Mohr's Circle For Plane Stress & Plane Strain

Mohr's Circle For Plane Stress & Plane Strain | Strength of Materials (SOM) - Mechanical Engineering PDF Download

Mohr’s circle is the locus of points representing the magnitude of normal and shear stress at the various plane in a given stress element. Graphically, a variation of normal stress and shear stress are studied with the help of Mohr's circle.
σ1 and σ2 are Principal Stresses,  then normal and shear stress on lane  which is inclined at angle ‘θ’ from major principal plane, then

Different Stress Diagram

Mohr's circle for plane Stress and StrainNormal Stress

Shear Stress

General State of Stress at an Element

If  σx and σy are normal stress on vertical and horizontal plane respectively and this plane is  accompanied by shear stress  then normal stress and shear stress on the plane, which is inclined at an angle θ from the plane of

then,

Let σx, σy be two normal stresses(both tensile) and τxy be shear stress then:

Maximum and Minimum Principal Stresses are:

Strength of Materials

Mohr's circle for plane stressed

Observations from Mohr's Circle

The following are the observations of Mohr's circle as:

• At point M on circle σn is maximum and shear stress is zero.
∴ Maximum principal stress ≡ coordinate of M
• At point N on circle, σn is minimum and shear stress τ is zero.
∴ minimum principal stress ≡ coordinate of N
• At point P on Circle τ is maximum.
Maximum shear stress ≡ ordinate of P(i.e. radius of circle)
• Also, normal stress on the plane of maximum shear stress:
σn = abscissa of P
Where σn ≡ Average stress
• Mohr's circle becomes zero at a point if radius of circle has the following consideration.
• If σx = σy, then radius of Mohr's circle is zero and τxy = 0.
• The sum of normal stresses acting on perpendicular faces of a plane stress elements is constant and independent of the angle θ.
σ1 + σ2 = σ1 + σ2

Strain analysis

Principle Strain

θ + ∈θ + 90º = ∈x + ∈y

Relation between Principle strain and stress

Strain Rosetts

• Rectangular Strain Rosette

x = ∈, ∈y = ∈90º and Ф = 2∈45º - (∈x + ∈y)

• Equiangular Strain Rosette (delta strain rosette)

θº = x

The document Mohr's Circle For Plane Stress & Plane Strain | Strength of Materials (SOM) - Mechanical Engineering is a part of the Mechanical Engineering Course Strength of Materials (SOM).
All you need of Mechanical Engineering at this link: Mechanical Engineering

Strength of Materials (SOM)

37 videos|39 docs|45 tests

FAQs on Mohr's Circle For Plane Stress & Plane Strain - Strength of Materials (SOM) - Mechanical Engineering

 1. What is Mohr's circle and how is it used to analyze plane stress and plane strain?
Mohr's circle is a graphical method used to analyze the stress states in a material under plane stress or plane strain conditions. It provides a visual representation of the stress components acting on a material at a specific point. By plotting the normal and shear stresses on a circle, Mohr's circle allows for the determination of principal stresses, maximum shear stresses, and the orientation of the principal planes.
 2. What is the difference between plane stress and plane strain?
Plane stress refers to a condition in which a material is subjected to stresses only within a single plane, while the stresses in the other two planes are negligibly small. On the other hand, plane strain refers to a condition in which a material is subjected to strains only within a single plane, while the strains in the other two planes are negligibly small. In plane stress, the material can freely deform in the other two directions, while in plane strain, it is constrained from deforming in the other two directions.
 3. How can Mohr's circle be used to determine the principal stresses?
Mohr's circle allows for the determination of principal stresses by finding the intersection points of the circle with the horizontal axis. These intersection points represent the maximum and minimum normal stresses acting on the material. The angles at which the intersection points occur provide the orientation of the principal planes.
 4. How is the maximum shear stress determined using Mohr's circle?
The maximum shear stress can be determined by the radius of the Mohr's circle. The maximum shear stress occurs at the 45-degree angle to the principal axes, and its magnitude is equal to half the difference between the maximum and minimum normal stresses.
 5. What are the applications of Mohr's circle in mechanical engineering?
Mohr's circle has various applications in mechanical engineering. It is commonly used in the analysis of structural components subjected to complex loading conditions, such as beams, plates, and shafts. It is also used in the design of materials and structures to ensure the safety and reliability of engineering systems. Additionally, Mohr's circle is valuable in geotechnical engineering for analyzing soil mechanics and rock mechanics problems.

Strength of Materials (SOM)

37 videos|39 docs|45 tests

Up next

 Explore Courses for Mechanical Engineering exam

Top Courses for Mechanical Engineering

Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Related Searches

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

;