Contoh Perhitungan Penulangan Tie Beam [PDF]

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PERENCANAAN TIE BEAM Data-data perencanaan tie beam       



Penampang balok tie beam arah x 35/70 Penampang balok tie beam arah y 45/80 Spesifikasi tulang longitudinal: fy=400MPa Spesifikasi tulangan transversal: fy=400Mpa Mutu beton: f’c = 35 MPa Berat jenis beton = 24 kN/m3 Tebal selimut beton = 75 mm [SNI 2847:2013 pasal 7.7.1]



Check dimensi tie-beam: Dimensi terkecil harus lebih besar atau sama dengan jarak bersih antara kolom yang diikat dibagi 20 tetapi tidak boleh melebihi 450 mm. [ACI 318-14 18.13.3.2] Jarak bersih antara kolom dibagi 20: 7000𝑚𝑚−800𝑚𝑚 20 8000𝑚𝑚−800𝑚𝑚 20



= 310 𝑚𝑚 ≤ 350𝑚𝑚 ≤ 450𝑚𝑚 (𝑂𝐾) = 360 𝑚𝑚 ≤ 450𝑚𝑚 ≤ 450𝑚𝑚 (𝑂𝐾)



Pembebanan pada Tie Beam  Beban Mati 1. Berat sendiri balok : qx = (0,7-0,125) × 0,35 × 2400 kg/m3 = 483 kg/m qy = (0,8-0,125) × 0,45 × 2400 kg/m3 = 729 kg/m 2. Berat pasangan dinding : qx = 250 kg/m2 × (3.5 - 0,7) = 700 kg/m qy = 250 kg/m2 × (3.5 - 0,8) = 675 kg/m 3. Beban pelat : a. Bagian tepi qx1 = 387 kg/m2 × 6m/2 × 1 = 1161 kg/m qx2 = 387 kg/m2 × 7m/2 × 1 = 1354,5 kg/m qy = 387 kg/m2 × 4m/2 × 1 = 774 kg/m b. Bagian tengah qx1 = 387 kg/m2 × 6m/2 × 2 = 2322 kg/m qx2 = 387 kg/m2 × 7m/2 × 2 = 2709 kg/m qy = 387 kg/m2 × 4m/2 × 2 = 1548 kg/m



4. Berat tangga : As B : Beban merata = 2530,025 kg/m Beban terpusat = 5072,5 kg/m  Beban Hidup Fungsi ruang parkiran = 200 kg/m2 (SNI 1727 : 2013 Tabel 4.1 halaman 26) 1. Beban pelat lantai : a. Bagian tepi qx1 = 200 kg/m2 × 6m/2 × 1 = 600 kg/m qx2 = 200 kg/m2 × 7m/2 × 1 = 700 kg/m qy = 200 kg/m2 × 4m/2 × 1 = 400 kg/m b. Bagian tengah qx1 = 200 kg/m2 × 6m/2 × 2 = 1200 kg/m qx2 = 200 kg/m2 × 7m/2 × 2 = 1400 kg/m qy = 200 kg/m2 × 4m/2 × 2 = 800 kg/m 2. Berat tangga : As B : Beban merata = 996,75 kg/m Beban terpusat = 1993,5 kg/m Kombinasi Beban 1. 1,4 DL 2. 1,2 DL + 1,6 LL 3. 1,3214 DL + 1 LL + 3 Eqx + 0,9 Eqy 4. 1,3214 DL + 1 LL + 3 Eqx – 0,9 Eqy 5. 1,3214 DL + 1 LL – 3 Eqx + 0,9 Eqy 6. 1,3214 DL + 1 LL – 3 Eqx – 0,9 Eqy 7. 1,3214 DL + 1 LL + 0,9 Eqx + 3 Eqy 8. 1,3214 DL + 1 LL – 0,9 Eqx + 3 Eqy 9. 1,3214 DL + 1 LL + 0,9 Eqx – 3 Eqy 10. 1,3214 DL + 1 LL – 0,9 Eqx – 3 Eqy 11. 0,7786 DL + 3 Eqx + 0,9 Eqy 12. 0,7786 DL + 3 Eqx – 0,9 Eqy 13. 0,7786 DL – 3 Eqx + 0,9 Eqy 14. 0,7786 DL – 3 Eqx – 0,9 Eqy 15. 0,7786 DL + 0,9 Eqx + 3 Eqy 16. 0,7786 DL – 0,9 Eqx + 3 Eqy 17. 0,7786 DL + 0,9 Eqx – 3 Eqy 18. 0,7786 DL – 0,9 Eqx – 3 Eqy



Pemodelan Tie Beam Akibat Beban Mati:



Member



Mz.i [KN-m]



Mz.pos [KN-m]



Mz.j [KN-m]



Fy.i [KN]



Fy.j [KN]



1 2 3 4 5 6 7 8 9 10 11



-36.7535 -72.4706 -95.8457 -81.4785 -81.1374 36.7535 -8.6668 14.3671 -14.3671 8.6668 -36.7535



50.9268 31.9524 61.7261 31.9524 50.9268 36.7535 4.3334 14.3671 7.1836 8.6668 18.3767



-81.1374 -81.4785 -95.8457 -72.4706 -36.7535 -18.3768 4.3334 -7.1836 7.1836 -4.3334 18.3768



58.3807 64.2767 80.731 67.2793 73.1753 -13.7826 3.2501 -5.3877 5.3877 -3.2501 13.7826



-73.1753 -67.2793 -80.731 -64.2767 -58.3807 -13.7826 3.2501 -5.3877 5.3877 -3.2501 13.7826



Akibat Beban Hidup:



Member



Mz.i [KN-m]



Mz.pos [KN-m]



Mz.j [KN-m]



Fy.i [KN]



Fy.j [KN]



1 2 3 4 5 6 7 8 9 10 11



-14.0392 -26.9875 -39.5905 -32.5135 -30.5674 14.0392 -3.58 7.0769 -7.0769 3.58 -14.0392



21.008 13.3595 28.8666 13.3595 21.008 14.0392 1.79 7.0769 3.5385 3.58 7.0196



-30.5674 -32.5135 -39.5905 -26.9875 -14.0392 -7.0196 1.79 -3.5385 3.5385 -1.79 7.0196



18.8003 20.634 29.3387 22.476 24.3097 -5.2647 1.3425 -2.6538 2.6538 -1.3425 5.2647



-24.3097 -22.476 -29.3387 -20.634 -18.8003 -5.2647 1.3425 -2.6538 2.6538 -1.3425 5.2647



Akibat Beban Gempa Kuat (ke kanan):



Member 1 2 3 4 5



Mz.i [KNm] 862.6438 394.011 482.7196 478.5919 586.0369



Mz.pos [KN-m] 862.6438 394.011 482.7196 478.5919 586.0369



Mz.j [KNm] -586.037 -478.592 -482.72 -394.011 -862.644



Fy.i [KN] -241.447 -145.434 -137.92 -145.434 -241.447



Fy.j [KN] -241.447 -145.434 -137.92 -145.434 -241.447



Akibat Beban Gempa Kuat (ke kiri):



Member 1 2 3 4 5



Mz.i



[KNm] -862.644 -394.011 -482.72 -478.592 -586.037



Mz.pos [KN-m]



Mz.j [KN-m]



586.0369 478.5919 482.7196 394.011 862.6439



586.0369 478.5919 482.7196 394.011 862.6438



Fy.i [KN] 241.4468 145.4338 137.9199 145.4338 241.4468



Fy.j [KN] 241.4468 145.4338 137.9199 145.4338 241.4468



Desain Tie Beam Desain Penulangan Tie Beam Semua pengikat harus memiliki kuat tarik/tekan desain sebesar 10 persen SDS kali beban mati terfaktor ditambah beban hidup terfaktor pur tiang atau kolom yang lebih besar. [SNI 1726-2012 Pasal 7.13.6.2] Nu kolom = 7030,68kN dan SDS = 0,607 10% 𝑁𝑢 𝑆𝐷𝑆 = 0,1 ∙ 7030,68 ∙ 0,607 = 426,7623 𝑘𝑁 𝐴𝑔 𝑓′𝑐 350 ∙ 700 ∙ 35 = = 857500 𝑁 = 857,5 𝑘𝑁 > 10% 𝑁𝑢 𝑆𝐷𝑆 (𝑂𝐾) 10 10 Gaya Dalam Tie Beam: Balok B36



Tumpuan Tumpuan Kiri Kiri + 655,874



B45



595,6299



184,3849



Lapangan -



Lapangan



Tumpuan Kanan



Tumpuan Kanan



473,506



244,358



Momen Lentur (kNm) 276,1252 135,7248 Gaya Lintang (kN) 45,099



103,4422



Tulangan Lentur (B36) Berdasarkan SNI 2847 : 2013 Pasal 21.5.2.1 𝐴𝑠 𝑚𝑖𝑛 =



1,4 1,4 𝑏𝑤 𝑑 = 450 ∙ 699,5 = 1101,7125 𝑚𝑚2 (𝑑𝑖𝑔𝑢𝑛𝑎𝑘𝑎𝑛) 𝑓𝑦 400



𝐴𝑠 𝑚𝑖𝑛 =



√𝑓′𝑐 √30 𝑏𝑤 𝑑 = 450 ∙ 699,5 = 1077,5586 𝑚𝑚2 4𝑓𝑦 4 ∙ 400



𝐴𝑠 𝑚𝑎𝑘𝑠 = 0,025 ∙ 𝑏𝑤 𝑑 = 0,025 ∙ 450 ∙ 699,5 = 7869,375  Tumpuan Kiri (tulangan atas / momen negatif) Mu = -655,874kNm 𝑀𝑢 655,874 ∙ 106 = = 2893,9278 𝑚𝑚2 0,9𝑓𝑦 0,9𝑑 0,9 ∙ 400 ∙ 0,9 ∙ 699.5 𝐴𝑠 𝑓𝑦 2893,9278 ∙ 400 𝑎= = = 100,8777 𝑚𝑚 0,85𝑓′𝑐 𝑏𝑤 0.85 ∙ 30 ∙ 450 𝑀𝑢 655,874 ∙ 106 𝐴𝑠 = = 2806,9347 𝑚𝑚2 𝑎 = 100,8777 0,9𝑓𝑦 (𝑑 − 2) 0,9 ∙ 400 (699.5 − ) 2 Digunakan tulangan 6D25 → As = 2945,2431 mm2 𝐴𝑠 =







Tumpuan Kiri (tulangan bawah / momen positif)



Mu = 595,6299kNm 𝑀𝑢 595,6299 ∙ 106 𝐴𝑠 = = = 2628,1113 𝑚𝑚2 0,9𝑓𝑦 0,9𝑑 0,9 ∙ 400 ∙ 0,9 ∙ 699.5 𝐴𝑠 𝑓𝑦 2628,1113 ∙ 400 𝑎= = = 91,6117 𝑚𝑚 0,85𝑓′𝑐 𝑏𝑤 0.85 ∙ 30 ∙ 450 𝑀𝑢 595,6299 ∙ 106 𝐴𝑠 = = 2531,0423 𝑚𝑚2 𝑎 = 91,6117 0,9𝑓𝑦 (𝑑 − 2) 0,9 ∙ 400 (699.5 − ) 2 Digunakan tulangan 6D25 → As = 2945,2431 mm2 



Lapangan (tulangan atas / momen negatif)



Mu = -276,1252 kNm 𝑀𝑢 276,1252 ∙ 106 = = 1218,3535 𝑚𝑚2 0,9𝑓𝑦 0,9𝑑 0,9 ∙ 400 ∙ 0,9 ∙ 699.5 𝐴𝑠 𝑓𝑦 1218,3535 ∙ 400 𝑎= = = 42,4698 𝑚𝑚 0,85𝑓′𝑐 𝑏𝑤 0.85 ∙ 30 ∙ 450 𝑀𝑢 276,1252 ∙ 106 𝐴𝑠 = = = 1114,4659 𝑚𝑚2 𝑎 42,4698 0,9𝑓𝑦 (𝑑 − ) 0,9 ∙ 400 (699.5 − ) 2 2 2 Digunakan tulangan 3D25 → As =1472,6216 mm 𝐴𝑠 =







Lapangan (tulangan bawah / momen positif)



Mu = 135,7248 kNm 𝑀𝑢 135,7248 ∙ 106 𝐴𝑠 = = = 598,8616 𝑚𝑚2 0,9𝑓𝑦 0,9𝑑 0,9 ∙ 400 ∙ 0,9 ∙ 699.5 𝐴𝑠 𝑓𝑦 598,8616 ∙ 400 𝑎= = = 20,8754 𝑚𝑚 0,85𝑓′𝑐 𝑏𝑤 0.85 ∙ 30 ∙ 450 𝑀𝑢 135,7248 ∙ 106 𝐴𝑠 = = 547,1397 𝑚𝑚2 𝑎 = 20,8754 0,9𝑓𝑦 (𝑑 − 2) 0,9 ∙ 400 (699.5 − 2 ) 𝐷𝑖𝑔𝑢𝑛𝑎𝑘𝑎𝑛 𝐴𝑠 𝑚𝑖𝑛 = 1101,7125 𝑚𝑚2 Digunakan tulangan 3D25 → As =1472,6216 mm2







Tumpuan Kanan (tulangan atas / momen negatif)



Mu = -473,506 kNm 𝑀𝑢 473,506 ∙ 106 𝐴𝑠 = = = 2089,2613 𝑚𝑚2 0,9𝑓𝑦 0,9𝑑 0,9 ∙ 400 ∙ 0,9 ∙ 699.5 𝐴𝑠 𝑓𝑦 2089,2613 ∙ 400 𝑎= = = 72,8283 𝑚𝑚 0,85𝑓′𝑐 𝑏𝑤 0.85 ∙ 30 ∙ 450 𝑀𝑢 473,506 ∙ 106 𝐴𝑠 = = 1983,596 𝑚𝑚2 𝑎 = 72,8283 0,9𝑓𝑦 (𝑑 − 2) 0,9 ∙ 400 (699.5 − 2 ) Digunakan tulangan 5D25 → As =2454,3693 mm2 



Tumpuan Kanan (tulangan bawah / momen positif)



Mu = 244,358 kNm 𝑀𝑢 244,358 ∙ 106 = = 1078,1864 𝑚𝑚2 0,9𝑓𝑦 0,9𝑑 0,9 ∙ 400 ∙ 0,9 ∙ 699.5 𝐴𝑠 𝑓𝑦 1078,1864 ∙ 400 𝑎= = = 37,5838 𝑚𝑚 0,85𝑓′𝑐 𝑏𝑤 0.85 ∙ 30 ∙ 450 𝑀𝑢 244,358 ∙ 106 𝐴𝑠 = = = 997,1561 𝑚𝑚2 𝑎 37,5838 0,9𝑓𝑦 (𝑑 − ) 0,9 ∙ 400 (699.5 − ) 2 2 𝐷𝑖𝑔𝑢𝑛𝑎𝑘𝑎𝑛 𝐴𝑠 𝑚𝑖𝑛 = 1101,7125 𝑚𝑚2 Digunakan tulangan 3D25 → As =1472,6216 mm2 𝐴𝑠 =



Tulangan Geser (B45) Berdasarkan SNI 2847:2013 pasal 11.4.6.3 𝑏𝑤 𝑠 𝐴𝑣 𝑚𝑖𝑛 350 𝑚𝑚2 ′ 𝐴𝑣 𝑚𝑖𝑛 = 0,062√𝑓 𝑐 → = 0,062√30 = 0,2971 𝑓𝑦𝑡 𝑠 400 𝑚𝑚′ 𝑏𝑤 𝑠 𝐴𝑣 𝑚𝑖𝑛 350 𝑚𝑚2 𝐴𝑣 𝑚𝑖𝑛 = 0,35 → = 0,35 = 0,3063 (𝑑𝑖𝑝𝑎𝑘𝑎𝑖) 𝑓𝑦𝑡 𝑠 400 𝑚𝑚′



𝑉𝑐 = 0.17𝜆√𝑓′𝑐 𝑏𝑤 𝑑 = 0.17√30 ∙ 350 ∙ 599.5 ∙ 10−3 = 195,374 𝑘𝑁 



Tumpuan Kiri Vu = 184,3849 kN 𝑉𝑢 𝑉𝑐 < = 245,8465 𝑘𝑁(𝑑𝑖𝑏𝑢𝑡𝑢ℎ𝑘𝑎𝑛 𝑡𝑢𝑙𝑎𝑛𝑔𝑎𝑛 𝑔𝑒𝑠𝑒𝑟) 0,75 𝑉𝑢 184,3849 𝑉𝑠 ≥ − 𝑉𝑐 = − 195,374 = 50,4726 𝑘𝑁 𝜙 0,75



𝐴𝑣 𝑓𝑦𝑡 𝑑 𝐴𝑣 𝑉𝑠 50,4726 ∙ 103 𝑚𝑚2 𝑉𝑠 = → = = = 0,2105 𝑠 𝑠 𝑓𝑦𝑡 𝑑 400 ∙ 599,5 𝑚𝑚′ 𝐴𝑣 𝑚𝑚2 𝑑𝑖𝑔𝑢𝑛𝑎𝑘𝑎𝑛 = 0,3063 𝑠 𝑚𝑚′ Spasi maksimum tulangan transversal 1) ¼ d = ¼ 599,5 = 149,875 mm 2) 6D = 6∙ 25 = 150 mm 3) 150mm Digunakan sengkang D13, 2 kaki (𝐴𝑣 = 265,4646 𝑚𝑚2 ) 𝐴𝑣 265,4646 = = 874,3893 𝑚𝑚 𝐴𝑣 0,3036 𝑠 Digunakan spasi tulangan transversal 125 mm Digunakan sengkang D13 – 125 mm 𝑆=







Lapangan Vu = 45,099 kN 𝑉𝑢 𝑉𝑐 > = 60,132 𝑘𝑁 (𝑡𝑖𝑑𝑎𝑘 𝑑𝑖𝑏𝑢𝑡𝑢ℎ𝑘𝑎𝑛 𝑡𝑢𝑙𝑎𝑛𝑔𝑎𝑛 𝑔𝑒𝑠𝑒𝑟) 0,75 𝑉𝑠 = 0 𝐴𝑣 𝑚𝑚2 𝑑𝑖𝑔𝑢𝑛𝑎𝑘𝑎𝑛 = 0,3063 𝑠 𝑚𝑚′ Spasi maksimum tulangan transversal 1) ¼ d = ¼ 599,5 = 149,875 mm 2) 6D = 6∙ 25 = 150 mm 3) 150mm Digunakan sengkang D13, 2 kaki (𝐴𝑣 = 265,4646 𝑚𝑚2 ) 𝐴𝑣 265,4646 = = 874,3893 𝑚𝑚 𝐴𝑣 0,3036 𝑠 Digunakan spasi tulangan transversal 125 mm Digunakan sengkang D13 – 125 mm 𝑆=







Tumpuan Kanan Vu = 103,4422kN 𝑉𝑢 𝑉𝑐 > = 137,9229 𝑘𝑁 (𝑡𝑖𝑑𝑎𝑘 𝑑𝑖𝑏𝑢𝑡𝑢ℎ𝑘𝑎𝑛 𝑡𝑢𝑙𝑎𝑛𝑔𝑎𝑛 𝑔𝑒𝑠𝑒𝑟) 0,75 𝑉𝑠 = 0



𝐴𝑣 𝑚𝑚2 𝑑𝑖𝑔𝑢𝑛𝑎𝑘𝑎𝑛 = 0,3063 𝑠 𝑚𝑚′ Spasi maksimum tulangan transversal 4) ¼ d = ¼ 599,5 = 149,875 mm 5) 6D = 6∙ 25 = 150 mm 6) 150mm Digunakan sengkang D13, 2 kaki (𝐴𝑣 = 265,4646 𝑚𝑚2 ) 𝐴𝑣 265,4646 = = 874,3893 𝑚𝑚 𝐴𝑣 0,3036 𝑠 Digunakan spasi tulangan transversal 125 mm Digunakan sengkang D13 – 125 mm 𝑆=