Mohr's Circle

Question 1

How can certain stress states be simply expressed?

Question 2

What is stress analysis?

Answer 2

Most practical engineering structures fo not have simple stress states, and need a way to relate complex stress states to known material properties aim to reduce the complexity of the stress state, then compare to material properties)

simply put: a way to reduce complexity in calculation

Question 3

What is conventions for normal stress?

Answer 3

For normal stresses tension is positive

Question 4

What is conventions for shear stresses?

Answer 4

For shear stresses clockwise is positive

Question 5

What is important thing to remember when using conventions?

Answer 5

The important thing is to use a consistent convention

Question 6

What are the assumptions made when using conventions

Answer 6

Stresses are:
- In equilibrium
- Static
The material is assumed to be:
- Homogenous
- Isotopic
- Linear elastic
Deflections are assumed to be small

Question 7

What is the transformation of axes?

Answer 7

The nature of stress and strain we see depends on how we look at an object

Question 8

What is the resolution of stresses 1?

Question 9

What is the resolution of stresses 2?

Question 10

What is principal stress?

Answer 10

There are always three principal stresses (always normal stresses). They lie in mutually perpendicular directions σ1 > σ2 > σ3. σ1 is the major principal stress, σ3 is the minor principle stress, σ2 is the intermediate principle stress.

Question 11

What happens in a plane stress system?

Answer 11

In plane stress systems one of the principle stresses will be zero, in this case use σ1 and σ2 as major and minor principles (because we are working in 2D)

Question 12

How can we find the principle stresses?

Answer 12

Can be found using Mohr’s circle

Question 13

How can uniaxial stresses be expressed?

Question 14

How can hydrostatic pressure be expressed?

Question 15

How can biaxial stress be expressed?

Question 16

How can pure shear be expressed?

Question 17

How can plane stress be expressed?

Question 18

Draw and label the mohrs circle

Question 19

How do we work out the radius of the circle of mohrs circle

Question 20

How do we work out the centre of Mohr’s circle?

Question 21

How do you work out the orientation of what angle you have to rotate your axis to get an axis set where the shear stresses go to zero?

Question 22

How do you calculate σ1?

Answer 22

σ1 = C + R

Question 23

How do you calculate σ2?

Answer 23

σ2 = C + R

Question 24

A thin plate of material is used in such a way that it experiences the following stress state (all values in MPa)
Identify the principle stresses σ1 and σ2, and determine their orientation with respect to the direction of the applied tensile force

Question 25

How do we draw Mohr’s circle for strain gauge rosettes?

Question 26

A 0°, 60° and 120° strain gauge rosette mounted on a thin plate records the following microstrains: 1400, 6500 and 3000 respectively during loading.
a) use this information to calculate the maximum and minimum principal strains on the plate at the point of measurement
b) the material has Young’s modulus 110GPa and a Poisson’s ratio of 0.34. Use this information and your results from part a) to calculate the maximum and minimum principal stresses on the plate at the point of measurement
c) the material is separately measured with a yield stress of 910MPa. using the Von Mises Criterion to determine whether the plate will yield or not