Cauchy Stress tensor (see eq. (5.82)): ##T = - \pi I + \mu (\frac{l_0^2}{4 \bar{\theta}^2 r^2} e_r...

I'm studying elasticity from classical Gurtin's book, and my professor gave us the following example, during lecture. Unfortunately, this is not present in our references, so I'm posting it here the beginning of the solution, and I will highlight at the end my questions. First I need to state...

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...

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

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...

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...

In order to use Solid65 in Ansys workbench for simulating concrete, we shall define the multi-linear isotropic stress-strain curve as well. I have the concrete compression stress-strain data in excel. I would like to ask that how could I get the multi-linear isotropic stress-strain curve in...

I don't understand the difference between the elastic limit and the yield point. I understand that if you stretch a material within the elastic limit, then the material should return to its normal shape. However, the yield point is described as the point at which a permanent increase in length...

Homework Statement E = 290 GNm-2 Yield Stress = 500 MPa Q. What pressure would a strain of 40 με indicate? Homework Equations Hoop Strain. εθ = 1/E (σθ − νσz) = 1/E (pr/t − ν(pr/2t). The Attempt at a Solution I am looking for some direction on how to determine the poisson ratio...

I have this fundamental question about stress and strain. If we apply same Force on two different objects of same geometry in the same configurations, will they experience the same stress? If yes, then does it imply that stress is independent of the internal material properties?

Homework Statement i can not find the N. what i can only found is: D0=0.02mm;V=0.25;E=10G Pa;A=π(0.02mm/2)2 ΔD=εshear×D0 εshear=εaxial×V εaxial=σaxial / E σaxial=N/A Homework EquationsThe Attempt at a Solution

Homework Statement The component shown in Fig 1 is made from a material with the following properties and is subjected to a compressive force of 5kN. Material Properties : Young’s Modulus of Elasticity – 200 GNm-2 Modulus of Rigidity – 90 GNm-2 Poisons ratio – 0.32 Calculate : (a) The stress in...

I am going through a literature where the terms like ( 'plastic yielding' , 'plastic yield strength', plastic strength' and 'plastic stress') are regularly used and I am confused. Are they different and if yes then how each term differs from the other? I also want to know relation of plastic...

Hello everyone, could you help me with this exercise? I am stuck, and I can't find anything on the internet that solves this. Your help is very much appreciated :) 1. Homework Statement Circular steel bar, clamped at extremities. Two parts: A(ab)=800mm² A(bc)=400mm² L(ab)=...

Unsure how to calculate in order to get the stress (N/mm2) and strain (%) if: a material has a length of 50mm diameter of 12mm Load: 11.5 kN Extension 0.025 mm Help on how to work this out would be very appreciated :)

Hello! I'm having some trouble understanding stress and strain rations in sheet metal forming. I understand that they're constants, but how do you calculate them? Or are they usually given? Thank you!

Hello this is my first post here so basically I've had my best crack at all the questions all I am really after is a bit or re assurance as to my answers and if any are wrong were I have gone wrong essentially. I've tried to include all my working out were possible. 1. Homework Statement The...

Hello--can anyone please help me estimate the PSI required in an air mattress to minimize or even prevent displacement if a person, say 220 lbs, walked across it? Mattress material and wall thickness variable. Surface area variable. Also, if scenarios where the person is standing still...

Homework Statement I'm not sure if this belongs here, sorry if it does not. I am trying to find the most amount of mass a bridge can hold before deforming/collapsing. I was trying to factor stress/ultimate tensile strength into it in a way. Is there a way I can calculate ultimate tensile...

Homework Statement A copper rod of length l_0 at 0 C is placed on a smooth surface.Now the rod is heated up to 100 C.FIND THE LONGITUDINAL STRAIN DEVELOPED ? The Attempt at a Solution What I did : strain = delta l/ l_0 = l_0 alpha(coefficient of linear expansion) delta T/l_0...

Can someone please help with hyperelastic theory, I need to know how changes in reversible work are related to energy density function and then to strain and stress tensors. A reference that explains the theories simply would also be appreciated. So far I have failed to find anything relatively...

By definition the UTS is the maximum stress a material can take. But how exactly can a material not break after reaching the UTS if it is so? Why is there a breaking stress and how come on the graph of stress against strain the stress seems to decreases before the braking stress?

I need help understanding a passage in my textbook, where the form of hookes law in continuous elastic media is explained. It says: "The absence of internal directions in isotopic matter tells us that there are only two tensors available to construct a linear relation between the the stress...

I am so confused about these quantities. For many theoretical setups you assume a linear relation (elastic materials) such that for example if you press on the side of a rectangular box, it makes the box contract in the normal direction to the induced stress. Also the box will expand in the...

Homework Statement A 2.75 KN tensile load is applied to at test coupon made from 1.6 mm flat steel plate (E=200 GPa, v=0.30). Determine the resulting change in the 50 mm gage length. Homework Equations εx = (σx/E) + (-Vσy/E) - (Vσz/E) εy = (-vσx/E) + (σy/E) - (Vσz/E) εz = (-vσx/E) - (Vσy/E)...

Homework Statement The component shown in Fig 1 is made from a material with the following properties and is subjected to a compressive force of 5kN. Material Properties : Young’s Modulus of Elasticity – 200 GNm-2 Modulus of Rigidity – 90 GNm-2 Poisons ratio – 0.32 Calculate : (a) The stress...

I am struggling with a question in my coursework, and would appreciate some guidance. The question is: The component shown in Fig 1 is made from a material with the following properties and is subjected to a compressive force of 5kN. Material Properties : Young’s Modulus of Elasticity – 200...

Im currently studying a course on the mechanics of solids..the reference book i use is by Popov..But i can't completely understand the concept of stress in an axial loading.Like for instance. If a weight W acts on a rod(ignore the rod's weight),stress will vary point to point along the...

Definition/Summary Stress is force per area, and is a tensor. It is measured in pascals (Pa), with dimensions of mass per length per time squared (ML^{-1}T^{-2}). By comparison, load is force per length, and strain is a dimensionless ratio, stressed length per original length...

A 30kg sledge hammer strikes a steel spike of 2.30 cm diameter while moving at 20.9 cm/s. The hammer rebounds with a speed of 10.0 cm/s after 0.110 s. What is the average strain in the spike during impact? 2. F = (mvf-mvi)/t S = (F/A)/(deltaL/initialL) Young's modulus for steel = 2 x...

A compound bar is made using stainless steel tube with an aluminium alloy bar positioned concentrically inside it, and rigidly fixed at each end. The cross sectional area of the tube is 400mm^2 and the cross sectional area of the bar is 300mm^2. The combination is in tension and limiting stress...

A light alloy bar is observed to increase in length by .35% when subjected to a tenstile stress of 280MN/m^2. Calculate youngs modulus for the material. σ=280MN/M^2 x=.35% ε=? E=? L=? I have too many unknowns where do I start?

Homework Statement A tunnel of length L = 151 m, height H = 7.7 m high, and width 6.2 m (with a flat roof) is to be constructed at distance d = 60 m beneath the ground. The tunnel roof is to be supported entirely by square steel columns, each with a cross-sectional area of 960 cm2. The mass of...

Hi all, This is a question regarding stress and strain. Can someone please explain the concepts of stress and strain in atomic level? My understanding is as follows.Let us consider a metal bar or rod that is subjected to tension.The load applied to the bar will be try to elongate the...

Hi all, This is a question regarding stress and strain. Can someone please explain the concepts of stress and strain in atomic level? My understanding is as follows.Let us consider a metal bar or rod that is subjected to tension.The load applied to the bar will be try to elongate the...

Hi all, This is my first post in PF I'm doing my ninth standard in India,My knowledge in physics is limited so please forgive me if I ask something basic Can anyone clearly explain me the relationship stress and strain,because I thought when a material deforms (even to the slightest...

Firstly, does a stress vs. strain graph for a material always take the same general shape as its load vs. extension graph (with the same important points, e.g. UTS, having the same shape and corresponding to the same thing)? Secondly, what do the stress-strain and load-extension graphs look...

Homework Statement For each material calculate the cross sectional area in m². Each sample is of rectangular cross section 20mm by 1mm. Produce Stress and Strain tables for the data. TEST DATA FOR X (N) EXTENSION (mm) 1000 0.48 2000 0.60 3000 0.70 4000 0.80 Homework...

Homework Statement Knowing that the stress and strain for an isotropic media can be related with the following expressions: \sigma_{xx} = (\lambda + 2\mu)\varepsilon_{xx} + \lambda\varepsilon_{yy} + \lambda\varepsilon_{zz} \sigma_{yy} = \lambda\varepsilon_{xx} + (\lambda +...

A 25mm diameter solid circular section bar made from given material tested is to be bored axially to produce a cylinder of uniform thickness. If this cylinder is then subjected to an axial tensile load of 75kN, what is the maximum diameter of the bore possible if the stress in the cylinder is...

1. Knowing that a 0.5 mm gap exists when the temperature is 20 degree celsius, Determine the tempature at which the normal stress in the aluminum bar will be equal to -90 MPa,And the corresponding exact length of the aluminum bar. The Attempt at a Solution I am not familiar with this topic...

Hi everyone, so I'm trying to understand how to use the (Cauchy I think?) stress tensor. The definition I have is that the element \sigma_{\alpha\beta} of the stress tensor σ is the force per unit area in the α direction on a surface that's normal to the β direction. I also have a...