P P A B 4 3 2 1

3U]\NáDG.UDWRZQLFD]áR*RQD
:\]QDF]\üUHDNFMH
P
P
3×l
4×l
5R]ZL]DQLH
=H VSRVREX SRGSDUFLD Z\QLND *H QLH]QDQH V VNáDGRZH UHDNFML 'OD XNLHUXQNRZDQLD
GDOV]\FK G]LDáD Z FHOX Z\]QDF]HQLD UHDNFML ]DFLHQLXMP\ WDUF]H V]W\ZQH WZRU]FH W
NUDWRZQLF
(IHNWWHJRG]LDáDQLDSRND]XMHU\VXQHNSRQL*HM
P
3
1
P
4
2
B
A
3U]HGVWDZLRQD NUDWRZQLFD VWDQRZL XNáDG SRáF]RQ\FK SU]HJXERZR HOHPHQWyZ V]W\ZQ\FK GZyFKWDUF]LGZXSU
WyZ5R]G]LHOP\Z\Uy*QLRQHWDUF]HXVXZDMFP\ORZRSU
W\L
L ]DVW
SXMF MH QLH]QDQ\PL RGG]LDá\ZDQLDPL 61
i S2 :SURZDG(P\ WDN*H UHDNFMH SRGSyU
2WU]\PDQ\XNáDGVLáSU]HGVWDZLDSRQL*V]\U\VXQHN
3l
l
P
P
S2
S2
3
4
S1
S1
1
HB
2
VB
y
2l
x
HA
VA
$E\ Z\HOLPLQRZDü ] UyZQDQLD QLHZLDGRPH 61
lewej równanie
∑P
lewa
iy
i S2 Z\NRU]\VWDP\ GOD Z\G]LHORQHM F]
FL
= 0 VNGRWU]\PDP\9A – P = 0 ⇒ VA = P.
i
:\NRU]\VWXMF WHUD] GRZROQH WU]\ UyZQDQLD UyZQRZDJL GOD FDáHJR XNáDGX PR*HP\
Z\]QDF]\üSR]RVWDáHQLHZLDGRPHUHDNFMH,WDNQS]UyZQD
∑M
iB
= 0 ⇒P Âl + P Â3l + HA Â2l – PÂ3l = 0
i
∑P
∑P
ix
= 0 ⇒ HA –HB = 0 ,
iy
= 0 ⇒VB-P –P +P = 0
i
i
REOLF]\P\*H
HA = - P/2, HB = - P/2, VB = P.
=QDQHZDUWRFLVNáDGRZ\FKUHDNFMLSR]ZDODMWHUD]QDZ\]QDF]HQLDVLáZSU
WDFKNUDWRZQLF\
MHGQ]H]QDQ\FKPHWRGSROHFDP\MDNRüZLF]HQLH
:DUWRFLLU]HF]\ZLVWH]ZURW\UHDNFMLSU]HGVWDZLDSRQL*V]\U\VXQHN
P
P
P/2
P
P/2
P
2