Mi
tP
TC
Ma
th
ca
dE
xp
re
ss
er
st e
m
= 1471.5 N
FG ≔ 150 kg ⋅ 9.81 ―
s2
llt.
BX ≔ 0
AX ≔ 0
AX ≔ -BX
ei t
er
2) ΣFY ＝ 0 ＝ -FG + AY + BY - FG
W
1) ΣFX ＝ 0 ＝ AX + BX
eI
3) ΣMA ＝ 0 ＝ -FG ⋅ 275 mm - BY ⋅ 1150 mm + FG ⋅ 1425 mm
n fo
rm
aus 3)
BY ＝ B
on
en
aus 2)
a ti
-FG ⋅ 275 mm + FG ⋅ 1425 mm
= 1471.5 N
BY ≔ ――――――――――
1150 mm
AY ＝ A
fi n
AY ≔ FG - BY + FG = 1471.5 N
de
nS
ie
un
ter
ww
w.
ma
th
ca
ΣFX ＝ 0 ＝ N
N≔0
x ≔ 275 mm
.
ΣMX ＝ 0 ＝ -M - FG ⋅ x
om
Q ≔ -FG
d.c
ΣFY ＝ 0 ＝ -FG - Q
ΣMX ＝ 0 ＝ -M - FG ⋅ x
Mi
M ≔ -FG ⋅ x = -404662.5 N·mm
tP
TC
Normalkraftverlauf
Ma
mF: 1471,5N = 30mm
th
mL: 2300mm = 100mm
100mm = 4,3mm
300mm = 12,9mm
575mm = 24,7mm
1150mm = 49,4mm
ca
dE
xp
re
ss
er
st e
llt.
W
ei t
er
eI
n fo
rm
a ti
en
fi n
mL: 2300mm = 100mm
on
Biegemomentenverlauf
mM: -404662,5Nmm = 40mm
de
nS
ie
un
ter
ww
w.
ma
th
ca
d.c
om
.
Mi
Belastungsfall 1
tP
m
kg ⋅ ―
s2
laut Tabb. S.32
σbF ≔ 330 ―――
mm 2
TC
S235JR ->
ν ≔ 1.2
Ma
σbF
N
= 275 ――
σbmaxzul ≔ ――
ν
mm 2
th
M
≤ σbmaxzul
σbvor ＝ ――
Wb
ca
dE
||M||
= 1471.5 mm 3
Wb ≔ ―――
σbmaxzul
xp
1471.5 mm 3 = 1.472 cm 3
re
ss
Wb ＝ WX
er
st e
llt.
laut Berechnung U30 x 15 laut Tabb. S.106
gewählt U65
W
ei t
er
eI
n fo
rm
a ti
on
en
fi n
de
nS
ie
d ≔ 10 mm
un
D ≔ 21 mm
ΣAiwi ≔ 22499 mm 3
ΣAi ≔ 758.9 mm 2
th
ca
om
ΣAiwi
= 29.647 mm
wS ≔ ―――
ΣAi
d.c
Ai*wi
3062.5
11687.5
3062.5
2343.25
2343.25
22499
ma
wi
17.5
42.5
17.5
35
35
----
w.
Ai
175
275
175
66.95
66.95
758.9
ww
i
1
2
3
4
5
Σ
ter
π
2
2
―⋅ ⎛⎝D - d ⎞⎠
4
= 66.955 mm 2
AHohlwelle ≔ ―――――
4
.
e1 ≔ 29.647 mm
e1 ≔ 29.647 mm
Mi
tP
e2 ≔ 45 mm - e1 = 15.353 mm
TC
Ma
Jy ＝ Jys + A ⋅ a 2
th
ca
5 mm ⋅ 35 3 mm 3
55 mm ⋅ 5 3 mm 3
5 mm
+ 175 mm 2 ⋅ ⎛⎝e1 - 17.5 mm ⎞⎠ 2 + ――――――
+ 275 mm 2 ⋅ ⎛⎝e2 - 2.5 mm ⎞⎠ 2 + ――
Jy ≔ ――――――
12
12
dE
xp
re
35 mm ⋅ 5 3 mm 3
5 mm ⋅ 55 3 mm 3
35 m
+ 175 mm 2 ⋅ ⎛⎝e1 - 17.5 mm ⎞⎠ 2 + ――――――
+ 275 mm 2 ⋅ ⎛⎝e2 - 2.5 mm ⎞⎠ 2 + ――
JZ ≔ ――――――
12
12
ss
er
Jy
Wy1 ≔ ―= 4889.778 mm 3
e1
st e
llt.
ei t
er
eI
JZ
= 4765.793 mm 3
Wz ≔ ――――
37.5 mm
W
Jy
Wy2 ≔ ―= 9442.275 mm 3
e2
n fo
rm
a ti
on
en
fi n
de
nS
ie
un
ter
ww
w.
ma
th
ca
d.c
om
.