=QDOH(ü URGHN FL *NRFL RVWURVáXSD IRUHPQHJR R SRGVWDZLH NZDGUDWX R Z\PLDUDFK MDN QD
U\VXQNXSRQL*HM
Rysunek 1
URGHNFL *NRFLEU\á\PR*QDREOLF]DüSRSUDZLDMFZ]RU\]]DGDQLD3RQL*HM
przestawiono Z]RU\ GR REOLF]H URGND FL *NRFL SR XZ]JO GQLHQLX WU]HFLHM ZVSyáU] GQHM
RUD]]DPLHQLDMFSROHILJXU\$QDREM WRüEU\á\9
3RáR*HQLHURGNDFL *NRFLEU\á\RNUHODVL QDSRGVWDZLHZ]RUyZ
6 \]
6
6
[]
[\
[ =
\ =
] =
,
(1)
F
F
F
9
9
9
JG]LHVWDW\F]QHPRPHQW\EH]ZáDGQRFLLSROHRNUHORQHVZ]RUDPL
6
= [ G9 6 =
\ G9
6
= ] G9 9 = G9
∫
∫
∫
∫ .
(2)
\]
[]
[\
9
9
9
9
'ODEU\á\VNáDGDMFHMVL ]EU\áGODNWyU\FK]QDQHMHVWSRáR*HQLHURGNyZFL *NRFLVWDW\F]QH
PRPHQW\EH]ZáDGQRFLPR*QDRNUHODüQDSRGVWDZLHZ]RUyZ
Q
Q
Q
6
=
9 [
6
∑
=
9 \
6
∑
=
9 ]
∑
(3)
\]
L
&
[]
L
&
[\
L
&
L=
L=
L=
gdzie Vi, xCi, yCi oraz zCiR]QDF]DMREM WRüLRGSRZLHGQLZVSyáU] GQURGNDFL *NRFLLWHM
EU\á\VNáDGRZHMZSU]\M W\PXNáDG]LHRVL
'ODEU\á\]U\VXQNXURGHNFL *NRFLOH*HüE G]LHQDRVLSLRQRZHMRVWURVáXSD:SU]\SDGNX
XV\WXRZDQLD XNáDGX RVL ZVSyáU] GQ\FK WDN DE\ R ] XNáDGX SRNU\ZDáD VL ] RVL V\PHWULL
EU\á\ ]QDOH(ü Z\VWDUF]\ W\ONR ZVSyáU] GQ SLRQRZ URGND FL *NRFL zc 3U]\URVW REM WRFL
G9RNUHOLP\MDNRREM WRüSURVWRSDGáRFLDQXSRáR*RQHJRQDZ\VRNRFL]RZ\VRNRFLdz i SRGVWDZLHNZDGUDWXRERNXE3RZ\*V]H]DáR*HQLDSU]HGVWDZLRQRQDU\VXQNX
:LHONRüESROLF]\P\]WZLHUG]HQLDTalesa w stosunku do boku podstawy a.
D
E
=
+
(+ − ])
D
E =
(+ − ])
+
3U]\URVWREM WRFLdV wynosi:
D
G9 = E G] =
(+ − ]) G]
+
Moment statyczny do policzenia zcPD]DWHPZDUWRü
+
+
D
+
D
D
+ ]
+]
]
6 =
] G9 =
]
(+ − ]) G]
∫
( +
]
+]
] )G]
=
∫
∫
9
+
=
−
+
=
−
+
+
+
=
D +
2EM WRüRVWURVáXSDSROLF]\P\WDN*H]DSRPRFFDáNL
+
+ D
+
D
D
]
9 =
G9 =
(+ − ]) G]
∫
∫
∫ (+
+]
] )G]
+
]
+]
= D +
9
+
=
−
+
=
−
+
+
+
:VSyáU] GQDSLRQRZDURGNDFL *NRFLRVWURVáXSDZ\QRVL]DWHP
2
D +
] =
= +
F
D +
3ROLF]RQZVSyáU] GQ]QDMGXMHP\ZXNáDG]LHZVSyáU] GQ\FK
Rysunek 3
3