PC-HOLLOW.xls

1. 설계조건 a. Concrete Precast PC : fck = 40 MPa Ec = 8500*(fck+4)^(1/3) = 30008 MPa fcki = 28 MPa Eci = 8500*(fcki+4)^(1/3) = 26986 MPa Topping Slab : fckt = 27 MPa Ect = 8500*(fckt+4)^(1/3) = 26702 MPa b. 철근 휨인장용철근 : SD400 ( fy = 400 MPa) Es = 205000 MPa 전단보강용철근 : SD400 ( fys = 400 MPa) c. 프리스트레스긴장재 : KS D 7002 38 31 27 Fpu1 = 183 이상 kn Fpu2 = 88.8 이상 kn Fpu3 = 38.2 이상 kn Fpy1 = 156 이상 kn Fpy2 = 75.5 이상 kn Fpy3 = 33.8 이상 kn Aps1 = 98.71 mm 2 /EA Aps2 = 51.61 mm 2 /EA Aps3 = 19.82 mm 2 /EA Eps = 200000 MPa Eps = 200000 MPa Eps = 200000 MPa 직경 ds1 = 12.7 mm 직경 ds2 = 9.3 mm 직경 ds3 = 2.9 mm fpu1 = Fpu1/Aps1= 1854 MPa fpu2 = Fpu2/Aps2= 1721 MPa fpu3 = Fpu3/Aps3= 1927 MPa fpy1 = Fpy1/Aps1= 1580 MPa fpy2 = Fpy2/Aps2= 1463 MPa fpy3 = Fpy3/Aps3= 1705 MPa 2. 허용응력도 - 콘크리트 a. 프리스트레스도입직후압축연단에서최대압축응력 0.6*fcki = 0.6*28 = 16.80 MPa 인장연단에서최대인장응력 0.25* fcki = 0.25* 28 = 1.32 MPa 단순지지부재단부의최대인장응력 0.50* fcki = 0.50* 28 = 2.65 MPa b. 모든프리스트레스손실을허용한후에사용하중하의응력압축연단에서최대압축응력 ( 긴장력 + 지속하중 ) 0.45*fck = 0.45*40 = 18.00 MPa (Precast 부재용 ) 0.45*fckt = 0.45*27 = 12.15 MPa (Topping Slab용 ) ( 긴장력 + 전체하중 ) 0.60*fck = 0.60*40 = 24.00 MPa (Precast 부재용 ) 0.60*fckt = 0.60*27 = 16.20 MPa (Topping Slab용 ) 압축프리스트레스가가해진인장영역내의최대인장응력 (- 일반적인경우 ) 0.63* fck = 0.63* 40 = 3.98 MPa (Precast 부재용 ) 0.63* fckt = 0.63* 27 = 3.27 MPa (Topping Slab용 ) 압축프리스트레스가가해진인장영역내의최대인장응력 (- 환산균열단면과 2개의선형으로이루어진모멘트-처짐관계를이용하여구한즉시처짐과장기처짐이규준을만족시키는경우 ) 1.0* fck = 1.0* 40 = 6.32 MPa - strand (1) SWPC 7B 7연선 12.7mm Initial jacking force Po1 = 0.70 *Fpu1 = 0.7*183 = 128.1 kn/strand MIN(0.80*Fpu1, 0.94*Fpy1) = 146.4 kn/strand at Release Pi1 = 0.90 *Po1 = 0.9*128.1 = 115.3 kn/strand MIN(0.74*Fpu1, 0.82*Fpy1) = 127.9 kn/strand Final Design Pt1 = 0.80 *Po1 = 0.8*128.1 = 102.5 kn/strand 0.5*Fpu1 = 91.5 kn/strand (2) SWPC 7A 7연선 9.30mm Initial jacking force Po2 = 0.70 *Fpu2 = 0.7*88.8 = 62.2 kn/strand MIN(0.80*Fpu2, 0.94*Fpy2) = 71.0 kn/strand at Release Pi2 = 0.90 *Po2 = 0.9*62.2 = 56.0 kn/strand MIN(0.74*Fpu2, 0.82*Fpy2) = 61.9 kn/strand Final Design Pt2 = 0.80 *Po2 = 0.8*62.2 = 49.8 kn/strand 0.5*Fpu2 = 44.4 kn/strand (3) SWPD 3 2.9mm 3연선 Initial jacking force Po3 = 0.70 *Fpu3 = 0.7*38.2 = 26.7 kn/strand MIN(0.80*Fpu3, 0.94*Fpy3) = 30.6 kn/strand at Release Pi3 = 0.90 *Po3 = 0.9*26.7 = 24.0 kn/strand MIN(0.74*Fpu3, 0.82*Fpy3) = 27.7 kn/strand Final Design Pt3 = 0.80 *Po3 = 0.8*26.7 = 21.4 kn/strand 0.5*Fpu3 = 19.1 kn/strand 1/9 쪽

3. Section Properties 16 * at Basic Section Ac y Ac*y D D1 Io (mm) (mm) (mm 2 ) (mm) (mm 3 ) (mm) (mm) (mm 4 ) 1160 40 211400 161.9 34225660 0.00 127.21 2419000000 416 245 1198 30 211400 34225660 2419000000 * at Topping Slab n = Ect/Ec = 0.890 1200 200 213600 415 88644000-125.89 712000000 (1068) 425000 122869660 3131000000 bw = 416 mm bf = 1200 mm h = 515 mm hf = 240 mm htop = 200 mm * 프리캐스트보 * 합성보 ( 프리캐스트보 +Topping) Ac = 211400 mm 2 Acc = 425000 mm 2 yb = 161.90 mm y1c = 25.89 mm : 프리캐스트부재상부 yt = 153.10 mm y2c = 289.11 mm : 프리캐스트부재하부 I = 2419000000 mm 4 y3c = 225.89 mm : Topping 상부 St = 15800131 mm 3 y4c = 25.89 mm : Topping 하부 Sb = 14941322 mm 3 Icc = 9937151191 mm 4 Z1c = 383821985 mm 3 1 dp' = 72.38 mm Z2c = 34371524 mm 3 e = 89.52 mm Z3c = 43991107 mm 3 db' = 0.00 mm Z4c = 383821985 mm 3 y A*D 2 A*D1 2 (mm 4 ) (mm 4 ) 0 3420955999 0 0 0 0 0 3420955999 3385195193 6806151191 bf 4 htop hf h 2 3 *at Strand * at Tensile Rebar TYPE 갯수 직경 면적 거리 면적 * 거리 Pi Pt 갯수 직경 면적 거리 면적 * 거리 (ea) (mm) Aps(mm 2 ) (mm) (mm 3 ) (kn) (kn) (ea) (mm) As(mm 2 ) (mm) (mm 3 ) 하부1 10 φ12.7 987.10 30 29613.00 1153.0 1025.0 하부2 - - 0.00 0.00 0.0 0.0 상부 4 φ9.3 206.44 275 56771.00 224.0 199.2 14 1193.54 86384.00 1377.0 1224.20 0 0 0.00 fpu = 1854 MPa fpy = 1580 MPa Aps = 10*Aps1*fpu1/fpu + 0 + 4*Aps2*fpu2/fpu = 10*98.71*1854/1854 + 0 + 4*51.61*1721/1854 = 1178.73 mm 2 ( 환산단면적 ) ds = MAX(strand직경 ) = 12.70 mm 4. Load and Moment/Shear Span L = 9000 mm Ln = 8500 mm Spa = 1200 mm 전단력보정계수 MF = 1.00 저감계수 ws 하중계수 wu Ms(kN-m) Mu(kN-m) Vu R.F (kn/m) L.F (kn/m) END MID END MID (kn) Self Weight 4.86 1.2 5.83 0.00 43.89 0.00 52.65 24.78 합성전 Dead Load 0.00 1.2 0.00 0.00 0.00 0.00 0.00 0.00 합성전 Topping Slab 5.76 1.2 6.91 0.00 52.02 0.00 62.41 29.37 합성전 Finish Load 1.56 1.2 1.87-10.25 8.05-12.28 9.65 7.95 합성후 Live Load 30.00 1.6 48.00-197.05 154.82-315.27 247.71 204.00 합성후 42.18 62.61-207.30 258.78-327.55 372.42 266.10 5. Required Prestress Force Ms = 43.89 + 0 + 52.02 = 95.91 kn-m Ms1 = 8.05 + 154.82 = 162.87 kn-m Ft = (Ms/Sb + Ms1/Z2c - 0.63* fck) / (1/Ac + e/sb) = (95.91*10^6 / 14941322 + 162.87*10^6 /( 34371524) - 0.63* 40) / (1/211400 + 89.52/14941322) * 1/10^3 = 669 kn Pt = 1224.2 kn (0.55) 6. 프리스트레스도입직후의프리캐스트보의응력 : Pi/Ac ± Pi*e/S ± Ms/S END : Ms = 0.00 kn-m ft = Pi/Ac - Pi*e/St = 1377*10^3/211400-1377*10^3*89.52/15800131 = 6.51-7.8 = -1.29 MPa / 인장 ft = 1.29 MPa 0.50* fcki = 2.65 MPa 2/9 쪽

fb = Pi/Ac + Pi*e/Sb = 1377*103/211400 + 1377*10^3*89.52/14941322 = 6.51 + 8.25 = 14.76 MPa / 압축 fb = 14.76 MPa 0.6*fcki = 16.8 MPa CENTER : Ms = 43.89 kn-m ft = Pi/Ac - Pi*e/St + Ms/St = 1377*10^3/211400-1377*10^3*89.52/15800131 + 43.89*10^6 /15800131 = 6.51-7.8 + 2.78 = 1.49 MPa / 압축 ft = 1.49 MPa 0.6*fcki = 16.8 MPa fb = Pi/Ac + Pi*e/Sb - Ms/Sb = 1377*10^3/211400 + 1377*10^3*89.52/14941322-43.89*10^6 /14941322 = 6.51 + 8.25-2.94 = 11.83 MPa / 압축 fb = 11.83 MPa 0.6*fcki = 16.8 MPa 7. 프리캐스트 PC보에 Topping Slab를타설한경우 : Pt/Ac ± Pt*e/S ± Ms/S END : Ms = 0.00 kn-m ft = Pt/Ac - Pt*e/St = 1224.2*10^3/211400-1224.2*10^3*89.52/15800131 = 5.79-6.94 = -1.15 MPa / 인장 ft = 1.15 MPa 0.63* fck = 3.98 MPa fb = Pt/Ac + Pt*e/Sb = 1224.2*10^3/211400 + 1224.2*10^3*89.52/14941322 = 5.79 + 7.33 = 13.13 MPa / 압축 fb = 13.13 MPa 0.45*fck = 18 MPa CENTER : Ms = 43.89+0+52.02 = 95.91 kn-m ft = Pt/Ac - Pt*e/St + Ms/St = 1224.2*10^3/211400-1224.2*10^3*89.52/15800131 + 95.91*10^6/15800131 = 5.79-6.94 + 6.07 = 4.93 MPa / 압축 ft = 4.93 MPa 0.45*fck = 18 MPa fb = Pt/Ac + Pt*e/Sb - Ms/Sb = 1224.2*10^3/211400 + 1224.2*10^3*89.52/14941322-95.91*10^6 /14941322 = 5.79 + 7.33-6.42 = 6.71 MPa / 압축 fb = 6.71 MPa 0.45*fck = 18 MPa 8. 합성보에마감하중이작용할경우 : Pt/Ac ± Pt*e/S ± Ms/S END : Ms = 0.00 kn-m Ms1 = -10.25 kn-m ft = Pt/Ac - Pt*e/St + Ms/St + Ms1/Z1c = 1224.2*10^3/211400-1224.2*10^3*89.52/15800131 + 0*10^6/15800131 + (-10.25)*10^6/(383821985) = 5.79-6.94 + 0 + (-0.03) = -1.17 MPa / 인장 ft = 1.17 MPa 0.63* fck = 3.98 MPa fb = Pt/Ac + Pt*e/Sb - Ms/Sb - Ms1/Z2c = 1224.2*10^3/211400 + 1224.2*10^3*89.52/14941322-0*10^6/14941322 - (-10.25)*10^6 /(34371524) = 5.79 + 7.33-0 - (-0.3) = 13.42 MPa / 압축 fb = 13.42 MPa 0.45*fck = 18 MPa CENTER : Ms = 43.89+0+52.02 = 95.91 kn-m Ms1 = 8.05 kn-m ft = Pt/Ac - Pt*e/St + Ms/St + Ms1/Z1c = 1224.2*10^3/211400-1224.2*10^3*89.52/15800131 + 95.91*10^6/15800131 + 8.05*10^6/(383821985) = 5.79-6.94 + 6.07 + (0.02) = 4.95 MPa / 압축 ft = 4.95 MPa 0.45*fck = 18 MPa fb = Pt/Ac + Pt*e/Sb - Ms/Sb - Ms1/Z2c = 1224.2*10^3/211400 + 1224.2*10^3*89.52/14941322-95.91*10^6/14941322-8.05*10^6 /(34371524) = 5.79 + 7.33-6.42 - (0.23) = 6.47 MPa / 압축 fb = 6.47 MPa 0.45*fck = 18 MPa 3/9 쪽

9. 최종사용하중시응력 : Pt/Ac ± Pt*e/S ± Ms/S END : Ms = 0.00 kn-m Ms1 = -10.25 + (-197.05) = -207.30 kn-m ft = Pt/Ac - Pt*e/St + Ms/St + Ms1/Z1c = 1224.2*10^3/211400-1224.2*10^3*89.52/15800131 + 0*10^6/15800131 + (-207.3)*10^6/(383821985) = 5.79-6.94 + 0 + (-0.54) = -1.69 MPa / 인장 ft = 1.69 MPa 0.63* fck = 3.98 MPa fb = Pt/Ac + Pt*e/Sb - Ms/Sb - Ms1/Z2c = 1224.2*10^3/211400 + 1224.2*10^3*89.52/14941322-0*10^6/14941322 - (-207.3)*10^6 /(34371524) = 5.79 + 7.33-0 - (-6.03) = 19.16 MPa / 압축 fb = 19.16 MPa 0.60*fck = 24 MPa CENTER : Ms = 43.89+0+52.02 = 95.91 kn-m Ms1 = 8.05 + 154.82 = 162.87 kn-m ft = Pt/Ac - Pt*e/St + Ms/St + Ms1/Z1c = 1224.2*10^3/211400-1224.2*10^3*89.52/15800131 + 95.91*10^6/15800131 + 162.87*10^6/(383821985) = 5.79-6.94 + 6.07 + (0.42) = 5.35 MPa / 압축 ft = 5.35 MPa 0.60*fck = 24 MPa fb = Pt/Ac + Pt*e/Sb - Ms/Sb - Ms1/Z2c = 1224.2*10^3/211400 + 1224.2*10^3*89.52/14941322-95.91*10^6/14941322-162.87*10^6 /(34371524) = 5.79 + 7.33-6.42 - (4.74) = 1.97 MPa / 압축 fb = 1.97 MPa 0.60*fck = 24 MPa 10. 슬래브상하단의응력 : Ms/S END : Ms = -10.25 + (-197.05) = -207.3 kn-m ft = n*ms/z3c = 0.89*(-207.3)*10^6 /(43991107) = -4.19 MPa / 인장 ft = 4.19 MPa > 0.63* fckt = 3.27 MPa / 철근보강 (As = 2668.57 cm²) fb = n*ms/z4c = 0.89*(-207.3)*10^6/(383821985) = -0.48 MPa / 인장 fb = 0.48 MPa 0.63* fckt = 3.27 MPa CENTER : Ms = 8.05 + 154.82 = 162.9 kn-m ft = n*ms/z3c = 0.89*162.9*10^6 /(43991107) = 3.30 MPa / 압축 ft = 3.3 MPa 0.60*fckt = 16.2 MPa fb = n*ms/z4c = 0.89*162.9*10^6/(383821985) = 0.38 MPa / 압축 fb = 0.38 MPa 0.60*fckt = 16.2 MPa 11. 탈형시검토 Lifting 위치 x = Ln/ 10 = 8500/10 = 850 mm Lifting ws = 4.86 kn/m SF = 1.5 M1 = -ws*x²/2 * SF = -4.86*(850/10^3)²/2 * 1.5 = -2.63 kn-m x M1 x M1 M2 = (ws*ln²/8 - ws*ln/2*x) * SF = (4.86*(8500/10^3)²/8-4.86*(8500/10^3)/2*(850/10^3))*1.5 = 39.50 kn-m M1 위치 M2 ft = Pi/Ac - Pi*e/St + M1/St = 1377*10^3/211400-1377*10^3*89.52/15800131 +( -2.63)*10^6 /15800131 = 6.51-7.8 + (-0.17) = -1.45 MPa / 인장 ft = 1.45 MPa 0.63* fcki = 3.33 MPa fb = Pi/Ac + Pi*e/Sb - M1/Sb = 1377*10^3/211400 + 1377*10^3*89.52/14941322 - (-2.630*10^6 /14941322 = 6.51 + 8.25 - (-0.18) = 14.94 MPa / 압축 fb = 14.94 MPa 0.6*fcki = 16.8 MPa 4/9 쪽

M2 위치 ft = Pi/Ac - Pi*e/St + M2/St = 1377*10^3/211400-1377*10^3*89.52/15800131 + 39.5*10^6 /15800131 = 6.51-7.8 + 2.5 = 1.21 MPa / 압축 ft = 1.21 MPa 0.6*fcki = 16.8 MPa fb = Pi/Ac + Pi*e/Sb - M2/Sb = 1377*10^3/211400 + 1377*10^3*89.52/14941322-39.5*10^6 /14941322 = 6.51 + 8.25-2.64 = 12.12 MPa / 압축 fb = 12.12 MPa 0.6*fcki = 16.8 MPa 12. Check Ultimate Strength φ = 0.85 dp = h - dp' = 515-72.38 = 442.6 mm db = 0.0 mm ρp = Aps/(bf*dp) = 1178.73/(1200*442.6) = 0.00222 ρ = As/(bf*db) = 0/(1200*0) = 0.00000 fpy/fpu = 1580/1854 = 0.852 0.85 γp = 0.4 β1 = 0.85 fps = fpu*[1 - (γp/β1)*(ρp*(fpu/fckt) + db/dp*ρ*fy/fckt)] = 1854*[1 - (0.4/0.85)*(0.00222*(1854/27) + 0/442.6*0*400/27)] = 1721 MPa a' = (Aps*fps + As*fy) / (0.85*fckt*bf) = (1178.73*1721 + 0*400) / (0.85*27*1200) = 73.66 mm hf = 240mm / 장방형보 φmn = φ*(aps*fps*(dp-a'/2) + As*fy*(db-a'/2)) = 0.85*(1178.73*1721*(442.6-73.66/2) + 0*400*(0-73.66/2)) /10^6 = 699.67 kn-m φmn = 699.67 kn-m Mu = 372.42 kn-m (0.53) 13. 철근비검토 gp = Aps/(bf*dp)*fps/fckt + db/dp*as/(bf*db)*fy/fckt = 1178.73/(1200*442.6)*1721/27 = 0.141 gp = 0.141 0.36*β1 = 0.36*0.85 = 0.306 * 단면의인장지배여부확인 c/dp = (a'/β1) / dp = (73.66/0.85) / 442.6 = 0.196 c/dp = 0.196 < 0.375 / 인장지배 14. 휨균열모멘트검토 fr = 0.63* fck = 0.63* 40 = 3.98 MPa Ms = 43.89 + 0 + 52.02 = 95.91 kn-m Mcr1 = (fr + Pt/Ac + Pt*e/Sb - Ms/Sb )*Z2c = (3.98 + 1224.2*10^3/211400 + 1224.2*10^3*89.52/14941322-95.91*10^6/14941322)*(34371524)*1/10^6 = 367.31 kn-m Mcr = Ms + Mcr1 = 95.91 + (367.31) = 463.22 kn-m φmn/mcr = 699.67/463.22 = 1.51 1.20 15. 부모멘트구간철근배근검토 φ = 0.850 Mu(-) = -327.55 kn-m USE : HD19 @100 (As = 3444 mm²) : 1200mm 폭당 As,min = 2154.66 mm² As = 2668.57 mm² bb = 1198 mm bw = 416 mm hb = 30 mm dt' = 60.00 mm dt = h-dt' = 515-60 = 455.00 mm a' = As*fy / (0.85*fck*bb) = 3444*400 / (0.85*40*1198) = 33.82 mm > hb = 30mm /T형보 Aw*fy = As*fy - 0.85*fck*hb*(bb-bw) = 3444*400-0.85*40*30*(1198-416) = 579960 N a = Aw*fy / (0.85*fck*bw) = 579960 / (0.85*40*416) = 41.00 mm φmn = φ*(aw*fy*(dt-a/2) + 0.85*fck*hb*(bb-bw)*(dt-hb/2)) = 0.85*(579960*(455-41/2)+ 0.85*40*30*(1198-416)*(455-30/2))/10^6 = 512.51 kn-m φmn = 512.51 kn-m Mu = 327.55 kn-m (0.64) 5/9 쪽

Asmin1 = 1.4/fy*bb*dt = 1.4/400*1198*455 = 1907.82 mm 2 Asmin2 = 0.25* fck/fy*bb*dt = 0.25* 40/400*1198*455 = 2154.66 mm 2 As,min = MAX(Asmin1, Asmin2) = MAX(1907.82, 2154.66) = 2154.66 mm 2 * 단면의인장지배여부확인 c = a/β1 = 41/0.85 = 48.24 mm εy = fy/es = 400/205000 = 0.00195 εt = (dt-c) / c*0.003 = (455-48.24)/48.24*0.003 = 0.0253 MAX(0.005,2.5*εy) = 0.005 < εt = 0.0253 ( 인장지배단면 ) 16. Check Deflection a. Instantaneous Camber Δ = Pi*e*Ln² / (8*Eci*I) = 1377*10^3*89.52*8500² / (8*26986*2419000000) = 17.054 mm b. 부재자중에의한처짐 Δ = 5*ws*Ln⁴ / (384*Eci*I) = 5*4.86*8500⁴ / (384*26986*2419000000) = 5.060 mm c. Dead Load에의한처짐 Δ = 5*ws*Ln⁴ / (384*Ec*I) = 5*0*8500⁴ / (384*30008*2419000000) = 0.000 mm d. Topping Slab에의한처짐 Δ = 5*ws*Ln⁴ / (384*Ec*I) = 5*5.76*8500⁴ / (384*30008*2419000000) = 5.393 mm e. Finish Load에의한처짐 Δ = 5*ws*Ln⁴ / (384*Ec*Icc) = 5*1.56*8500⁴ / (384*30008*9937151191) = 0.356 mm f. Live Load에의한처짐 Δ = 5*(1-RF)*ws*Ln⁴ / (384*Ec*Icc) = 5*(1-0)*30*8500⁴ / (384*30008*9937151191) = 6.838 mm g. Determine Long term Effects of Creep (from Fig 4-6-3, PCI HANDBO) * Release * at Erection * Final Condition Δi(mm) C.F Δ(mm) Δi(mm) C.F Δ(mm) Δi(mm) C.F Δ(mm) -17.054 1.00-17.054-17.054 1.80-30.697-17.054 2.20-37.519 5.060 1.00 5.060 5.060 1.85 9.361 5.060 2.40 12.144-11.994 0.000 1.00 0.000 0.000 2.30 0.000 5.393 1.00 5.393 5.393 2.30 12.404 0.356 1.00 0.356 0.356 3.00 1.068-15.587-11.903 Deflection(LL) 6.838-5.065 ΔTL = (-11.903-(-15.587)) + 6.838 = 10.522 mm ( 모든지속하중에의한장기처짐 + 추가적인활하중에의한순간처짐 ) h. Check Δ allowable Ln/360 = 8500/360 = 23.61 mm ΔLL = 6.838 mm Ln/480 = 8500/480 = 17.71 mm ΔTL = 10.522 mm 6/9 쪽

16. Check Shear φ = 0.75 0 50*ds 1/12*L 2/12*L 3/12*L 4/12*L 5/12*L 6/12*L 위험단면 거리 0.00 635.00 708.33 1416.67 2125.00 2833.33 3541.67 4250.00 220.00 (mm) Vu 266.09 226.34 221.74 177.39 133.05 88.70 44.35 0.00 252.32 (kn) Mu 0.00 156.35 172.77 314.14 424.08 502.62 549.74 565.45 57.03 (kn-m) dp 442.60 442.60 442.60 442.60 442.60 442.60 442.60 442.60 442.60 (mm) d = MAX(0.8*h, dp) 442.60 442.60 442.60 442.60 442.60 442.60 442.60 442.60 442.60 (mm) Vu*dp/Mu 1.00 0.64 0.57 0.25 0.14 0.08 0.04 0.00 1.00 Prestress force P 0 1224.20 1224.20 1224.20 1224.20 1224.20 1224.20 1224.20 424.13 (kn) fpc = P/Ac 0.00 5.79 5.79 5.79 5.79 5.79 5.79 5.79 2.01 (MPa) Vp 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 (kn) φvc1 720.32 476.72 429.36 212.83 138.40 97.80 70.73 43.67 720.32 (kn) φvc2 253.28 493.14 493.14 493.14 493.14 493.14 493.14 493.14 336.54 (kn) φvc3 145.56 145.56 145.56 145.56 145.56 145.56 145.56 145.56 145.56 (kn) φvc4 363.90 363.90 363.90 363.90 363.90 363.90 363.90 363.90 363.90 (kn) φvc 253.28 363.90 363.90 212.83 145.56 145.56 145.56 145.56 336.54 (kn) φvc /2 126.64 181.95 181.95 106.42 72.78 72.78 72.78 72.78 168.27 (kn) φvs 12.81 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 (kn) ( 불필요 ) ( 불필요 ) ( 불필요 ) ( 불필요 ) ( 불필요 ) ( 불필요 ) ( 불필요 ) ( 불필요 ) φ*2/3* fck*bw*d 582.24 (kn) () φ*1/3* fck*bw*d 291.12 (kn) leg leg stirrup S1 0 0 0 0 0 0 0 0 0 (mm) S2 0 0 0 0 0 0 0 0 0 (mm) S3 0 0 0 0 0 0 0 0 0 (mm) S4 0 0 0 0 0 0 0 0 0 (mm) S5 #N/A (mm) S = MIN(S1,S2,S3,S4,S5) #N/A 0 0 0 0 0 0 0 0 (mm) USE (mm) 7/9 쪽

400.00 350.00 300.00 전단보강여부검토 (Half Span) Vu(kN) φvc(kn) 위험단면 φvc/2(kn) Vu(kN) or ΦVc(kN) 250.00 200.00 150.00 100.00 50.00 0.00 0.00 500.00 1000.00 1500.00 2000.00 2500.00 3000.00 3500.00 4000.00 4500.00 거리 (mm) a. Use leg- HD (Av = 0.00 mm 2 ) Smax1 = 0 mm Smax2 = Av*fys / (0.0625* fck*bw) = 0*400 / (0.0625* 40*416) = 0 mm Smax3 = Av*fys / (0.35*bw) = 0*400/(0.35*416) = 0 mm Smax4 = Av / ((Aps/80)*(fpu/fys)*(1/d) * (d/bw)) = 0 / ((1178.73/80)*(1854/400)*(1/442.6) * (442.6/416)) = 0 mm Smax = MIN(Smax1, Smax2, Smax3, Smax4) = MIN( 0, 0, 0, 0) = 0 mm b. 콘크리트전단강도 dp = 442.60 mm d = MAX(dp, 0.8*h) = MAX(442.6, 0.8*515) = 442.60 mm 위험단면 CS = 220.00 mm Vu = MF*wu*Ln/2 - MF*wu*CS = 1*62.61*(8500/10^3)/2-1*62.61*(220/10^3) = 252.32 kn Mu = MF*wu*CS*(L-CS) / 2 = 1*62.61*(220/10^3)*((8500/10^3)-(220/10^3))/2 = 57.03 kn-m Vu/Mu*dp = MIN(252.32*(442.6/1000) / 57.03, 1.0) = MIN(1.96, 1.0) = 1.00 전달길이 50*ds = 50*12.7 = 635.00 mm 프리스트레스힘 P = Pt/(50*ds)*CS = 1224.2/(50*12.7)*220 = 424.13 kn fpc = P / Ac = 424.13*10^3/211400 = 2.01 MPa Vp = P*slope = 424.13*(442.6-442.6)/(4250-0) = 0.00 kn φvc1 = φ*(0.05* fck + 4.9*Vu/Mu*dp)*bw*d = 0.75*(0.05* 40 + 4.9*1)*416*442.6/10^3 = 720.32 kn φvc2 = φ*((0.29* fck + 0.3*fpc)*bw*d + Vp) = 0.75*(0.29* 40 + 0.3*2.01)* 416*442.6/10^3 + 0) = 336.54 kn φvc3 = φ*1/6* fck*bw*d = 0.75 * 1/6 * 40*416*442.6/10^3 = 145.56 kn φvc4 = φ*5/12* fck*bw*d = 0.75*5/12* 40*416*442.6/10^3 = 363.90 kn φvc = MIN( MAX( MIN(Vc1, Vc2), Vc3), Vc4 ) = MIN( MAX( MIN( 720.32, 336.54), 145.56), 363.9) = 336.54 kn c. 전단보강근의전단강도 φvs = Vu - φ*vc = 252.32-336.54 = -84.22 kn 전단보강불필요 8/9 쪽

17. 수평전단설계 (1) τnh = 0.56 MPa 1). 최소전단연결재가없으면서접촉면이청결하고부유물이없으며접촉면을의도적으로거칠게만든경우 ----------- τnh = 0.56 MPa 2). 최소전단연결재가있으면서접촉면이청결하고부유물이없으며접촉면을의도적으로거칠게만들어지지않은경우 ----------- τnh = 0.56 MPa 3). 최소전단연결재가있으면서접촉면이청결하고부유물이없으며접촉면을의도적으로거칠게만든경우 ----------- τnh = 3.5 MPa C = 0.85*fckt*bf*htop = 0.85*27*1200*200/10^3 = 5508.0 kn T1 = Aps*fps = 1178.73*1721/10^3 = 2028.59 kn T2 = As*fy = 0*400/10^3 = 0.00 kn T = T1 + T2 = 2028.59 + 0 = 2028.59 kn Fh = MIN(C, T) = MIN( 5508, 2028.59 ) = 2028.59 kn bv = 1200 mm Lvh = 4250.00 mm φvnh = φ*τnh*bv*lvh = 0.75*0.56*1200*4250/1000 = 2142.00 kn Fh/φVnh = 2028.59 / 2142 = 0.947 1.00 9/9 쪽