Lecture 31: Stress transformation â Principal …...transformations Top-Drop-Sweep the Clock Sec...

11
ME 323 Mechanics of Materials

Transcript of Lecture 31: Stress transformation â Principal …...transformations Top-Drop-Sweep the Clock Sec...

Page 1: Lecture 31: Stress transformation â Principal …...transformations Top-Drop-Sweep the Clock Sec 12.9 Mohr's Circle To help you remember this method, we're even going to give ita

ME 323 Mechanics of Materials

Page 2: Lecture 31: Stress transformation â Principal …...transformations Top-Drop-Sweep the Clock Sec 12.9 Mohr's Circle To help you remember this method, we're even going to give ita

0, 0, 0 0, 0, 0x y xy z xz yz

Page 3: Lecture 31: Stress transformation â Principal …...transformations Top-Drop-Sweep the Clock Sec 12.9 Mohr's Circle To help you remember this method, we're even going to give ita

, ,n t nt

, ,x y xy

2 2cos sin in s2s con x y xy

2 2cos sin sios ncnt x y xy

cos 22 2

sin 2x y x yn xy

cos 22 2

sin 2x y x yyt x

sin 22

cos 2x yxynt

, ,n t nt, ,x y xy

i j00ij

Page 4: Lecture 31: Stress transformation â Principal …...transformations Top-Drop-Sweep the Clock Sec 12.9 Mohr's Circle To help you remember this method, we're even going to give ita
Page 5: Lecture 31: Stress transformation â Principal …...transformations Top-Drop-Sweep the Clock Sec 12.9 Mohr's Circle To help you remember this method, we're even going to give ita

cos 22 2

sin 2x y x yn xy

n

Page 6: Lecture 31: Stress transformation â Principal …...transformations Top-Drop-Sweep the Clock Sec 12.9 Mohr's Circle To help you remember this method, we're even going to give ita

nt

sin 22

cos 2x yxynt

Page 7: Lecture 31: Stress transformation â Principal …...transformations Top-Drop-Sweep the Clock Sec 12.9 Mohr's Circle To help you remember this method, we're even going to give ita

x

y

x

y

Page 8: Lecture 31: Stress transformation â Principal …...transformations Top-Drop-Sweep the Clock Sec 12.9 Mohr's Circle To help you remember this method, we're even going to give ita
Page 9: Lecture 31: Stress transformation â Principal …...transformations Top-Drop-Sweep the Clock Sec 12.9 Mohr's Circle To help you remember this method, we're even going to give ita

1 1 1

o2 2 1

2 22

in c

0

s os

9

xy x yp ave p p

p ave p p

R R

R

R

1 2 0nt p nt p

2x y

ave

2

2

4x y

xyR

, ,x y xy

Page 10: Lecture 31: Stress transformation â Principal …...transformations Top-Drop-Sweep the Clock Sec 12.9 Mohr's Circle To help you remember this method, we're even going to give ita

, ,x y xy

o1 1 1 1 1

o2 2 1

sin co45 2 2

90

s2x y xy

max s s p s s

min s max s s

RR R

R

2x y

avg

2

2

4x y

xyR

1, 21, 2n s s t avgs s

/ 2ave x y

Page 11: Lecture 31: Stress transformation â Principal …...transformations Top-Drop-Sweep the Clock Sec 12.9 Mohr's Circle To help you remember this method, we're even going to give ita