Mechanika Budowli II - Projekty (rok III), Mechanika - Zadanie Projektowe Nr2, Politechnika Gdańska

Politechnika Gdańska Rok akademicki 1999/2000

Wydział Budownictwa Lądowego

Mechanika Budowli II

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Zadanie projektowe NR 2

Michał Rzodkiewicz

WBL III sem. V TOB2

Rozwiązanie zadania

przy pomocy programu

DSM

PROGRAM D-S-M 97, C.J.Branicki

==============================

Datafile: MICHAL1 7-12-1999

==============================

Projekt 2.0 Michal Rzodkiewicz

No. of elements Ne= 6

No. of unknowns n= 6

Element type: BEAM

Element data table:

EI L

1.5 6

1.5 5.4

1.5 4

1 4

1 3.2

Allocation vectors:

va fa vb fb

0 1 0 2

0 2 0 3

0 3 0 4

6 3 0 0

0 5 6 2

0 0 6 4

Fixed-end forces, Sjo

Va Ma Vb Mb

-15 -15 -15 15

0 0 0 0

Vector of external nodal loads, R:

12 0 0 0 0 14

-----------------------------------------------------------------------------

Vector of effective nodal loads, P=R-ΣSjgo:

27.0000 -15.0000 0.0000 0.0000 0.0000 14.0000

Nodal displacements, q:

30.4300 -6.8600 -2.9788 6.3737 15.6647 26.1008

Final element end-forces, Sj=Kj-Dj+Sjo:

j Va Ma Vb Mb

1 -9.1075 12.0000 -20.8925 23.3550

2 -3.0367 -9.2771 3.0367 -7.1209

3 1.9096 0.3120 -1.9096 7.3263

4 3.7768 6.8089 -3.7768 8.2984

5 -4.3994 0.0000 4.3994 -14.0779

6 -5.8238 -11.3099 5.8238 -7.3263

End of problem

Sprawdzenie schematu przy użyciu programu FRANK

PROGRAM F-R-A-N-K

C. BRANICKI 1986-1994 12-19-1999

==================================

DATA FROM FILE: DSMMRZ.FRA

==================================

PROBLEM TITLE: Projekt 2.1 Michal Rzodkiewicz

NODES= 7

N X Y

1 0 0

2 6 0

3 11.4 0

4 15.4 0

5 6 3.2

6 11.4 -4

7 15.4 3.2

E= 1

TYPES= 3

T AREA I H

1 1.00000E+05 1.50000E+00 11

2 1.00000E+05 1.00000E+00 01

3 1.00000E+05 1.00000E+00 11

ELEMENTS= 6

El A B (T)

1 1 2 1

2 2 3 1

3 3 4 1

4 3 6 3

5 5 2 2

6 7 4 3

SUPPORTS= 4

N CODE

1 Y

5 XY

6 FIX

7 FIX

SPRINGS= 0

WARNING! SINGULAR NODE - REPEATED 1 TIME(S)

DO NOT LOAD IT WITH A MOMENT

SYSTEM STATISTICS

~~~~~~~~~~~~~~~~~

NO OF NODES.................. 7

NO OF ELEMENTS............... 6

NO OF RIGID SUPPORT LINKS.... 9

NO OF ACTIVE SPRINGS......... 0

NO OF NODAL RESTRAINTS....... 9

STIFFNESS MATRIX VOLUME..... 55 ELEMENTS

MEMORY USED............... 1282 BYTES

STATICAL INDETERMINACY....... 6

============

LOAD CASE No 1 : / Projekt 2.1 Michal Rzodkiewicz

============

LOCAL ELEMENT LOADS

EL (CODE X0 V (DIR))

1 UDL 0 5 YS

END *{LOCAL}

GLOBAL NODAL LOADS

NN (CODE V )

1 X 14

1 M 12

END *{GLOBAL}

---------------------------------------------------------

Resultant of external loads: SPX SPY

14.0000 30.0000

---------------------------------------------------------

G L O B A L D I S P L A C E M E N T S

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

N U V FI

1 2.6102277E+01 0.0000000E+00 3.0430168E+01

2 2.6101437E+01 7.6573016E-04 -0.6859954E+01

3 2.6100918E+01 -0.1978431E-03 -0.2978915E+01

4 2.6100685E+01 6.1103978E-05 6.3737099E+00

5 0.0000000E+00 0.0000000E+00 0.0000000E+00

6 0.0000000E+00 0.0000000E+00 0.0000000E+00

7 0.0000000E+00 0.0000000E+00 0.0000000E+00

L O C A L E L E M E N T E N D - F O R C E S

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

EL (NA) NB=N VA VB MA MB

1 -14.00000 -9.107510 -20.892490 12.00000 23.35494

2 -9.60059 -3.036578 3.036578 -9.27683 -7.12069

3 -5.82376 1.909499 -1.909499 0.31176 7.32623

4 -4.94608 3.776829 -3.776829 6.80893 8.29839

5 -23.92907 -4.399410 4.399410 0.00000 -14.07811

6 -1.90950 -5.823761 5.823761 -11.30980 -7.32623

R I G I D S U P P O R T R E A C T I O N S

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

NODE DIRECTION VALUE

5 X -4.3994

6 X -3.7768

7 X -5.8238

1 Y -9.1075

5 Y -23.9291

6 Y 4.9461

7 Y -1.9095

6 M 8.2984

7 M -11.3098

---------------------------------------------------------

RESULTANT OF SUPPORT REACTIONS: SRX SRY

-14.0000 -30.0000

---------------------------------------------------------

END OF PROGRAM RUN

Wymiarowanie przekrojów elementów - reanaliza układu dla udokładnionych wartości EA i EI

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M₁ = 12 kNm

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x

R_a

M₁ + R_a ⋅x - = 12 + 9,1075 ⋅ x - 0,5 ⋅ 5x²

12 + 9,1075 ⋅ x - 2,5x² = 0

9,1075 - 5x = 0

x = 1,8215

M_MAX (x = 1,8215) = 12 + 9,1075 ⋅ (1,8215) - 2,5 ⋅ (1,8215²) = 22,2946 kNm

Moment przęsłowy nie jest momentem maksymalnym, zatem nie uwzględniamy go do obliczeń.

Obliczenia powtórzono dla każdego przypadku.

Wymiarowanie wstepne przekroju: Stal St3S, dwuteownik normalny

Tytul: Projekt 2.2 Michal Rzodkiewicz

El N M Profil A Wx Jy sigma

1. -14.000 23.3550 I-180 27.9 161.0 1450 155.10

2. -9.6006 9.2771 I-140 18.3 81.9 573 123.77

3. -5.8238 7.3263 I-120 14.2 54.7 328 142.14

4. -4.9461 8.2984 I-140 18.3 81.9 573 106.73

5. -23.929 14.0779 I-160 22.8 117.0 935 141.31

6. -1.9095 11.3099 I-140 18.3 81.9 573 140.18

Koniec wymiarowania

PROGRAM D-S-M 97, C.J.Branicki

============================

Datafile: RZODKWW1: 14-12-1999

============================

Title: Projekt 2.3 Michal Rzodkiewicz

No. of elements Ne= 6

No. of unknowns n=12

Element type: FRAME

Element data table:

EA EI L c1 c2

585900 3045 6 1 0

384300 1203.3 5.4 1 0

298200 688.8 4 1 0

384300 1203.3 4 0 -1

478800 1963.5 3.2 0 -1

384300 1203.3 3.2 0 -1

Allocation vectors:

ua va fa ub vb fb

7 0 1 8 9 2

8 9 2 10 11 3

10 11 3 6 12 4

10 11 3 0 0 0

0 0 5 8 9 2

0 0 0 6 12 4

Fixed-end forces Sjo:

Na Va Ma Nb Vb Mb

0 -15 -15 0 -15 15

0 0 0 0 0 0

Nodal loads R:

12 0 0 0 0 0

14 0 0 0 0 0

Vector of effective nodal loads P=R-ΣSjo:

27.0000 -15.0000 0.0000 0.0000 0.0000 0.0000

14.0000 0.0000 15.0000 0.0000 0.0000 0.0000

Nodal displacements q:

1.4838E-02 -2.9993E-03 -4.4277E-03 8.3417E-03 1.2722E-02 2.3768E-02

2.4085E-02 2.3942E-02 1.5241E-04 2.3830E-02 -2.9438E-05 8.3774E-06

Final element end-forces Sj=Sjo+Kj-Dj:

j Na Va Ma Nb Vb Mb

1 14.0000 -9.0175 12.0000 -14.0000 -20.9825 23.8950

2 7.9708 -1.8222 -4.6016 -7.9708 1.8222 -5.2382

3 4.5924 1.0061 -0.1867 -4.5924 -1.0061 4.2110

4 2.8283 3.3785 5.4250 -2.8283 -3.3785 8.0889

5 22.8047 -6.0292 0.0000 -22.8047 6.0292 -19.2933

6 1.0061 -4.5924 -10.4845 -1.0061 4.5924 -4.2110

End of problem

Wymiarowanie wstepne przekroju: Stal St3S, dwuteownik normalny

Tytul: Projekt 2.4 Michal Rzodkiewicz

El N M Profil A Wx Jy sigma

1. -14.000 23.8950 I-200 33.5 214.0 2140 120.02

2. -7.9708 5.2382 I-120 14.2 54.7 328 106.99

3. -4.5924 4.2110 I-100 10.6 34.2 171 131.79

4. -2.8283 8.0889 I-120 14.2 54.7 328 151.86

5. -22.804 19.2933 I-180 27.9 161.0 1450 136.18

6. -1.0061 10.4845 I-140 18.3 81.9 573 129.12

Koniec wymiarowania

PROGRAM D-S-M 97, C.J.Branicki

============================

Datafile: RZODKWW1: 14-12-1999

============================

Title: Projekt 2.5 Michal Rzodkiewicz

No. of elements Ne= 6

No. of unknowns n=12

Element type: FRAME

Element data table:

EA EI L c1 c2

703500 4494 6 1 0

298200 688.8 5.4 1 0

222600 359.1 4 1 0

298200 688.8 4 0 -1

585900 3045 3.2 0 -1

384300 1203.3 3.2 0 -1

Allocation vectors:

ua va fa ub vb fb

7 0 1 8 9 2

8 9 2 10 11 3

10 11 3 6 12 4

10 11 3 0 0 0

0 0 5 8 9 2

0 0 0 6 12 4

Fixed-end forces Sjo:

Na Va Ma Nb Vb Mb

0 -15 -15 0 -15 15

0 0 0 0 0 0

Nodal loads R:

12 0 0 0 0 0

14 0 0 0 0 0

Vector of effective nodal loads P=R-ΣSjo:

27.0000 -15.0000 0.0000 0.0000 0.0000 0.0000

14.0000 0.0000 15.0000 0.0000 0.0000 0.0000

Nodal displacements q:

9.3780E-03 -6.7096E-04 -5.4103E-03 1.0349E-02 1.2594E-02 2.5966E-02

2.6270E-02 2.6151E-02 1.2204E-04 2.6040E-02 -2.0358E-05 5.5232E-06

Final element end-forces Sj=Sjo+Kj-Dj:

j Na Va Ma Nb Vb Mb

1 14.0000 -8.5089 12.0000 -14.0000 -21.4911 26.9467

2 6.1112 -0.8544 -1.7024 -6.1112 0.8544 -2.9114

3 4.1455 0.6633 -0.0882 -4.1455 -0.6633 2.7414

4 1.5177 1.9656 2.9996 -1.5177 -1.9656 4.8629

5 22.3455 -7.8888 -0.0000 -22.3455 7.8888 -25.2443

6 0.6633 -4.1455 -10.5244 -0.6633 4.1455 -2.7414

End of problem

Wymiarowanie wstepne przekroju: Stal St3S, dwuteownik normalny

Tytul: Projekt 2.6 Michal Rzodkiewicz

El N M Profil A Wx Jy sigma

1. -14.000 26.9467 I-200 33.5 214.0 2140 134.28

2. -6.1112 2.9114 I-100 10.6 34.2 171 96.66

3. -4.1455 2.7414 I-100 10.6 34.2 171 87.98

4. -1.5177 4.8629 I-100 10.6 34.2 171 145.05

5. -22.345 25.2443 I-200 33.5 214.0 2140 131.30

6. -0.6633 10.5244 I-140 18.3 81.9 573 129.23

Koniec wymiarowania

PROGRAM D-S-M 97, C.J.Branicki

============================

Datafile: RZODKWW1: 14-12-1999

============================

Title: Projekt 2.7 Michal Rzodkiewicz

No. of elements Ne= 6

No. of unknowns n=12

Element type: FRAME

Element data table:

EA EI L c1 c2

703500 4494 6 1 0

222600 359.1 5.4 1 0

222600 359.1 4 1 0

222600 359.1 4 0 -1

703500 4494 3.2 0 -1

384300 1203.3 3.2 0 -1

Allocation vectors:

ua va fa ub vb fb

7 0 1 8 9 2

8 9 2 10 11 3

10 11 3 6 12 4

10 11 3 0 0 0

0 0 5 8 9 2

0 0 0 6 12 4

Fixed-end forces Sjo:

Na Va Ma Nb Vb Mb

0 -15 -15 0 -15 15

0 0 0 0 0 0

Nodal loads R:

12 0 0 0 0 0

14 0 0 0 0 0

Vector of effective nodal loads P=R-ΣSjo:

27.0000 -15.0000 0.0000 0.0000 0.0000 0.0000

14.0000 0.0000 15.0000 0.0000 0.0000 0.0000

Nodal displacements q:

8.7097E-03 6.5539E-04 -5.1901E-03 9.6828E-03 1.1132E-02 2.4262E-02

2.4568E-02 2.4448E-02 1.0153E-04 2.4332E-02 -1.6808E-05 5.0254E-06

Final element end-forces Sj=Sjo+KjúDj:

j Na Va Ma Nb Vb Mb

1 14.0000 -8.0109 12.0000 -14.0000 -21.9891 29.9346

2 4.8039 -0.3318 -0.5072 -4.8039 0.3318 -1.2847

3 3.8646 0.6035 -0.1282 -3.8646 -0.6035 2.5423

4 0.9354 0.9394 1.4128 -0.9354 -0.9394 2.3447

5 22.3209 -9.1961 0.0000 -22.3209 9.1961 -29.4274

6 0.6035 -3.8646 -9.8243 -0.6035 3.8646 -2.5423

End of problem

Wymiarowanie wstepne przekroju: Stal St3S, dwuteownik normalny

Tytul: Projekt 2.8 Michal Rzodkiewicz

El N M Profil A Wx Jy sigma

1. -14.000 29.9346 I-200 33.5 214.0 2140 148.24

2. -4.8039 1.2847 I-100 10.6 34.2 171 46.63

3. -3.8646 2.5423 I-100 10.6 34.2 171 81.63

4. -0.9354 2.3447 I-100 10.6 34.2 171 70.32

5. -22.320 29.4274 I-200 33.5 214.0 2140 150.84

6. -0.6035 9.8243 I-140 18.3 81.9 573 120.61

Koniec wymiarowania

PROGRAM D-S-M 97, C.J.Branicki

============================

Datafile: RZODKWW1: 14-12-1999

============================

Title: Projekt 2.9 Michal Rzodkiewicz

No. of elements Ne= 6

No. of unknowns n=12

Element type: FRAME

Element data table:

EA EI L c1 c2

703500 4494 6 1 0

222600 359.1 5.4 1 0

222600 359.1 4 1 0

222600 359.1 4 0 -1

703500 4494 3.2 0 -1

384300 1203.3 3.2 0 -1

Allocation vectors:

ua va fa ub vb fb

7 0 1 8 9 2

8 9 2 10 11 3

10 11 3 6 12 4

10 11 3 0 0 0

0 0 5 8 9 2

0 0 0 6 12 4

Fixed-end forces Sjo:

Na Va Ma Nb Vb Mb

0 -15 -15 0 -15 15

0 0 0 0 0 0

Nodal loads R:

12 0 0 0 0 0

14 0 0 0 0 0

Vector of effective nodal loads P=R-ΣSjo:

27.0000 -15.0000 0.0000 0.0000 0.0000 0.0000

14.0000 0.0000 15.0000 0.0000 0.0000 0.0000

Nodal displacements q:

8.7097E-03 6.5539E-04 -5.1901E-03 9.6828E-03 1.1132E-02 2.4262E-02

2.4568E-02 2.4448E-02 1.0153E-04 2.4332E-02 -1.6808E-05 5.0254E-06

Final element end-forces Sj=Sjo+Kj-Dj:

j Na Va Ma Nb Vb Mb

1 14.0000 -8.0109 12.0000 -14.0000 -21.9891 29.9346

2 4.8039 -0.3318 -0.5072 -4.8039 0.3318 -1.2847

3 3.8646 0.6035 -0.1282 -3.8646 -0.6035 2.5423

4 0.9354 0.9394 1.4128 -0.9354 -0.9394 2.3447

5 22.3209 -9.1961 0.0000 -22.3209 9.1961 -29.4274

6 0.6035 -3.8646 -9.8243 -0.6035 3.8646 -2.5423

End of problem

Wymiarowanie wstepne przekroju: Stal St3S, dwuteownik normalny

Tytul: Projekt 2.10 Michal Rzodkiewicz

El N M Profil A Wx Jy sigma

1. -14.000 29.9346 I-200 33.5 214.0 2140 148.24

2. -4.8039 1.2847 I-100 10.6 34.2 171 46.63

3. -3.8646 2.5423 I-100 10.6 34.2 171 81.63

4. -0.9354 2.3447 I-100 10.6 34.2 171 70.32

5. -22.320 29.4274 I-200 33.5 214.0 2140 150.84

6. -0.6035 9.8243 I-140 18.3 81.9 573 120.61

Koniec wymiarowania

Profile elementów powtarzają się - wymiarowanie jest więc zakończone.

Uwaga: Wartości momentów M są to momenty mak