PRESTRESSED CONCRETE BETON PRA-TEKAN BETON PRA-TEGANG

KONSEP GARIS TEKANCOMPRESSION LINE (C Line)PRESSURE LINE (P Line)THRUST LINE (T Line)06/04/2015Prestressed Concrete / AN / ISTN106/04/2015Prestressed Concrete / AN / ISTN2PPC Line (P) = CGSCGCqLPiPiPiPiPie1e3e3e1C LINE AKIBAT GAYA PRA-TEKANe2e206/04/2015Prestressed Concrete / AN / ISTN3PPC Line (Transfer)CGCPiPiPiPiPieD1 = MD1 / PieD2eD1C LINE PADA TAHAP TRANSFERMD3MD2MD1MD1MD2MD3Momen akibat beban mati (berat sendiri)eD2 = MD2 / PieD3 = MD3 / PieD3CGCC Line (P) = CGS06/04/2015Prestressed Concrete / AN / ISTN4PPC Line (Service)CGCPefPefPefPefPefeT1 = MT1 / PefeT2eT1C LINE PADA TAHAP SERVICEMT3MT2MT1MT1MT2MT3Momen akibat beban kerja (beban mati + beban hidup)eT2 = MT2 / PefeT3 = MT3 / PefeT3CGCCGSDAERAH AMAN TITIK TEKANDAERAH AMAN GARIS TEKAN (C Line)06/04/2015Prestressed Concrete / AN / ISTN5CGCBatas Kern Atas = kaBatas Kern Bawah = kbDaerah aman titik tekan / garis tekan / C-linePenampang beton mengalami tegangan tekan, apabila titik tekan / garis tekan / C-line berada dalam batas kern atas dan kern bawah.06/04/2015Prestressed Concrete / AN / ISTN6hbL qLCGCDiketahui::L = 12 md = 10 cmb = 30 cmh = 90 cmqL = 15 kN/mgc = 24 kN/m3 (berat jenis beton)Kehilangan gaya pra-tekan 20%Mutu beton: fc = 35 MPa. fci = 70% fcLATIHAN 3 : Rencanakan balok pra-tekan dengan metode load balancing?ABKarakteristik Penampang:Ac = b.h = 30.90 = 2700 cm2Ix = b.h3/12 = 30 (cm).903 (cm3) / 12Ix = 1822500 cm4ya= yb = .h = .90 = 45 cmTegangan tarik = fct = 0 ka = kb = (I) / (Ac. ya) = 15 cm = h / 6

06/04/2015Prestressed Concrete / AN / ISTN7yb = .hya = .hbkayaybkbCGCKonsep load balancing Rencanakan beban pengganti (imbang) = qp = qD + 0,4 qLqP = (0,3. 0,9. 24) + (0,4. 15) = 12,48 kN / mKondisi Unbalance :1.Beban minimal = qD

2.Beban maksimal = qD + qL 06/04/2015Prestressed Concrete / AN / ISTN8qDqP = qD + 0,4.qL 0,4.qLMDmax = (0,4.15).(122) / (8)MDmax =108 kN.mqDqP = qD + 0,4.qL 0,6.qLqLMTmax = (0,6.15).(122) / (8)MTmax =162 kN.m06/04/2015Prestressed Concrete / AN / ISTN9kakbyaybCGCPMTmax Pef = MTmax / ka = 16200 / 15 = 1080 kNPi = Pef / (1 0,2) = 1350 kNGunakan Pi = 1400 kN Pef = 0,8. 1400 = 1120 kNEksentrisitas CGS = e = (qP.L2) / (8.Pef) e = (12,48. 122) / (8. 1120) = 0,20 mMENGHITUNG GAYA PRA-TEKAN (P)CGCCGS2006/04/2015Prestressed Concrete / AN / ISTN10CGCCGSe cS kbkaC-Line (Service)TAHAP PEMERIKSAAN C - LineTahap transfer:Tahap service:MqDmax = 116,64 kN.m Mmax = 386,64 kN.m Pi = 1400 kNPef=1120 kNcT = 11664 / 1400 = 8,33 cmcS=34,52 cmKesimpulan:C-Lina dalam batas kern seluruh penampang beton mengalami tegangan tekan.cT C-Line (Transfer)BATAS KERNKERN LIMIT06/04/2015Prestressed Concrete / AN / ISTN11MENENTUKAN BATAS KERN PENAMPANG06/04/2015Prestressed Concrete / AN / ISTN12PCGCkaPP.kafccfctf cc = (P / Ac) + (P.ka.ya) / If cc =(P / Ac) + (P. ka.ya).(Ac / Ac ) / If cc =(P / Ac) {1 + (ka.ya) / (I / Ac)}f cc (Ac / P) = 1 + (ka).(ya / i2)ka=(i2 / ya) {f cc (Ac / P) 1}f ct = (P / Ac) (P. ka.yb) / If ct =(P / Ac) (P. ka.yb).(Ac / Ac ) / If ct =(P / Ac) {1 (ka.yb) / (I / Ac)}f ct (Ac / P) = 1 (ka).(yb / i2)ka=(i2 / yb) {1 f ct (Ac / P)}f ct =0 ka = (i2 / yb)Batas kern penampang:ka =(i2 / yb)=(I) / (Ac.yb)kb = (i2 / ya)= (I) / (Ac.ya)MENENTUKAN GAYA PRA-TEKAN Mmax & Mmin SEARAH06/04/2015Prestressed Concrete / AN / ISTN13kakbacdyaybCGCPenampang : Ac ; ya ; yb ; I ; WTegangan tarik beton = fct = 0 ka & kbSelimut beton = d > 10 cmMekanika struktur Mmax & MminASUMSI titik tekan P pada posisi selimut beton d c = yb kb d. a = ka + kb + cMminMmaxMenghitung P :P1 (Mmin) / (c)P2 (Mmax) / (a)P3 (Mmax Mmin) / (ka + kb)PMENENTUKAN GAYA PRA-TEKAN Mmax & Mmin TIDAK SEARAH06/04/2015Prestressed Concrete / AN / ISTN14kakbcdyaybCGCPenampang : Ac ; ya ; yb ; I ; WTegangan tarik beton = fct = 0 ka & kbSelimut beton = d > 10 cmc = yb kb d. a = ka + kb + cMekanika struktur Mmax & MminMminMmaxMenghitung gaya pra-tekan, ASUMSI titik tekan P dalam batas kern.P (Mmax + Mmin) / (ka + kb)PMENENTUKAN DAERAH AMAN POSISI CGS06/04/2015Prestressed Concrete / AN / ISTN15kakbacdyaybCGCa =(Mmax / Pef) c=(Mmin / Pef)MminMmaxPPDaerah aman posisi CGSMENENTUKAN DAERAH AMAN POSISI CGS06/04/2015Prestressed Concrete / AN / ISTN16kakbacdyaybCGCa =(Mmax / Pef) c=(Mmin / Pef)MminMmaxPefDaerah aman posisi CGSPefNOTASI BETON PRA-TEKAN06/04/2015Prestressed Concrete / AN / ISTN17h/2bh/2eCGC = Center of Gravity of ConcreteCGS = Center of Gravity of SteelBaja pra-tekand (selimut beton)06/04/2015Prestressed Concrete / AN / ISTN18hbL qSIDLCGCDiketahui::L = 12 md = 10 cmb = 30 cmh = 90 cmqSIDL = 4 kN/mTL = 70 kN/mgc = 24 kN/m3 (berat jenis beton)Kehilangan gaya pra-tekan 20%Mutu beton: fc = 35 MPa. fci = 70% fcLATIHAN 4 :Hitung berapa gaya pra-tekan efektif yang diperlukan dan tentukan posisi CGS yang memenuhi syarat?

ABTL3 KARAKTERISTIK PENAMPAPANGAc = b.h = 30.90 = 2700 cm2Ix = b.h3/12 = 30 (cm).903 (cm3) / 12Ix = 1822500 cm4ya= yb = .h = .90 = 45 cmTegangan tarik = fct = 0 ka = kb = (I) / (Ac. ya) = 15 cm = h / 6

06/04/2015Prestressed Concrete / AN / ISTN19yb = .hya = .hbkacdyaybkbc = 20 cmCGC06/04/2015Prestressed Concrete / AN / ISTN20116,6487,48105157,5336Beban mati berat sendiriqD = 6,48 kN/mBeban hidupTL = 70 kN/mIII7254Beban mati tambahanqSIDL = 4 kN/mMEKANIKAN STRUKTUR BALOK BETON PRA-TEKANPERENCANAAN Selalu pada tahap service (layan) Pef06/04/2015Prestressed Concrete / AN / ISTN21KOMBINASI PEMBEBANANMI MIIBeban minimal Beban matiqDL 87,48116,64 qSIDL 54,0072,00Momen beban minimal141,48188,64Beban maksimal Beban total (mati + hidup)1.qDL 87,48116,64qSIDL 54,0072,00TL 157,50105,00Momen beban maksimal298,98293,64kayaybkbCGCMb.minMb.maxcdCARA NON LOAD BALANCING Untuk menghitung Pef , maka asumsi posisi titik tekan Pef pada jarak d06/04/2015Prestressed Concrete / AN / ISTN22kayaybkbCGCMb.minMb.maxcdPefPada potongan I (x = 3 m) MmaxP1 (14148 / 20) 707,4 kNP2 (29898) / (15 + + 15 + 20) 597,9 kNP3 (29898 14148) / (15 + 15) 525 kNP1P2P3 597,9 kN Pef 707,4 kN Ambil Pef = 700 kN Pi = Pef / (1 0,2) = 875 kN525597,9707,4PefMENENTUKAN DAERAH AMAN POSISI CGS Potongan - I06/04/2015Prestressed Concrete / AN / ISTN23kakbacdyaybCGCa =(Mmax / Pef)=29898 / 700= 42,7 cmc=(Mmin / Pef)=14148 / 700= 20,2 cmDaerah aman posisi CGS (tidak melebihi selimut beton)(yb + ka a = 14 cm)MENENTUKAN DAERAH AMAN POSISI CGS Potongan - II06/04/2015Prestressed Concrete / AN / ISTN24kakbacdyaybCGCa =(Mmax / Pef)=29364 / 700= 41,9 cmc=(Mmin / Pef)=18864 / 700= 26,9 cmDaerah aman posisi CGS (tidak melebihi selimut beton)(yb + ka a = 14,9 cm)06/04/2015Prestressed Concrete / AN / ISTN25IIIBatas aman posisi CGS14,917,3kakbCGCd = 101042,741,9CARA LOAD BALANCINGAsumsi beban imbang atau gaya pengganti = qDL + qSIDL Beban minimal beban mati (DL + SIDL)

Beban maksimal beban mati + beban hidup (DL + SIDL + LL)

06/04/2015Prestressed Concrete / AN / ISTN26qDL qP qSIDL qDLqSIDLTLqP TLPERENCANAAN SELALU PADA KONDISI SERVICE (LAYAN) Pef06/04/2015Prestressed Concrete / AN / ISTN27Kombinasi BebanMI MIIBeban minimal Beban mati Kondisi balance Momen beban minimal00

Beban maksimal Beban total1. TL 157,5105,0Momen beban maksimal157,5105,0kayaybkbCGCMmaxcdPefMENGHITUNG GAYA PRA-TEKAN06/04/2015Prestressed Concrete / AN / ISTN28Pef Mmax / ka (15750 / 15) 1050 kN Ambil Pef = 1100 kNKehilangan gaya pra-tekan 20% Pi = Pef / (1 0,2) = 1375 kNTinggi parabola = e Pef. e = (qP. L2 / 8) e = (10,48. 122) / (8. 1100) = 0,17 m17CGCCGS12,75PEMERIKSAAN TAHAP TRANSFERCara Non Load Balancing Gaya pra-tekan = Pi = 1375 kNBeban kerja = qDL + qSIDL

Potongan IPotongan II

06/04/2015Prestressed Concrete / AN / ISTN29CGCCGCMmax.IPiMmax.IIPi1712,75Mmax.I = 141,48 kN.mMmax.II = 188,64 kN.m4,25 MPa5,92 MPa+3,98 MPa6,20 MPa+Tegangan Tekan Transfer:ct= 0,60. f'ci = 0,60. (70%. 35) = 14,7 MPaPEMERIKSAAN TAHAP SERVICE (LAYAN) BEBAN KERJA MINIMALCara Load Balancing Gaya pra-tekan = Pef = 1100 kNBeban kerja = qDL + qSIDL MinimalBeban imbang=- qP Potongan IPotongan II

06/04/2015Prestressed Concrete / AN / ISTN30CGCPefMmax.I = 0 kN.mMmax.II = 0 kN.m4,07 MPa+4,07 MPa+Tegangan Tekan Service:cs= 0,45. f'c = 0,45. 35 = 15,75 MPaCGCPefPEMERIKSAAN TAHAP SERVICE (LAYAN) BEBAN KERJA MAKSIMALCara Load Balancing Gaya pra-tekan = Pef = 1100 kNBeban kerja = qDL + qSIDL + TLL MaksimalBeban imbang=- qP Potongan IPotongan II

06/04/2015Prestressed Concrete / AN / ISTN31CGCMmax.IPefMmax.I = 157,5 kN.mMmax.II = 105 kN.m7,96 MPa+6,66 MPa1,48 MPa+Tegangan Tekan Service:cs= 0,45. f'c = 0,45. 35 = 15,75 MPaCGCMmax.IIPef0,18 MPa06/04/2015Prestressed Concrete / AN / ISTN32CGCTUGAS 8 : Hitung gaya pra-tekan efektif dan rencanakan daerah aman posisi CGS yang memenuhi syarat.TLDiketahui::L = 12 md = 12,5 cmgc = 24 kN/m3 (berat jenis beton)qSIDL = 8 kN/mTL=50 kNMutu beton: fc = 35 MPa. fci = 70% fcKehilangan gaya pra-tekan 20%20 50 7030qSIDLL1 = 8 mL2 = 4 m 06/04/2015Prestressed Concrete / AN / ISTN33CGCTUGAS 9 : Hitung gaya pra-tekan efektif dan tentukan posisi CGS dengan cara load balancing, dimana qP = qBS + 0,6 qSIDLTLDiketahui::L = 12 md = 12,5 cmgc = 24 kN/m3 (berat jenis beton)qSIDL = 8 kN/mTL=50 kNMutu beton: fc = 35 MPa. fci = 70% fcKehilangan gaya pra-tekan 20%20 50 7030qSIDLL1 = 8 mL2 = 4 m