metode ubahan sudu tMETODE UBAHAN SUDUT JARAK10.0015.0012.008.001.50PERHITUNGAN MOMEN PRIMER BENTANG D-EMD-50.00L:-75.00BENTANG D-CMFCD0.00MFDC0.00BENTANG B-CMFBC.-1/2 q x2-840.00MFCB.1/12qx2840.00BENTANG A-BBEBAN TERBAGI RATA BEBAN TERPUSAT MFAB-2992.50MFAB-288.00MFBA1732.50MFBA192.00PERSAMAAN UBAHAN SUDUT MAB : MFAB + 2EI/L ( 2OA + OB ) MFAB-3280.50.+ 2EI/L ( 2 OA + OB )0.48O A0.24O B MBA : MFBA + 2EI/L ( 2 OB + OA ) MFBA 1924.50+ 2EI/L ( 2 OB + OA ) 0.48OB0.24O A MBC : MFBC + 2EI/L ( 2 OB + OC )MFBC-840.00+ 2EI/L ( 2 OB + OC )0.67O B 0.33O C MCB : MFBC + 2EI/L ( 2 OC + OB ) MFBC 840.000.67O C 0.33OB MCD : MFCD + 2EI/L ( 2 OC + OB )MFCD0.00 + 2EI/L ( 2 OC + OB )0.50O C0.25O DMDC : MFDC + 2 EI / L ( 2 OD + OC ) MFDC0.00+ 2 EI / L ( 2 OD + OC ) 0.50O D 0.25O C SYARAT PERLETAKAN PERLETAKAN DI A MAB = 00.48OA +0.24O B =3280.50..1PERLETAKAN DI B MBA + MBC = 01.15O B.+0.24O A .+0.33O C :-1084.50..2PERLETAKAN DI C MCB+MCD = 01.17O C.+0.33O B .+0.25O D :-840.003PERLETAKAN DI DM DC + 75 = 00.50O D .+0.25 O C : -75.00.4ELEMINASI PERSAMAAN 1 DAN 2 0.48OA .+0.24O B :3280.501.000.24O A .+1.15O B .+0.33O C : -1084.502.000.48OA .+0.24O B 0.00:3280.500.48OA .+2.29O B .+0.67O C : -2169.00-2.05O B -0.67O C 5449.505ELEMINASI PERSAMAAN 3 DAN 4 1.17O C.+0.33O B .+0.25O D :-840.002.000.25 O C .+0.00O B .+0.50O D :-75.001.002.33O C .+0.67O B .+0.50O D :-1680.000.25 O C .+0.00O B .+0.50O D :-75.002.08O C .+0.67O B .+0.00O D :-1605.006ELEMINASI PERSAMAAN 5 DAN 6 -2.05O B .--0.67O C :5449.501.000.67O B .+2.08O C :-1605.003.08-2.05O B .--0.67O C :5449.502.05O B .+6.42O C :-4943.400.00O B 5.75O C 506.10OC : 88.020.50O D .+0.25 O C : -75.00.40.50O D .+22.00:-75.00O D :-97.00-194.010.501.17O C.+0.33O B .+0.25O D :-840.00.3102.690.33O B -48.50:-840.00O B :-894.18:-2682.550.330.48OA +0.24O B =3280.500.00..1-643.81O A : 3924.31:8175.650.48HASIL ROTASI

O A : 8175.65O B :-2682.55O C : 88.02O D :-194.01

MOMEN DARI PERSAMAAN UBAHAN SUDUT

MAB : MFAB + 2EI/L ( 2OA + OB ) -3280.50.+0.48O A .+0.24O B :-0.00MBA : MFBA + 2EI/L ( 2 OB + OA ) 1924.50.+0.48O B .+0.24O A :2599.03MBC : MFBC + 2EI/L ( 2 OB + OC )-840.00.+0.67O B .+0.33O C :-2599.03MCB : MFBC + 2EI/L ( 2 OC + OB ) 840.00.+0.67O C .+0.33O B :4.49MCD : MFCD + 2EI/L ( 2 OC + OB )0.00.+0.50O C.+0.25O D:-4.49MDC : MFDC + 2 EI / L ( 2 OD + OC ) 0.00.+0.50O D .+0.25O C : -75.00

METODE UBAHAN SUDUT REVISIMETODE UBAHAN SUDUT JARAK10.00015.00012.0008.0001.500PERHITUNGAN MOMEN PRIMER BENTANG D-EMD50.000L:75.000BENTANG D-CMFCD0.000MFDC0.000BENTANG B-CMFBC.-1/2 q x2-840.000MFCB.1/12qx2840.000BENTANG A-BBEBAN TERBAGI RATA BEBAN TERPUSAT MFAB-1732.500MFAB-288.000MFBA2992.500MFBA192.000PERSAMAAN UBAHAN SUDUT MAB : MFAB + 2EI/L ( 2OA + OB ) MFAB-2020.500.+ 2EI/L ( 2 OA + OB )0.480O A0.240O B MBA : MFBA + 2EI/L ( 2 OB + OA ) MFBA 3184.500+ 2EI/L ( 2 OB + OA ) 0.480OB0.240O A MBC : MFBC + 2EI/L ( 2 OB + OC )MFBC-840.000+ 2EI/L ( 2 OB + OC )0.667O B 0.333O C MCB : MFBC + 2EI/L ( 2 OC + OB ) MFBC 840.0000.667O C 0.333OB MCD : MFCD + 2EI/L ( 2 OC + OB )MFCD0.000 + 2EI/L ( 2 OC + OB )0.500O C0.250O DMDC : MFDC + 2 EI / L ( 2 OD + OC ) MFDC0.000+ 2 EI / L ( 2 OD + OC ) 0.500O D 0.250O C SYARAT PERLETAKAN PERLETAKAN DI A MAB = 00.480OA +0.240O B =2020.500..1PERLETAKAN DI B MBA + MBC = 01.147O B.+0.240O A .+0.333O C :-2344.500..2PERLETAKAN DI C MCB+MCD = 01.167O C.+0.333O B .+0.250O D :-840.0003PERLETAKAN DI DM DC + 75 = 00.500O D .+0.250 O C : 75.000.4ELEMINASI PERSAMAAN 1 DAN 2 0.480OA .+0.240O B :2020.5001.0000.240O A .+1.147O B .+0.333O C : -2344.5002.0000.480OA .+0.240O B 0.000:2020.5000.480OA .+2.293O B .+0.667O C : -4689.000-2.053O B -0.667O C 6709.5005ELEMINASI PERSAMAAN 3 DAN 4 1.167O C.+0.333O B .+0.250O D :-840.0002.0000.250 O C .+0.000O B .+0.500O D :75.0001.0002.333O C .+0.667O B .+0.500O D :-1680.0000.250 O C .+0.000O B .+0.500O D :75.0002.083O C .+0.667O B .+0.000O D :-1755.0006ELEMINASI PERSAMAAN 5 DAN 6 -2.053O B .--0.667O C :6709.5001.000-2.053O B .--0.667O C :6709.5003.1250.667O B .+2.083O C :-1755.0003.0800.667O B .+2.083O C :-1755.0001.000-2.053O B .--0.667O C :6709.500-6.417O B - -2.083 O C : 20967.1882.053O B .+6.417O C :-5405.4000.667O B .+2.083O C :-1755.0000.000O B 5.750O C 1304.100-5.750O B 19212.188OC : 226.800OB = -3341.2500.500O D .+0.250 O C : 75.000.40.500O D .+56.700:75.000O D :18.30036.6000.5001.167O C.+0.333O B .+0.250O D :-840.000.3264.6000.333O B 9.150:-840.000O B :-1113.750:-3341.2500.3330.480OA +0.240O B =2020.5000.000..1-801.900O A : 2822.400:5880.0000.480HASIL ROTASI

O A : 5880.000O B :-3341.250O C : 226.800O D :36.600

MOMEN DARI PERSAMAAN UBAHAN SUDUT

MAB : MFAB + 2EI/L ( 2OA + OB ) -2020.500.+0.480O A .+0.240O B :-0.000MBA : MFBA + 2EI/L ( 2 OB + OA ) 3184.500.+0.480O B .+0.240O A :2991.900MBC : MFBC + 2EI/L ( 2 OB + OC )-840.000.+0.667O B .+0.333O C :-2991.900MCB : MFBC + 2EI/L ( 2 OC + OB ) 840.000.+0.667O C .+0.333O B :-122.550MCD : MFCD + 2EI/L ( 2 OC + OB )0.000.+0.500O C.+0.250O D:122.550MDC : MFDC + 2 EI / L ( 2 OD + OC ) 0.000.+0.500O D .+0.250O C : 75.000

PERSAMAAN 3 MOMEN PERSAMAAN 3 MOMEN 2.2.BJARAK 10.000M15.000M12.000M8.000M1.500MBATANG A - BJARAK 10.000M15.000MEI3.000REAKSI TUMPUANMB =0MA = 0CEK V = 0RA. 25 - 80.15 - 1/2 Q (L - X ) ^2 = 0RB. 25 - 80 . 10 - 70. 15. 17,5 = 01130.000:1130.000RA = 9075.000:363.000KN RB =19175.000:767.000KN 25.00025.000MOMENMX = RA. X X = 0.000M0.000KNMX = 10.000M3630.000KNMLUAS A1 = 1/2 3630.10:18150.000KNM A2 = 2/3 15. 3630:36300.000KNM BATANG B - C JARAK12.000MMOMENMX = 1/8. Q . L^2MMAKS: 1260.000KNM LUAS : A3 = 2/3. 12.1260 = 10080.000BATANG C - D JARAK =8.000MMX =0.000BATANG D -E MX = -P.X MD = -75.000KNM PERSAMAAN 3 MOMEN PADA BENTANG A B C LUAS A1 = 18150.000A2 = 36300.000A3 = 10080.000MA ( L/I ).+ 2MB ( L1/I1 + L2/I2 ) .+MC ( L2/I2 ) : MA = 028.667MB6MC:-9680.000-45375.000-15120.000

REVISI 28.667MB.+6MC: -85032.500..1-85032.500

PERSAMAAN 3 MOMEN PADA BENTANG B -C - DLUAS = A3 = 10080.000MD = -75 KN 6.000MB.+28.000MC .+MD:-15120.0006.000MB.+28.000MC .+-600.000:-15120.0006.000MB.+28.000MC .+:-14520.000.2ELEMINASI PERSAMAAN 1 DAN 2 28.667MB.+6.000MC : -85032.5004.6676.000MB.+28.000MC :-14520.0001.000133.778MB.+28.000MC 0.0000.000: -396818.3336.000MB.+28.000MC 0.0000.000:-14520.000127.778MB.+0.000MC : -382298.333MB = -382298.333:-2991.900KNM127.778 28.667MB.+6MC: -85032.5000.000..16.000MB.+28.000MC .+0.000:-14520.000-85767.800-17951.400MC = 735.300:122.550KNM M C= 3431.400:122.5506.00028.000HASIL MOMEN AKIBAT PERSAMAAN 3 MOMENTMA =0.000MB = -2991.900MC = 122.550MD = -75.000KURVA ELASTIS METODE PERSAMAAN 3 MOMEN MOMENMA = 0.000MB = -2991.900MC = 122.550MD = -75.000BAGIAN A - B PANJANG BATANG 10.000M15.000MJUMLAH PANJANG 25.000MINERSIA =3.000AKIBAT MOMEN -2991.900

LUAS =37398.750

RAKSI TUMPUAN MB = 0RA = O A MA = 0 RB = OB 0A = -4155.417OB = 8310.833AKIBAT BEBAN LUAR

LUAS MOMEN REVISI : A1A2A3A4A5A6A1 = 2400.00044000.00036000.000288750.000180731.25025913.672177261.328A2 = 3600.000A3 = 15750.000JUMLAH = 752656.250 = 10035.417REAKSI TUMPUAN = SUDUT ROTASI A4 = 14175.00075.000MB = 0RA = O A 0.000MA = 0 RB = OB A5 = 2126.2500A = 10035.417OB = -11652.083A6 = 27011.250A1A2A3A4A5A616000.00054000.000105000.000173643.75027242.578498019.922BAGIAN B - CJUMLAH =873906.250 = 11652.08375.000PANJANG BATANG = 12.000MINERSIA = 2.000EI

MOMEN KIRI = 2991.900MOMEN KANAN = 122.550AKIBAT MOMEN KIRIAKIBAT MOMEN KANAN

LUAS = 17951.400LUAS = 735.300

REAKSI TUMPUAN = SUDUT ROTASI REAKSI TUMPUAN = SUDUT ROTASI MC = 0RB = OB MB = 0RC = OC MC = O RB = OB MB = 0 RC = OC OB = -5983.800OC = 2991.900OB = 122.550OC = -245.100AKIBAT BEBAN LUAR

LUAS MOMENT = A 7 = 10080.000

REAKSI TUMPUAN = SUDUT ROTASI MC = 0RB = OB 0.000MB = 0RC = OC OB = 2520.000OC = -2520.000

BENTANG C - D MOMENT = KIRI = 122.550KANAN = 75.000

MOMEN KIRI = 122.550MOMEN KANAN = 75.000 LUAS = 490.200LUAS = 300.000

REAKSI TUMPUAN = SUDUT ROTASI REAKSI TUMPUAN = SUDUT ROTASI MD = 0 RC = OC MC = 0 RD = OD MD = 0 RC = OC 0.000MC = 0 RD = OD OC = 326.800OD = -163.400OC = -100.000OD = 200.000

HASIL ROTASI

OAB = -4155.417 + 10035.417 = 5880.000OBA = 8310.833 + -11652.083 = -3341.250OBC = -5983.800 + 122.550 + 2520.000 = -3341.250OCB = 2991.900 + -245.100 + -2520.000 = 226.800OCD = 326.800 + -100.000 = 226.800ODC = -163.400 + 200.000 = 36.600

SULIH PERSAMAAN 3 MONEN PERSAMAAN 3 MOMEN 2.2.BJARAK 10.000M15.000M12.000M8.000M1.500MBATANG A - BJARAK 10.000M15.000MEI3.000REAKSI TUMPUANMB =0MA = 0CEK V = 0RA. 25 - 80.15 - 1/2 Q (L - X ) ^2 = 0RB. 25 - 80 . 10 - 70. 15. 17,5 = 01130.000:1130.000RA = 9075.000:363.000KN RB =19175.000:767.000KN 25.00025.000MOMENMX = RA. X X = 0.000M0.000KNMX = 10.000M3630.000KNMLUAS A1 = 1/2 3630.10:18150.000KNM A2 = 2/3 15. 3630:36300.000KNM BATANG B - C JARAK12.000MMOMENMX = 1/8. Q . L^2MMAKS: 1260.000KNM LUAS : A3 = 2/3. 12.1260 = 10080.000BATANG C - D JARAK =8.000MMX =0.000BATANG D -E MX = -P.X MD = -75.000KNM PERSAMAAN 3 MOMEN PADA BENTANG A B C LUAS A1 = 18150.000A2 = 36300.000A3 = 10080.000MA ( L/I ).+ 2MB ( L1/I1 + L2/I2 ) .+MC ( L2/I2 ) : MA = 028.667MB6MC:-9680.000-45375.000-15120.000

REVISI 28.667MB.+6MC: -85032.500..1-85032.500

PERSAMAAN 3 MOMEN PADA BENTANG B -C - DLUAS = A3 = 10080.000MD = -75 KN 6.000MB.+28.000MC .+MD:-15120.0006.000MB.+28.000MC .+-600.000:-15120.0006.000MB.+28.000MC .+:-14520.000.2ELEMINASI PERSAMAAN 1 DAN 2 28.667MB.+6.000MC : -85032.5004.6676.000MB.+28.000MC :-14520.0001.000133.778MB.+28.000MC 0.0000.000: -396818.3336.000MB.+28.000MC 0.0000.000:-14520.000127.778MB.+0.000MC : -382298.333MB = -382298.333:-2991.900KNM127.778 28.667MB.+6MC: -85032.5000.000..16.000MB.+28.000MC .+0.000:-14520.000-85767.800-17951.400MC = 735.300:122.550KNM M C= 3431.400:122.5506.00028.000HASIL MOMEN AKIBAT PERSAMAAN 3 MOMENTMA =0.000MB = -2991.900MC = 245.230MD = -75.000KURVA ELASTIS METODE PERSAMAAN 3 MOMEN MOMENMA = 0.000MB = -2991.900MC = 245.230MD = -75.000BAGIAN A - B PANJANG BATANG 10.000M15.000MJUMLAH PANJANG 25.000MINERSIA =3.000AKIBAT MOMEN -2991.900

LUAS =37398.750

RAKSI TUMPUAN MB = 0RA = O A MA = 0 RB = OB 0A = -4155.417OB = 8310.833AKIBAT BEBAN LUAR

LUAS MOMEN REVISI : A1A2A3A4A5A6A1 = 2400.00044000.00036000.000288750.000180731.25025913.672177261.328A2 = 3600.000A3 = 15750.000JUMLAH = 752656.250 = 10035.417REAKSI TUMPUAN = SUDUT ROTASI A4 = 14175.00075.000MB = 0RA = O A 0.000MA = 0 RB = OB A5 = 2126.2500A = 10035.417OB = -11652.083A6 = 27011.250A1A2A3A4A5A616000.00054000.000105000.000173643.75027242.578498019.922BAGIAN B - CJUMLAH =873906.250 = 11652.08375.000PANJANG BATANG = 12.000MINERSIA = 2.000EI

MOMEN KIRI = 2991.900MOMEN KANAN = 245.230AKIBAT MOMEN KIRIAKIBAT MOMEN KANAN

LUAS = 17951.400LUAS = 1471.380

REAKSI TUMPUAN = SUDUT ROTASI REAKSI TUMPUAN = SUDUT ROTASI MC = 0RB = OB MB = 0RC = OC MC = O RB = OB MB = 0 RC = OC OB = -5983.800OC = 2991.900OB = 245.230OC = -490.460AKIBAT BEBAN LUAR

LUAS MOMENT = A 7 = 10080.000

REAKSI TUMPUAN = SUDUT ROTASI MC = 0RB = OB 0.000MB = 0RC = OC OB = 2520.000OC = -2520.000

BENTANG C - D MOMENT = KIRI = 245.230KANAN = 75.000

MOMEN KIRI = 245.230MOMEN KANAN = 75.000 LUAS = 980.920LUAS = 300.000

REAKSI TUMPUAN = SUDUT ROTASI REAKSI TUMPUAN = SUDUT ROTASI MD = 0 RC = OC MC = 0 RD = OD MD = 0 RC = OC 0.000MC = 0 RD = OD OC = 653.947OD = -326.973OC = -100.000OD = 200.000

HASIL ROTASI

OAB = -4155.417 + 10035.417 = 5880.000OBA = 8310.833 + -11652.083 = -3341.250OBC = -5983.800 + 245.230 + 2520.000 = -3218.570OCB = 2991.900 + -490.460 + -2520.000 = -18.560OCD = 653.947 + -100.000 = 553.947ODC = -326.973 + 200.000 = -126.973

PERSAMAAN 3 MOMEN SULIHAIPERSAMAAN 3 MOMEN 2.2.BJARAK 10.000M15.000M12.000M8.000M1.500MBATANG A - BJARAK 10.000M15.000MEI3.000REAKSI TUMPUANMB =0MA = 0CEK V = 0RA. 25 - 80.15 - 1/2 Q (L - X ) ^2 = 0RB. 25 - 80 . 10 - 70. 15. 17,5 = 01130.000:1130.000RA = 9075.000:363.000KN RB =19175.000:767.000KN 25.00025.000MOMENMX = RA. X MMAKS = 3858.750X = 0.000M0.000KNMREVISIX = 10.000M3630.000KNMA1 = 2400.000A2 = 3600.000A3 = 15750.000LUAS A4 = 14175.000A1 = 1/2 3630.10:18150.000KNM A5 = 2126.250A2 = 2/3 15. 3630:36300.000KNM A6 = 27011.250

BATANG B - C JARAK12.000MMOMENMX = 1/8. Q . L^2MMAKS: 1260.000KNM LUAS : A3 = 2/3. 12.1260 = 10080.000BATANG C - D JARAK =8.000MMX =0.000BATANG D -E MX = -P.X MD = -75.000KNM REVISI

PERSAMAAN 3 MOMEN PADA BENTANG A B C A1 = 2400.000-1280.000A2 = 3600.000-4320.000A3 = 15750.000-8400.000LUAS A1 = 18150.000A4 = 14175.000-13891.500A2 = 36300.000A5 = 2126.250-2179.406A3 = 10080.000A6 = 27011.250-39841.594A7 = 10080.000-15120.000

MA ( L/I ).+ 2MB ( L1/I1 + L2/I2 ) .+MC ( L2/I2 ) : MA = 028.667MB6MC:-9680.000-45375.000-15120.00028.667MB.+6MC: -85032.500..1-85032.500PERSAMAAN 3 MOMEN PADA BENTANG B -C - DLUAS = A3 = 10080.000MD = -75 KN 6.000MB.+28.000MC .+MD:-15120.0006.000MB.+28.000MC .+-600.000:-15120.0006.000MB.+28.000MC .+:-14520.000.2ELEMINASI PERSAMAAN 1 DAN 2 28.667MB.+6.000MC : -85032.5004.6676.000MB.+28.000MC :-14520.0001.000133.778MB.+28.000MC 0.0000.000: -396818.3336.000MB.+28.000MC 0.0000.000:-14520.000127.778MB.+0.000MC : -382298.333MB = -382298.333:-2991.900KNM127.778 28.667MB.+6MC: -85032.5000.000..1-85767.800MC = 735.300:122.550KNM 6.000HASIL MOMEN AKIBAT PERSAMAAN 3 MOMENTMA =0.000MB = -2991.900MC = 122.550MD = -75.000

Sheet2

PERSAMAAN 3 MOMEN REVISI BENTANG A BBEBAN TERPUSATBEBAN TERBAGI RATAMOMEN = RA.X480KNMMB = 0MA = 0LUAS =A1 = 2400RA = 7875: 315KN RB = 735KNA2 = 360025MOMEN = RA . X X = 103150KNMMMAKS = JARAK X MAKS = 10.5M LUAS BIDANG MOMEN MMAKS = 3858.75KNMA3 = 15750A4 = 14175A5 = 2126.25A6 = 27011.25A7 = 10080PERSAMAAN 3 MOMEN PADA BENTANG A - B - CLUAS = A1 = 2400A2 = 3600A3 = 15750A4 = 14175A5 = 2126.25A6 = 27011.252MB(25/3 + 12/2 ).+MC (12/2)-1280-4320-8400-13891.5-2179.40625-39841.59375-1512028.6666666667MB.+6MC:-85032.5