* Given the strain components e x, e y, and e xy, this calculator computes the principal strains e 1 and e 2, the principal angle q p, the maximum shear strain e xy max and its angle q s*. It also illustrates an approximate Mohr's cirlce for the given strain state In addition to identifying principal strain and maximum shear strain, Mohr's circle can be used to graphically rotate the strain state. This involves a number of steps. On the horizontal axis, plot the circle center at ε avg = (ε x + ε y)/2. Plot the either the point (ε x, γ xy /2) or (ε y, -γ xy /2)

German physicist Otto Mohr developed a method to graphically interpret the general state of stress at a point. This method is named as Mohr's circle and can be used to evaluate principal stress, maximum shear stresses and normal and tangential stresses at any plane Example: The state of plane stress at a point is represented by the stress element below. Draw the Mohr's circle, determine the principal stresses and the maximum shear stresses, and draw the corresponding stress elements. 80 MPa 80 MPa 50 MPa x y 50 MPa 25 MPa σ τ 15 2 80 50 2 =− − + = + = = x y c avg σ σ σ c A (θ=0) A B B (θ=90. Strains at a point in the body can be illustrated by Mohr's Circle. The idea and procedures are exactly the same as for Mohr's Circle for plane stress. The two principal strains are shown in red, and the maximum shear strain is shown in orange

Solid Mechanics: Strain Mohr's Circle for Plane Strain Mohr's Circle Strains at a point in the body can be illustrated by Mohr's Circle. The idea and procedures are exactly the same as for Mohr's Circle for plane stress. The two principal strains are shown in red, and the maximum shear strain is shown in orange. Recall that the normal strains. * Mohr's Circle for 2-D Stress Analysis If you want to know the principal stresses and maximum shear stresses, you can simply make it through 2-D or 3-D Mohr's cirlcles! You can know about the theory of Mohr's circles from any text books of Mechanics of Materials*. The following two are good references, for examples Determine: a) The principal planes. b) The principal stresses. c) The maximum shear stress and the corresponding normal stress. Mohr's Circle for Plane Stress: The transformation equations for plane stress can be represented in a graphical format known as Mohr's circle. This representation is useful in visualizing the relationship

Determine the principal stresses using Mohr's circle. The minimum principal stress is - D M Pa, and the maximum principal stress is [ MPa. Problem 07.031.c - Determine the planes of maximum in-plane shear stress for the given state of stress. Determine the orientation of the planes of maximum in-plane shearing stress using Mohr's circle The construction steps are exactly the same as the Mohr's circle for stress: Like the Mohr's circle for stress, you can obtain θp, θs and also strains based on other θ (e.g. θ = 30o) from the Mohr's circle for strain. And again, like the Mohr's circle for stress, we have the 3D strain Mohr's circle. 3D Mohr's circle for strain Mohr's Circle Equation •The circle with that equation is called a Mohr's Circle, named after the German Civil Engineer Otto Mohr. He also developed the graphical technique for drawing the circle in 1882. • The graphical method is a simple & clear approach to an otherwise complicated analysis Mohr's circle is often used in calculations relating to mechanical engineering for materials' strength, geotechnical engineering for strength of soils, and structural engineering for strength of built structures. It is also used for calculating stresses in many planes by reducing them to vertical and horizontal components. These are called principal planes in which principal stresses are.

To help understand this strain state, a Mohr's circle will be constructed and used to find the 1) principal direction and principal strains, 2) maximum shear strain direction and the maximum shear strain, and 3) the strain state if the element is rotated 30 o (counter-clockwise) [MUSIC] This is module 33 of Mechanics of Materials part one. And today's learning outcome is now given the plane strain conditions a point, we're going to determine the principal strains, the principal planes, and the maximum sheer strain, using Mohr's Circle. And so here's where we left off last time The Mohr's circle is used to determine the principle angles (orientations) of the principal stresses without have to plug an angle into stress transformation equations. To draw a Mohr's Circle for a typical 2-D element, we can use the following procedure to determine the principal stresses. Define The Shear Stress Coordinate System: 1

Draw the Mohr's circle, determine the principal stresses and the maximum shear stresses, and draw the corresponding stress elements. = -15 -80+50 65 +25 = 69.6 A (9 50 MPa 80 MPa 25 MPa 50 MPa =c+R -15+69.6 01,2 = = 54.6 MPa = -84.6 MPa B (0=90) = R = 69.6 MPa 15 MPa max 80 MP Now, today, we're going to go ahead, and use Mohr's Circle to find the principal strains, max in-planes, shear strain, and the orientation of the principal planes. So, here is our in-plane strains and what I'd like you to do now is to draw a small element and show the strains on that element and comment back Principal Strains Mohr's Circle. 13 B it is possible to find principal strains and their directions. • If the material obeys Hooke's Law, the principal strains can be used to find the principal stresses. • Strain measurement can be direct (using electrical-type gauge

- e the principal planes using Mohr's circle. The principal planes are at O ' and Problem 07.031.b - Deter
- Mohr's Circle for mutually perpendicular tensile stresses The figure shown above is the Mohr's circle for a body which is subjected to 2 mutually perpendicular principal tensile stresses. Both the stresses are of unequal intensities
- One of the principal stresses must be σ33, and the other two are easy to find by solving the quadratic equation inside the square brackets for \ (\xi \). Alternatively, when there are only two principal stresses to find, such as in this example, we can use Mohr's circle
- e the stresses on a plane 20o to the plane of the larger stress. SOLUTION Since there is no shear stress, x and y are the principal stresses and are at the edge of the circle
- LECTURE 08Playlist for MEEN361 (Advanced Mechanics of Materials):https://www.youtube.com/playlist?list=PL1IHA35xY5H5AJpRrM2lkF7Qu2WnbQLvSPlaylist for MEEN462..
- Derivation of Mohr's Circle (cont'd) 6. Mohr's Circle Equation • The circle with that equation is called a Mohr's Circle, named after the German Civil Engineer Otto Mohr. He also developed the graphical technique for drawing the circle in 1882. • The graphical method is a simple & clear approach to an otherwise complicated analysis. 7

- Principal plane, shear plane ,principal stress, shear stress, normal stress,MOHR CIRCLE .-----Max. Shear Stress theory|| https:..
- e the normal stresses σ n and σ t and the shearing stress τ nt at this point if they act on the rotated stress element shown in Figure 12b. The Stress Transformatio
- 5. Assertion (A): Mohr's circle of stress can be related to Mohr's circle of strain by some constant of proportionality. Reason (R): The relationship is a function of yield stress of the material. (a) Both A and R are individually true and R is the correct explanation of

**Mohr's** **circle** **is** a graphical representation of a general state of stress at a point. It is a graphical method used for evaluation of **principal** stresses, maximum shear stress; normal and tangential stresses on any given plane. Following important points must be noted for graphical analysis by **Mohr's** **circle** of Mohr's Circle. In this paper, an emphasis is given to identify the source of pedagogical difficulty and a simple rule-based method is presented as a new approach for effective teaching as well as learning. It is a viable method to understand the Mohr's Circle and its application to plane stress transformation The Mohr stress circle: Determining stress and stress states The goal of this lab is to reinforce concepts discussed in lecture on the topic of stress and give students a hands on intuition of the relationships between the principal stresses, the normal and shear stresses, and the interaction of these quantities on planes of varying orientation Intro and Derivation Mohr's circle is a geometric representation of plane (2D) stress transformation and allows us to quickly visualize how the normal (σ) and shear (τ) stress components change as their plane changes orientation. German civil engineer Otto Mohr developed this method from the good ol' stress transformation equations

- Two-dimensional state of stress at a point in a plane stressed element is represented by a Mohr circle of zero radius. Then both principal stresses (a) Are equal to zero (b) Are equal to zero and shear stress is also equal to zer
- • Using Mohr's Circle you can also calculate principal stresses, maximum shear stresses and stresses on inclined planes. 3. Stress Transformation Equations sx1 - sx +sy 2 = sx -sy 2 cos2q +txy sin2q tx1y1 = - sx +sy 2 sin2q +txy cos2q 1 2 4
- e point A' ( y, yx) : coordinate when = 90 4. Draw circle connecting A and A' with C as the centre 5. The datum (reference line) in Mohr circle is line AC 6. All angles must be deter

- According to Eq. (10.24), if one wants to measure one of the principal strains, the simplest method is to place sensors along the direction of the desired strain.For example, if ε 1 is desired, the sensor will be placed along this direction. Then we have α 1 = 0 and α 2 = α 3 = π/2. The influence of other strains (ε 2 and ε 3) will be cancelled
- or principal stress is horizontal, equal to cell pressure, and major principal stress is vertical. It is not possible to deter
- e the principal strains and their directions is: A. 1. B. QUESTION: 5. Assertion (A): Mohr's construction is possible for stresses, strains and area moment of inertia. Mohr's circle of stress can be related to Mohr's circle of strain by some.
- In order to calculate the normal and shear stresses acting on any plane, through Mohr's circle diagram, it is necessary to know the direction cosines of the normal unit vector of the plane with respect to the principal directions
- A 2D graphical representation for Cauchy stress tensor is said to be as Mohrs circle. It is used to analyse and find the stress components acting on a coordinate point. Abscissa, σ n and ordinateτ n are the magnitudes of normal and shear stress. Find the mean, maximum, principal and Von Mises stress with this this mohrs circle calculator
- or principal plane. Hence, point A represents
- Each circle plots the stress components in a plane perpendicular to one of the principle axes, for example, circle C1 plots possible stress states in planes perpendicular to the first principal stress (σ 1) axis. Allowable stress components on all planes must lie inside the largest circle and outside the two smaller circles as shown by the.

2d (6 pts) Compute the principal stress magnitudes using: Show your work. Check to be sure that your results are consistent with your Mohr circle in (2c). 2e (6 pts) Compute the principal stress directions using: Remember that α1 and α3 are the angles between the X 1-axis and the directions in which σ1 and σ3 act, respectively Principal Stresses and Strains - Mechanical Engineering (MCQ) questions and answers Which of the following formulae is used to calculate tangential stress, when a member is subjected to stress in mutually perpendicular axis and accompanied by a shear stress? The graphical method of Mohr's circle represents shear stress (τ) on _____ a. An alternative graphical method to calculate the normal and shear stress is to use the pole point on Mohr's circle. Two pole points can be established on Mohr's circle. The first pole point is related with the directions of the stresses and the second is related with the planes on which the stresses act. Consider the case of Fig. 1 The Principal Stresses have a nice graphical representation, first devised by Otto Mohr, and this is called as Mohr's Circle. Mohr's Circle is drawn with the normal stress components being represented on the x-axis and the shear stress component on the y-axis. Figure shows a typical Mohr's Circle for a two-dimensional state of stress

33 Slide No. 64 Mohr's Circle for Plane Stress Example 6 For the state of plane stress shown, (a) construct Mohr's circle, determine (b) the principal planes, (c) the principal stresses, (d) the maximum shearing stress and the corresponding normal stress and the normal stress acting on the planes of maximum shear stress are x + y ave = CCC = 27 MPa 2 7.4 Mohr's Circle for Plane Stress the transformation of plane stress can be represented in graphical form, known as Mohr's circle the equation of Mohr's circle can be derived from the transformation equations for plane stress x + y x - C7.4 3D Mohr's Circle and τ abs-max. So far we've only looked at 2D plane-stress scenarios, but in the real world stresses act in a 3D manner, with a general state-of-stress that looks like:. The full-blown transformation for this scenario is not within the scope of this course (phew) Mohr's Circle The data needed to construct Mohr's circle are the same as those needed to compute the preceding values, because the graphical approach is an exact analogy to the computations. Mohr's Circle Mohr's circle is actually a plot of the combination of normal and shearing stresses that exist on a stress element for all possible.

**principal** stress ratio K = σ. 2 / σ. 1 (typically . σ. 2. represents the horizontal stress . σ. h, and . σ. 1. represents the vertical stress . σ. v). It is thus more convenient on occasion to express the Mohr-C criterion in terms of K Stresses and Shears, Determine Coefficients, Principal Stress, Principal Shear Stress, Stress Tensor, Three Mohr's Circles, Direction Cosine Matrix Related Resources: Design Engineering Stresses in Three Dimensions Excel Spreadsheet Calculato Using Mohr's circle, determine (a) the principal stresses and (b) the maximum shear stress and associated normal stress at the point in Figure 4. Specify and sketch the orientation of the element in each case. The directions of the stress components are as indicated in Figure 4. 20 MPа 60 MP ** Then, the Mohr circle of stress at failure for the sample can be drawn using the known values of the principal stresses**. If data from several tests, carried out on different samples upto failure is available, a series of Mohr circles can be plotted. It is convenient to show only the upper half of the Mohr circle Determine the principal and maximum shear st/tiitresses/strains in 2Db M h' i lD by Mohr's circle Determine the principal and maximum shear stresses/strains in 3D by linear algebra Calculate Tresca and von Mises stresses Review of stress and deformation in axially loade

- or σ III principal stresses, or (2) normal stress σ and shear stress τ on the failure plane.
- A yield criterion is a hypothesis defining the limit of elasticity in a material and the onset of plastic deformation under any possible combination of stresses.. There are several possible yield criteria. We will introduce two types here relevant to the description of yield in metals. To help understanding of combinations of stresses, it is useful to introduce the idea of principal stress space
- or principal stress (s 3), and the axial stress (s a) is the major principal stress (s 1). To visualise the normal and shear stresses acting on any plane within the soil sample, a graphical representation of stresses called the Mohr circle is obtained by plotting the principal stresses
- e which principal stresses will produce this combination of shear and normal stress, and the angle of the plane in which this will occur. According to the principle of normality the stress introduced at failure will be perpendicular to the line describing the fracture condition
- Solution. First, Mohr's circle for the transformation of stress in the xy plane is sketched in the usual manner as shown, centered at C 2 with diameter A 2 A 3 ().Next, we complete the three-dimensional Mohr's circle by drawing two additional circles of diameters A 1 A 2 and A 1 A 3 in the figure. Referring to the circle, the principal stresses are s 1 = 100 MPa, s 2 = 40 MPa, and s 3 = -60 MPa
- e the stresses ox, Oy, and txy, and show them on a stress element. (b) Deter
- ing the principal and maximum shear stresses graphically. It also facilitates in getting stress along any plane inclined to vertical at a particular angle

** Thus, the normal stresses σxand σyare equal to the membrane stress σand the normal stress σzis zero**. The principal stresses are and σ3= 0. Any rotation element about the zaxis will have a shear stress equals to zero. t pr 1 2 2 σ σ σ = = = Stresses at the Outer Surfaces. To obtain the maximum shear stresses, we mus 572 CHAPTER 7 Analysis of Stress and Strain Problem 7.2-3 Solve Problem 7.2-1 for an element in plane stresssubjected to stresses s x 5700 psi, s y 2300 psi, and t xy 2500 psi, as shown in the figure. Determine the stresses acting on an element oriented at an angle u 50˚ from the x axis, where the angle u is positive when counterclockwise. Show these stresses on a sketc Answer to: Using Mohr's circle, for the given state of stress, determine (a) The principal planes (all angles are between -90 o and 90 o ), (b).. 1. Determine the state of stress at points A and B 2. Represent the state of stress at points A and B in three-dimensional differential stress elements. Using the Mohr's circle, determine: 3. The principal stresses and principal angles for the states of stress at A and B

mohr circle calculation for a three dimensional state of stress, mohr 3D - Granit Engineerin The state of stress at a point P in a two dimensional loading is such that the Mohr's circle is a point located at 175 MPa on the positive normal stress axis. Question 3. Determine the maximum and minimum principle stresses respectively from the Mohr's circle (A) +175 MPa, -175 MPa (B) +175 MPa, +175 MPa (C) 0,-175 MPa (D) 0, In Fig. 7.3(b) the Mohr circle has been drawn, A and B representing the major and minor principal stresses respectively. By drawing line A O P parallel to the major principal plane the origin of planes O P may be located. (a) The maximum shear stress may be calculated from equation (7.3) or it may simply be read from the Mohr circle. Clearly τ.

Mohr's Circle for Plane Stress • With Mohr's circle uniquely defined, the state of stress at other axes orientations may be depicted. • For the state of stress at an angle θwith respect to the xy axes, construct a new diameter X'Y' at an angle 2θwith respect to XY. • Normal and shear stresses are obtained from the coordinates X. The added axial stress at failure ( s d) f is practically the same regardless of the chamber confining pressure. This property is shown in Figure 12.33. The failure envelope for the total stress Mohr's circles u Bs 3 A¢s d Bs 3 A1s 1 s 32 ¢u d A¢s d u u c ¢u d f f B B 55 A Shear stress (kN/m 2) Normal stress (kN/m2) 105 125 175A Effective.

- Mohr Theory Some materials have compressive strengths different from tensile strengths Mohr theory is based on three simple tests: tension, compression, and shear Plotting Mohr's circle for each, bounding curve defines failure envelope Fig. 5−1
- Q. Add the following 2-D stress states, and find the principal stresses and directions of the resultant stress state. A. Step 4: Plotting the Mohr circle for the combined stress state and reading off the principal stresses and the principal directions gives the required values 1 = 37.4 MPa 2= 27 6 MP
- e (a) the principal planes, (b) the principal stresses. Probs. 7.9 For the given state of stress, deter
- 3.5.1. Setting up and interpreting a Mohr circle. When a Mohr circle is constructed, eventually it is possible to know that type of tension or compression present by simply looking at the position of the circle. Firstly a set of axes need to be drawn. The horizontal one will represent the normal stress, and the vertical one the shear stress

Here is the simple technique to draw M ohr's Circle in Excel. Let us consider this example below: For the initial stress element shown, draw the mohr's circle and also determine the principle stresses and the maximum shear stres - Mohr's circle method is a graphical method used to determine principal stresses, normal, tangential and resultant stresses. - Direct stress (σ) is represented on X-axis and shear stress (τ) is represented on Y-axis in Mohr's circle. - Centre of this circle can be determined by using the formula: C = (σ x - σ y) / Calculator which draws Mohr's Circle very neatly for plane stress and strain in both 2D and 3D. Also includes a graph of the element orientation for principal. Bending Moment and Shear Force Diagram Calculator The first free, easy to use customizable Bending Moment Diagram and Shear Force Diagram Calculator for simply supported Beams. The Mohr Circle construction is quite simple in this case. The two endpoints of the radius will be at (0,0) and (20,0) and the circle is drawn as shown below We see by simple visual inspection of the Mohr circle that we are already in the principal stress state (i.e. all shear stresses are equal to zero), so we do not need t 1.Drawthestresssquare,notingthevaluesonthexandyfaces;Fig.5(a)showsahypo-theticalcaseforillustration.For the purpose of Mohr's circle only, regardashearstres

- ) τ MAX [MPa] Maximum shear stress : σ VM [MPa] Von Mises stres
- e the moments and product of inertia for any other rectangular axes including the principal axes and principal moments and products of inertia
- } \] This applies in both 2-D and 3-D. The maximum shear always occurs in a coordinate system orientation that is rotated 45° from the principal coordinate system. For the principal strain.
- e (a) thein-plane principal strains and (b) the maximum in-plane shear strain and average normal strain. In each case specify the orientation of the element and show how the strains deform the element within the x-y plane.-825110-62.
- This is found by finding the average stress, using either the average of the principal stresses or one third of the trace (both are equivalent): This can also be found graphically as the center of the largest circle in the image of Mohr's circle, below
- e the location of maximum stress

6 LECTURE 22. FAILURE CRITERIA: MOHR'S CIRCLE AND PRINCIPAL STRESSES (7.4) Slide No. 10 Principal Stresses and Maximum ENES 220 ©Assakkaf Shearing Stress Variation of Stresses as Functions of θ-20-10 0 10 20 30 40 0 60 120 180 240 300 36 When the Mohr's circles for plane stresses and plane strains are combined, a powerful tool for finding principal stresses and strains is formed. Alternatively, one can transform either stresses or strains and then employ the constitutive law to find the transformed strains or stresses, respectively Radius of Mohr's circle is equal to the maximum shear stress. 11. Determine the principal planes and the principal stresses. Also de-termine the maximum sgear stress and planes on which it acts. Minor principal stress, ( ) ( ) 12 2 2 n2 1 2 2 2 2 n2 1 4q 2 2 70 35 1 70 35 4 17.5 2

Employ Mohr's circle to determine (a) the magnitude and orientation of the principal stresses and (b) the magnitude and orientation of the maximum shearing stresses and associated normal stresses. In each case, show the results on a properly oriented element; represent the stress tensor in matrix form. Figure 1.16 Example 1.3 Mohr circle for strain. very rigid elongated objects such as belemnite fossils and toumaline crustals may undergo boudinage during strain. It is possible to determine the original length of the object by adding up the lengths of all the boudins. The strains along the strain axes are the three principal strains. The principal stretches. Calculate σ 1, σ 2, τ max in-plane and θ p1, θ s1. Use the Mohr's circle. Use the Mohr's circle. Calculate σ 1 , σ 2 , τ max in-plane and θ p1 , θ s1 Values of normal stress and shear stress must relate to a particular planewithin an element of soil. In general, the stresses on another plane will be different. To visualise the stresses on all the possible planes, a graph called the Mohr circle is drawn by plotting a (normal stress, shear stress) point for a plane at every possible angle A stress element has σ x = 80 MPa & τ xy = 50 MPa cw. a. Using Mohr's circle, find the principal stresses & directions, and show these on a stress element correctly aligned wrt xy coordinates. Draw another stress element to show τ 1 & τ 2, find corresponding normal stresses, and label the drawing completely. b. Repeat part a usin

The test specimen is subjected to all around lateral pressure (). The deviatric stress applied be. Then total vertical stress is, A mohr's circle is drawn by plotting and in x- axis and the shear stress is the y-axis. Mohr's rupture envelope is obtained by drawing the tangent to the circles obtained 4.2.3 Mohr's Circle for Strain Because of the similarity between the stress transformation equations 3.4.9 and the strain transformation equations 4.2.2, Mohr's Circle for strain is identical to Mohr's Cirlce for stress, section 3.5.5, with replaced by (and replaced by xy). 4.2.4 Problems 1 form of Mohr's circles (Fig. 2) where the normal stress is plotted on the horizontal axis and the shear stress plotted on the vertical axis. Three principal circles are possible between the principal stress pairs σ1 - σ2, σ2 - σ3, and σ1 - σ3. In failure theorems, the principal stress pair 1 to 3 is regarded as the mos The Mohr Theory of Failure, also known as the Coulomb-Mohr criterion or internal-friction theory, is based on the famous Mohr's Circle. Mohr's theory is often used in predicting the failure of brittle materials, and is applied to cases of plane stress. Mohr's theory suggests that failure occurs when Mohr's Circle at a point in the bod • Determine the principal components of stress, 2 σ 1 and σ. • Determine the magnitude of ′ τ xy′. • Draw the Mohr's circle for this state of stress. Show the location of the x'−axis in your Mohr's circle. From this, determine the rotation angle θ. • Determine the absolute maximum shear stress for this state of stress. x a.

It becomes very easy to understand this case if you are used to of visualizing the Mohr' Circleimagine a body having sigma x and sigma y in x and y direction along with shear stress in such a way that at some angle theta, we are getting minimum a.. ** Mohr's Circle for Plane Stress • From Mohr's circle we can find state of stress at other axes orientations**. • For state of stress at angle qwith respect to the xy axes, construct a new diametral line X'Y' at angle 2qwith respect to XY. • Coordinates of X', Y' are the transformed normal and shear stresses

For the state of plane stress shown, (a) construct Mohr's circle, determine (b) the principal planes, (c) the principal stresses, (d) the maximum shearing stress and the corresponding normal stress. SOLUTION: •Construction of Mohr's circle 30 40 50MPa 502030MPa 40MPa 20MPa 2 50 10 2 2 2 R CX CF FX x y ave V V Mohr's Circle It can be Drawn for the following Cases A body in which two mutually perpendicular principal stresses of unequal intensities act. A body subjected to two mutually perpendicular principal stresses which are unequal and unlike. A body subjected to two mutually perpendicular principal tensile stresses and a simple shear stress

For each of the plane stress states listed below, draw a Mohr's circle diagram properly labeled, find the principal normal and shear stresses, and determine the angle from the x axis to σ1. Draw stress elements as in Fig. 3-11c and d and label all details. (a) σx = 20 kpsi, σy = −10 kpsi, τxy = 8 kpsi c 1.3 Mohr's Circle for Stress The stress states at a point within a soil mass can be represented graphically by a very useful and widely used devise known as Mohr's circle for stress . The stress state at a point is the set of stress vectors corresponding to all planes passing through that point Concept of normal and shear stress, principal stress, plane stress, Mohr's circle, stress invariants and stress equilibrium relations are discussed in analysis of stress section while strain-displacement relationship for normal and shear strain, compatibility of strains are discussed in analysis of strain section through geometrical. Mohr's circle. In Mohr's circle, the shear strain axis is drawn in the reverse direction such that positive axis points downward. Similar to the equations in (2), Mohr's circle can be used to transform strain components ( ó Ñ, ó Ò, Û Ñ Ò) in a X-Y coordinate frame to the corresponding components ( ó, ó, Û) in an X*-Y* coordinat ** Draw Mohr's circle of strain and determine principal normal and shear strains and their directions for the elements having the strains as in Table 2**. Verify your results analytically. Also, determine principal normal and shearing stresses. Take E=200 GPa and =0.3

** The principal normal stress will occur when the shear stress is zero**, which means The principal shear stress is simply the square root term An alternative to using these equations for the principal stresses is to use a graphical method known as Mohr's Circle is a principal stress Azimuth of is N60 W Friction angle = 30. SOLUTION First, recognize the planes of and and their orientations with respect to the geographical coordinate system. The plane of in this case is a horizontal plane (plane, a principal stress) and the plane of is a vertical plane perpendicular to It's a situation when various types of stress (or in other words various types of load) act on a single structure at the same time. These are the possible kinds of stress: * axial: tensile or compressive * bending * torsional * shear All possible. The stress components on the right-hand face of the element are the coordinates of the reference point A (—20, 60), = 00, Fig. 15—19b. Applying the Pythagorean theorem to the shaded triangle to determine the circle's radius CA, we have = Principal Stresses. The principal stresses are represented by points B and D in Fig. 15—19b

From this stage of the test, as well as the shear strength being determined, the values of cohesion (c') and phi (φ') can be determined using **Mohr** **circle** and stress path plots. Figure 10 - **Mohr** **Circle** Plot with Cohesion and Phi Results. 15 Advantages of a VJ Tech Automatic Triaxial Syste proportional to the deviatoric stress, a point in principal stress space does not directly indicate the value of shear stress on a plane. However, each point on the failure sur-face in principal stress space corresponds to a Mohr circle tangent to the failure envelope (Fig. 2a). For the particular case where r 2 is the intermediate principal. 1. For the state of plane stress shown the maximum and minimum principal stresses are: (a) 60 MPa and -30 MPa (b) 50 MPa and 10 MPa (c) 40 MPa and 20 MPa (d) 70 MPa and -30 MPa 2. Normal stresses of equal magnitude p, but of opposite signs, It is possible to evaluate the principal stresses on these planes by substituting equation 1.14 into equation 1.12, noting that equation 1.14 gives are principal strains. Determine the. •Calculate the stress at the point of interest due to each internal resultant •Combine the individual stresses, and draw the stress element •For example, •Use Mohr's circle to determine the principal stresses, max shear stress, etc. •Make sure you identify the plane corresponding to the state of plane stress 13 ( ) () x x F x x M x yz