Civil Engineering Reference
In-Depth Information
Fortsetzung
n
³
2
I
=
z
⋅
dA
1
∑
y
I
=⋅
(y
⋅ − ⋅⋅
z
y
z )
axiales
Trägheitsmoment
y
i
i+1
i+1
i
(A)
12
i1
=
2
2
⋅+⋅+
(z
z
z
z
)
i
i
i+1
i+1
n
³
2
I
=
y
⋅
dA
1
∑
z
I
=⋅
(y
⋅ − ⋅⋅
z
y
z )
z
i
i+1
i+1
i
12
(A)
=
i1
2
2
⋅+⋅+
(
y
y
y
y
)
i
i 1
i
i+1
n
³
I
=
y
⋅
z dA
⋅
1
∑
Zentrifugalmoment
oder
Deviationsmoment
yz
I
=⋅
(y
⋅ − ⋅⋅
z
y
z )
yz
i
i+1
i+1
i
24
(2yz yz
(A)
i1
=
⋅⋅⋅+⋅
+
y
⋅+⋅
z 2y
⋅
z)
i
i
i
i 1 i 1i
i 1i 1
³
2
polares
Trägheitsmoment
I
=
r
⋅
dA
I
=+
py
I
I
p
z
(A)
S
y
a
=
y
A
Schwerpunktsabstand
S
z
a
=
z
A
2I
⋅
Neigung der Hauptachsen gegenüber beliebigen Schwer-
punktsachsen y, z
yz
tan(2 ij )
⋅
=−
−
I )
0
(I
yz
(I
−
I )
Neigung der Achsen mit größtem Deviationsmoment
gegenüber beliebigen Schwerachsen
yz
tan(2 ij )
⋅
=
⋅
1
2I
yz
A
A
S
y
= S
+ b · A
S
= S
y
· cos
ϕ
- S
z
· sin
ϕ
η
η
S
z
= S
+ a · A
S
ζ
= S
z
· cos
ϕ
+ S
y
· sin
ϕ
ζ
I
+
I
I
−
I
+ b
2
· A
I
y
= I
+ 2 · b · S
η
yz yz
η
I
=
+
⋅
cos(2 ij)I in(2ij)
⋅
−
⋅
⋅
+ 2 · b · S
y
- b
2
· A
= I
Ș
yz
2
2
η
+ a
2
· A = I
I
+
I
I
−
I
I
z
= I
+ 2 · a S
+ 2 · a · S
z
-
yz yz
ζ
ζ
ζ
I
=
−
⋅
cos(2 ij)I in(2ij)
⋅
+
⋅
⋅
a
2
· A
ȗ
yz
2
2
=⋅
I
I
yz
I
yz
= I
+ b · S
z
+ a · S
y
- a · b · A
I
sin(2ij)I cos(2ij)
+⋅
ηζ
Șȗ
yz
2
