3U]\NáDG%HONDZROQRSRGSDUWD]HZVSRUQLNLHP

3ROHFHQLH Z\]QDF]\ü UHDNFMH SRGSRURZH GOD SRQL*V]HM EHONL REFL*RQHM REFL*HQLHP

FLJá\PRVWDá\PQDW *HQLX q RUD]VLáVNXSLRQ P = ql.

P = ql

q

4 l

l

l

Przyjmujemy oznaczenia podpór: A i B.

P = ql

q

B

A

4 l

l

l

5R]ZL]\ZDQLH ]DGDQLD UR]SRF]\QDP\ RG RVZRERG]HQLD EHONL RG ZL ]yZ ]DVW SXMF

SRGSRU\ UHDNFMDPL /HZD SRGSRUD R]QDF]RQD OLWHU A MHVW SRGSRU SU]HJXERZ

QLHSU]HVXZQ =DWHP Z SXQNFLH A G]LDáDM GZLH QLH]DOH*QH RG VLHELH VNáDGRZH UHDNFML

pionowa VA i pozioma HA 3UDZD SRGSRUD R]QDF]RQD OLWHU B MHVW SRGSRU SU]HJXERZ

SU]HVXZQ : SXQNFLH B Z\VW SXMH UHDNFMD RB NWyUHM OLQLD G]LDáDQLD MHVW SLRQRZD

SURVWRSDGáD GR NLHUXQNX PR*OLZHJR SU]HVXZX : FHOX XSURV]F]HQLD ]DSLVX UyZQD

UyZQRZDJL ]DVWSLP\ REFL*HQLH FLJáH q VLá Z\SDGNRZ NWyUHM NLHUXQHN L ]ZURW MHVW

]JRGQ\ ] NLHUXQNLHP L ]ZURWHP REFL*HQLD FLJáHJR :DUWRü Z\SDGNRZHM MHVW UyZQD SROX

ILJXU\ SRG Z\NUHVHP UR]NáDGX QDW *HQLD REFL*HQLD FLJáHJR QDWRPLDVW OLQLD G]LDáDQLD VLá\

Z\SDGNRZHMSU]HFKRG]LSU]H]URGHNFL *NRFLWHMILJXU\:UR]SDWU\ZDQ\PSU]\NáDG]LHVLáD

wypadkowa jest równa W = q  l = 4 ql2GOHJáRüOLQLLG]LDáDQLDZ\SDGNRZHMRGSRGSRU\ A wynosi 2 l.

W = 4 ql

P = ql

y

A

B

HA

VA

RB

x

2 l

3 l

l

%HONDREFL*RQDMHVWGZLHPDVLáDPL]HZQ WU]Q\PLNWyU\FKZLHONRFLV]QDQHR]QDF]RQ\PL

NRORUHPF]DUQ\PRUD]WU]HPDUHDNFMDPLR]QDF]RQ\PLNRORUHPSRPDUDF]RZ\P1LH]QDQH

ZDUWRFL UHDNFML Z\]QDF]\P\ ] WU]HFK UyZQD UyZQRZDJL GOD SáDVNLHJR GRZROQHJR XNáDGX

VLá =DSLV]HP\ GZD UyZQDQLD U]XWyZ VLá QD RVLH XNáDGX ZVSyáU] GQ\FK RUD] UyZQDQLH

PRPHQWyZ2VWDWQLH]Z\PLHQLRQ\FKUyZQDQDMNRU]\VWQLHMMHVW]DSLVDüZ]JO GHPSXQNWX A

lub B /LQLH G]LDáDQLD UHDNFML VA i HA SU]HFKRG] SU]H] SXQNW A, zatem te niewiadome nie Z\VWSL Z UyZQDQLX PRPHQWyZ Z]JO GHP SXQNWX A PRPHQW VLá\ Z]JO GHP SXQNWX

OH*FHJRQDOLQLLG]LDáDQLDWHMVLá\MHVWUyZQ\]HUX:WDN]DSLVDQ\PUyZQDQLXZ\VWSLW\ONR

jedna niewiadoma RB3RGREQLHZUyZQDQLXPRPHQWyZZ]JO GHPSXQNWX BQLHZ\VWSLá\E\

reakcje RB i HA JG\* LFK OLQLH G]LDáDQLD SU]HFKRG] SU]H] SXQNW B .RU]\VWDMF ] WHJR

UyZQDQLDPR*QDE\Z\]QDF]\üUHDNFM VA.

∑

14

M

: R

ql = 2,8 ql

iA = 0

B Â l í W Â l í P Â l = 0 ⇒ RB = 5

i

:QDVW SQ\PUyZQDQLXUyZQRZDJLNRU]\VWDP\]Z\]QDF]RQHMZDUWRFLUHDNFML RB.

∑

11

P

: V

ql = 2,2 ql

iy = 0

A + RB í W í P = 0 ⇒ VA = 5

i

=UyZQDQLDU]XWyZVLáQDRSR]LRPZ\]QDF]DP\QLHZLDGRP HA.

∑ P

: H

ix = 0

A = 0

i

: FHOX VSUDZG]HQLD SRSUDZQRFL Z\NRQDQ\FK REOLF]H ]DSLV]HP\ UyZQDQLH UyZQRZDJL ]

NWyUHJRZF]HQLHMQLHNRU]\VWDOLP\

W = 4 ql

P = ql

A

B

HA = 0

VA = 2,2 ql

RB = 2,8 ql

2 l

3 l

l

∑ M

: W Â l í P Â l í V

iB = 0

A  l = 4 ql  l í ql  l í ql  l = 12 ql2 í ql2 í ql2 = 0

i

5yZQDQLHVSHáQLRQHMHVWWR*VDPRFLRZR

2