3U]\NáDG.UDWRZQLFD]áR*RQD

:\]QDF]\üUHDNFMH

P

P

4

×

l

3

×

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

P

A

B

4

3

2

1

3U]HGVWDZLRQD NUDWRZQLFD VWDQRZL XNáDG SRáF]RQ\FK SU]HJXERZR HOHPHQWyZ V]W\ZQ\FK

GZyFKWDUF]LGZXSUWyZ5R]G]LHOP\Z\Uy*QLRQHWDUF]HXVXZDMFP\ORZRSUW\L

L ]DVWSXMF MH QLH]QDQ\PL RGG]LDá\ZDQLDPL 6

1

i S

2

:SURZDG(P\ WDN*H UHDNFMH SRGSyU

2WU]\PDQ\XNáDGVLáSU]HGVWDZLDSRQL*V]\U\VXQHN

2

P

P

S

2

S

1

H

B

1

2

V

A

H

A

3

V

B

S

2

S

1

4

3l

2l

l

x

y

$E\ Z\HOLPLQRZDü ] UyZQDQLD QLHZLDGRPH 6

1

i S

2

Z\NRU]\VWDP\ GOD Z\G]LHORQHM F]FL

lewej równanie

0

P

i

lewa

iy

=

∑

VNGRWU]\PDP\9

A

– P = 0

⇒

V

A

= P.

:\NRU]\VWXMF WHUD] GRZROQH WU]\ UyZQDQLD UyZQRZDJL GOD FDáHJR XNáDGX PR*HP\

Z\]QDF]\üSR]RVWDáHQLHZLDGRPHUHDNFMH,WDNQS]UyZQD

M

iB

i

∑

=

0

⇒

P

Â

l + P

Â

3l + H

A

Â

2l – P

Â

3l = 0

0

P

i

ix

=

∑

⇒

H

A

–H

B

= 0 ,

0

P

i

iy

=

∑

⇒

V

B

-P –P +P = 0

REOLF]\P\*H

H

A

= - P/2, H

B

= - P/2, V

B

= P.

=QDQHZDUWRFLVNáDGRZ\FKUHDNFMLSR]ZDODMWHUD]QDZ\]QDF]HQLDVLáZSUWDFKNUDWRZQLF\

MHGQ]H]QDQ\FKPHWRGSROHFDP\MDNRüZLF]HQLH

:DUWRFLLU]HF]\ZLVWH]ZURW\UHDNFMLSU]HGVWDZLDSRQL*V]\U\VXQHN

P

P

P/2

P

P

P/2