3U]\NáDGURGHNFL *NRFLXNáDGXRELHNWyZ
=QDOH(ü URGHN FL *NRFL XNáDGX RELHNWyZ SU]HGVWDZLRQHJR QD U\VXQNX QU RVWURVáXSD
3
IRUHPQHJR R SRGVWDZLH WUyMNWD L FL *DU]H ZáDFLZ\P NJP , nr2 – pionowej tarczy w 2
NV]WDáFLH SURVWRNWD R FL *DU]H SRZLHU]FKQLRZ\P NJP , nr3 – pionowej tarczy w 2
NV]WDáFLHSURVWRNWDRFL *DU]HSRZLHU]FKQLRZ\PNJP QU±XNRQLHXáR*RQHMWDUF]\Z
2
NV]WDáFLHWUyMNWDRFL *DU]HSRZLHU]FKQLRZ\PNJP QU±SU WDRFL *DU]Hkg/m, nr6 –
SU WDRFL *DU]HNJP.ROHMQHRELHNW\]D]QDF]RQRNRORUDPLZ\PLDU\LSU W\QULQURUD]
SU]\M WH 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
Q
Q
Q
6
=
4 [
6
∑
=
4 \
6
∑
=
4 ]
∑
(1)
\]
L
&
[]
L
&
[\
L
&
L=
L=
L=
gdzie Qi, xCi, yCi oraz zCiR]QDF]DMFL *DULRGSRZLHGQLZVSyáU] GQURGNDFL *NRFLLWHJR
RELHNWXVNáDGRZHJRZSU]\M W\PXNáDG]LHRVL
3RáR*HQLHURGNDFL *NRFLXNáDGXRNUHODVL QDSRGVWDZLHZ]RUyZ
6 \]
6
6
[]
[\
[ =
\ =
] =
,
(2)
F
F
F
4
4
4
*G]LH4R]QDF]DáF]Q\FL *DUZV]\VWNLFKRELHNWyZ
2EOLF]DP\QDMSLHUZNROHMQRFL *DU\SRV]F]HJyOQ\FKRELHNWyZPQR*FLFKFL *DU\ZáDFLZH
SU]H] RGSRZLHGQLR REM WRü EU\á\ SRZLHU]FKQL ILJXU\ L GáXJRü NU]\ZHM =D Z\MWNLHP
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
+
=
≅
&L *DU\NROHMQ\FKRELHNWyZZ\QRV]RGSRZLHGQLR
NJ
4 =
P P P
= NJ
P
NJ
4 = P P
= NJ
P
NJ
4 = P P
= NJ
P
NJ
4 =
P
P
=
NJ
P
NJ
4 = P
= NJ
P
NJ
4 = P
= NJ
P
2NUHOP\ WHUD] SRáR*HQLH URGNyZ FL *NRFL NROHMQ\FK RELHNWyZ Z SU]\M W\P XNáDG]LH
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
P
&
=
\
= + P P
&
=
]
= + P P
&
=
URGHNFL *NRFLWUyMNWQHMUyZQRUDPLHQQHMWDUF]\QUOH*\QDRGFLQNX.0LMHVWRGGDORQ\RG
ERNXSRGVWDZ\RMHGQWU]HFLZ\VRNRFLK4:VSyáU] GQHURGNDFL *NRFLWDUF]\Z\QRV]
[
=
P =
P
&
\
= P
&
]
= + P P
&
=
3RáR*HQLH URGNyZ FL *NRFL SR]RVWDá\FK RELHNWyZ MHVW áDWZH GR RGF]\WDQLD ] Z\PLDUyZ
XNáDGX
2
'DQH GRW\F]FH SRV]F]HJyOQ\FK RELHNWyZ RUD] REOLF]HQLD VWDW\F]Q\FK PRPHQWyZ
EH]ZáDGQRFLPR*QDZáDWZ\VSRVyESU]HGVWDZLüWDEHODU\F]QLH
Numer
&L *DU
:VSyáU] GQHURGNyZ
6WDW\F]QHPRPHQW\EH]ZáDGQRFL
obiektu obiektu –
FL *NRFLRELHNWyZ
obiektów
Qi [kg]
xCi [m]
yCi [m]
zCi [m]
Qi xCi [kgm]
Qi yCi [kgm] Qi zCi [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]JO GHP NROHMQ\FK SáDV]F]\]Q Z\QRV] ]DWHP
odpowiednio:
6
=
NJP
\]
6
=
NJP
[]
6
=
NJP
[\
2EOLF]DMFZVSyáU] GQHURGNDFL *NRFLRWU]\PXMHP\
6
\]
NJP
[ =
=
≅
P
F
4
NJ
6
NJP
[]
\ =
≅
≅
P
F
4
NJ
6
[\
NJP
] =
≅
≅
P
F
4
NJ
1D U\VXQNX SU]HGVWDZLRQR SU]HU\ZDQ\PL OLQLDPL RGPLHU]HQLH NROHMQ\FK ZVSyáU] GQ\FK
URGNDFL *NRFLXNáDGXRELHNWyZ]U\VXQNX
3
4