What is Normal stress: Definition and 43 Discussions

In continuum mechanics, stress is a physical quantity that expresses the internal forces that neighbouring particles of a continuous material exert on each other, while strain is the measure of the deformation of the material. For example, when a solid vertical bar is supporting an overhead weight, each particle in the bar pushes on the particles immediately below it. When a liquid is in a closed container under pressure, each particle gets pushed against by all the surrounding particles. The container walls and the pressure-inducing surface (such as a piston) push against them in (Newtonian) reaction. These macroscopic forces are actually the net result of a very large number of intermolecular forces and collisions between the particles in those molecules. Stress is frequently represented by a lowercase Greek letter sigma (σ).
Strain inside a material may arise by various mechanisms, such as stress as applied by external forces to the bulk material (like gravity) or to its surface (like contact forces, external pressure, or friction). Any strain (deformation) of a solid material generates an internal elastic stress, analogous to the reaction force of a spring, that tends to restore the material to its original non-deformed state. In liquids and gases, only deformations that change the volume generate persistent elastic stress. However, if the deformation changes gradually with time, even in fluids there will usually be some viscous stress, opposing that change. Elastic and viscous stresses are usually combined under the name mechanical stress.

Significant stress may exist even when deformation is negligible or non-existent (a common assumption when modeling the flow of water). Stress may exist in the absence of external forces; such built-in stress is important, for example, in prestressed concrete and tempered glass. Stress may also be imposed on a material without the application of net forces, for example by changes in temperature or chemical composition, or by external electromagnetic fields (as in piezoelectric and magnetostrictive materials).
The relation between mechanical stress, deformation, and the rate of change of deformation can be quite complicated, although a linear approximation may be adequate in practice if the quantities are sufficiently small. Stress that exceeds certain strength limits of the material will result in permanent deformation (such as plastic flow, fracture, cavitation) or even change its crystal structure and chemical composition.
In some branches of engineering, the term stress is occasionally used in a looser sense as a synonym of "internal force". For example, in the analysis of trusses, it may refer to the total traction or compression force acting on a beam, rather than the force divided by the area of its cross-section.

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  1. Moara

    Engineering Maximum normal stress and shear stress

    First, I am trying to find the external reactions in A and B, but I have only one equation relating ##V_A## and ##V_B##, what other relation could I use ? Once I find the reactions, I can find the external moment as well. Then, I may draw the diagram of moments in each cross section and then...
  2. Tapias5000

    How to calculate the normal stress of a Howe reinforcement?

    This is the structure I already made the calculation of all the bars T = tension and C = compression, these are the results. now I am asked to calculate the normal stress in all the bars but I don't understand where to start, could you tell me how? here is the diagram of the first node but I...
  3. Q

    Normal Stress in Rods Experiencing Temperature Changes

    Now here is the part where I'm sort of stumped myself: Could someone let me know if my reasoning is valid? The professor explained it during office hours and all I got out of that was that something cancels out and the answer is 0.
  4. person123

    I Normal Stress Vectors: Sketch 1 vs Sketch 2

    Let's say you have a material element with normal and shear stress. These stresses were computed using stress transformation. When the material deforms, should the normal stress vectors remain normal to the surface (sketch 1) or parallel to the other surface (sketch 2)? Which would be more...
  5. E

    I Pressure vs Normal Stress: Exploring Bird Transport Phenomena

    What's really the difference between pressure and normal stress? Also I know pressure acts normal to a surface from the outside Do normal stress acts from inside? I'm reading bird transport phenomena and this is confusing
  6. R

    Finding Average Normal Stress in Rod

    Homework Statement Here's a snapshot of the problem: Homework Equations + Newton's 2nd Law. The Attempt at a Solution My question is: why does the delta P term have only a single 40 kN force considered, whereas for delta EF there's an F/2? Thanks for your time.
  7. T

    Normal Stress Balance at a Fluid-fluid Interface

    I am trying to determine a normal stress balance at an axisymmetric and dynamic fluid-fluid interface, ##z(r,t)##. For a static, free surface, this simplifies to the Young-Laplace equation: $$ \Delta p=\rho gz-\sigma2H=\rho gz-\frac{\sigma}{r}\frac{\partial}{\partial r}\left(r\frac{\partial...
  8. K

    Why Euler-Bernoulli beam theory does not work in this case?

    Hello, i would like to ask You a question about difference in results between Euler-Bernoulli method of analysis of stress in short slender beam and 3D FEA method mentioned in ansys aim tutorial here: https://confluence.cornell.edu/pages/viewpage.action?pageId=33636829 The problem looks like...
  9. A

    Ratio of shear stress to normal stress along principle place

    Homework Statement "In a component under multi-axial state of stress, the ratio of shear stress to normal stress along principle places is _____. A) 0.0 B) 0.5 C) 1.0 D) 1.5 E)2.0" Homework Equations σx' = (σx+σy)/2 + ((σx-σy)/2)*cos(2θ) + τxy*sin(2θ) σy' = (σx+σy)/2 - ((σx-σy)/2)*cos(2θ)...
  10. R

    Direction & magnitude of normal stress

    Homework Statement For the state of stress shown in the figure, normal stress acting on the plane of maximum shear stress is? Homework Equations Normal stress σn = σcos2θ 3. The Attempt at a Solution Plane of maximum shear stress is 45o relative to the max stress of 100MPa. So the total...
  11. B

    What is the cause of normal stress on a fluid element?

    In the derivation of Navier Stokes equation there is a term for normal stress acting on the fluid element. While the cause of normal stress is the static pressure which is already present in the equation doesn't this mean that the same force on the fluid element is repeated twice with different...
  12. G

    Find Axial Force P: Stress Concentration Homework

    Homework Statement The stress distribution along the section of a bar is shown below. From this distribution, find the approximate axial force P in kip. Homework Equations δavg=P/A A= (.6+.6)(.5) δavg=30ksi[/B]The Attempt at a Solution P=(30ksi)(.6in2)=18kip It says this answer is wrong...
  13. D

    Normal Stress: Compression vs Tension

    Homework Statement Homework Equations Equation of Equilibrium (Horizontal and Vertical Forces, Moments) Normal Stress = F/A The Attempt at a Solution I have already solved the solution for this problem. For part (a), I simply found the force in the link, and used the cross area where the...
  14. C

    Calculating Area of Normal Stress: Solving for σBC in a Thin Rectangular Rod

    Homework Statement For σBC end , i don't understand how the author get (20mm)(40mm-25mm) = 300x10^-6 (m^2) ... Homework EquationsThe Attempt at a Solution IMO, , the area should be the circled part (thin rectangular part of the rod) , but i only know one dimension only , which is 40mm , i don't...
  15. C

    Finding shear and normal stress after rotation

    Homework Statement http://ocw.nthu.edu.tw/ocw/upload/8/256/Chapter_7-98.pdf refer to page 3 in the 2nd, 3rd pictures, i have problem of finding σx'Homework EquationsThe Attempt at a Solution why can't use the formula to find σs ? it's given that σx' = ( σx+ σy)(0.5) + (0.5)( σx- σy)cos2θ +...
  16. C

    Angle of shear stress vs normal stress

    Homework Statement why the angle of shear stress ( θs) is given by θp - 45 ?? Homework EquationsThe Attempt at a Solution the difference in angle of shear stress and normal stress is90 degree , am i right? why it's negative 45 degree? is it wrong?
  17. F

    Shear stress and normal stress

    Homework Statement why the shear stress is maximum at the center ? while the normal stress is maximum at the boundary ? Homework EquationsThe Attempt at a Solution why shouldn't the shear stresss maximum at the boundary ? this is because shear stress is to pull the 2 surface apart [/B]
  18. Polar Bear

    Welding shear and normal stress calculations

    Hello, Does anybody know how to compute shear and normal stresses which take place due to applied load? My case is a simply supported beam (120x120x6.5 length: 4.2m) reinforced by a plate (20x120 length: 2m). Plate is welded on a top of a beam and external force (F=15 kN) is applied to the...
  19. I

    (Composite) In plane principal stress or normal stress?

    Hey everybody, I went through a discussion with a colleague today about Finite element modeling of composite structures and how to interpret the stress analysis. I understand that for isotropic materials, principal stresses could be used against the allowable stresses to see if failure will...
  20. C

    Calculating normal stress in a beam

    Hello So I've done some calculations, I'd like to see if my stuff is right. Thanks :) Please view attached http://i.imgur.com/AfMZyr0.jpg area = (pi)(9^2) = 254.46 Cos53.13=15/CG CG=25kN Normal stress = 25000/254.46 =98.25
  21. A

    Pressure and normal stress in fluid mechanics

    Hi, everyone. I am learning fluid mechanics. One book says that for a infinitesimal fluid cell, surface force includes 1) the pressure, which is imposed by the outside fluids surrounding the concerned fluid cell 2) the shear and normal stress, which result in shear deformation and volume...
  22. T

    Normal stress boundary condition at fluid/vacuum interface

    Homework Statement Stuck on two similar problems: "State the normal stress boundary condition at an interface x_3-h(x_1,x_2,t)=0between an invisicid incompressible fluid and a vacuum. You may assume that the interface has a constant tension." The second question in the same but the fluid is...
  23. Z

    Elasticity: Determine zero normal stress plane

    Given the stress tensor in a point, determine the zero normal stress plane. ...2 3 0 T= 3 2 0 ...0 0 5 ---------------------- Eigenvalues: σ1=σ2=5, σ3=-1 It must be simple, but I don't know how to determine the normal vector of that plane analytically. I know σ=0. t=Tn=σ+τ=τ If normal stress...
  24. B

    Normal Stress In A Simple Beam

    Homework Statement In a prismatic bar (same cross sectional area throughout the entire length), the load applied to both ends is 100 N causing the member to be in tension. If the cross sectional area of the member is 5 cm2. What is the normal stress in the in kPa? Homework Equations...
  25. N

    Finding the Force P from Normal Stress

    Homework Statement In the steel structure shown, a 6‐mm‐diameter pin is used at C and 10‐mm‐diameter pins are used at B and D. The ultimate shearing stress is 150 MPa at all connections, and the ultimate normal stress is 400 MPa in link BD. Knowing that a factor of safety of 3.0 is desired...
  26. T

    Max value of the average normal stress in the links.

    Homework Statement Here is the problem along with the solution: I am confused about part (a). Why is it that the area used is 2*0.008*(0.036-0.016). If you draw a cross section at just one of the holes, wouldn't that give you the max average stress? So the area used should instead be...
  27. Z

    Problem: Determine the maximum value of the average normal stress

    Hi guys. Please look at the uploaded picture. Normal stress is difined as: σ= P/A. And the Maximum normal stress σ = P/ (b*h/cos(θ)) ?? The right answers should be σAB= 97,7 MPa and σBC = -66,5 MPa. But how do I calculate it? What I have tried: Force AB: 40* sin(60deg) = 34,641 kN...
  28. R

    Material shear and normal stress question

    Homework Statement Everything needed is written in the question ( Open the attached image ) Nyhow the required is to find the value of P.Homework Equations Shear stress = \frac{ \Delta V }{\Delta A} eq 1 normal stress = \frac{ \Delta N }{\Delta A} eq 2The Attempt at a SolutionFor the...
  29. X

    Normal Stress Help: Find Normal Stress for 15kN & 20kN Plate of AISI 1010 Steel

    Homework Statement A 12cm X 12 cm square plate of AISI 1010 steel (E=200 GPa) us subjected to normal tensile forces of 15 kN and 20 kN on the top and right edges as shown in figure P22. The thickness of the plate is 5mm, and the left and bottom edges of the plate are fixed. Find the normal...
  30. T

    Finding the max value of the average normal stress

    Homework Statement Here is the question with the solution: The Attempt at a Solution I understand the first part where they find the forces by summation of moments. However I don't understand how they got that area. Why would they take the diameter (0.016) and subtract it from the length...
  31. N

    Finding normal stress in composite bar

    Homework Statement The 2000 mm long composite bar shown in Fig. 1 consists of an aluminum bar having a modulus of elasticity EAl = 70 GPa and length LAl = 500 mm, which is securely fastened to a steel bar having modulus of elasticity ESt = 210 GPa and length LSt = 1500 mm. After the force P...
  32. A

    How to calculate normal stress and shear stress on the beams.

    This is the my homework.Who can solve this for me ? i upload my solutions and the problem .Thanks.
  33. S

    What is the maximum normal stress in a W18x46 beam?

    Homework Statement Homework Equations σ=P/A σ=My/I τ=VQ/ItThe Attempt at a Solution I'm on part C, pretty sure I have A and B, so I'm using a W18x46 Beam. I have drawn shear and moment diagrams. I just want to be clear on what part C is asking... I'm assuming this point is at the end of...
  34. T

    Normal stress on cantilever beam

    Homework Statement Homework Equations \sigma_x = -\frac{M(x)y}{I} I = \frac{bh^3}{3} The Attempt at a Solution For point A, I did the following: I = \frac{t(2h)^3}{3} I = \frac{8th^3}{3} \sigma_x = -\frac{3\tau_0}{4th} \tau_{yx} = -\tau_0 \sigma_y = 0 Are my...
  35. H

    Normal stress problem, Help me

    Normal stress problem,.. Help me :( link BD CONSIST OF SINGLE BAR 30MM WIDE AND 12MM THICK. KNOWING THAT EACH PIN HAS 10MM DIAMETER. DET MAX VALUE OF AVE. NORMAL STRESS IN LINK BD IF A.) ANGLE = 0 DEGREES, B.) ANGLE = 90 DEGREES.. http://i356.photobucket.com/albums/oo7/hids0902/fcdsafdsa.jpg
  36. P

    Max Normal Stress of Beam: 1.879N | Modulus of Elasticity 100Gp

    Homework Statement What is the maximum normal stress in the beam and where is it located? The beam is 1m long, 0.2m high, and 0.05m thick (out of the page). The Modulus of Elasticity is 100Gp. The force is applied at an angle of 20 degrees with horizontal. | |____________ |...
  37. C

    How Does Temperature Affect Stress Distribution in Bonded Metals?

    length: 20mm thickness = 0.5mm delta t = 100 celsius thickness of adhesive = 50 mm and a picture of a Silion on top of a Copper Questions: How to calculate the distribution of shearing and normal stress? Any helps and ideas will be appreciated.
  38. 3

    Is there any normal stress on torsional member?

    Homework Statement is there any normal stress on torsional member? Homework Equations The Attempt at a Solution My professor showed me a circular rod made up of rubber and she made a rectangular hole on the side of it and asked whether there is any normal stress on the torsional...
  39. K

    Normal Stress question - Mechanics of Materials

    Homework Statement Conceptual question - When considering beam connected to something say a wall by a cylindar shaped pin, why is it when the beam is in tension near the pin the stress is high as the load is applied over a smaller cross section (normal cross section - profile of the pin) but...
  40. A

    Solve Normal Stress Problem: Width of 30kN Offset Link, 73MPa Max

    Homework Statement An offset link supports a load of 30 kN as shown in figure 6. Determine its required width w if the total (combined) normal stress is not to exceed 73 MPa? The cross section of the link is rectangular and has thickness of 40 mmHomework Equations stress= N/A I have tried...
  41. R

    Normal Stress in members of a stystem

    Diagram: http://i177.photobucket.com/albums/w222/77whtrocco/NORMALSTRESS.jpg Given: members AB, CD, and EF have x-sectional area of 25 mm^2. E = 200 GPa. Neglect deformation in member GH. Find: Normal Stresses in members AB, CD, and EF. I know that I need to determine the axial forces in these...
  42. C

    How is normal stress measured in biological tissues?

    ok...my engineering professor just gave us this crazy homework problem. he wants use to design a tool to measure the normal stress in a biological tissue. now it doesn't have to be extremely detailed in any way, but...we don't even know how normal stress is measured. the problem asks for it...
  43. F

    What Is the Correct Calculation of Stress in Welded Cylindrical Rods AB and BC?

    Two solid cylinderical rods AB & BC are welded together at B & loaded as shown. Knowing that d(1)=30mm & d(2)=50mm, find the average normal stress in the midsection of (a)rod AB, (b) rod BC. B____________C 125kN--->| | A______________|...