3U]\NáDGURGHNFL*NRFLXNáDGXRELHNWyZ

=QDOH(ü URGHN FL*NRFL XNáDGX RELHNWyZ SU]HGVWDZLRQHJR QD U\VXQNX QU RVWURVáXSD

IRUHPQHJR R SRGVWDZLH WUyMNWD L FL*DU]H ZáDFLZ\P NJP

3

, nr2 – pionowej tarczy w

NV]WDáFLH SURVWRNWD R FL*DU]H SRZLHU]FKQLRZ\P NJP

2

, nr3 – pionowej tarczy w

NV]WDáFLHSURVWRNWDRFL*DU]HSRZLHU]FKQLRZ\PNJP

2

QU±XNRQLHXáR*RQHMWDUF]\Z

NV]WDáFLHWUyMNWDRFL*DU]HSRZLHU]FKQLRZ\PNJP

2

QU±SUWDRFL*DU]H

kg/m, nr6 –

SUWDRFL*DU]HNJP.ROHMQHRELHNW\]D]QDF]RQRNRORUDPLZ\PLDU\LSUW\QULQURUD]

SU]\MWH RVLH XNáDGX ZVSyáU]GQ\FK NRORUHP F]DUQ\P OLQLH SRPRFQLF]H V SU]HU\ZDQH 1D

U\VXQNX]D]QDF]RQR URGNL FL*NRFL ZV]\VWNLFK RELHNWyZ -HGQRVWN XNáDGX ZVSyáU]GQ\FK

jest 1.0 metr.

Rysunek 1

'OD XNáDGX VNáDGDMFHM VL ] RELHNWyZ GOD NWyU\FK ]QDQH MHVW SRáR*HQLH URGNyZ FL*NRFL

VWDW\F]QHPRPHQW\EH]ZáDGQRFLPR*QDRNUHODüQDSRGVWDZLHZ]RUyZ

6

4 [

6

4 \

6

4 ]

\]

L

&

L

Q

[]

L

&

L

Q

[\

L

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L

Q

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=

=

=

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∑

∑

∑

(1)

gdzie Q

i

, x

Ci

, y

Ci

oraz z

Ci

R]QDF]DMFL*DULRGSRZLHGQLZVSyáU]GQURGNDFL*NRFLLWHJR

RELHNWXVNáDGRZHJRZSU]\MW\PXNáDG]LHRVL

3RáR*HQLHURGNDFL*NRFLXNáDGXRNUHODVLQDSRGVWDZLHZ]RUyZ

[

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6

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2

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ZLHONRFLZ\VRNRFLWDUF]\QUZV]\VWNLHZ\PLDU\RELHNWyZPR*QDRGF]\WDüEH]SRUHGQLR]

U\VXQNX :\VRNRü WUyMNWD WDUF]\ QU PR*QD REOLF]\ü ] WUyMNWD SURVWRNWQHJR R

ZLHU]FKRáNDFK./L0

K

P

P

P

= 

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=

≅

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4

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ZVSyáU]GQ\FK URGHN FL*NRFL RVWURVáXSD QU RGGDORQ\ MHVW RG MHJR SR]LRPHM SRGVWDZ\ R

MHGQF]ZDUWZ\VRNRFL± RGFLQND ./ RUD] RG ERF]QHM SLRQRZHM SRGVWDZ\ R MHGQF]ZDUW

Z\VRNRFL±RGFLQND/1:VSyáU]GQHWHZ\QRV]]DWHP

[

P

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&

=

+



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\

P

P

&

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+



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

 =

]

P

P

&

=

+







 =

URGHNFL*NRFLWUyMNWQHMUyZQRUDPLHQQHMWDUF]\QUOH*\QDRGFLQNX.0LMHVWRGGDORQ\RG

ERNXSRGVWDZ\RMHGQWU]HFLZ\VRNRFLK

4

:VSyáU]GQHURGNDFL*NRFLWDUF]\Z\QRV]

[

P

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+



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 =

3RáR*HQLH URGNyZ FL*NRFL SR]RVWDá\FK RELHNWyZ MHVW áDWZH GR RGF]\WDQLD ] Z\PLDUyZ

XNáDGX

3

'DQH GRW\F]FH SRV]F]HJyOQ\FK RELHNWyZ RUD] REOLF]HQLD VWDW\F]Q\FK PRPHQWyZ

EH]ZáDGQRFLPR*QDZáDWZ\VSRVyESU]HGVWDZLüWDEHODU\F]QLH

:VSyáU]GQHURGNyZ

FL*NRFLRELHNWyZ

6WDW\F]QHPRPHQW\EH]ZáDGQRFL

obiektów

Numer

obiektu

&L*DU

obiektu –

Q

i

[kg]

x

Ci

[m]

y

Ci

[m]

z

Ci

[m]

Q

i

x

Ci

[kgm]

Q

i

y

Ci

[kgm] Q

i

z

Ci

[kgm]

1

30

3.125

2.5

3.75

93.75

75

112.5

2

42

5

2

1.5

210

84

63

3

30

2.5

4

1.5

75

120

45

4

31.28

0.833

2

4

26.06

62.56

125.12

5

25

2.5

0

3

62.5

0

75

6

24

0

0

1.5

0

0

36

Suma

182.28

467.31

341.56

456.62

: RVWDWQLHM JUXSLH NROXPQ SROLF]RQR LORF]\Q\ FL*DUX RELHNWyZ L NROHMQ\FK ZVSyáU]GQ\FK

LFK URGNyZ FL*NRFL : RVWDWQLP ZLHUV]X WDEHOL SU]HGVWDZLRQR VXP Z\UD]yZ ]

SRV]F]HJyOQ\FK NROXPQ FL*DUX RELHNWyZ L LFK VWDW\F]Q\FK PRPHQWyZ EH]ZáDGQRFL

6WDW\F]QH PRPHQW\ EH]ZáDGQRFL Z]JOGHP NROHMQ\FK SáDV]F]\]Q Z\QRV] ]DWHP

odpowiednio:

6

NJP

\]

=

6

NJP

[]

=

6

NJP

[\

=

2EOLF]DMFZVSyáU]GQHURGNDFL*NRFLRWU]\PXMHP\

[

6

4

NJP

NJ

P

F

\]

=

=

≅

\

6

4

NJP

NJ

P

F

[]

=

≅

≅

]

6

4

NJP

NJ

P

F

[\

=

≅

≅

1D U\VXQNX SU]HGVWDZLRQR SU]HU\ZDQ\PL OLQLDPL RGPLHU]HQLH NROHMQ\FK ZVSyáU]GQ\FK

URGNDFL*NRFLXNáDGXRELHNWyZ]U\VXQNX

4

Rysunek 2