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σ11

σ12

σ13

σ21

σ22

σ23

σ31

σ32

σ33

 

i=1 dσ11dx1+dσ21dx2+dσ31dx3+F1=0

-F2= -1,010 + 1,810x32 - 0,210·2·x3=

-1,010 + 1,810·(-1,710)2 - 0,210·2·(-1,710) = 5,008MN/m3 

F2 = - 5,0008MN/m3

i=2 dσ12dx1+dσ22dx2+dσ32dx3+F2=0

i=3 dσ13dx1+dσ23dx2+dσ33dx3+F3=0

 

ε11=du1dx1ε12=ε21=12du2dx1+du1dx2,     ε32=ε23=12du3dx2+du2dx3,     ε22=du2dx2

ε32=12du3dx2+du2dx3=121,310x1-0,510x1∙2x3=121,310∙0,110-0,510∙0,110∙2∙5,990=-0,2640·10-4

 

 

 

2,020 - σ2

0

3,030

 

0

-2,230 - σ2

0

=0

3,030

0

-6,060 - σ2

 

 

(2,020 - σ2)·(-2,230 - σ2)·(-6,060 - σ2) – 3,0302·(-2,230 - σ2)=0   → σ2=-2,230 ˅ σ2=3,030 ˅ σ2=-7,070

 

2,020 – (-7,070)

0

3,030

 

9,090

0

3,030

0

-2,230 - (-7,070)

0

=

0

4,840

0

3,030

0

-6,060 - (-7,070)

 

3,030

0

1,010

 

 

9,090

0

3,030

0

4,840

0

3,030

0

1,010

n1

n2

n3

 

9,09 n1+ 3,03 n3=0    →   n1= -0,333n3

n12+ n22+ n32=1   →   (-0,333n3)2...

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