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Betonske konstrukcije - <strong>EC2</strong>ε c2 (%o) ε s1 (‰) ξ=x/d ζ=z/d μ sd-3.5 10.5 0.250 0.896 0.154-3.5 10.0 0.259 0.892 0.159-3.5 9.5 0.269 0.888 0.164-3.5 9.0 0.280 0.884 0.170-3.5 8.5 0.292 0.879 0.177-3.5 8.0 0.304 0.874 0.183-3.5 7.5 0.318 0.868 0.190-3.5 7.0 0.333 0.861 0.197-3.5 6.5 0.350 0.854 0.206-3.5 6.0 0.368 0.847 0.214-3.5 5.5 0.389 0.838 0.224-3.5 5.0 0.412 0.829 0.235-3.5 4.5 0.438 0.818 0.247-3.5 4.0 0.467 0.806 0.259-3.5 3.5 0.500 0.792 0.272-3.5 3.0 0.538 0.776 0.287-3.5 2.5 0.583 0.757 0.304-3.5 2.0 0.636 0.735 0.322-3.5 1.5 0.700 0.709 0.342-3.5 1.0 0.778 0.676 0.362-3.5 0.5 0.875 0.636 0.3832
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Betonske konstrukcije - <strong>EC2</strong>Tablice <strong>za</strong> odabir armature (ploča, zid)RazmakšipakaPovršina presjeka u cm 2 na širini ploče od 100 cmPromjer šipke u mmt 6 7 8 10 12 14 16 18 207.0 4.04 5.50 7.18 11.22 16.16 21.99 28.73 36.36 44.877.5 3.77 5.13 6.70 10.47 15.08 20.52 26.81 33.93 41.888.0 3.53 4.81 6.28 9.82 14.14 19.24 25.14 31.81 39.268.5 3.33 4.53 5.91 9.24 13.31 18.11 23.66 29.94 36.959.0 3.14 4.28 5.59 8.73 12.57 17.10 22.34 28.28 34.909.5 2.98 4.05 5.29 8.27 11.90 16.20 21.17 26.79 33.0610.0 2.83 3.85 5.03 7.85 11.31 15.39 20.11 25.45 31.4110.5 2.69 3.67 4.79 7.48 10.77 14.66 19.15 24.24 29.9111.0 2.57 3.50 4.57 7.14 10.28 13.99 18.28 23.14 28.5511.5 2.46 3.35 4.37 6.83 9.84 13.39 17.49 22.13 27.3112.0 2.36 3.21 4.19 6.54 9.42 12.83 16.76 21.21 26.1712.5 2.26 3.08 4.02 6.28 9.05 12.32 16.09 20.36 25.1313.0 2.17 2.96 3.87 6.04 8.70 11.84 15.47 19.58 24.1613.5 2.09 2.85 3.72 5.82 8.38 11.40 14.90 18.85 23.2714.0 2.02 2.75 3.59 5.61 8.08 11.00 14.36 18.18 22.4414.5 1.95 2.65 3.47 5.42 7.80 10.62 13.87 17.55 21.6615.0 1.89 2.57 3.35 5.24 7.54 10.26 13.41 16.97 20.9415.5 1.82 2.48 3.24 5.07 7.30 9.93 12.97 16.42 20.2716.0 1.77 2.41 3.14 4.91 7.07 9.62 12.57 15.90 19.6416.5 1.71 2.33 3.05 4.76 6.85 9.33 12.19 15.42 19.0417.0 1.66 2.26 2.96 4.62 6.65 9.05 11.83 14.97 18.4817.5 1.62 2.20 2.87 4.49 6.46 8.79 11.49 14.54 17.9518.0 1.57 2.14 2.79 4.36 6.28 8.55 11.17 14.14 17.4618.5 1.53 2.08 2.72 4.25 6.11 8.32 10.87 13.76 16.9419.0 1.49 2.03 2.65 4.13 5.95 8.10 10.58 13.39 16.5419.5 1.45 1.97 2.58 4.03 5.80 7.89 10.31 13.05 16.1120.0 1.41 1.92 2.51 3.93 5.65 7.69 10.05 12.72 15.724
Betonske konstrukcije - <strong>EC2</strong>Tablice <strong>za</strong> odabir armature (grede)Fi(mm) kg/m 1 2 3 4 5 6 7 8 9 10 11 12 13 14 158 0,405 0,50 1,01 1,51 2,01 2,51 3,02 3,52 4,02 4,52 5,03 5,53 6,03 6,54 7,04 7,5410 0,634 0,79 1,57 2,36 3,14 3,93 4,71 5,50 6,20 7,07 7,85 8,64 9,42 10,21 11,00 11,7812 0,911 1,13 2,26 3,39 4,52 5,66 6,79 7,92 9,05 10,18 11,31 12,44 13,57 14,70 15,83 16,9714 1,242 1,54 3,08 4,62 6,16 7,70 9,24 10,78 12,32 13,86 15,39 16,93 18,47 20,01 21,55 23,0916 1,621 2,01 4,02 6,03 8,04 10,05 12,06 14,07 16,09 18,10 20,11 22,12 24,13 26,14 28,15 30,1618 2,170 2,54 5,09 7,63 10,18 12,72 15,27 17,81 20,36 22,90 25,45 27,99 30,54 33,08 35,63 38,1719 2,288 2,84 5,67 8,51 11,34 14,18 17,01 19,85 22,68 25,52 28,35 31,19 34,02 36,86 39,69 42,5320 2,536 3,14 6,28 9,43 12,57 15,71 18,85 21,99 25,13 28,27 31,42 34,56 37,70 40,84 43,98 47,1222 3,058 3,80 7,60 11,40 15,21 19,01 22,81 26,64 30,41 34,21 38,01 41,81 45,62 49,42 53,22 57,0224 3,652 4,52 9,05 13,57 18,10 22,62 27,14 31,67 36,19 40,72 45,24 49,76 54,29 58,81 63,34 67,8625 3,951 4,91 9,82 14,73 19,64 24,54 29,45 34,36 39,27 44,18 49,09 54,00 58,90 63,81 68,72 73,6328 4,956 6,16 12,32 18,47 24,63 30,79 36,95 43,10 49,26 55,42 61,58 67,73 73,88 80,05 86,21 92,3632 6,474 8,04 16,09 24,13 32,17 40,21 48,26 56,30 64,34 72,38 80,42 88,47 96,50 104,55 112,60 120,6436 8,200 10,18 20,36 30,54 40,72 50,89 61,07 71,25 81,43 91,61 101,79 111,97 122,15 132,32 142,50 152,68razmak armature/m 100,00 50,00 33,34 25,00 20,00 16,67 14,30 12,50 11,11 10,00 9,10 8,33 7,70 7,14 6,676
Betonske konstrukcije - <strong>EC2</strong>Tablice <strong>za</strong> odabir armature grede.kom φ (mm) A s2 8 1.013 8 1.512 10 1.574 8 2.012 12 2.263 10 2.365 8 2.512 14 3.084 10 3.143 12 3.395 10 3.932 16 4.024 12 4.523 14 4.625 12 5.652 19 5.673 16 6.034 14 6.162 20 6.282 22 7.605 14 7.704 16 8.043 19 8.513 20 9.422 25 9.825 16 10.054 19 11.343 22 11.402 28 12.324 20 12.575 19 14.183 25 14.734 22 15.215 20 15.712 32 16.083 28 18.475 22 19.014 25 19.632 36 20.363 32 24.135 25 24.544 28 24.633 36 30.545 28 30.794 32 32.175 32 40.214 36 40.725 36 50.897
Betonske konstrukcije - <strong>EC2</strong>R mrežeTip Profili (mm) Razmaci (mm) Dimenzije (m) kg/m2 kg/komR 131 5,0x4,2 150x250 6,00x2,20 1,50 19,80R 131 5,0x4,6 150x250 6,00x2,20 1,63 21,50R 139 4,2x4,2 100x250 6,00x2,20 1,55 20,50R 166 4,6x4,2 100x250 6,00x2,20 1,76 23,30R 166 4,6x4,6 100x250 6,00x2,20 1,85 24,50R 188 6,0x4,2 150x250 6,00x2,20 1,96 26,00R 188 6,0x4,6 150x250 6,00x2,20 2,08 27,50R 196 5,0x4,2 150x250 6,00x2,20 2,00 26,50R 226 6,0x4,2 125x250 6,00x2,20 2,27 30,00R 257 7,0x5,0 150x250 6,00x2,20 2,72 35,80R 283 6,0x4,6 100x250 6,00x2,20 2,77 36,60R 283 6,0x5,0 100x250 6,00x2,20 2,88 38,00R 335 8,0x5,0 150x250 6,00x2,20 3,33 44,00R 335 8,0x6,0 150x250 6,00x2,20 3,63 48,00R 385 7,0x5,0 100x250 6,00x2,20 3,68 48,60R 424 9,0x6,0 150x250 6,00x2,20 4,34 57,30R 503 8,0x5,0 100x200 6,00x2,20 4,77 63,00R 503 8,0x5,0 100x250 6,00x2,20 4,58 60,50R 503 8,0x6,0 100x250 6,00x2,20 4,89 64,60R 524 10,0x6,0 150x250 6,00x2,15 5,15 68,00R 636 9,0x6,0 100x250 6,00x2,15 5,95 78,50R 785 10,0x6,0 100x250 6,00x2,15 7,35 97,00R 785 10,0x6,0 100x200 6,00x2,20 7,39 97,50Q mrežeTip Profili (mm) Razmaci (mm) Dimenzije (m) kg/m2 kg/komQ 069 4,2x4,2 200x200 6,00x2,20 1,10 14,50Q 131 5,0x5,0 150x150 6,00x2,20 2,12 28,00Q 139 4,2x4,2 100x100 6,00x2,20 2,20 29,05Q 166 4,6x4,6 100x100 6,00x2,20 2,64 34,90Q 188 6,0x6,0 150x150 6,00x2,20 3,06 40,40Q 196 5,0x5,0 100x100 6,00x2,15 3,07 40,50Q 226 6,0x6,0 125x125 6,00x2,20 3,63 48,00Q 257 7,0x7,0 150x150 6,00x2,20 4,16 55,00Q 283 6,0x6,0 100x100 6,00x2,20 4,48 59,15Q 335 8,0x8,0 150x150 6,00x2,20 5,45 72,00Q 385 7,0x7,0 100x100 6,00x2,20 6,10 80,60Q 424 9,0x9,0 150x150 6,00x2,20 6,81 90,00Q 503 8,0x8,0 100x100 6,00x2,20 8,03 106,00Q 524 10,0x10,0 150x150 6,00x2,20 8,40 110,90Q 636 9,0x9,0 100x100 6,00x2,20 10,08 133,05Q 785 10,0x10,0 100x100 6,00x2,20 12,46 164,508
Betonske konstrukcije - <strong>EC2</strong>Tablice <strong>za</strong> proračun ploča nosivih u dva okomita smjera opterećenihravnomjerno podijeljenim opterećenjem po cijeloj pločiλ =llyxMxmaks=qlϕ2xxMymaks2qly= qx=κ◊q qy=(1-kx)qϕy______________±±±±±±±±±±±±± upeti ležaj----------------------slobodno položeni ležajSlučaj 1 l j 1x D j 1y D k 1x D1 2 3 4 5 6 70.500.550.600.650.700.75169.17125.1094.9475.3161.6051.698.8146.0313.9272.7411.98310.5711.3512.3013.4414.7916.350.1560.1900.2280.2700.3130.05880.08380.11470.15150.19360.24040.00500.00620.00730.00840.00930.800.850.900.951.0043.9738.2934.2630.4427.431.5441.1360.8070.7640.60218.0120.1522.3624.7927.430.3310.4270.4440.4860.5270.29060.34300.39620.44890.50000.01000.01050.01060.01050.01021.101.201.301.401.5022.7919.4517.0215.2213.870.4640.3340.2440.1800.13533.3740.3448.6058.4570.220.5940.6970.8260.9851.1760.59420.67470.74070.79350.83510.00940.00800.00660.00530.00421.601.701.801.902.0012.8812.0611.4510.9710.570.0990.0820.0610.0480.04084.43100.77121.69143.00169.171.4211.6342.0922.1312.6170.86660.89310.91300.92870.94120.00330.00250.00200.00160.00129
Betonske konstrukcije - <strong>EC2</strong>Slučaj 2 l j 2x D j 2y D k 2x D8 9 10 11 12 13 140.500.550.600.650.700.75140.91107.3785.3070.5959.2450.866.7074.4142.9422.2701.67611.2812.3813.7015.2917.1919.410.2170.2660.3200.3790.4440.13510.18620.24470.30860.37510.44170.01020.01170.01280.01330.01330.800.850.900.951.0044.5639.7035.7432.5429.931.2590.9710.7920.6400.52221.9924.9628.3732.3036.750.5160.5950.6830.7860.8900.50590.56610.62120.67060.71430.01290.01210.01100.00990.00871.101.201.301.401.5026.0223.3321.4320.0419.020.3910.2690.1910.1380.10347.5861.3878.75100.28126.641.0831.3811.7362.1532.6360.78540.83830.87720.90570.92680.00710.00530.00390.00290.0021ly UVIJEK PARALELNO SUKLIJEŠTENIM RUBOM1.601.701.801.902.0018.3017.6317.0516.6716.500.0710.0670.0590.0370.021158.52196.69239.81295.08357.033.1893.8174.3125.5276.1950.94250.95430.96330.97020.97560.00160.00120.00090.00070.0005Slučaj 3 l j 3x D j 3y D k 3x D15 16 17 18 19 20 210.500.550.600.650.700.75136.06107.4287.6273.7663.6956.165.7283.9602.7722.0141.50512.4814.1016.1218.6021.1625.240.3230.4040.4960.6030.7250.23810.31390.39320.47160.54560.61270.01520.01590.01570.01480.01340.800.850.900.951.0050.4245.9742.4839.7037.471.1480.8910.6980.5550.44629.5634.6640.6547.6455.740.8641.0211.1991.3981.6200.67090.72300.76640.80290.83330.01160.01040.00870.00730.00611.101.201.301.401.5034.1831.9330.3429.1828.310.3290.2250.1590.1160.08775.33101.68134.65175.88226.651.9592.6353.2984.1235.0770.87980.91200.93460.95050.96200.00460.00320.00230.00160.0012l y UVIJEK PARALELNO SUKLIJEŠTENIM RUBOM1.601.701.801.902.0027.6427.1226.7126.3726.090.0670.0520.0410.0340.028288.36362.50450.72555.49675.816.1717.4148.82210.37712.1320.97040.97660.98130.98490.98770.00080.00060.00050.00040.000310
Betonske konstrukcije - <strong>EC2</strong>Slučaj 4 l j 4x D j 4y D k 4x D22 23 24 25 26 27 280.500.550.600.650.700.75271.75194.98145.73112.9290.1673.996.7074.4142.9422.2701.67616.9817.8418.8920.1621.6523.410.1710.2090.2540.2980.3530.05880.08380.11470.15150.19360.24040.00500.00620.00730.00840.00930.800.850.900.951.0062.1853.3446.5841.5237.151.2591.7681.3521.0520.83325.4727.8430.5633.6537.150.4110.4650.5430.6190.7000.29060.34300.39620.44890.50000.01000.01050.01060.01050.01021.101.201.301.401.5031.0927.0124.1722.1220.620.6060.4080.2850.2040.15045.5256.0169.0284.99104.380.8371.0631.2871.5961.9400.59420.67470.74070.79350.83510.00940.00800.00660.00530.00421.601.701.801.902.0019.4918.6217.9517.4116.980.1130.0870.0680.0530.043127.72155.54188.41226.93271.752.3342.7823.2873.8524.8820.86760.89310.91300.92870.94120.00330.00250.00200.00160.0012Slučaj 5 l j 5xD j 5yD k 5x D29 30 31 32 33 34 350.500.550.600.650.700.75246.42186.97138.61110.3090.6576.5811.8919.6715.6613.9312.81417.8819.1220.6822.6024.9227.690.2510.3130.3840.4640.5550.11110.15470.20580.26310.32440.38760.00870.01020.01140.01230.01260.800.850.900.951.0066.2458.4652.5147.8644.182.0681.5561.1910.9800.73630.9834.8439.3544.5650.570.6580.7720.9001.0431.2010.45030.51080.56750.61960.66670.01250.01210.01140.01040.0094l y UVIJEK PARALELNO SASLOBODNO POLOŽENIMRUBOM1.101.201.301.401.501.601.701.801.902.0038.8435.2732.7931.0129.7128.7327.9727.3826.9226.540.5350.3570.2480.1780.1300.0930.0750.0590.0470.03865.3084.25108.24138.11174.79219.29272.66336.02410.58497.611.4741.8952.3982.9873.6694.4505.3376.3377.4568.7020.74540.80570.85100.88480.91010.92910.94350.95450.96310.96970.00790.00600.00450.00380.00250.00190.00140.00110.00090.000711
Betonske konstrukcije - <strong>EC2</strong>Slučaj 6 l j 6x D j 6y D k 6x D36 37 38 39 40 41 420.500.550.600.650.700.75436.53310.15229.50175.97139.24113.3025.27616.13010.7067.3465.18927.2828.3829.7431.4133.4335.850.2200.2730.3340.4040.4830.05880.08380.11470.15150.19360.24040.00500.00620.00730.00840.00930.800.850.900.951.0094.5180.6070.1062.0455.743.7572.7822.1001.6141.25938.7142.0846.0050.5355.740.5730.6730.7840.9071.0430.29060.34300.39620.44890.50000.01000.01050.01060.01050.01021.101.201.301.401.5046.7740.9036.8934.0832.040.8970.5880.4000.2820.20468.4884.80105.38130.92162.221.2741.6322.0572.5553.1300.59420.67470.74070.79350.83510.00940.00800.00660.00530.00421.601.701.801.902.0030.5429.4028.5227.7527.280.1510.1140.0880.0770.047200.13245.53299.38362.69436.533.7904.5405.3856.3317.3840.86760.89310.91300.92870.94120.00330.00250.00200.00160.001212
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Betonske konstrukcije - <strong>EC2</strong>PRIJENOS OPTEREĆENJA S PLOČE NOSIVE U DVA SMJERA NA GREDE I ZIDOVELežajni pritisak pravokutnih ploča na grede ili zidove kontinuirano je promjenljiv oblika parabole.Za potrebe prakse ovo opterećenje <strong>za</strong>mjenjuje se trapeznim (<strong>za</strong> dužu stranu ploče) ili trokutnim (<strong>za</strong>kraću stranu ploče). Grede se radi jednostavnosti proračuna nadalje mogu proračunavati sa<strong>za</strong>mjenjujućim jednolikim kontinuiranim opterećenjem (<strong>prema</strong> izrazima danim na slici). Ovim<strong>za</strong>mjenjujućim opterećenjem dobiju se isti momenti savijanja, ali oko 25% veće poprečne sile.24
Betonske konstrukcije - <strong>EC2</strong>Prosta greda:R A,g =R B,g =V A,g =V B,g = 0.5◊g◊LR A,q =R B,q =V A,q =V B,q = 0.5◊q◊LM 1,g = 0.125◊g◊L 2M 1,q = 0.125◊g◊L 2M Sd =1.35◊M g +1.5◊M qV Sd =1.35◊V g +1.5◊V qProsta greda s jednim prepustom:gR = V = ⋅ L −L2⋅LRAq,= VAq,= 0.5⋅q⋅LgR ( ) 2Bg ,= ⋅ L+Lk2⋅LqR ( ) 2Bq ,= ⋅ L+Lk2⋅Lg 2 2VBlg,,= ⋅ ( L + Lk)2⋅Lq 2 2VBlq,,= ⋅ ( L + Lk)2⋅LV = g⋅LV2 2( )A, g A,g kBd , , gBdq , ,= q⋅Lkk2RA,gM1,g=2 ⋅ g2M1, = 0.125⋅q⋅LqM2, g= −0.5⋅g⋅LM2, q= −0.5⋅q⋅L2k2k25
Betonske konstrukcije - <strong>EC2</strong>Prosta greda s dva prepusta:RRVVAg ,Aq ,A,,lgA,,lq( 2 )g⋅ L+ ⋅Lk=2q⋅ L+ 2⋅Lk=2= g⋅L= q⋅L( )V = R − VA, dg , Ag , Alg , ,V = R − VA, dq , Aq , Alq , ,kkM1, g= 0.125⋅g⋅L −0.5⋅g⋅LM1, = 0.125⋅q⋅LqM2, g= −0.5⋅g⋅LM2,= −0.5⋅q⋅Lq2 2k22k2kKontinuirani nosač preko dva raspona:R = V = 0.375⋅g ⋅ LA,gA,qA,gR = V = 0.438⋅q ⋅ LRB,gRB,qVB,gVB,qA,q= 1.25⋅g⋅L= 1.25⋅q⋅L= 0.625⋅g ⋅ L= 0.625⋅q ⋅ LM1,gM1,q= 0.070⋅g ⋅ L= 0.096⋅q ⋅ L22M2,gM2,q= −0.125⋅g ⋅ L= −0.125⋅q ⋅ L2226
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