3 m

3 m

4 m

4 m

2 m

2 m

5 kNm

18 kN

10

kN

m

A

B

C

F

G

H

4 m

D

E

45

11,25

60

5

55

45,5

M(x)

M(x)

15

15

15

15

13,75

13,75

13,75

4,75

22,75

4,75

22,75

Q(x)

1. Dane

R

300MPa

:=

Rt

150MPa

:=

E

210GPa

:=

wdop

2 0cm

,

:=

Qmax

22.75kN

:=

Mmax

60kN m

⋅

:=

2. Oblicznie wymiarów przekroju

A

3 a

⋅ 1.5

⋅ a a 4

⋅ a

⋅

+

4a a

⋅

+

collect

12.5 a

2

⋅

→

:=

a

A

12.5a

2

:=

a

Sy

3 a

⋅ 1.5

⋅

a

⋅ 0.75

⋅

a

⋅

4 a

⋅ a

⋅ 3.5

⋅ a

+

4 a

⋅ a

⋅ 6

⋅ a

+

collect

41.375 a

3

⋅

→

:=

a

Sy

41.375a

3

:=

a

z0

41.375a

3

12.5a

2

collect

3.31 a

⋅

→

:=

a

z0

3.31a

:=

a

Iy

4 a

⋅ a

3

⋅

12

4 a

2

⋅

3.19a

0.5a

−

(

)

2

⋅

+

a 4 a

⋅

(

)

3

⋅

12

+

4 a

2

⋅

3 a

⋅

3.19a

−

(

)

2

⋅

+

3 a

⋅ 1.5 a

⋅

(

)

3

⋅

12

+

4.5a

2

3.31a

−

(

⋅

+

:=

a

Iy

65.09 a

4

⋅

:=

a

Napre

ż

enie normalne

σx R

≤

Mmax

Iy

z0

⋅

R

≤

Wy

Iy

z0

:=

Iy

Wy

65.09 a

4

⋅

3.31a

collect

→

=

Wy

19.66 a

3

⋅

:=

a

Mmax

19.66a

3

R

≤

60kNm

19.66a

3

300MPa

≤

a

≥

3

60kN m

⋅

19.66 300

⋅

MPa

2.167 cm

⋅

=

Napr

ęż

enia styczne

τxz

Qmax Sy z

( )

⋅

b z

( ) Iy

⋅

Rt

≤

:=

Sy

Sy z

( )

4 a

⋅ a

⋅ 2.69

⋅

a

a 1.69

⋅

a

1.69

2

⋅

a

+

collect

12.18805 a

3

⋅

→

:=

a

Sy z

( )

12.19a

3

:=

a

22.75kN 12.19

⋅

a

3

a 55.57

⋅

a

4

⋅

150MPa

<

expand

4.9905074680583048407 kN

⋅

a

2

150 MPa

⋅

<

→

a

≥

2

4.99 kN

⋅

150MPa

0.577 cm

⋅

=

Maksymalne gui

ę

cie

Wdop

wmax

E Iy

⋅

≥

wmax

1312

:=

1312

210 10

9

⋅

65.09

⋅

a

4

⋅

2cm

≤

expand

9.5984314758319981857e-11

a

4

2 cm

⋅

≤

→

a

4

0.96

2

0.832

=

:=

a

0.832cm

≥

Przyjmuje a=3cm

0.75a)

2

collect

65.090416666666666667 a

4

⋅

→

*