A VD VD HD HD HA VA VB HB VC HC ∑ ∑
Transkrypt
A VD VD HD HD HA VA VB HB VC HC ∑ ∑
3U]\NáDG5DPDÄWUyMSU]HJXERZD´±SU]\SDGHN]áR*RQ\ :\]QDF]\üUHDNFMH q E l D l A C B 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 VD HA HD VD C HC D B A VA HB VC 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: ∑ M iDI = 0 i ∑ M iEIprawa = 0 . i i 0DMRQHSRVWDü VC 2l + HC l –2ql l = 0 VC l + HC 2l –ql l/2 = 0. = XNáDGX WHJR REOLF]\P\ *H HC= - 1/3 ql i VC=7/6ql. =QDN Ä´R]QDF]D *H ]ZURW UHDNFML +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 HB HA VA : FHOX REOLF]HQLD SR]RVWDá\FK 1/3ql VB UHDNFML 7/6 ql SRZWyU]\P\ WRN SRVW SRZDQLD GOD XNáDGX „trójprzegubowego”. Do obliczenia reakcji pionowych wykorzystamy równania ∑ M iA = 0 i ∑ M iB = 0 . i i 3U]\MPXMRQHSRVWDü VB 2l +7/6ql 3l –3ql 3/2l = 0 i -VA 2l +3ql 1/2l +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 II I E V1 HD VD HD VD A D C 1/3ql D HA 7/6ql B E H1 V1 H1 B C A 4/3ql E D H2 V2 C V2 A H2 HB III 1/2ql 3LHUZV]\]SU]HGVWDZLRQ\FKSRG]LDáyZZ\NRU]\VWDOLP\GRREOLF]HQLDUHDNFML9C 'UXJL ] W\FK SRG]LDáyZ Z\NRU]\VWDP\ GR Z\]QDF]HQLD UHDNFML +A . Równanie i HC. ∑ M iDII = 0 i SU]\MPLHSRVWDüTO l + HA l + ql l/2 LVWG 2 HA = 5/6 ql. 7U]HFLSRG]LDáSR]ZROLZ\]QDF]\üUHDNFM +B Z równania ∑ III M iD . = 0 Z\QLND*Hòql l- HB l = 0 i HB = ½ ql. i =HVWDZLHQLH REOLF]RQ\FK UHDNFML SU]HGVWDZLD U\VXQHN 'OD XáDWZLHQLD VSUDZG]HQLD ZLHONRFL UHDNFMLVSURZDG]RQHVGRZVSyOQHJRPLDQRZQLND q y x 5/6 ql 8/6 ql 3 3/6 ql 2/6 ql 3/6 ql 7/6 ql