1. 설계조건 a. Concrete Precast PC : fck = 35 MPa Ec = 8500*(fck+4)^(1/3) = 28825 MPa fcki = 24.5 MPa Eci = 8500*(fcki+4)^(1/3) = 25964 MPa Topping Slab : fckt = 24 MPa Ect = 8500*(fckt+4)^(1/3) = 25811 MPa b. 철근 휨인장용철근 : SD400 ( fy = 400 MPa) 전단보강용철근 : SD400 ( fys = 400 MPa) c. 프리스트레스긴장재 : KS D 7002 38 Fpu = 183 이상 kn fpu = Fpu/Aps1 = 183*10^3/98.71 = 1854 MPa Fpy = 156 이상 kn fpy = Fpy/Aps1 = 156*10^3/98.71 = 1580 MPa Aps1 = 98.71 mm 2 Eps = 200000 MPa 직경 ds = 12.7 mm 2. 허용응력도 - 콘크리트 a. 프리스트레스도입직후 압축연단에서최대압축응력 0.6*fcki = 0.6*24.5 = 14.70 MPa 인장연단에서최대인장응력 0.25* fcki = 0.25* 24.5 = 1.24 MPa 단순지지부재단부의최대인장응력 0.50* fcki = 0.50* 24.5 = 2.47 MPa b. 모든프리스트레스손실을허용한후에사용하중하의응력 압축연단에서최대압축응력 ( 긴장력 + 지속하중 ) 0.45*fck = 0.45*35 = 15.75 MPa (Precast Beam용 ) 0.45*fckt = 0.45*24 = 10.80 MPa (Topping Slab용 ) ( 긴장력 + 전체하중 ) 0.60*fck = 0.60*35 = 21.00 MPa (Precast Beam용 ) 0.60*fckt = 0.60*24 = 14.40 MPa (Topping Slab용 ) 압축프리스트레스가가해진인장영역내의최대인장응력 (- 일반적인경우 ) 0.63* fck = 0.63* 35 = 3.73 MPa (Precast Beam용 ) 0.63* fckt = 0.63* 24 = 3.09 MPa (Topping Slab용 ) 압축프리스트레스가가해진인장영역내의최대인장응력 (- 환산균열단면과 2개의선형으로이루어진모멘트-처짐관계를이용하여구한즉시처짐과장기처짐이규준을만족시키는경우 ) 1.0* fck = 1.0* 35 = 5.92 MPa - strand Initial jacking force Po = 0.75 *Fpu = 0.75*183 = 137.3 kn/strand MIN(0.80*Fpu, 0.94*Fpy) = 146.4 kn/strand at Release Pi = 0.90 *Po = 0.9*137.3 = 123.6 kn/strand MIN(0.74*Fpu, 0.82*Fpy) = 127.9 kn/strand Final Design Pt = 0.80 *Po = 0.8*137.3 = 109.8 kn/strand 0.5*Fpu = 91.5 kn/strand 3. Section Properties : 유효폭고려입력 * at Basic Section Ac y Ac*y D D1 Io A*D 2 A*D1 2 (mm) (mm) (mm 2 ) (mm) (mm 3 ) (mm) (mm) (mm 4 ) (mm 4 ) (mm 4 ) 125 550 68750 275 18906250 135.19 230.09 1733072917 1256498107 3639721807 50 550 13750 367 5046250 43.19 138.09 231076389 25648921 262196661 125 550 68750 275 18906250 135.19 230.09 1733072917 1256498107 3639721807 50 550 13750 367 5046250 43.19 138.09 231076389 25648921 262196661 2400 50 120000 575 69000000-164.81-69.91 25000000 3259480332 586488972 285000 116905000 3953298611 5823774388 8390325908 * at Topping Slab n = Ect/Ec = 0.895 2400 90 193320 645 124691400-139.91 130491000 3784201902 (2148) 478320 241596400 4083789611 12174527810 bw = 300 mm bf = 2400 mm bf h = 690 mm hf = 140 mm ht = 90 mm 6 ht * 프리캐스트보 * 합성보 ( 프리캐스트보 +Topping) 5 hf Ac = 285000 mm 2 Acc = 478320 mm 2 2 4 h 1 3 yb = 410.19 mm y1c = 94.91 mm : 프리캐스트부재상부 y yt = 189.81 mm y2c = 505.09 mm : 프리캐스트부재하부 I = 9777072999 mm 4 y3c = 184.91 mm : Topping 상부 bw/2 bw/2 St = 51509789 mm 3 y4c = 94.91 mm : Topping 하부 Sb = 23835474 mm 3 Icc = 16258317421 mm 4 Z1c = 171302470 mm 3 dp' = 100.00 mm Z2c = 32188951 mm 3 e = 310.19 mm Z3c = 87925571 mm 3 db' = 50.00 mm Z4c = 171302470 mm 3 1/7 쪽
*at Strand * at Tensile Rebar 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 ) 2 φ12.7 197.42 50 9871.00 247.2 219.6 2 HD19 574 50 28700.00 2 φ12.7 197.42 100 19742.00 247.2 219.6 2 φ12.7 197.42 150 29613.00 247.2 219.6 0 0 6 592.26 59226.00 741.60 658.80 2 574 28700.00 4. Load and Moment/Shear Span L = 10000 mm Ln = 9500 mm Spa = 2400 mm 전단력보정계수 MF = 1.00 저감계수 ws 하중계수 wu Ms Mu Vu R.F (kn/m) L.F (kn/m) (kn-m) (kn-m) (kn) Self Weight 6.84 1.2 8.21 77.16 92.62 39.00 합성전 : M = w*l 2 /8 Dead Load 0.00 1.2 0.00 0.00 0.00 0.00 합성전 : V = w*l/2 Topping Slab 5.18 1.2 6.22 58.44 70.17 29.55 합성전 Finish Load 0.72 1.2 0.86 8.12 9.70 4.09 합성후 Live Load 0 14.40 1.6 23.04 162.45 259.92 109.44 합성후 27.14 38.33 306.17 432.41 182.08 5. Required Prestress Force Ms = 77.16 + 0 + 58.44 = 135.60 kn-m Ms1 = 8.12 + 162.45 = 170.57 kn-m Ft = (Ms/Sb + Ms1/Z2c - 0.63* fck) / (1/Ac + e/sb) = (135.6*10^6 / 23835474 + 170.57*10^6 / 32188951-0.63* 35) / (1/285000 + 310.19/23835474) * 1/10^3 = 439 kn N = Ft/Pt = 439/109.8 = 4 ea N = 4 ea 6 ea 6. 프리스트레스도입직후의프리캐스트보의응력 : Pi/Ac ± Pi*e/S ± Ms/S Ms = 77.16 kn-m END ft = Pi/Ac - Pi*e/St = 741.6*10^3/285000-741.6*10^3*310.19/51509789 = 2.6-4.47 = -1.86 MPa / 인장 ft = 1.86 MPa 0.50* fcki = 2.47 MPa fb = Pi/Ac + Pi*e/Sb = 741.6*103/285000 + 741.6*10^3*310.19/23835474 = 2.6 + 9.65 = 12.25 MPa / 압축 fb = 12.25 MPa 0.6*fcki = 14.7 MPa ft = Pi/Ac - Pi*e/St + Ms/St = 741.6*10^3/285000-741.6*10^3*310.19/51509789 + 77.16*10^6 /51509789 = 2.6-4.47 + 1.5 = -0.37 MPa / 인장 ft = 0.37 MPa 0.25* fcki = 1.24 MPa fb = Pi/Ac + Pi*e/Sb - Ms/Sb = 741.6*10^3/285000 + 741.6*10^3*310.19/23835474-77.16*10^6 /23835474 = 2.6 + 9.65-3.24 = 9.02 MPa / 압축 fb = 9.02 MPa 0.6*fcki = 14.7 MPa 7. 프리캐스트 PC보에 Topping Slab를타설한경우 : Pt/Ac ± Pt*e/S ± Ms/S Ms = 77.16+0+58.44 = 135.60 kn-m END ft = Pt/Ac - Pt*e/St = 658.8*10^3/285000-658.8*10^3*310.19/51509789 = 2.31-3.97 = -1.66 MPa / 인장 ft = 1.66 MPa 0.63* fck = 3.73 MPa fb = Pt/Ac + Pt*e/Sb = 658.8*10^3/285000 + 658.8*10^3*310.19/23835474 = 2.31 + 8.57 = 10.89 MPa / 압축 fb = 10.89 MPa 0.45*fck = 15.75 MPa 2/7 쪽
ft = Pt/Ac - Pt*e/St + Ms/St = 658.8*10^3/285000-658.8*10^3*310.19/51509789 + 135.6*10^6/51509789 = 2.31-3.97 + 2.63 = 0.98 MPa / 압축 ft = 0.98 MPa 0.45*fck = 15.75 MPa fb = Pt/Ac + Pt*e/Sb - Ms/Sb = 658.8*10^3/285000 + 658.8*10^3*310.19/23835474-135.6*10^6 /23835474 = 2.31 + 8.57-5.69 = 5.20 MPa / 압축 fb = 5.2 MPa 0.45*fck = 15.75 MPa 8. 합성보에마감하중이작용할경우 : Pt/Ac ± Pt*e/S ± Ms/S Ms = 77.16+0+58.44 = 135.60 kn-m Ms1 = 8.12 kn-m ft = Pt/Ac - Pt*e/St + Ms/St + Ms1/Z1c = 658.8*10^3/285000-658.8*10^3*310.19/51509789 + 135.6*10^6/51509789 + 8.12*10^6/171302470 = 2.31-3.97 + 2.63 + 0.05 = 1.02 MPa / 압축 ft = 1.02 MPa 0.45*fck = 15.75 MPa fb = Pt/Ac + Pt*e/Sb - Ms/Sb - Ms1/Z2c = 658.8*10^3/285000 + 658.8*10^3*310.19/23835474-135.6*10^6/23835474-8.12*10^6 /32188951 = 2.31 + 8.57-5.69-0.25 = 4.94 MPa / 압축 fb = 4.94 MPa 0.45*fck = 15.75 MPa 9. 최종사용하중시응력 : Pt/Ac ± Pt*e/S ± Ms/S Ms = 77.16+0+58.44 = 135.60 kn-m Ms1 = 8.12 + 162.45 = 170.57 kn-m ft = Pt/Ac - Pt*e/St + Ms/St + Ms1/Z1c = 658.8*10^3/285000-658.8*10^3*310.19/51509789 + 135.6*10^6/51509789 + 170.57*10^6/171302470 = 2.31-3.97 + 2.63 + 1 = 1.97 MPa / 압축 ft = 1.97 MPa 0.60*fck = 21 MPa fb = Pt/Ac + Pt*e/Sb - Ms/Sb - Ms1/Z2c = 658.8*10^3/285000 + 658.8*10^3*310.19/23835474-135.6*10^6/23835474-170.57*10^6 /32188951 = 2.31 + 8.57-5.69-5.3 = -0.10 MPa / 인장 fb = 0.1 MPa 0.63* fck = 3.73 MPa 10. 슬래브상하단의응력 : Ms/S Ms = 8.12 + 162.45 = 170.6 kn-m ft = n*ms/z3c = 0.895*170.6*10^6 /87925571 = 1.74 MPa / 압축 ft = 1.74 MPa 0.60*fckt = 14.4 MPa fb = n*ms/z4c = 0.895*170.6*10^6/171302470 = 0.89 MPa / 압축 fb = 0.89 MPa 0.60*fckt = 14.4 MPa 11. 탈형시검토 Lifting 위치 x = Ln/ 10 = 9500/10 = 950 mm Lifting ws = 6.84 kn/m SF = 1.5 M1 = -ws*x²/2 * SF = -6.84*(950/10^3)²/2 * 1.5 = -4.63 kn-m x M1 x M1 M2 = (ws*ln²/8 - ws*ln/2*x) * SF = (6.84*(9500/10^3)²/8-6.84*(9500/10^3)/2*(950/10^3))*1.5 = 69.45 kn-m M1 위치 M2 ft = Pi/Ac - Pi*e/St + M1/St = 741.6*10^3/285000-741.6*10^3*310.19/51509789 +( -4.63)*10^6 /51509789 = 2.6-4.47 + (-0.09) = -1.95 MPa / 인장 ft = 1.95 MPa 0.63* fcki = 3.12 MPa fb = Pi/Ac + Pi*e/Sb - M1/Sb = 741.6*10^3/285000 + 741.6*10^3*310.19/23835474 - (-4.630*10^6 /23835474 = 2.6 + 9.65 - (-0.19) = 12.45 MPa / 압축 fb = 12.45 MPa 0.6*fcki = 14.7 MPa 3/7 쪽
M2 위치 ft = Pi/Ac - Pi*e/St + M2/St = 741.6*10^3/285000-741.6*10^3*310.19/51509789 + 69.45*10^6 /51509789 = 2.6-4.47 + 1.35 = -0.52 MPa / 인장 ft = 0.52 MPa 0.63* fcki = 3.12 MPa fb = Pi/Ac + Pi*e/Sb - M2/Sb = 741.6*10^3/285000 + 741.6*10^3*310.19/23835474-69.45*10^6 /23835474 = 2.6 + 9.65-2.91 = 9.34 MPa / 압축 fb = 9.34 MPa 0.6*fcki = 14.7 MPa 12. Check Ultimate Strength φ = 0.85 dp = h - dp' = 690-100 = 590.0 mm db = h - db' = 690-50 = 640.0 mm ρp = Aps/(bf*dp) = 592.26/(2400*590) = 0.00042 ρ = As/(bf*db) = 574/(2400*640) = 0.00037 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)*(0.00042*(1854/24) + 640/590*0.00037*400/24)] = 1820 MPa a' = (Aps*fps + As*fy) / (0.85*fckt*bf) = (592.26*1820 + 574*400) / (0.85*24*2400) = 26.71 mm hf = 140mm / 장방형보 φmn = φ*(aps*fps*(dp-a'/2) + As*fy*(db-a'/2)) = 0.85*(592.26*1820*(590-26.71/2) + 574*400*(640-26.71/2)) /10^6 = 650.63 kn-m φmn = 650.63 kn-m Mu = 432.41 kn-m 13. 철근비검토 gp = Aps/(bf*dp)*fps/fckt + db/dp*as/(bf*db)*fy/fckt = 592.26/(2400*590)*1820/24 + 640/590*574/(2400*640)*400/24 = 0.038 gp = 0.038 0.36*β1 = 0.36*0.85 = 0.306 * 단면의인장지배여부확인 c/dp = (a'/β1) / dp = (26.71/0.85) / 590 = 0.053 c/dp = 0.053 < 0.375 / 인장지배 14. 휨균열모멘트검토 fr = 0.63* fck = 0.63* 35 = 3.73 MPa Ms = 77.16 + 0 + 58.44 = 135.60 kn-m Mcr1 = (fr + Pt/Ac + Pt*e/Sb - Ms/Sb )*Z2c = (3.73 + 658.8*10^3/285000 + 658.8*10^3*310.19/23835474-135.6*10^6/23835474)*32188951*1/10^6 = 287.32 kn-m Mcr = Ms + Mcr1 = 135.6 + (287.32) = 422.92 kn-m φmn/mcr = 650.63/422.92 = 1.54 1.20 15. Check Deflection a. Instantaneous Camber Δ = Pi*e*Ln² / (8*Eci*I) = 741.6*10^3*310.19*9500² / (8*25964*9777072999) = 10.223 mm b. 부재자중에의한처짐 Δ = 5*ws*Ln⁴ / (384*Eci*I) = 5*6.84*9500⁴ / (384*25964*9777072999) = 2.858 mm c. Dead Load에의한처짐 Δ = 5*ws*Ln⁴ / (384*Ec*I) = 5*0*9500⁴ / (384*28825*9777072999) = 0.000 mm d. Topping Slab에의한처짐 Δ = 5*ws*Ln⁴ / (384*Ec*I) = 5*5.18*9500⁴ / (384*28825*9777072999) = 1.949 mm e. Finish Load에의한처짐 Δ = 5*ws*Ln⁴ / (384*Ec*Icc) = 5*0.72*9500⁴ / (384*28825*16258317421) = 0.163 mm 4/7 쪽
f. Live Load에의한처짐 Δ = 5*(1-RF)*ws*Ln⁴ / (384*Ec*Icc) = 5*(1-0)*14.4*9500⁴ / (384*28825*16258317421) = 3.259 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) -10.223 1.00-10.223-10.223 1.80-18.401-10.223 2.20-22.491 2.858 1.00 2.858 2.858 1.85 5.287 2.858 2.40 6.859-7.365 0.000 1.00 0.000 0.000 2.30 0.000 1.949 1.00 1.949 1.949 2.30 4.483 0.163 1.00 0.163 0.163 3.00 0.489-11.002-10.660 Deflection(LL) 3.259-7.401 ΔTL = (-10.66-(-11.002)) + 3.259 = 3.601 mm ( 모든지속하중에의한장기처짐 + 추가적인활하중에의한순간처짐 ) h. Check Δ allowable Ln/360 = 9500/360 = 26.39 mm ΔLL = 3.259 mm Ln/480 = 9500/480 = 19.79 mm ΔTL = 3.601 mm 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 0.00 635.00 791.67 1583.33 2375.00 3166.67 3958.33 4750.00 345.00 (mm) Vu 182.07 157.73 151.72 121.38 91.03 60.69 30.34 0.00 168.84 (kn) Mu 0.00 107.89 132.13 240.23 324.31 384.36 420.40 432.41 60.53 (kn-m) dp 590.00 590.00 590.00 590.00 590.00 590.00 590.00 590.00 590.00 (mm) d = MAX(0.8*h, dp) 590.00 590.00 590.00 590.00 590.00 590.00 590.00 590.00 590.00 (mm) Vu*dp/Mu 1.00 0.86 0.68 0.30 0.17 0.09 0.04 0.00 1.00 Prestress force P 0 658.80 658.80 658.80 658.80 658.80 658.80 658.80 357.93 (kn) fpc = P/Ac 0.00 2.31 2.31 2.31 2.31 2.31 2.31 2.31 1.26 (MPa) Vp 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 (kn) φvc1 689.74 598.68 481.59 234.41 149.85 97.81 65.29 39.27 689.74 (kn) φvc2 227.75 319.75 319.75 319.75 319.75 319.75 319.75 319.75 277.93 (kn) φvc3 130.89 130.89 130.89 130.89 130.89 130.89 130.89 130.89 130.89 (kn) φvc4 327.23 327.23 327.23 327.23 327.23 327.23 327.23 327.23 327.23 (kn) φvc 227.75 319.75 319.75 234.41 149.85 130.89 130.89 130.89 277.93 (kn) φvc /2 113.88 159.88 159.88 117.21 74.93 65.45 65.45 65.45 138.97 (kn) φvs 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 (kn) ( 최소 ) ( 불필요 ) ( 불필요 ) ( 최소 ) ( 최소 ) ( 불필요 ) ( 불필요 ) ( 불필요 ) ( 최소 ) φ*2/3* fck*bw*d (kn) φ*1/3* fck*bw*d (kn) leg 2 2 2 2 2 2 2 2 2 leg stirrup HD10 HD10 HD10 HD10 HD10 HD10 HD10 HD10 HD10 S1 517 517 517 517 517 517 517 517 517 (mm) S2 512 512 512 512 512 512 512 512 512 (mm) S3 540 540 540 540 540 540 540 540 540 (mm) S4 1741 1741 1741 1741 1741 1741 1741 1741 1741 (mm) S5 (mm) S = MIN(S1,S2,S3,S4,S5) 512 512 512 512 512 512 512 512 512 (mm) USE @200 @200 @200 @200 @200 @200 @200 @200 @200 (mm) 5/7 쪽
350.00 300.00 250.00 전단보강여부검토 (Half Span) Vu(kN) φvc(kn) 위험단면 φvc/2(kn) Vu(kN) or ΦVc(kN) 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 5000.00 거리 (mm) a. Use 2leg- HD10 (Av = 142.00 mm 2 ) Smax1 = MIN(3/4*h, 600) = MIN(3/4*690, 600) = 517 mm Smax2 = Av*fys / (0.0625* fck*bw) = 142*400 / (0.0625* 35*300) = 512 mm Smax3 = Av*fys / (0.35*bw) = 142*400/(0.35*300) = 540 mm Smax4 = Av / ((Aps/80)*(fpu/fys)*(1/d) * (d/bw)) = 142 / ((592.26/80)*(1854/400)*(1/590) * (590/300)) = 1741 mm Smax = MIN(Smax1, Smax2, Smax3, Smax4) = MIN( 517, 512, 540, 540) = 512 mm b. 콘크리트전단강도 dp = 590.00 mm d = MAX(dp, 0.8*h) = MAX(590, 0.8*690) = 590.00 mm 위험단면 CS = 345.00 mm Vu = MF*wu*Ln/2 - MF*wu*CS = 1*38.33*(9500/10^3)/2-1*38.33*(345/10^3) = 168.84 kn Mu = MF*wu*CS*(L-CS) / 2 = 1*38.33*(345/10^3)*((9500/10^3)-(345/10^3))/2 = 60.53 kn-m Vu/Mu*dp = MIN(168.84*(590/1000) / 60.53, 1.0) = MIN(1.65, 1.0) = 1.00 전달길이 50*ds = 50*12.7 = 635.00 mm 프리스트레스힘 P = Pt/(50*ds)*CS = 658.8/(50*12.7)*345 = 357.93 kn fpc = P / Ac = 357.93*10^3/285000 = 1.26 MPa Vp = P*slope = 357.93*(590-590)/(4750-0) = 0.00 kn φvc1 = φ*(0.05* fck + 4.9*Vu/Mu*dp)*bw*d = 0.75*(0.05* 35 + 4.9*1)*300*590/10^3 = 689.74 kn φvc2 = φ*((0.29* fck + 0.3*fpc)*bw*d + Vp) = 0.75*(0.29* 35 + 0.3*1.26)* 300*590/10^3 + 0) = 277.93 kn φvc3 = φ*1/6* fck*bw*d = 0.75 * 1/6 * 35*300*590/10^3 = 130.89 kn φvc4 = φ*5/12* fck*bw*d = 0.75*5/12* 35*300*590/10^3 = 327.23 kn φvc = MIN( MAX( MIN(Vc1, Vc2), Vc3), Vc4 ) = MIN( MAX( MIN( 689.74, 277.93), 130.89), 327.23) = 277.93 kn c. 전단보강근의전단강도 φvs = Vu - φ*vc = 168.84-277.93 = -109.09 kn 최소전단보강근 6/7 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*ht = 0.85*24*2400*90/10^3 = 4406.4 kn T1 = Aps*fps = 592.26*1820/10^3 = 1077.91 kn T2 = As*fy = 574*400/10^3 = 229.60 kn T = T1 + T2 = 1077.91 + 229.6 = 1307.51 kn Fh = MIN(C, T) = MIN( 4406.4, 1307.51 ) = 1307.51 kn bv = 2400 mm Lvh = 4750.00 mm φvnh = φ*τnh*bv*lvh = 0.75*0.56*2400*4750/1000 = 4788.00 kn Fh/φVnh = 1307.51 / 4788 = 0.273 1.00 7/7 쪽