(Solved): Draw three Mohr circles representing stress states in which the mean stresses are the same but the ...

Draw three Mohr circles representing stress states in which the mean stresses are the same but the deviatoric stresses vary. Draw three Mohr circles representing stress states in which the least compressive principal stress has the same magnitude but the most compressive principal stress varies. (a) Draw a Mohr circle representing given physical plane diagram below (

(b) Use Mohr circle to determine Principal stress orientations in the given physical diagram. Draw a Mohr circle, and locate and label the points on the circle that represent the planes that experience the maximum shear stress. a. What are the magnitudes of the normal stresses acting on the planes that experience maximum shear stress? b. What angles do the planes that experience maximum shear stress make with the plane that experiences the most compressive normal stress? What angles do the planes that experience maximum shear stress make with the plane that experiences the least compressive normal stress? c. Draw a physical plane diagram corresponding to the Mohr circle you have drawn, and identify the pole to the Mohr circle that ties your physical plane drawing to your Mohr circle. If the most compressive

and least compressive (

) principal stresses acting on planes within an object have the same magnitude, what is the magnitude of the maximum shear stress acting on any plane within that object? Imagine that you have a cubic block of tar

long along each edge; the area of each face of the cube is

. Now imagine that you place a granite cube with the same size on top of the block of tar. The force that the block of granite exerts on the block of tar is equal to its weight (i.e.

its density

volume

gravitational acceleration; assume a density of 2.85

and a gravitational acceleration of

). This force is applied equally across the 1

area of the top of the block of tar. The pressure exerted by the atmosphere is

(i.e. 1 bar), and the total pressure across the top of the block of tar is equal to the standard atmospheric pressure plus the pressure due to the weight block of granite. a. Draw the appropriate Mohr circle that representing this situation. b. Draw the physical space diagram representing this situation. Find the pole of this Mohr circle, and use it to determine the magnitudes of the stress components acting on planes (in the tar) dipping first

and then

to the left. Imagine now that we place a s ESS 3113: Structural Geology Lab 8 Mohr Circles Please use graph paper for all your plots, and please draw them as accurately as possible. Treat all the situations described in these problems as two dimensional situations, i.e. ignore all stresses acting in the third dimension. Compression positive along

-axis and

positive along

-axis in Mohr space. (a)

Draw a Mohr circle using normal and shear stresses acting on planes a and

. **Draw physical plane diagram (X1 parallel to

) corresponding to the Mohr circle you have drawn.

Draw planes of maximum shear stresses on physical plane diagram using the Mohr circle you have drawn. (b) **Draw a Mohr circle using normal and shear stresses acting on planes

, c' and

. **Draw physical plane diagram (X1 parallel to

) corresponding to the Mohr circle you have drawn. **Draw planes of maximum shear stresses on physical plane diagram using the Mohr circle you have drawn. rigure s.?/ ricturea nere is a vertical stress

or magnitude 40 Irra ana a horizontal stress

of magnitude

. The lines labeled

and

to

are traces of planes at

intervals. Stress

, normal stress

, and shear stress

have been calculated for each of the planes to show the systematic variations.