3U]\NáDGURGHNFL *NRFLILJXU\SáDVNLHM±]DGDQLH
=QDOH(üURGHNFL *NRFLILJXU\SU]HGVWDZLRQHMSRQL*HM
Rysunek 1
: FHOX SROLF]HQLD ZVSyáU] GQ\FK URGND FL *NRFL ILJXU\ ] U\VXQNX SU]\M WR XNáDG RVL L
SRG]LHORQRMQDWU]\ILJXU\VNáDGRZHMDNQDU\VXQNX
Rysunek 2
=QDQH V SRáR*HQLD URGNyZ FL *NRFL ILJXU\ L URGHN FL *NRFL üZLDUWNL NRáD OH*\ QD
GZXVLHF]QHM NWD SURVWHJR JG\* MHVW WR R V\PHWULL ILJXU\ QLH]QDQH V MHGQDN MHJR
ZVSyáU] GQH
3ROLF]P\ ]DWHP RJyOQLH ZVSyáU] GQH URGND FL *NRFL Z\FLQND NRáD R NFLH ZHZQ WU]Q\P
3 1D U\VXQNX SU]HGVWDZLRQR Z\FLQHN NRáD ZUD] ] SU]\M W\P XNáDGHP ZVSyáU] GQ\FK
RUD]ZSURZDG]RQ\PLGODXáDWZLHQLDREOLF]HZVSyáU] GQ\PLELHJXQRZ\PL
Rysunek 3
Przy obliczaniu momentów statycznych Sx i SySRGVWDZLDP\QDVW SXMFR
[ = U FRVα \ = U VLQ α
G$ = GU U Gα = U GU Gα
Pole powierzchni G$SROLF]RQH]RVWDáRMDNGODSURVWRNWDRERNDFK dr i UGα GáXJRüERF]QHM
FLDQNLLGáXJRüáXNXFRGODPDá\FKZLHONRFLNWD Gα jest prawdziwe.
3U]HG]LDá\ ]PLHQQRFL GOD ZVSyáU] GQ\FK ELHJXQRZ\FK GOD UR]SDWU\ZDQHJR Z\FLQND NRáD
Z\QRV]
U ∈< 5 > α ∈< −ϕ ϕ > .
/LF]HQLHZVSyáU] GQHMxCPR*QDSRPLQüJG\*URGHNFL *NRFLILJXU\OH*\QDRVL\
3R SRGVWDZLHQLX ZVSyáU] GQ\FK ELHJXQRZ\FK X]\VNDQH FDáN ZH Z]RU]H QD Sx PR*QD
REOLF]\üQLH]DOH*QLHGODRE\GZXZVSyáU] GQ\FK
π +
π
ϕ
5
+
ϕ
π
π
5
6 = π
U VLQ α GU Gα =
U (− FRVα )
= − 5
∫
FRV
+ ϕ
FRV
ϕ =
−ϕ ∫
[
π
−
−
−ϕ
= −
(
5
VLQ ϕ
VLQ ϕ
5 VLQ ϕ
[ − ( )− ( ) ]=
( )
2
3ROHSRZLHU]FKQLILJXU\PR*QDSROLF]\üZVWRVXQNXGRSRZLHU]FKQLFDáHJRNRáD
ϕ
$ = π 5
= ϕ 5
π
:VSyáU] GQDSLRQRZDURGNDFL *NRFLILJXU\ZSU]\M W\FKRVLDFK[\Z\QRVL
5 VLQ(ϕ)
6
5 VLQ ϕ
[
( )
\ =
=
=
F
$
ϕ 5
ϕ
π
π
'ODüZLDUWNLNRáD]QDMGXMHP\ZVSyáU] GQy
=
ϕ =
CSRGVWDZLDMF ϕ
, bo
:
π
5 VLQ
5
5
\ =
=
=
F
π
π
π
:UDFDMFGRILJXU\]U\VXQNXZVSyáU] GQHURGNDFL *NRFLILJXU\SU]\SU]\M W\FKMDNQD
U\VXQNXRVLDFKXNáDGXZVSyáU] GQ\FKZ\QRV]
5
5
[
= \ =
=
&
&
π
π
6WRVXMFPHWRG JUXSRZDQLDILJXURWU]\PXMHP\Z]RU\QDVWDW\F]QHPRPHQW\EH]ZáDGQRFL
π 5 5
6 =
5
5 +
+ 5 − 5
5
5
5
5
[
π
=
+
−
=
π
5 5
6
= 5 − 5
5
5
5
5
5
5
\
+
+
= −
+
+
=
π
Pole powierzchni wynosi:
π 5
π
+
$ =
5 +
+ 5 =
5
:VSyáU] GQHURGNDFL *NRFLZ\QRV]
6
5
\
[
=
=
5 ≅ 5
&
+
=
οπ
$
π
( + )
5
5
6
[
\
=
=
5 ≅ 5
&
+
=
οπ
$
π
( + )
5
=QDMGXMFQDU\VXQNXURGHNFL *NRFLX]\VNXMHP\
3
4