ANALISIS STRUKTUR JEMBATAN BAB IV PERENCANAAN ABUTMENT (PANGKAL JEMBATAN) 4.1 Data Beban (dari hitungan terdahulu) Beban Mati QD = 5,6273 + 13,8590 = 19,4863 ton Beban Hidup QH = 12.9500 + 11.0989 = 24,0489 ton 4.2 Data Lokasi dan Rencana Abutment Data lokasi dapat dilihat pada gambar 4.1. Ketentuan abutment sebagai berikut : a. Tipe Abutmen = Cantilever Retaining Wall (CRW) tanpa angkur dan counterfort. b. Tinggi Abutment = 7 m c. Pondasi = sumuran d. f’c = 25 MPa e. fy = 390 MPa f. γ beton = 2,4 t/m3 g. kedalaman muka air tanah = -3,0 m Gambar 4.1 Topografi dan Rencana Abutment 27 PERENCANAAN ABUTMENT ANALISIS STRUKTUR JEMBATAN 4.3 Analisi Data Tanah Koefisien tanah aktif (tekanan tanah pasif diabaikan) Ka = tan2 (45o – ϕ/2) = tan2 (45o – 30o/2) = 1/3 Data karakteristik tanah a. γ tanah = 1,90 ton/m3 b. Sudut gesek tanah = 30o c. Kadar air ( w ) = 0,25 d. Angka pori ( n ) = 0,43 Berat Jenis tanah adalah sbb : γk = γs (1 - n) = 1,90 (1 - 0,43) = 1,0830 t/m3 γb = γk (1 + w) = 1,0830 (1 + 0,25) = 1,3538 t/m3 γsat = γk + n = 1,0830 + 0,43 = 1,5130 t/m3 γ’ = γsat - 1 = 1,5130 - 1 = 0,5130 t/m3 4.4 Analisa Mekanika Gambar 4.2 Diagram tekanan tanah aktif dan pembebanan abutment 28 PERENCANAAN ABUTMENT ANALISIS STRUKTUR JEMBATAN h = 7 m h1 = 3 m h2 = 4 m γk γb γsat γ’ P = 4,36364 t Q = 0,8000 t/m2 = = = = 1,0830 1,3538 1,5130 0,5130 t/m3 t/m3 t/m3 t/m3 h’ = l tan (45o +ϕ/2) – l tan ϕ = 2,5 tan (45 o +30 o/2) – 2,5 tan 30 o = 4,33 – 1,44 = 2,89 Tekanan tanah aktif Ea1 = h q Ka Ea4 = ½ h22 γw Ea2 = ½ h12 γb Ka Ea5 = ½ h22 γ’ Ka Ea3 = h1 h2 γb Ka Ea6 = ½ P K a h’ Tabel 4.1 Perhitungan Gaya Horisontal (Ea) dan Momen (t-m), ditinjau untuk tiap 1 m h b Akibat beban merata 1 7 0,8000 2 3 4,0614 3 4 4,0614 4 4 4,0000 5 4 2,0520 Akibat baban titik 6 2,89 2,5193 H (ton) Ka 1/3 1/3 1/3 1/3 ke A (m) Momen (t-m) b h Ka ½ b h Ka b h Ka ½bh ½ b h Ka 1,8667 2,0307 5,4152 8,0000 1,3680 3,5000 5,0000 2,0000 1,3333 1,3333 6,5334 10,1535 10,8304 10,6664 1,8240 ½bh 3,6404 22,3210 4,5967 16,7338 56,7415 Tabel 4.2 Perhitungan Gaya vertikal dan Momen (t-m) Abutment 1 2 3 4 5 h 0,3 1,1 1,6 4,8 0,8 b 0,5 0,8 0,8 0,8 6,0 ΣA= Titik berat abutment, A (m2) 0,15 0,88 0,64 3,84 4,80 10,31 x = 2,881 m y = 2,317 m Berat abutment = 10,31 × 1,0 × 2,4 = 24,7440 ton Momen terhadap pusat dasar abutment = 24,7440 × ( 3,0 – 2,881 ) = 2,9445 t-m 29 PERENCANAAN ABUTMENT ANALISIS STRUKTUR JEMBATAN Tanah pengisi a b c d e f Berat (ton) 1,8 × 0,3 × 1,0 × 1,90 = 1,0260 0,3 × 0,3 × 1,0 × 1,90 = 0,1710 1,8 × 1,1 × 1,0 × 1,90 = 3,7620 1,8 × 1,6 × 1,0 × 1,90 = 5,7420 ½ 0,8 × 1,6 × 1,0 × 1,90 = 1,2160 2,6 × 3,2 × 1,0 × 0,5130 = 4,2682 = 16,1852 Lengan (m) Momen (t-m) 2,10 2,1546 1,05 0,1796 2,10 7,9002 2,10 11,4912 0,93 1,1309 1,70 7,2559 30,1121 A. Kontrol Tegangan tanah Kontrol tegangan tanah di dasar abutment sebelum jembatan dipasang V = 24,7440 + 16,1852 = 40,9292 ton M = - 2,9445 - 30,1121 + 56,7415 = 23,6849 t-m A = 6 × 1 = 6 m2 W = 1/6 × 1,0 × 62 = 6 m3 σ = V M ± A W σ maks = 40,9292 23,6849 + = 10,7690 t/m2 6 6 σ min = 40,9292 23,6849 − = 2,8741 t/m2 6 6 Kontrol tegangan-tegangan tanah di dasar abutment setelah jembatan dipasang Kombinasi 1 (100% qa) Jarak titik berat beban mati dan beban hidup terhadap titik berat tumpuan = 3,0-2,881 = 0,119 m Beban Mati Hidup Abutment Tanah pengisi Tekanan tanah aktif V (ton) 19,4863 24,0489 24,7440 16,1852 84,4644 σ maks = M (t-m) 2,3187 2,8618 - 2,9445 - 30,1121 56,7415 28,1909 84,4644 28,1909 + = 18,7759 t/m2 6 6 30 PERENCANAAN ABUTMENT ANALISIS STRUKTUR JEMBATAN σ min = 84,4644 28,1909 − = 9,3789 t/m2 6 6 di dasar sumuran, Berat jenis beton siklop = 2,2 t/m3 σ maks = 84,4644 5,6 × 0,6 × 6 × 0,5130 ((6 × 1) − (5,6 × 0,6)) × 6 × 2,2 + + 6 6 6 σ maks = 14,0774 + 1,7237 + 5,8080 = 21,6091 t/m2 < qa = 2,25 kg/cm2 (22,5 t/m2) Kombinasi 2 (125% qa) Jarak titik berat beban mati dan beban hidup terhadap titik berat tumpuan = 3,0-2,881 = 0,119 m gaya memanjang karena gesekan tumpuan = 0,25 × M = 0,25 × 19,4863 = 4,8716 ton Momen = 4,8716 × 0,119 = 0,5797 tm Beban Mati Abutment Tanah pengisi Tekanan tanah aktif F V (ton) 19,4863 24,7440 16,1852 60,4155 M (t-m) 2,3187 - 2,9445 - 30,1121 56,7415 0,5797 26,5833 σ maks = 60,4155 26,5833 + = 14,4998 t/m2 6 6 σ min = 60,4155 26,5833 − = 5,6387 t/m2 6 6 didasar sumuran, Berat jenis siklop = 2,2 t/m3 σ maks = 60,4155 5,6 × 0,6 × 6 × 0,5130 ((6 × 1) − (5,6 × 0,6)) × 6 × 2,2 + + 6 6 6 σ maks = 10,0693 + 1,7237 + 5,8080 = 17,6010 t/m2 < 1,25 qa = 2,8125 kg/cm2 (28,125 t/m2) B. Kontrol Stabilitas terhadap Penggulingan Momen yang menggulingkan = 56,7415 + 0,5797 = 57,3212 tm Momen yang menahan guling (titik penggulingan pada tepi luar) a. b. c. d. Abutment Tanah pengisi Mati Hidup = 24,7440 × (6 – 2,881) = = 19,4863 × 3 24,0489 × 3 = = = = = 77,1765 30,1121 58,4589 72,1467 237,8942 tm tm tm tm tm 31 PERENCANAAN ABUTMENT ANALISIS STRUKTUR JEMBATAN Angka keamanan terhadap penggulingan, n = 237,8942 = 4,15 > 1,5 O K 57,3212 C. Kontrol Stabilitas terhadap Penggeseran Gaya geser = 22,3210 ton Gaya geser penahan = Σ V tan ϕ (diasumsikan ϕ = 30o) = (24,7440 + 16,1852 ) tan 30o = 23,6305 ton Angka keamanan terhadap penggeseran, n = 23,6305 = 1,06 22,3210 4.5 Penulangan Abutment A. Penulangan Titik I Tabel 4.3 Perhitungan Gaya Horisontal (Ea) dan Momen (t-m), ditinjau untuk tiap 1 m thd ttk I h b Akibat beban merata 1 6,2 0,8000 2 3 4,0614 3 3,2 4,0614 4 3,2 4,0000 5 3,2 2,0520 Akibat baban titik 6 2,89 2,5193 H (ton) Ka 1/3 1/3 1/3 1/3 ke I (m) Momen (t-m) b h Ka ½ b h Ka b h Ka ½bh ½ b h Ka 1,6533 2,0307 4,3322 6,4000 1,0944 3,1000 4,2000 1,6000 1,0667 1,0667 5,1252 8,5289 6,9315 6,8269 1,1674 ½bh 3,6404 3,7967 13,8215 42,4014 Perhitungan baja tulangan M h d k ρb ρmaks ρmin = 424,0140 KNm = 800 mm = 740 mm = 0,9679 MPa = 0,028069 = 0,02105175 = 3,5897 × 10-3 ρperlu Asperlu Tulangan pokok Asterpakai Tulangan bagi = = = = = 2,5410 × 10-3 2656,3780 mm2 ∅16-75 2800,8253 ∅16-250 32 PERENCANAAN ABUTMENT ANALISIS STRUKTUR JEMBATAN B. Penulangan Titik J Tabel 4.4 Perhitungan Gaya Horisontal (Ea) dan Momen (t-m), ditinjau untuk tiap 1 m thd ttk J h b Akibat beban merata 1 3,0 0,8000 2 3,0 4,0614 Akibat baban titik 6a 1,56 1,3599 6b 1,56 1,1594 H ke J (m) b h Ka ½ b h Ka 0,8 2,0307 1,5000 1,0000 1,2000 2,0307 ½bh bh 1,0607 1,8087 1,04 0,78 1,1031 1,4108 5,7446 Ka 1/3 1/3 Momen (tm) Perhitungan baja tulangan M h d k ρb ρmaks ρmin = 57,4460 KNm = 800 mm = 740 mm = 0,1311 MPa = 0,028069 = 0,02105175 = 3,5897 × 10-3 ρperlu Asperlu Tulangan pokok Asterpakai Tulangan bagi = = = = = 3,3720 × 10-3 2656,3780 mm2 ∅16-75 2800,8253 ∅16-250 C. Penulangan Titik K Tabel 4.5 Perhitungan Gaya Horisontal (Ea) dan Momen (t-m), ditinjau untuk tiap 1 m thd ttk K h b Akibat beban merata 1 1,4 0,8000 2 1,4 4,0614 Ka 1/3 1/3 b h Ka ½ b h Ka H ke J (m) 0,3733 0,9477 0,7000 0,4667 Momen (tm) 0,2613 0,4423 0,7036 Perhitungan baja tulangan M h d k ρb ρmaks ρmin = 7,0360 KNm = 500 mm = 440 mm = 0,0454 MPa = 0,028069 = 0,02105175 = 3,5897 × 10-3 ρperlu Asperlu Tulangan pokok Asterpakai Tulangan bagi = = = = = 1,1653 × 10-4 1579,4680 mm2 ∅16-125 1680,4952 ∅16-250 33 PERENCANAAN ABUTMENT ANALISIS STRUKTUR JEMBATAN D. Penulangan Dasar Abutment 2,6 m 0,8 m y2 2,6 m y1 9,3789 y1 = 9,3789 + 3,4 9,3970 = 14,7039 t/m2 6 y 2 = 9,3789 + 2,6 9,3970 = 13,4509 t/m2 6 18,7759 bagian depan dinding 2,6 ⎞ ⎛ 1 2 × 2,6 ⎞ ⎛ M maks = ⎜14,7039 × 1,0 × 2,6 × ⎟ + ⎜ × (18,7759 − 14,7039 ) × 1,0 × 2,6 × ⎟ 2 ⎠ ⎝2 3 ⎠ ⎝ = 49,6992 + 9,1756 = 58,8748 tm Perhitungan baja tulangan M h d k ρb ρmaks ρmin = = = = = = = 588,7480 KNm 800 mm 740 mm 1,3439 MPa 0,028069 0,02105175 3,5897 × 10-3 ρperlu Asperlu Tulangan pokok Asterpakai Tulangan bagi = = = = = 3,5623 × 10-3 2656,3780 mm2 ∅16-75 2800,8253 ∅16-250 bagian belakang dinding 1.momen akibat tanah pengisi a b c d e f Berat (ton) 1,8 × 0,3 × 1,0 × 1,90 = 1,0260 0,3 × 0,3 × 1,0 × 1,90 = 0,1710 1,8 × 1,1 × 1,0 × 1,90 = 3,7620 1,8 × 1,6 × 1,0 × 1,90 = 5,7420 ½ 0,8 × 1,6 × 1,0 × 1,90 = 1,2160 2,6 × 3,2 × 1,0 × 0,5130 = 4,2682 = 16,1852 Lengan (m) Momen (t-m) 1,70 1,7442 0,65 0,1112 1,70 6,3954 1,70 9,7614 0,5333 0,6485 1,30 5,5487 24,2094 2. momen akibat berat abutment = 24,7440 × ( 2,881 – 2,6 ) = 6,9531 t-m 34 PERENCANAAN ABUTMENT ANALISIS STRUKTUR JEMBATAN 3. momen akibat tekanan tanah h b Akibat beban merata 1 6,2 0,8000 2 3 4,0614 3 3,2 4,0614 4 3,2 4,0000 5 3,2 2,0520 Akibat baban titik 6 2,89 2,5193 H (ton) Ka 1/3 1/3 1/3 1/3 ke I (m) Momen (t-m) b h Ka ½ b h Ka b h Ka ½bh ½ b h Ka 1,6533 2,0307 4,3322 6,4000 1,0944 3,1000 4,2000 1,6000 1,0667 1,0667 5,1252 8,5289 6,9315 6,8269 1,1674 ½bh 3,6404 3,7967 13,8215 42,4014 Momen total = 42,4014 – (24,2094 + 6,9531) = 11,2389 tm Perhitungan baja tulangan = = = = = = = M h d k ρb ρmaks ρmin 112,3890 KNm 800 mm 740 mm 0,2565 MPa 0,028069 0,02105175 3,5897 × 10-3 ρperlu Asperlu Tulangan pokok Asterpakai Tulangan bagi = = = = = 6,6171 × 10-4 2656,3780 mm2 ∅16-75 2800,8253 ∅16-250 E. Penulangan Sayap Bentuk garis leleh disederhanakan sebagai berikut : A B im 6,2 m E m b im C D 2,6 m 35 PERENCANAAN ABUTMENT ANALISIS STRUKTUR JEMBATAN Perhitungan Gaya Horisontal (Ea) dan Momen (t-m), ditinjau untuk tiap 1 m h b Akibat beban merata 1 6,2 0,8000 2 3 4,0614 3 3,2 4,0614 4 3,2 4,0000 5 3,2 2,0520 Akibat baban titik 6 2,89 2,5193 H (ton) Ka 1/3 1/3 1/3 1/3 ke I (m) Momen (t-m) b h Ka ½ b h Ka b h Ka ½bh ½ b h Ka 1,6533 2,0307 4,3322 6,4000 1,0944 3,1000 4,2000 1,6000 1,0667 1,0667 5,1252 8,5289 6,9315 6,8269 1,1674 ½bh 3,6404 3,7967 13,8215 42,4014 im = m ρ min = 1,4 1,4 = = 3,5897 × 10 −3 f y 390 As = ρ x b x d = 3,5897 x10-3 x 1000 x 140 = 502,558 mm2 a= As × f y 0,85 × f × b ' c = 502,558 × 390 = 9,2 mm 0,85 × 25 × 1000 mu = φ × As × f y (d − a2 ) = 0,8 × 502,558 × 390 × (140 − 92, 2 ) × 10 −6 = 21,2305 KNm Bagian CDE (im + m ) × 2,6 = qu ( 12 × 2,6 × b ) × b3 qu = 254,766 b2 1) Bagian ABCE (im + m ) × 6,2 = qu ( 12 × 2,6 × b ) × 23,6 + qu ((6,2 − b ) × 2,6) × 22,6 qu = 1579,5492 125,736 − 13,52b 2) 1) = 2) 254,766 1579,5492 = 2 125,736 − 13,52b b 1579,5492b 2 + 3444,4363b − 32033,2578 = 0 b = 3,5431 m 36 PERENCANAAN ABUTMENT ANALISIS STRUKTUR JEMBATAN qu = 254,766 = 20,2943 KN/m 3,54312 Arah CD m = 20,2943 × ( 12 × 2,6 × 3,5431) × 3,5431 = 110,3985 KNm (untuk lebar plat 2,6 m) 3 M = 110,3985 KNm h = 200 mm d = 200 - 60 = 140 mm M 110,3985 × 10 6 k= = = 2,7080 MPa φ × b × d 2 0,8 × 2600 × 140 2 ρ b = 0,85 f c' × β1 × fy 0,003 0,003 + fy = 0,85 25 × 0,85 × 390 Es 0,003 = 0,028069 390 0,003 + 200000 ρmaks = 0,75 ρb = 0,75 x 0,028069 = 0,02105175 ρ perlu = 0,85 ρ min = f c' fy ⎛ 2k ⎜1 − 1 − ⎜ 0,85 f c' ⎝ ⎞ 25 ⎛ 2 × 2,7080 ⎞ ⎟ = 0,85 ⎟ = 7,4534 × 10 −3 ⎜1 − 1 − ⎜ ⎟ 390 ⎝ 0,85 × 25 ⎟⎠ ⎠ 1,4 1,4 = = 3,5897 × 10 −3 f y 390 As = ρ x b x d = 7,4534 x10-3 x 2600 x 140 = 2713,0376 mm2 Dipakai tulangan ∅16 (As = 210,0619 mm2), dengan jarak antar tulangan s perlu = 210,0619 × 2600 = 201,3098 mm 2713,0376 dipakai tulangan ∅16-200 mm As = 210,0619 × 2600 = 2730,8047 mm2 200 tulangan bagi = 20 % × 2730,8407 = 546,1609 mm2 dipakai tulangan ∅16-250 mm Arah AC m = qu ( 12 × 2,6 × b ) × 23,6 + qu ((6,2 − b ) × 2,6) × 22,6 = 263,2617 KNm (untuk lebar plat 6,2 m) M = 263,2617 KNm h = 200 mm k= d = 200 - 60 = 140 mm M 263,2617 × 10 6 = = 2,7080 MPa φ × b × d 2 0,8 × 6200 × 140 2 37 PERENCANAAN ABUTMENT ANALISIS STRUKTUR JEMBATAN ρ b = 0,85 f c' × β1 × fy 0,003 0,003 + fy = 0,85 25 × 0,85 × 390 Es 0,003 = 0,028069 390 0,003 + 200000 ρmaks = 0,75 ρb = 0,75 x 0,028069 = 0,02105175 ρ perlu = 0,85 ρ min = f c' fy ⎛ 2k ⎜1 − 1 − ⎜ 0,85 f c' ⎝ ⎞ 25 ⎛ 2 × 2,7080 ⎞ ⎟ = 0,85 ⎜1 − 1 − ⎟ = 7,4534 × 10 −3 ⎜ ⎟ 390 ⎝ 0,85 × 25 ⎟⎠ ⎠ 1,4 1,4 = = 3,5897 × 10 −3 f y 390 As = ρ x b x d = 7,4534 x10-3 x 6200 x 140 = 6469,5512 mm2 Dipakai tulangan ∅16 (As = 210,0619 mm2), dengan jarak antar tulangan s perlu = 210,0619 × 6200 = 201,3098 mm 6469,5512 dipakai tulangan ∅16-200 mm As = 210,0619 × 6200 = 6511,9189 mm2 200 tulangan bagi = 20 % × 6511,9189 = 1302,3838 mm2 dipakai tulangan ∅16-250 mm Tabel 4.6. Penulangan Abutment No. 1 2 3 4 5 Elemen struktur Dinding (titik I) (titik J) Parapet (titik K) Dasar abutment Bagian depan dinding Bagian belakang dinding Sayap Tulangan pokok ∅16-75 ∅16-75 ∅16-125 bagi ∅16-250 ∅16-250 ∅16-250 ∅16-75 ∅16-75 ∅16-200 ∅16-250 ∅16-250 ∅16-250 38 PERENCANAAN ABUTMENT