Transformation av spänningar - Tillämpad fysik och elektronik ...

N = 20kN
60 ◦
σn = 9.9 MP a τn = 17.1 MP a
N = 200 kN
30 ◦
σn = 50 MP a τn = 29 MP a
σx = 45 MP a σy = 45 MP a
τ = −20 MP a
28 ◦
x − axeln
σn = 28.4 MP a τt = −11.2 MP a
−38 ◦
x − axeln
σn = 25.6 MP a τt = −4.84 MP a
σ1 = 65 MP a σ2 = 25 MP a σ3 = 0 MP a
σx = 90MP a
τxy = 60 MP a
σ1 = 120 MP a σ2 = 0MP a σ3 = −30MP a
σx = 70 MP a σy = 120 MP a
τxy = 60 MP a
σ1 = 160 MP a Φ1 = 56.3 ◦ σ2 = 30 MP a Φ2 = 146.3 ◦
σx = σy = 200 MP a
σ(α) = 200 MP a τ(α) = 0

σx = 9 MP a σy = 3 MP a τxy = 3 √ 3 MP a
σ1 = 12MP a Φ1 = 30 ◦ σ2 = 0 Φ2 = 120 ◦
Mv a h
σ1 = − Mv
2πa 2 h σ2 = Mv
2πa 2 h σ3 = 0
p
Mv = πpa 3 2a
h
σ1,2 = (1 ± √ 2) pa
2h Φ1 = 112, 5 ◦ Φ2 = 22, 5 ◦
p Mv = πpa 3
a h
σ1,2 = (3 ± √ 5) pa
4h Φ1 = 121.7 ◦ Φ2 = 31.7 ◦
45 ◦
σu = 330 MP a
Mv = 1.75 kNm
a h
π/9
Mv
σ(φ) = Mv
2πa2h sin 40◦ τ(φ) = Mv
2πa2 cos 40◦ h
a
h
Mv
x ρ
σ1,2 = ρgx
2 ±
( ρgx
2 )2 + ( Mv
2πa2h )2
τmax = ( ρgx
2 )2 + ( Mv
2πa2h )2

L = 9 m a = 1, 5 m h = 15 mm
Θ p = 1 MP a
G = 75 MP a
Θmax = pL
Gh √ = 0.324◦
2

σx = 70 MP a σy = 120 MP a
τxy = 60 MP a
σ T e = 160 MP a σ vM
e
= 147 MP a
Mv
σ T e = Mv
πa 2 h
MP a σvM
e
=
√ 3
2
Mv
πa 2 h
MP a
2a h
p p
σs
ps =
σsh
a √ 1−ν+ν 2
(E, ν, σs)
σx = σs σx = σs
σy
σy (0 < σy < σs)