## MOHR DIAGRAM

#### I. USES OF DIAGRAM: (MOHR)

A. With known principal stresses we can find stress components acting on any inclined plane

 e.g., s1 = 5kb s 3 = 2kb stress with q = 47o with 2q = 94o

B. From general state of stress we can find the magnitudes and directions of principal stresses

 ex: given     4.5 sxx 1.5 txy -1.5 tyx 1.5 syy

#### II. CONVERSIONS: (h.w.)

A. 1 dyne/cm2 = 10-9 kbars

B. 1 dyne/cm2 = 14.503 X 10-6 pounds/in2

C. 1 dyne/cm2 = 10-10 gig. pa

D. 1 lb/in2 = 6.895 X 105 kb

#### III. TYPES OF STRESS: - (6) states

A. Uniaxial stress - one direction / s 1

1.

2. Principal stresses

s1> 0 s2 = s3 º 0

3. Mohr diagram

4. Stress ellipse - is a straight line

B. Biaxial stress - 2 directions

1.

2. s1 > s2 > s3 = 0

3.

4.

C. Triaxial stress - 3 directions

1. Real world

2. s1 > s2 > s3 not equal to 0

3.

4. Axis lengths not equal

D. Hydrostatic (special) - 3 equal directions of stress

1.

2. s1 = s2 = s3 = s

3.

4. Axes length equal (sphere)

a. What a submarine feels

b. With rocks it is lithostatic pressure

E. Pure shear - special biaxial

1.

2. s1 = -s3 neither = 0 but s2 = 0

3.

4. No stress ellipsoid due to (-) axis

F. Axial stress - (most rock experiments done with this)

1. Two cases:

a.

b. s1 > s2 and s2 = s3

c.

d.

2. Second case

a.

b. s1 = s2 > s3

c.

d.