3U]\NáDG5DPD]DPNQL WD]HFLJLHP

:\]QDF]\üUHDNFMH

l

q

ql

l

l

l

5R]ZL]DQLH

8NáDGVLáRWU]\PDQ\SRXZROQLHQLX]ZL ]yZSU]HGVWDZLRQ\MHVWQDU\VXQNXSRQL*HM

3

4

2

q

ql

1

A

B

x

HA

MB

VA

VB

2EOLF]P\ UHDNFM +

∑ =

A MHG\Q SR]LRP Z\NRU]\VWXMF UyZQDQLH

P

0 . Przyjmuje ono

ix

i

SRVWDü+A - ql = 0 ⇒ HA = ql.

'R Z\]QDF]HQLD SR]RVWDá\FK UHDNFML NRQLHF]QH MHVW UR]G]LHOHQLH SRGSyU $ L % : roz-ZD*DQ\P XNáDG]LH HOHPHQW\ UDP\ WZRU] REZyG ]DPNQL W\ 3RZRGXMH WR *H GOD

Z\RGU EQLHQLD GZX UR]áF]Q\FK F] FL QLH Z\VWDUF]\ UR]G]LHOHQLH MHGQHJR SRáF]HQLD

3RG]LHOP\XNáDGZSU]HJXEDFKL=DQLPZSURZDG]LP\VLá\Z]DMHPQHJRRGG]LDá\ZDQLDZ

W\FK SXQNWDFK SU]HDQDOL]XMP\ HOHPHQW\ L 6 WR SU W\ QLHREFL*RQH ]DNRF]RQH

SU]HJXEDPL=ZDUXQNXLFKUyZQRZDJLZ\QLND*HUHDNFMHQDNRFDFKPXV]PLHüNLHUXQHN

RVLSU WyZ3URZDG]LWRGRXNáDGXVLáSU]HGVWDZLRQHJRQDSRQL*V]\PU\VXQNX

I

S2

S2

2

q

S1

S1

ql

ql

MB

VA

VB

x

Z równania

M I

∑

= 0 PR*QD Z\]QDF]\ü QLH]QDQ\ PRPHQW UHDNF\MQ\ 0

i2

B (w punkcie 2

i

SU]HFLQDM VL OLQLH G]LDáDQLD QLH]QDQHM UHDNFML 9B i niewiadomych S1 i S2, co eliminuje je z równania):

M I

∑

= 0 ⇒ -M

i2

B –ql l = 0 ⇒ MB = – ql.

i

=QDMF 0B PR*HP\ WHUD] ] UyZQD

M

∑

= 0 i

M

∑

= 0 REOLF]\ü UHDNFMH SLRQRZH

iA

iB

i

i

5yZQDQLDWHSU]\MPXMSRVWDü VB 2l - MB+ ql l – ql l/2 = 0

-VA 2l + ql 3/2l + ql l – MB = 0, co daje VB = – 3/4 ql i VA =7/4 ql

=HVWDZLHQLHREOLF]RQ\FKZLHONRFLSU]HGVWDZLDU\VXQHN

q

ql

ql

ql2

7/4 ql

3/4 ql

2