Veza naprezanja i deformacija
Veza naprezanja i deformacija
Veza naprezanja i deformacija
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τ<br />
τ<br />
τ<br />
xy<br />
yz<br />
zx<br />
= Gγ<br />
= Gγ<br />
= Gγ<br />
xy<br />
yz<br />
zx<br />
Tenzor <strong>naprezanja</strong> je:<br />
(b) modul kompresije<br />
3<br />
3<br />
3<br />
<strong>Veza</strong> izmeñu <strong>naprezanja</strong> i <strong>deformacija</strong> - 21 -<br />
−4<br />
= 80.<br />
77 ⋅10<br />
⋅ 2⋅<br />
0.<br />
3⋅10<br />
−4<br />
= 80.<br />
77 ⋅10<br />
⋅ 2⋅<br />
0.<br />
8⋅10<br />
−4<br />
= 80.<br />
77 ⋅10<br />
⋅ 2⋅<br />
( −0.<br />
5)<br />
⋅10<br />
=<br />
4.<br />
86<br />
MPa<br />
= −8.<br />
46 MPa<br />
= 12.<br />
9 MPa<br />
[ σ ] =<br />
⎢<br />
4.<br />
86 77.<br />
7 −8.<br />
16<br />
⎥<br />
MPa<br />
ij<br />
⎡58.<br />
5<br />
⎢<br />
⎢⎣<br />
12.<br />
9<br />
4.<br />
86<br />
−8.<br />
16<br />
Modul kompresije odreñen je izrazom iz tablice 4.1:<br />
PRIMJER 4.2<br />
12.<br />
9<br />
58.<br />
48<br />
E 210<br />
K = =<br />
= 175 GPa<br />
3<br />
( 1−<br />
2ν)<br />
3(<br />
1−<br />
2⋅<br />
0.<br />
3)<br />
Stanje <strong>naprezanja</strong> u točki zadano je tenzorom <strong>naprezanja</strong>:<br />
Tijelo je zagrijano za ΔT = 20 o C.<br />
80<br />
⎤<br />
⎥<br />
⎥⎦<br />
[ σ ] =<br />
⎢<br />
− 60 30 20<br />
⎥<br />
MPa<br />
ij<br />
⎡<br />
⎢<br />
⎢⎣<br />
− 40<br />
− 60<br />
Zadano je: E = 210 GPa, ν = 0.3; α = 1.2 . 10 -5 1/ o C<br />
Napisati tenzor deformacije.<br />
20<br />
− 40⎤<br />
⎥<br />
50⎥⎦
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