3U]\NáDG5DPDÄWUyMSU]HJXERZD´±SU]\SDGHN]áR*RQ\

:\]QDF]\üUHDNFMH

q

E

l

D

l

A

B

C

l

l

l

5R]ZL]DQLH

3U]HGVWDZLRQD UDPD GZXQDZRZD MHVW XNáDGHP ]áR*RQ\P ] WDUF] $' '% '( L (& SRáF]RQ\FK SU]HJXERZR =QDQ\ MX* XNáDG ÄWUyMSU]HJXERZ\´ MHVW WXWDM ]ZLHORNURWQLRQ\ 3R

UR]G]LHOHQLXZSU]HJXELH'SRZVWDMGZDXNáDG\ÄWUyMSU]HJXERZH´LSRXZROQLHQLX]ZL ]yZ

RWU]\PXMHP\QDVW SXMFHXNáDG\VLá

I

E

HD

V

VD

D

HD

C HC

D

HA

VC

A

B

HB

VA

VB

:MDNLVSRVyEZ\]QDF]DVL QLHZLDGRPHUHDNFMHZXNáDG]LHÄWUyMSU]HJXERZ\P´ZLHP\MX*

] SU]\NáDGX =DMPLHP\ VL ]DWHP WDNLP XNáDGHP ± F] FL , 'R Z\]QDF]HQLD UHDNFML

podpory C wykorzystamy równania równowagi:

∑MI = 0 i ∑MIprawa = 0 .

iD

iE

i

i

0DMRQHSRVWDü

VC 2 l + HC l –2 ql l = 0

VC l + HC 2 l – ql l/2 = 0.

=XNáDGXWHJRREOLF]\P\*HHC= - 1/3 ql i VC=7/6ql. =QDNÄŔ]QDF]D*H]ZURWUHDNFML+C

MHVWSU]HFLZQ\GR]DáR*RQHJR

: WHQ VSRVyE Z XNáDG]LH Z\MFLRZ\P X]\VNDOLP\ XNáDG VLá SU]HGVWDZLRQ\ QD SRQL*V]\P

rysunku .

E

D

HA

HB

1/3ql

VA

VB

7/6 ql

: FHOX REOLF]HQLD SR]RVWDá\FK UHDNFML SRZWyU]\P\ WRN SRVW SRZDQLD GOD XNáDGX

„trójprzegubowego”. Do obliczenia reakcji pionowych wykorzystamy równania M

∑

= 0 i

M

∑

= 0 .

iA

iB

i

i

3U]\MPXMRQHSRVWDü

VB 2 l +7/6ql 3 l –3 ql 3/2 l = 0 i -VA 2 l +3 ql 1/2 l +7/6ql l –= 0, VNGREOLF]DP\ZDUWRFLVB= 1/2 ql i VA=4/3ql.

'R REOLF]HQLD UHDNFML SR]LRP\FK PDM ZVSyOQ OLQL G]LDáDQLD SRWU]HEQ\ MHVW MHV]F]H MHGHQ

SRG]LDá :\NRU]\VWDP\ SRZWyUQLH SU]HJXE ' 3RáF]HQLH Z SXQNFLH ' MHVW SU]HJXEHP

ZLHORNURWQ\P JG\* áF]\ ZL FHM QL* GZD HOHPHQW\ 3RG]LDá Z W\P SRáF]HQLX PR*H E\ü SU]HSURZDG]RQ\QDNLONDVSRVREyZSU]HGVWDZLRQ\FKQDU\VXQNX2GG]LDá\ZDQLDZND*G\P

]W\FKSU]\SDGNyZVLQQH

E

I

II

H1

E

HD

V1

V

V

1

D

V

B

C

D

H

D

H1

D

C 1/3ql

HA

A

D

7/6ql

A

B

4/3ql

E

D

H2

V2

C

A

V2

H2

HB

III

1/2ql

3LHUZV]\]SU]HGVWDZLRQ\FKSRG]LDáyZZ\NRU]\VWDOLP\GRREOLF]HQLDUHDNFML9C i HC.

II

'UXJL ] W\FK SRG]LDáyZ Z\NRU]\VWDP\ GR Z\]QDF]HQLD UHDNFML +A. Równanie M

∑

= 0

iD

i

SU]\MPLHSRVWDüTO l + HA l + ql l/2 LVWGHA = 5/6 ql.

2

7U]HFLSRG]LDáSR]ZROLZ\]QDF]\üUHDNFM +B.

Z równania

M III

∑

= 0

iD

Z\QLND*Hòql l- HB l = 0 i HB = ½ ql.

i

=HVWDZLHQLHREOLF]RQ\FKUHDNFMLSU]HGVWDZLDU\VXQHN'ODXáDWZLHQLDVSUDZG]HQLDZLHONRFL

UHDNFMLVSURZDG]RQHVGRZVSyOQHJRPLDQRZQLND

y

q

x

5/6 ql

3/6 ql

2/6 ql

8/6 ql

3/6 ql

7/6 ql

3