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# 66532198 bahan-ajar-mekanika-rekayasa-1-d3-sipil-15-8-2011-didik

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### 66532198 bahan-ajar-mekanika-rekayasa-1-d3-sipil-15-8-2011-didik

1. 1. PROGRAMDIPLOMA3TEKNIKSIPILFTSPITS2011MEKANIKA REKAYASA 1BAHANAJARDIDIKHARIJANTOPROGRAMDIPLOMA3TEKNIKSIPILFTSPITS2011MEKANIKA REKAYASA 1BAHANAJARDIDIKHARIJANTOKAMPUSD3TEKNIKSIPILJLNMENUR127SURABAYA
5. 5. PROGRAM DIPLOMA TEKNIK SIPILFAKULTAS TEKNIK SIPIL DAN PERENCANAANINSTITUT TEKNOLOGI SEPULUHNOPEMBERMATAKULIAHDANKELAS:MEKANIKAREKAYASA1 -YKODEMK:RC090308DOSEN1.DIDIKHARIJANTOSKSKONTRAKKULIAH& MATERI PEMBELAJARAN2.3MINGGUKEKOMPETENSI1MATERIPEMBELAJARANPENGAMPU21231 -4Mampumengidentifikasigaya,menghitungresultantegaya,momen,mengidentifikasimacambeban,perletakan,mampumenghitungreaksiperletakandangayadalamPengertiangaya,
10. 10. RITTERV13EVALUASI34
12. 12. ditetapkandiborangini.DIDIKHARIJANTO5
13. 13. PENGERTIANGAYAGAYAADALAHSUATUBESARANVEKTORYANGMEMPUNYAIBESARAN,TITIKTANGKAPDANGARISKERJAGAYA.GAYADAPATDIPINDAHKANSEPANJANGGARISKERJANYA.GariskerjaGariskerjagayaTitiktangkapgayaPENJUMLAHANGAYA(RESULTANTEGAYA)CARAANALITISRY=P1SIN a +P2SIN ßRX=P1COS a +P2COS ßR=.... .............. ........... .
14. 14. 5T3TDIKETAHUIDUAGAYAP1=5TDENGANSUDUT450DANP2=3TDENGANSUDUT300HITUNGBESARRESULTANTEGAYATERSEBUTDIATAS.00RY=5SIN45+3SIN30=5.0,7071+3.0,5=3,5355+1,5=5,0355T00RX=5COS45+3COS30=5.07071+3.0,866=3,5355+2,5981=6,1335T=7,936T..25,3562.. 37,6198 =....5,0335..6,1335..=................R=0=39,38 .. 0,8209..RRYX....TgCARAGRAFISUNTUKCARAGRAFISHARUS
17. 17. SEHINGGAMB= -5SIN a .6= -5.4/5.6= -24TM.DARIPENYELESAIANDIATASDISARANKANMENGURAIKANDAHULUGAYAMIRINGAGARPENYELESAIANMENJADILEBIHMUDAH.
19. 19. D
20. 20. 4M3M2MABCD6T5T3T2TABCD6T5T3T2T15TM-3.3+2.9=6.4-=.....B6TBB5T2TACD53TM-5.3+2.2=6.7-=.....6TAC5TBC2TCD
25. 25. PPPPSATUANBERATKG,TONDANLAINLAIN.qBEBANMERATAqSATUANT/M,KG/M,KG/CMDANLAINLAINq=TINGGIATAULEBARDARIBENTUKBEBAN(LIHATGAMBAR)BEBANTIDAKMERATAMISALBEBANSEGITIGAqqSATUANMAUPUNARTIq
27. 27. PERLETAKANSENDIHVMEMPUNYAIREAKSITEGAKLURUSLANDASANDANSEJAJARLANDASAN,ARTINYAPERLETAKANSENDITIDAKDAPATBERGERAKTEGAKLURUSMAUPUNSEJAJARLANDASAN.ROLVMEMPUNYAIREAKSITEGAKLURUSLANDASAN,ARTINYAPERLETAKANROLTIDAKDAPATBERGERAKARAHTEGAKLURUSLANDASAN.JEPIT
32. 32. ingat-+VAMISAL=0.....+VA.103.8+4.3=0VA=1,2T-VC.10+4.13+3.2=0VC=5,8T=0.....(OK)7=0-7=03+5,84-+1,2=0..SKONTROL
33. 33. ..45° .A4T5T5v2..5 T 2M3T2M7M3MBCDE3M4M=0...=0.....HEMISAL+HE3-5=0HE=8TVDMISAL+VD.103.14.125.35.3=0VD=8,1TES....=0VEMISALD4T4T5T5T5T5T3T3T-VE.10 -3.2+8.1 -5.4+5.74.2=0VE=0,9TD4T4T5T5T5T5T3T8T8T=0...+8,145+0,9=099=0(OK)17
35. 35. 4.129.84.2+2.1=0VB=3T=0.....-VD.10+2.11+4.8+9.2+4.2=0VD=8T=O...+4+394+82=01515=0(
36. 36. OK)
42. 42. tg a=3/4ABCD4M6M2M4TX1X23TX34TABCD4T1T6T4T+4TN1T1T++D2T2T8TMM4TM
43. 43. HAMISAL+HA+44=0HA=4TVAMISAL+VA.103.6+4.2=0VA=1T=0...=0.....=0.....VCMISAL-VC.10+3.4+4.12=0VB=6TBIDANGN,DDANMLIHATKIRIPOTONGANNX1=0VA=1TX1=0NA=0X1=4NB=0DX1=+1TMX1=+1.X1X1=0DA=+1TX1=0MA=0
44. 44. X1=4DB=+1TX1=4MB=1.4=4TMLIHATKANANPOTONGAN4TX2NX2=+4TCD2MVC=6T4TX1X2=0NC=+4TX2=6NB=+4TDX2=+46= -2TMX2= -4.(2+X2)+6.X2X2=0DC= -2TX2=0MC= -4.(2
45. 45. +0)+6.0=-8TMX2=6DB= -2TX2=6MC= -4.(2+6)+6.6=+4TMLIHATKANANPOTONGAN4TX3NX3=+4T4TX3=0ND=+4TDX3=2NC=+4TDX3=+4TMX3= -4.X3
46. 46. X3=0DD=+4TX3=0MD=0X3=2MC=+4TX3=2MD= -4.2= -8TM23
47. 47. X1q=1t/mX2X34T2TABCDHCMISAL=0..S2M8M2M+HC2=0HC=2TVAMISAL..0....SN+VA.108.4+2.12T2T+4.2=0VA=2,2TS....=0VCMISAL6TD4T-VC.10+8.6+2.112,2T+4.12=0VC=11,8T=0...D=0M2,2T5,8T10TM4,4TM2,28+11,84 -4=01414=0(OK)
51. 51. 11,8.X21X2.1/2X2LIHATKANANPOTONGANX2=0MC= -4.22.1+11,8.01.0.1/2.0= -10TMX2=8MB= -4.102.9+11,8.81.8.1/2.8=+4,4TMX2=5,8MMAX= -4.7,82.6,8+11,8.5,81.5,8.1/2.5,8= -31,2 -13,6= -31,213,6+68,4416,82=6,82TMNX3=+2TLIHATKANANPOTONGANX3=0ND=+2TX3=2NC=+2TDX3=
52. 52. +4+1.X3MX3= -4.X31.X3.1/2.X3X3=0DD=+4X3=0MD=0X3=2DC=+4+1.2=6TX3=2MC= -4.21.2.1/2.2= -10TMX34T2T25
53. 53. q=1t/mX1X2AC4M6MBQHA=0=0...Q=1/2.6.1=3T=0.....VA.103.(2/3.6)=01,21,2VA=1,2T-VC.10+3(4+1/3.6)D=0VC=1,8T1,8LIHATKIRIPOTONGANDX1=+1,2TX1=0DA=+1,2TX1=4DB=+1,2TMX1=+1,2.X1X1=0MA=0
54. 54. 4,8X1=4MB=1,2.4=4,8TMMMMAX=5.58=0....S
55. 55. LIHATKANANPOTONGAN1T/MX2C1,86MaQQ=1/2.X2.a....X....a=X2/6Q=1/2.X2.X2/6=X...=...X22DX2= -1,8+X2=0DC= -1,8T12...X2=6DB= -1,8+=+1,2T...X...2
56. 56. DX2=0 -1,8+.....0X2=21,6X2=4,65MDARITITIKCTERJADIMMAX.......MX2=+1,8X2Q.1/3X2=1,8X2..X2....X2=0MC=0.....X2=6MB=1,8.6-.... ..6=4,8TM..4,6521X2=4,65MMAX=1,8.4,65.3 .4,65=5,58TM12
60. 60. .
62. 62. =0.....=0.....VS.8+4.2=0VS= -1TVS=1T-VC.8+4.10=0VC=5T
64. 64. 1TX2=2DB=1SMX2=+1.X2X2=0MS=0X2=2MB=+2TMDX3= -1TLIHATKIRIPOTONGANSX3X3=0DS= -1TX3=8DC= -1TVS=1TMX3= -1.X3X3=0MS=0LIHATKANANPOTONGANX3=8MC= -8TDX4=+4TMX4= -4.X4X44TX4=0DD=+4TX4=0MD=0X4=2DC=+4TX4=2MC= -8TM
67. 67. SETELAH6,833TDIDAPATMBC=5TMDANMBA=6TMDARIHASILFREEBODYDIATAS,MAKABIDANGNORMAL,LINTANGMAUPUNMOMENDAPATDIGAMBARDENGANMUDAHDANHARUSTETAPMENGGUNAKANATURANARAHBIDANGM,NMAUPUND.32
69. 69. T6TM5TM1TM5TM6TM2,167T2,35TM3TM1TMDMMX=2,167X1.X.1/2.X1TX=2,167MMAX=2,167.2,1671.2,167.1/2
70. 70. .2,167=2,35TMMD= -1.3= -3TM33
71. 71. Aq=1t/m2T3TBCD+HE+2=0HE=2T=0...31,5=0+VE=0...4M+VE=4,5T+ME+3.1+2.4+1,5.4,75=0E2MME=18,125TM3M1M1,5M=0.....3S......0+MBD+1,5.1,75=0MBD=2,625TMBATANGBA18,125TMS....=0+MBA3.2=0MBA=6TMq=1t/mABCDE4,5T3T1,5T2T2T2,625TM6TM2T3,375TMBATANG
72. 72. BDHE=2T=0,DIDAPAT....SDENGANMENGGUNAKANVE=4,5TMBE=3,375TMBDEB=4,5COS a +2SIN a =4,5.3/5+2.4/5=2,7+1,6=4,3TNEB= -4,5SIN a +2COS a = -4,54/5+2.3/5= -3,6+1,2= -2,4T2COS aaa4,5SIN a
73. 73. EHE=2T2SIN a4,5COS aVE=4,5T34
74. 74. 2T2,4TN2,4T2T2T2,4TN2,4T2T1,5T1,5TD4,3T4,3T3T6TM1,125TM2,625TMM18,125TM3,375TM
75. 75. BEBANATAUMUATANTIDAKLANGSUNG.q=1t/mq=1t/m4TABCDEF.2m1m5 .=20MGel.melintangGel.memanjang4TABBCCDDEEFCONTOH221,50,53122BC23,53,5122..0.....VB.42.3=0ABCDE
78. 78. .36
79. 79. M
87. 87. MENEKANTITIKCSCFSIN a1,875T=a1,5/SINSCF==0aSCFSIN-1,5=0...SCF=1,875T(TARIK)=0a+SCD+SCFCOS=0...SCD+(1,875.3/5)=0SCD=-1,125TSCD=1,125T(TEKAN)TITIKDS..=0SDEDSDF=01,125TSDE+1,125=0=0...TITIKC1,5TSCDSCFSCFCOS aCSDFSDE=-1,125TSDE=1,125T(TEKAN)
88. 88. TITIKFSFESIN aS V=0-1,5+1,875.4/5+SFESIN a=0SCF=1,8751,875COS a1,875SINaSFESFECOS aSFGF1,5T-1,5+1,5+SFE.4/5=0SFE=0SFG+SFECOS a - 1,875COS a =0=0...SFG= -0.3/5+1,875.3/5=1,125T(TARIK)TITIKG1,5+SGE=0-=0..SSGESFG=1,125SGB1,5TGSGE=1,5T(TARIK)1,125+SGB=0-=0...
89. 89. SGB=1,125T(TARIK)TITIKEESDE=1,125SEG=1,5SEBSEBSIN a=0aSEBSIN1,5-=0...SEBCOS aSEB= -1,875TSEB=1,875T(TEKAN)KONTROL=0a1,125+SEBCOS=0...1,125+( -1,875.3/5)=01,125 -1,125=0(OK)
95. 95. UNTUKMENCARIBATANGSGF,SGEDANSEB,DIPOTONGKETIGABATANGTERSEBUT.LIHATKANANPOTONGAN.SEBESIN a =a/3a=3SIN aBSGESGFSEBaG4Ma=3.4/5=12/5M1,5T1,5T3MMENGHITUNGSGFMENGHITUNGSEBMENGHITUNG
96. 96. SGE=0.....=0.....=0.....+SGF.41,5.3=0SGF=1,125T(TARIK)-SEB.12/51,5.3=0SEB= -1,875TSEB=1,875(TEKAN)+SGE.31,5.3=0SGE=1,5T(TARIK)UNTUKMENGHITUNGSGEDAPATDIPAKAICARALAINDENGANMEMOTONGSEPERTIGAMBARDIBAWAHINIMESKIPUNBATANGBATANGYANG
98. 98. GARISPENGARUHREAKSIPERLETAKANBIDANGDAKIBATBEBANMATIBIDANGMGARISPENGARUHREAKSIPERLETAKANGARISPENGARUHDAKIBATBEBANBERJALANGARISPENGARUHMCONTOHAPLIKASIDILAPANGANBALOKJEMBATANKITAAKANMENCARIREAKSIDIAUNTUKMERENCANAKANKEPALAJEMBATANDIA.BebanberjalanP=20t
103. 103. ATAUVA,DIDAPATGPRA/GPVA.P=1P=1P=1P=1DIAS....=0VA.101.10=0A10MB2MCVA=1P=1DIBS....=0VA.101.0=0VA=0P=1DICS....=0VA.10+1.2=0VA= -2/10GPRA/GPVAGPRB/GPVB12/101=0....S
106. 106. luasluasandibawahbeban2/102m=(1+8/10).1/2.22Ingatluastrapesium=jumlhsisisejajarkalisetengahtinggiLuas=1,8mq=2t/mRAMAX=2X1,8=3,6TM.GAMBARGARISPENGARUHSELALULURUSTIDAKPERNAHTERPUTUS.112/10GAMBARGPRBYANGBENAR......BUKTI
107. 107. ..../.......10M2M1ingat:perbandingansegitigaGAMBARGPRBYANGSALAH
111. 111. PERLUMENGHITUNGREAKSIDIAMAUPUNDIB
112. 112. GPDCDANGPMCABCDP=1DIA3M3M7MS....=0-VD.101.3=0VD= -3/10GPDC7/10CD3/107m3/103/10DC=+3/10GPMCMC= -3/10.7= -21/10P=1DIBVD=0DC=0MC=021/1021/10P=1DISEDIKITSEBELAHKIRICD7mCVD=3/10=0VD.10+1.3-=0.....DC= -3/10MC=+3/10.7=21/10
113. 113. 3/10P=1DISEDIKITSEBELAHKANANCAVB=7/10VB.101.7=0=0.....DC=+7/10MC=+7/10.3=21/10BC7/103mP=1DIDVB=0DC=0MC=0=0.....
114. 114. AEBC2M1MKARENAPOTONGANTERLETAKDIANTARAPERLETAKANSNDIDANBEBAS,MAKAUNTUKMUDAHNYAMELIHATSAJAKEARAHBEBAS.P=1DILETAKKANDITITIKA,E,B,C.AEBC2mP=1P=1P=1P=1P=1P=1DITITIKADE= -1ME= 1.2= -2P=1DITITIK
115. 115. SEDIKITSEBELAHKIRIEDE= -1ME= -1.0=0P=1DITITIKSEDIKITSEBELAHKANANEDE=0ME=0P=1DITITIKBDANTITIKCDE=0ME=0AEBCGPDE112GPME
120. 120. HITUNGDANGAMBARGARISPENGARUHDCP=1DIAS.......-RD.101.2=0RD=2/10DC= -2/10c1c2e2/10c1.. 22c1=2/10P=1DISEDIKITKIRICDC=2/10c2=12/10=8/10P=1DISEDIKITSEBELAHKANANCDC= -8/10....e......./..... ......P=1DIEDC=3/10../...
121. 121. ..........CD2/10HITUNGDANGAMBARGARISPENGARUHMCecP=1DIARD=2/10MC= -2/10.8= -16/10P=1DIC...../..... ..c=16/10MC=16/10P=1DIE..... /..... ..e
122. 122. =6/10MC=6/10
124. 124. DiusahakanordinatY1=Y2untuka2-amendapatkanMmax2m8m..... .......,.................... ..,..................Y1=Y212+2a=168a10a=4a=0,4.
125. 125. Y1=1,6(20,4)/2=1,28LUASTRAPESIUM=(1,28+1,6)1/2.0,4+(1,28+1,6)1/2.(2-0,4)=0,576+2,304=2,88m2MCmax=q.luasandibawahbebanberjalan=2.2,88=5,76TM
129. 129. GPRBP=1DIA... ....8/6.2M6M3MP=1DIA..RB=8/6GPMDP=1DIA.MB=0-VS.61.2=08/6-VS= -2/6==MD
130. 130. = -2/6.4= -8/6P=1DID.../... ..b=8/6P=1DIDMD=+8/64MGPDEP=1DIA.... ..P=1DIADE=+2/6c=2/6Lihathal51
131. 131. GARISPENGARUHRANGKABATANGCDEHITUNGDANGAMBARGARISPENGARUHSCD,SCG,4mDANSFG.ABUNTUKMENCARIGAYABATANGFHG3m3m3m3mDIATAS,PAKAICARA
133. 133. SCD= -18/48=-3/8=0a=0+3/12+SCGSIN...SCG=-.....-15/48.... /..MC=0 -3/12.12+SFG.4=0SFG=+3/4
134. 134. P=1DIG=0.....VA=1/2=0.....1/2.6+SCD.4=0SCD= -3/4CG6mSFG=+3/8P=1DIHSCDSFGSCGSIN a1/2=0...1/2SCGSIN a=0../..SCG=.. .../..=0.....1/2.3SFG.4=0=0.....3/12.6+SCD.4=0..0....SVA.121.3=0VA=3/12
135. 135. SCD= -6/4=0...3/12SCGSIN a =0C6mSCGSIN a3mSCD../..... ...SCG=SFG../....=0.....1/4.3SFG.4=0GSFG=+3/16
138. 138. =1DIG=0...SDG -1=0SDG=1P=1DIH,I,BSDG=0GPSEHAGHIBLIHATKEATASPOTONGANSEHAGHIBP=1DIA,G,H,I,BSEH=060
140. 140. SFE=-2.(1/2.3.9/24)= -27/24TM61
145. 145. TUGAS1DHITUNGBESARMOMENDIA,B,C,D,E,FDARIKEDUASOAL6TßBdA..v.. .3T0a=45tg ß=3/4b4TcdaaNRPBERAKHIRANambmcmdm0
146. 146. 53584712456293368343256862266
147. 147. TUGAS2HITUNGBESARREAKSIREAKSIPERLETAKANDARIKONSTRUKSIDANBEBANSEPERTITERGAMBARDIBAWAHINI.4T6T5Tßa6V2Ta =450TG ß=3/43M4M6M3M4TABCD2M2M3M4M3M6TABa Ca=3003T5T6T2T3T3ME1m2m65
148. 148. TUGAS3HITUNGBESARREAKSI2PERLETAKANDARIKONSTRUKSIDANBEBANSEPERTIDIBAWAHINI.PV2Tqt/mß =450ABCDßPTPT3m8m2m2t/m4Tßtg ß=3/43TABC4m1t/mD
149. 149. 2T5TEamcm3mbmNomorpokokambmcmPtonqt/mGASAL62452GENAP3364166