Mohr Circles F 3 F 2 T N V F 4 F 1 H F 5 N Area = sin H T - - PDF document

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Mohr Circles F 3 F 2 T N V F 4 F 1 H F 5 N Area = sin H T - - PDF document

Nov 15, 2022 227 likes •519 views

Mohr Circles F 3 F 2 T N V F 4 F 1 H F 5 N Area = sin H T Area = cos F H T cos Nsin 0 H F V T sin Ncos 0 V V 1 Area = sin x

SLIDE 1

Mohr Circles

SLIDE 2

F1 F2 F3 F4 F5  H V N T

SLIDE 3

H V N T Area = sin  Area = cos 



           

 

H V

F H T cos Nsin F V T sin Ncos

SLIDE 4

y  cos    1   1 Area = sin  Area = cos 



   

                 

x y

sin cos sin cos sin cos

x  sin 

SLIDE 5

 

               

x y x y x y

cos2 2 2 sin2 2

Double Angle Formulas

SLIDE 6

  

x y

2     

x y

2  2

 

 

  ,

SLIDE 7

Mohr Circle Examples

SLIDE 8

(32,0) (52,0) (12,0) 35 (39,18.6)

SLIDE 9

20

(52,0) (39,18.6) +15 (32,20)

SLIDE 10

(6,2) (-4,-2)

SLIDE 11

  1 2 3

SLIDE 12

Mohr-Coulomb

SLIDE 13

 

SLIDE 14

  1 3 ½13) ½13) (ffff) Pole  f f 

SLIDE 15

  1 3 (ffff) Pole  f (ff–ff) –f

SLIDE 16

+f –f

SLIDE 17

ff   1 3 Pole  f f f

SLIDE 18

ff   1 3 Pole  f f f

SLIDE 19

ff   1 3 Pole  f f f

SLIDE 20

(ffff)   1 3 Pole  ff = c c

SLIDE 21

Obliquity Relationships

SLIDE 22

D R

cot c 







3 f



1 f



Cohesive Soil

SLIDE 23

       

1 3 1 3 1 3 1 3

1 2 sin 1 2 cot cot 2         

f f f f f f f f

R D c c           

Cohesive Soil

SLIDE 24

D R







3 f



1 f



Cohesionless Soil

SLIDE 25

       

1 3 1 3 1 3 1 3

1 2 sin 1 2       

f f f f f f f f

R D         

Cohesionless Soil

SLIDE 26

   

1 2 3

1 sin tan 45 1 sin 2            

f f

    

   

3 2 1

1 sin tan 45 1 sin 2            

f f

    

Obliquity Relationships

SLIDE 27

 

R



Angle of Obliquity

SLIDE 28

Example

A conventional triaxial compression test is conducted on

a medium-dense sandy silt with  = 32.

If the cell pressure (3) is 40 kPa, what is the major

principal stress at failure?

What is the normal stress on the failure plane at failure?

 

2 2 1 3 tan

45 40tan 61 130 kPa 2              

f f

SLIDE 29

85 45





Cohesionless Soil

 

85 45sin 32 61kPa      ff

40 130 32°