GEOMETRIJSKE KARAKTERISTIKE POPRE^NOG PRESEKA

Globalni sistem X0-Y0 osa Lokalni sistem te`i{nih Xt-Yt osa

Povr{ina preseka - A= 0.375 Polo`aj te`i{ta X0t= 0.000 Odstojanje gornje ivice preseka - yg= 0.600Stat.moment oko X0 ose- Sx0= 0.225 Polo`aj te`i{ta Y0t= 0.600 Odstojanje donje ivice preseka - yd= -0.600Stat.moment oko Y0 ose - Sy0= 0.000 Moment inercije oko Xt ose - Ixt= 0.061 Visina preseka - D= 1.200

Moment inercije oko X0 ose - Ix0= 0.196 Moment inercije oko Yt ose - Iyt= 0.005 Otporni moment oko gornje ivice - Wg= 0.102Moment inercije oko Y0 ose - Iy0= 0.01 Centrifugalni moment - Ixyt= 0.000 Otporni moment oko donje ivice - Wd= 0.102

Centrifugalni moment inercije -Ixy0= 0.00 Odstojanje gornje ta~ke jezgra preseka - Kg= 0.273Odstojanje donje ta~ke jezgra preseka - Kd= 0.273

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Spolja{nji uticaji

L= 20.00g= 9.375

16.000p= 8.500

x Mg Mp Mqm kNm kNm kNm kNm

0.00 0 0 0 01.00 65.63 112.00 59.50 237.132.00 121.88 208.00 110.50 440.383.00 168.75 288.00 153.00 609.754.00 206.25 352.00 187.00 745.255.00 234.38 400.00 212.50 846.886.00 253.13 432.00 229.50 914.637.00 262.50 448.00 238.00 948.508.00 262.50 448.00 238.00 948.509.00 253.13 432.00 229.50 914.63

10.00 234.38 400.00 212.50 846.8811.00 206.25 352.00 187.00 745.2512.00 168.75 288.00 153.00 609.7513.00 121.88 208.00 110.50 440.3814.00 65.63 112.00 59.50 237.1315.00 0.00 0.00 0.00 0.0016.00 -75.00 -128.00 -68.00 -271.0017.00 -159.38 -272.00 -144.50 -575.8818.00 -253.13 -432.00 -229.50 -914.6319.00 -356.25 -608.00 -323.00 -1287.2520.00 -468.75 -800.00 -425.00 -1693.75

Trasa kabla

L= 20.000xB= 20.000yB= 0.450f= 0.400

x ym m Gornja kontura nosa~a

0.00 0.000 x y1.00 -0.053 0.00 0.62.00 -0.099 20.00 0.63.00 -0.1374.00 -0.1665.00 -0.1886.00 -0.201

Dg=

MDg

7.00 -0.2078.00 -0.2049.00 -0.194 Donja kontura nosa~a

10.00 -0.175 x y11.00 -0.149 0.00 -0.612.00 -0.114 20.00 -0.613.00 -0.07214.00 -0.02115.00 0.03716.00 0.10417.00 0.17918.00 0.26119.00 0.35220.00 0.450

Samo za crtanje, promena znaka

0.00 0.00 0.00 0.00-65.63 -112.00 -59.50 -237.13

-121.88 -208.00 -110.50 -440.38-168.75 -288.00 -153.00 -609.75-206.25 -352.00 -187.00 -745.25-234.38 -400.00 -212.50 -846.88-253.13 -432.00 -229.50 -914.63-262.50 -448.00 -238.00 -948.50-262.50 -448.00 -238.00 -948.50-253.13 -432.00 -229.50 -914.63-234.38 -400.00 -212.50 -846.88-206.25 -352.00 -187.00 -745.25-168.75 -288.00 -153.00 -609.75-121.88 -208.00 -110.50 -440.38

-65.63 -112.00 -59.50 -237.130.00 0.00 0.00 0.00

75.00 128.00 68.00 271.00159.38 272.00 144.50 575.88253.13 432.00 229.50 914.63356.25 608.00 323.00 1287.25468.75 800.00 425.00 1693.75

Sila prethodnog naprezanja - trenje Uticaji prethodnog naprezanja

Nk0= 3540 tgalfa= 0.0800 qksr= 27.005L= 20.00 alfa= 0.0798 we= 0.95k= 0.0030 we*qksr= 25.654m= 0.2200 Nksr= 3375.57

Faza peth.napr.x Nk(x) Nkx/Nk0 x Mk0m rad kN m kNm

0.00 0.0000 3540.00 1.000 0.00 0.001.00 0.0080 3523.20 0.995 1.00 -179.582.00 0.0160 3506.49 0.991 2.00 -333.513.00 0.0239 3489.85 0.986 3.00 -461.784.00 0.0319 3473.29 0.981 4.00 -564.405.00 0.0399 3456.81 0.976 5.00 -641.366.00 0.0479 3440.40 0.972 6.00 -692.67

q(x)

7.00 0.0559 3424.08 0.967 7.00 -718.328.00 0.0639 3407.83 0.963 8.00 -718.329.00 0.0718 3391.66 0.958 9.00 -692.67

10.00 0.0798 3375.57 0.954 10.00 -641.3611.00 0.0878 3359.55 0.949 11.00 -564.4012.00 0.0958 3343.61 0.945 12.00 -461.7813.00 0.1038 3327.75 0.940 13.00 -333.5114.00 0.1118 3311.96 0.936 14.00 -179.5815.00 0.1197 3296.24 0.931 15.00 0.0016.00 0.1277 3280.60 0.927 16.00 205.2317.00 0.1357 3265.03 0.922 17.00 436.1218.00 0.1437 3249.54 0.918 18.00 692.6719.00 0.1517 3234.12 0.914 19.00 974.8620.00 0.1597 3218.78 0.909 20.00 1282.72

Uticaji prethodnog naprezanja UKupni uticaji u presecima

w= 0.8we*w*qksr 20.52

Faza peth.napr. Faza ekspl. Faza peth.napr. Faza ekspl.Nk0 Mkt Nkt x M0 N0 Mt NtkN kNm kN m kNm kN kNm kN

3363.00 0.00 2690.40 0.00 0.00 3363.00 0.00 2690.403347.04 -143.66 2677.63 1.00 -113.96 3347.04 93.46 2677.633331.16 -266.81 2664.93 2.00 -211.63 3331.16 173.57 2664.933315.35 -369.42 2652.28 3.00 -293.03 3315.35 240.33 2652.283299.62 -451.52 2639.70 4.00 -358.15 3299.62 293.73 2639.703283.97 -513.09 2627.17 5.00 -406.98 3283.97 333.79 2627.173268.38 -554.13 2614.71 6.00 -439.54 3268.38 360.49 2614.71

3252.88 -574.66 2602.30 7.00 -455.82 3252.88 373.84 2602.303237.44 -574.66 2589.95 8.00 -455.82 3237.44 373.84 2589.953222.08 -554.13 2577.66 9.00 -439.54 3222.08 360.49 2577.663206.79 -513.09 2565.43 10.00 -406.98 3206.79 333.79 2565.433191.58 -451.52 2553.26 11.00 -358.15 3191.58 293.73 2553.263176.43 -369.42 2541.14 12.00 -293.03 3176.43 240.33 2541.143161.36 -266.81 2529.09 13.00 -211.63 3161.36 173.57 2529.093146.36 -143.66 2517.09 14.00 -113.96 3146.36 93.46 2517.093131.43 0.00 2505.14 15.00 0.00 3131.43 0.00 2505.143116.57 164.19 2493.26 16.00 130.23 3116.57 -106.81 2493.263101.78 348.90 2481.43 17.00 276.75 3101.78 -226.98 2481.433087.06 554.13 2469.65 18.00 439.54 3087.06 -360.49 2469.653072.42 779.89 2457.93 19.00 618.61 3072.42 -507.36 2457.933057.84 1026.17 2446.27 20.00 813.97 3057.84 -667.58 2446.27

C-linije

Samo za crtanje

t=0 tM0 Mt x C0 Ct Klasi~no jezgro preseka

m m m0.00 0.00 0.00 0.000 0.000 K2 0

113.96 -93.46 1.00 -0.034 0.035 20.000211.63 -173.57 2.00 -0.064 0.065 K1 0293.03 -240.33 3.00 -0.088 0.091 20.000358.15 -293.73 4.00 -0.109 0.111406.98 -333.79 5.00 -0.124 0.127439.54 -360.49 6.00 -0.134 0.138

455.82 -373.84 7.00 -0.140 0.144455.82 -373.84 8.00 -0.141 0.144439.54 -360.49 9.00 -0.136 0.140406.98 -333.79 10.00 -0.127 0.130358.15 -293.73 11.00 -0.112 0.115293.03 -240.33 12.00 -0.092 0.095211.63 -173.57 13.00 -0.067 0.069113.96 -93.46 14.00 -0.036 0.037

0.00 0.00 15.00 0.000 0.000-130.23 106.81 16.00 0.042 -0.043-276.75 226.98 17.00 0.089 -0.091-439.54 360.49 18.00 0.142 -0.146-618.61 507.36 19.00 0.201 -0.206-813.97 667.58 20.00 0.266 -0.273

Pro{ireno jezgro preseka

t=0 t=tKlasi~no jezgro preseka x K1 K2 K1 K2

m m m m m0.273 0.00 -0.273 0.273 -0.273 0.2730.273 1.00 -0.273 0.273 -0.273 0.273

-0.273 2.00 -0.273 0.273 -0.273 0.273-0.273 3.00 -0.273 0.273 -0.273 0.273

4.00 -0.273 0.273 -0.273 0.2735.00 -0.273 0.273 -0.273 0.2736.00 -0.273 0.273 -0.273 0.273

7.00 -0.273 0.273 -0.273 0.2738.00 -0.273 0.273 -0.273 0.2739.00 -0.273 0.273 -0.273 0.273

10.00 -0.273 0.273 -0.273 0.27311.00 -0.273 0.273 -0.273 0.27312.00 -0.273 0.273 -0.273 0.27313.00 -0.273 0.273 -0.273 0.27314.00 -0.273 0.273 -0.273 0.27315.00 -0.273 0.273 -0.273 0.27316.00 -0.273 0.273 -0.273 0.27317.00 -0.273 0.273 -0.273 0.27318.00 -0.273 0.273 -0.273 0.27319.00 -0.273 0.273 -0.273 0.27320.00 -0.273 0.273 -0.273 0.273

Kontrola napona

t=0 t=t Dopu{teni naponixm MPa MPa MPa MPa Faza prethodnog naprezanja

0.00 9.0 9.0 7.2 7.21.00 10.0 7.8 6.2 8.1 Prit.2.00 11.0 6.8 5.4 8.83.00 11.7 6.0 4.7 9.4 Zat.4.00 12.3 5.3 4.2 9.95.00 12.7 4.8 3.7 10.36.00 13.0 4.4 3.5 10.5 Faza eksploatacije

sb10 sb20 sb1t sb2t

7.00 13.1 4.2 3.3 10.68.00 13.1 4.2 3.3 10.6 Prit.9.00 12.9 4.3 3.4 10.4

10.00 12.5 4.6 3.6 10.1 Zat.11.00 12.0 5.0 3.9 9.712.00 11.3 5.6 4.4 9.113.00 10.5 6.4 5.0 8.414.00 9.5 7.3 5.8 7.615.00 8.4 8.4 6.7 6.716.00 7.0 9.6 7.7 5.617.00 5.6 11.0 8.8 4.418.00 3.9 12.5 10.1 3.119.00 2.1 14.2 11.5 1.620.00 0.2 16.1 13.0 0.0

max= 13.1 16.1 13.0 10.6min= 0.2 4.2 3.3 0.0

Dopu{teni naponi

Faza prethodnog naprezanja

0.00 17.320.00 17.3

0.00 0.020.00 0.0

Faza eksploatacije

0.00 17.320.00 17.3

0 0.0020.00 0.00

0 2 4 6 8 10 12 14 16 18 20

-1500

-1000

-500

0

500

1000

1500

2000Momenti

Ukupno - faza preth.naprezanjaUkupno - faza eksploatacijegq

x (m)

Mom

ent

(kN

m)

0 2 4 6 8 10 12 14 16 18 200.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

18.0

20.0Ivi~ni naponi

Donja ivica t=0Gornja ivica t=0Donja ivica t=t

x (m)

Nap

on

(M

Pa)

0 2 4 6 8 10 12 14 16 18 20

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

C - linijeK1 - t=0K2 - t=0K1 - t=tK2 - t=tC - t=0C - t=t

x (m)

document.xls 04/08/2023 03:22:00

Page 19

Kontinualni nosa~ sa dva jednaka poljaAnaliza efekata simetri~nog prethodnog naprezanja

V.Alendar - Prethodno napregnuti beton - Ve`be 2003 - Primer 5.11.3

Grupa kablova - A (utezanje sa obe strane)

Sila na ~elu - Nk0 = 3540 kN

Koef.trenja na pravcu - k = 0.003 1/m <-(0.003)0.220 1/rad <-(0.220)

0.9500.800

POLJE L f e(m) (m) (m)

1 20.00 0.400 0.450 27.00

Spolja{nja optere}enjaSopstvena te`ina g= 9.38 kN/mDodatno stalno 16.00 kN/mPovremeno p= 8.50 kN/m

PresekFaza utezanja MB 35

Dop. napon zatezanja = 0.00 MPaDop. napon pritiska = 17.30 MPa

Faza eksploatacije MB 45Dop. napon zatezanja = 0.00 MPa

Dop. napon pritiska = 17.30 MPaIvi~ni naponi

Visina preseka d (m)= 1.200 Faza prethodnog naprezanja MPa16.11 < 17.30

0.375 0.102 0.273 0.20 < 0.00

0.600 0.102 0.273 Faza eksploatacije0.600 0.546 13.05 < 17.30

0.00 < 0.00

V.Alendar, novembar 2003.

Koef.trenja na krivini - m =

Elasti~ni gubici - we=Vremenski gubici - w=

qksr=

Dg=

maxs0 =F (m2)= W2 (m3)= K2 (m)= mins0 =Yt (m)= W1 (m3)= K1 (m)=

d-Yt (m)= K1+K2= maxst =minst =

0 2 4 6 8 10 12 14 16 18 20

-1.00

-0.50

0.00

0.50

1.00 Trasa kablova

0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00 20.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80 C-linije

t=0

x (m)