Stress and the Mohr diagram (D&R, 98-122)

1. AnnouncementsNext week lab: 1-3 PM Mon. and Tues. with Andrew McCarthy. Please start on lab before class and come prepared with specific questionsCottonwood wash ex. Due on Mon. in lectureThere will be NO lecture next Wed., Oct. 2.Please use the time to:1) Study important terms/concepts at end of Powerpoint lectures2) Work on practice problems (perhaps as a group in this room)3) Fault project

2. Stress and the Mohr diagram(D&R, 98-122) 1. Why learn about stress? 2. What is stress?3. Lithostatic stress4. Important stress tractions and stress ellipse 5. Stress Mohr circle

3. Why study stress? Dynamic/mechanical analysis: Interpret the stresses that produce deformation- Tectonic stresses andprocesses

4. - Rock deformation

5. Force vs. Stress Force:That which changes, or tends to change, body motionNewton's first law of motion: F=ma mass in kg; acceleration in m/s21 Newton (1N) = 1kg m/s2Forces are vector quantities; they have magnitude and direction.

6. Body forces: act on every point within a body GRAVITY! F = mg Surface forces: act on a specific surface in a body

7. Stress:that which tends to deform a bodyhow is it different than force?Deformation depends on how force is distributed!

8. Stress may be thought of as a description of force concentration Stress on a plane (traction), s = F/A what about units of stress? 1N/m2 = 1 Pa 100 MPa = 1 kbar

9. lithostatic stress vertical force = rVg = rL3g vertical stress = rL3g/L2 = rgL rgL = (2700 kg/m3)(10m/s2)(1500m) = 40500000 Pa = 40.5 MPa = .405 kbar

10. a stress traction is a vector, like force normal stress (traction): stress perpendicular to planeshear stress (traction): stress parallel to plane

11. A complete definition of Stress = a description of tractions at a given point on all possible surfaces going through the point s1 s1: Principal axis of greatest compressive stresss3: Principal axis of least compressive stress s3 s3 s1 and s3 always perpendicularand always perpendicular to planes of no shear stress s1

12. The goal of stress analysis is to determine the normal and shear stresses on any plane of any orientation, given the directions and magnitudes of the principal stresses

13. Analytical approach: Fundamental stress equations q = angle of plane from s1 Equation for a circle!

14. Geometric approach: Mohr Stress Diagram a plot of ss vs. sn first step: plot s1 and s3 recalling that they are in directions of no shear stress; draw Mohr circle

15. second step: Draw a line representing the plane at 2q, measured from s3.

16. differential stress: (s1-s3) diameter of circlecauses distortion mean stress: (s1+s3)/2 center of circlecauses dilation deviatoric stress: (s1-s3)/2 radius of circlecauses distortion

17. Mohr circles are useful for visualizing states of stress hydrostatic: equal stress magnitude in all directions

19. pore fluid pressure: serves to decrease confining pressure effective stress= confining pressure – fluid pressure

20. Next Lecture Stress and Deformation( D&R, 122-126; 226-252)

21. Important terminology/concepts force vs. stress static vs. dynamic equilibrium body forces vs. contact forces lithostatic stress definition of stress greatest/least principal stress directions normal stress (traction) shear stress (traction) Mohr circle stress diagram mean stress differential stress deviatoric stress effective stress pore fluid pressure hydrostatic state of stress dynamic/mechanical analysis

22. Ratio of sS/sN can be used to evaluate if failure is going to occur!