Arbeitsblätter zur Vorlesung Stahlbau

1
1
Lösungen zum Arbeitsblatt Nr.1
1.1
Aufgabe 1
S235(St37) :
HEA140 :
fyk
=
23, 5 kN/cm2
fuk
=
36, 0 kN/cm2
A
=
31, 4 cm2
Anet
= 31, 4 − 4 · 0, 85 · 1, 8
Npl,Rd =
Nu,Rd
1.2
1.2.1
=
=
A · fyk 31, 4 · 23, 5
=
γm0
1, 0
0, 9 · Anet · fuk 0, 9 · 25, 3 · 36, 0
=
γm2
1, 25
25, 3 cm2
= 737, 9 kN
= 655, 8 kN (maßgebend)
Aufgabe 2
Stabnachweis
fy
=
23, 5 kN/cm2
fu
=
36, 0 kN/cm2
NEd
= 1, 35 · 55
L 7 0 x 7
A *
3 0
S235(St37) :
1 8
fuk
=
A∗
1, 8
) · 0, 7 = 1, 47 cm2
2
36, 0
= 84, 7 kN
= 2, 94 ·
1, 25
74
=
= 0, 87 < 1
84, 7
NEd
Nt,Rd
4 0
γM2
= (3, 0 −
7
7 0
Nachweis des Knotenbleches
23, 5 kN/cm2
fuk
=
36, 0 kN/cm2
A
= 2 · 5, 3 · 0, 6
=
6, 36 cm2
Anet
= 6, 36 − 0, 6 · 1, 8
=
5, 28 cm2
Npl,Rd =
=
NEd
Nt,Rd
=
B r u c h lin ie
l = 5 5 .c o s 1 5 °
= 149, 5 kN
= 136, 9 kN
=
0, 54 < 1
1 5 °
Nu,Rd
6, 36 · 23, 5
1, 0
0, 9 · 5, 28 · 36, 0
1, 25
74
136, 9
1 5 °
1 5
=
4 0
fyk
4 0
S235(St37) :
⇒
74 kN
4 0 + 5 5 .t a n 1 5 ° =
5 5
1.2.2
=
Nu,Rd
Nu,Rd
⇒
2 · A∗ ·
5 5
2
Aufgabe 3
1.3.1
Stabnachweis
S235(St37) :
2 × U160 :
fyk
=
23, 5 kN/cm2
fuk
=
36, 0 kN/cm2
NEd
=
A
= 2 · 24, 0
=
48, 0 cm2
Anet
= 48, 0 − 4 · 0, 75 · 2, 2 =
41, 4 cm2
Npl,Rd =
⇒
NEd
Nt,Rd
=
= 1.128, 0 kN
=
1073, 0 kN
=
0, 84 < 1
Nachweis des Knotenbleches im Schnitt I-I
900
3
NEd
=
A
= (2 · 6, 6 + 7, 0) · 1, 5 =
30, 3 cm2
Anet
= 30, 3 − 2 · 1, 5 · 2, 2
23, 7 cm2
=
B r u c. h l i n i e I - I
l= 7 0 c o s 2 0 ° = 6 6
4 5
=
= 614, 3 kN
l = 1 2 9 .c o s 2 0 ° = 1 2 1
0, 49 < 1
3 5
NEd
Nt,Rd
= 712, 1 kN
B r u c h lin ie III- III
3 5
=
=
7 0
Nu,Rd
30, 3 · 23, 5
1, 0
0, 9 · 23, 7 · 36, 0
1, 25
300
614, 3
300 kN
4 5 + 7 0 .t a n 2 0 ° =
Npl,Rd =
⇒
=
48, 0 · 23, 5
1, 0
0, 9 · 41, 4 · 36, 0
1, 25
900
1073
1 2 9
1.3.2
Nu,Rd
900 kN
4 5 + 2 3 0 .t a n 2 0 ° =
1.3
Nachweis des Knotenbleches im Schnitt III-III
4 5
1.3.3
NEd
=
A
= (2 · 12, 1 + 7, 0) · 1, 5 =
46, 8 cm2
Anet
= 46, 8 − 2 · 1, 5 · 2, 2
40, 2 cm2
⇒
Nu,Rd
=
NEd
Nt,Rd
=
46, 8 · 23, 5
1, 0
0, 9 · 40, 2 · 36, 0
1, 25
900
1042
=
= 1.099, 8 kN
= 1.042, 0 kN
=
0, 86 < 1
2 0 °
Npl,Rd =
900 kN
8 0
8 0
7 0