Staticki proracun

KRAJWI NOSA^I: minLkn2 15.31= m SREDWI NOSA^I: minLsn2 15.46= m

maxLkn2 16.32= m maxLsn2 16.17= m

1. SOPSTVENA TE@INA MONTA@NIH NOSA^A

- KRAJWI NOSA^:

gkn 0.65 0.75⋅ 0.30 0.10⋅+ 0.15 0.20+( ) 0.5⋅ 0.60⋅+[ ] 25.0⋅=

gkn 15.56= kN/m

TE@INE KRAJWIH NOSA^A U KRAJWIM POQIMA:

minGkn1 gkn minLkn1⋅= maxGkn1 gkn maxLkn1⋅=

minGkn1 252.89= kN maxGkn1 268.61= kN

TE@INE KRAJWIH NOSA^A U SREDWIM POQIMA:

minGkn2 gkn minLkn2⋅= maxGkn2 gkn maxLkn2⋅=

minGkn2 238.26= kN maxGkn2 253.98= kN

STATI^KI PRORA^UN

20 140770

1090160 160

20140

12595

65606560656065606560656065606560 60

94010

50 6015

7510

1. PRORA^UN RASPONSKE KONSTRUKCIJE

[IRINA KOLOVOZA: Bk 7.70= m

[IRINA KOLOVOZNE PLO^E: Bpl 9.40= m

DU@INA MOSTA: Lm 82.70= m

1.1 ANALIZA OPTERE]EWA

FAZA MONTA@E•

- DU@INE MONTA@NIH NOSA^A SU PROMENQIVE U OKVIRU JEDNOG POQA

DU@INE MONTA@NIH NOSA^A U KRAJWIM POQIMA:

KRAJWI NOSA^I: minLkn1 16.25= m SREDWI NOSA^I: minLsn1 16.40= m

maxLkn1 17.26= m maxLsn1 17.11= m

DU@INE MONTA@NIH NOSA^A U SREDWIM POQIMA:

1

0.10 24.0⋅ 2.40= kN/m2

- KAMENI IVI^WAK 0.15 0.25⋅ 28.0⋅ 1.05= kN/m

- PE[A^KA STAZA: 0.365 1.45⋅ 0.285 0.15⋅+ 2 π⋅ 0.06752⋅−( ) 25.0⋅ 13.58= kN/m

- PE[A^KA OGRADA: 0.30 kN/m

4. POKRETNO OPTERE]EWE

MOST PRIPADA II KATEGORIJI MOSTOVA - RA^UNSKA [EMA OPTERE]EWA V 600

50

160

770

200

50

150

160

150 150 150

x Kd

p2

V 600

600

300

470

p2

p2

p1

P' 100= kN

p' 5.00= kN/m2

p'' 3.00= kN/m2

L4 17.00⋅ 14.00+

5=

L 16.40= m

Kd 1.4 0.008 L⋅−=

Kd 1.269=

P P' Kd⋅= P 126.88= kN

p1 p' Kd⋅= p1 6.34= kN/m2

p2 p''= p2 3.00= kN/m2

- SREDWI NOSA^:

gsn 1.25 0.10⋅ 0.65 0.50⋅+( ) 25.0⋅=

gsn 11.25= kN/m

TE@INE SREDWIH NOSA^A U KRAJWIM POQIMA:

minGkn11 gsn minLsn1⋅= maxGkn1 gsn maxLsn1⋅=

minGkn1 252.89= kN maxGkn1 192.49= kN

TE@INE SREDWIH NOSA^A U SREDWIM POQIMA:

minGkn2 gsn minLsn2⋅= maxGkn2 gsn maxLsn2⋅=

minGkn2 173.93= kN maxGkn2 181.91= kN

2. KOLOVOZNA PLO^A I ISPUNA

- ZA KRAJWI NOSA^: gplk 0.30 0.65⋅ 25.0⋅= gplk 4.88= kN/m

- ZA SREDWI NOSA^: gpls 1.25 0.15⋅ 2 0.30⋅ 0.50⋅+( ) 25.0⋅= gpls 12.19= kN/m

FAZA EKSPLOATACIJE•

3. DODATNO STALNO OPTERE]EWE

- KOLOVOZNI ZASTOR:

2

kT 0.858=

qmt1012ρ⋅ Vm5010 kt⋅ kT⋅( )2⋅ 10 3−

⋅= qmt10 0.158= kN/m2

- FAKTOR TOPOGRAFIJE TERENA: Sz 1.5=

- VISINA OBJEKTA: z 17.50= m

- FAKTORI HRAPAVOSTI TERENA: b 0.5=( ZA TEREN KLASE "S"): α 0.22=

- FAKTOR EKSPOZICIJE:

Kz bz

10⎛⎜⎝

⎞⎟⎠

α⋅= Kz 0.800=

OSREDWENI AERODINAMI^KI PRITISAK VETRA:•

- ZA NEOPTERE]EN MOST

qmtz' qmt10' Sz2⋅ Kz2

⋅= qmtz' 0.309= kN/m2

- ZA OPTERE]EN MOST

qmtz qmt10 Sz2⋅ Kz2

⋅= qmtz 0.227= kN/m2

OPTERE]EWE VETROM:•

- ZA NEOPTERE]EN MOST

- [IRINA KOLOVOZNE PLO^E: b 10.90= m

- VISINA KONSTRUKCIJE: hk 0.75= m

5. ZAUSTAVQAWE I POKRETAWE VOZILA

Sk1

20Bk⋅ Lm⋅ 3.00⋅= Sk 95.52= kN

Sk 0.3 600⋅= Sk 180.0= kN

6. RAVNOMERNA PROMENA TEMPERATURE

t 25= oC αt 10 5−= 1/oC

7. OPTERE]EWE VETROM

- NADMORSKA VISINA: Hs 385= mnm

- GUSTINA VAZDUHA: ρ 1.1884= kg/m3

- OSNOVNA BRZINA VETRA: Vm5010 19= m/s

- FAKTOR VREMENSKOG OSREDWAVAWA

OSNOVNE BRZINE VETRA ZA TEREN KLASE "S": kt 1.0=

OSNOVNI PRITISAK VETRA:•

- ZA NEOPTERE]EN MOST

- FAKTOR POVRATNOG PERIODA

OSNOVNE BRZINE VETRA: kT' 1.0=

qmt10'12ρ⋅ Vm5010 kt⋅ kT'⋅( )2⋅ 10 3−

⋅= qmt10' 0.215= kN/m2

- ZA OPTERE]EN MOST

- FAKTOR POVRATNOG PERIODA

OSNOVNE BRZINE VETRA:

3

W1 qmtz Gh⋅ Cf1 hk⋅ Cf2 hs⋅+( )⋅= W1 3.01= kN/m

- ZA STUBOVE: W2 qmtz Gh⋅ Cf1⋅ d⋅= W2 0.61= kN/m

8. SEIZMIKA

PROJEKTNA SEIZMI^NOST - VIII ZONA

ZA SREDWE TLO: Kc 0.05=

G 18532.64= kN

ΔG 1.05 13.58+ 0.30+( ) 2⋅ Lm⋅ 2.40 Bk⋅ Lm⋅+=

ΔG 3997.72=

Q G ΔG+= Q 22530.36= kN

Sz 1.5 Kc⋅ Q⋅= Sz 1689.78= kN

- U PODU@NOM PRAVCU

Sz'SzBpl

= Sz' 179.76= kN/m

- U POPRE^NOM PRAVCU

Sz''SzLm

= Sz'' 20.43= kN/m

UTICAJI U SVIM ELEMENTIMA MOSTA DOBIJENI SU U PROGRAMU SOFiSTiK.

- PRE^NIK STUBA: d 1.00= m

- KOEFICIJENT SILE

MOSTOVSKE KONSTRUKCIJE: Cf 1 1.6hkb

⋅+= Cf 1.11=

- DINAMI^KI KOEFICIJENT: Gh 2.0=

- ZA RASPONSKU KONSTRUKCIJU: W1' qmtz' Gh⋅ Cf⋅ hk⋅= W1' 0.51= kN/m

- ZA STUBOVE: W2' qmtz' Gh⋅ Cf⋅ d⋅= W2' 0.69= kN/m

- ZA OPTERE]EN MOST

- KOEFICIJENT SILE

MOSTOVSKE KONSTRUKCIJE: Cf1 1.35=

- KOEFICIJENT SILE

SAOBRA]AJNE TRAKE: Cf2 1.60=

- VISINA SAOBRA]AJNE TRAKE: hs 3.50= m

- ZA RASPONSKU KONSTRUKCIJU:

4

Mu 129.38−= kNm

kh

Mu 102⋅

b fb⋅

= k 7.867= ea / eb = 10.0 / 0.650 o/oo

μ' 1.769%=

Aa' μ' b⋅ h⋅fbσv⋅= Aa' 5.09= cm2

minAa' 0.20b d⋅100⋅= minAa' 9.75= cm2

USVOJENA ARMATURA U GORWOJ ZONI: 7 RA ∅ 28 ( Aa' 43.12= cm2 )

KRAJWE POQE - FAZA MONTA@E ( NOSA^I KAO PROSTE GREDE )•

65

95

6510

30 60

75

b 65.0= cm d 75.0= cm a 5.5= cm

h d a−= h 69.5= cm

DU@INA MONTA@NOG NOSA^A: maxL 17.26= m

RASPON MONTA@NOG NOSA^A: maxLo 16.61= m

1.2. PRORA^UN KRAJWIH NOSA^A

MB 40 ⇒ fb 25.50= MPa τr 1.30= MPa Eb 34= GPa

RA 400/500-2 ⇒ σv 400= MPa

KRAJWE POQE - FAZA PODIZAWA NOSA^A•

( NOSA^I KAO GREDE SA PREPUSTIMA )

65

95

6510

30 60

75

b 65.0= cm d 75.0= cm a 5.5= cm

h d a−= h 69.5= cm

DU@INA MONTA@NOG NOSA^A: maxL 17.26= m

RASPON MONTA@NOG NOSA^A: maxLo 10.21= m

- PRESEK NA MESTU HVATAWA

1. SOPSTVENA TE@INA MONTA@NOG NOSA^A: Mkgo' 80.86−= kNm

Mu 1.6 Mkgo'⋅=

5

Tkgo 129.63= kN Tkpl 40.65= kN

Tu 1.6 Tkgo Tkpl+( )⋅= Tu 272.45= kN

τnTub z⋅

10⋅= τn 0.67= MPa < τr 1.30= MPa

NIJE POTREBNO OSIGURAWE OD TRANSVERZALNIH SILA.

PRORA^UN DEFORMACIJA

Ib 0.0343= m4

SOPSTVENA TE@INA NOSA^A:

gkn 15.56= kN/m

Ug5

384gkn maxLo4

⋅ 102⋅

Eb 106⋅ Ib⋅

⋅= Ug 1.32= cm

TE@INA KOLOVOZNE PLO^E I ISPUNE:

gplk 4.88= kN/m

Upl5

384gplk maxLo4

⋅ 102⋅

Eb 106⋅ Ib⋅

⋅= Upl 0.41= cm

UKUPNI UGIB KRAJWEG NOSA^A U FAZI MONTA@E:

Ukn Ug Upl+= Ukn 1.74= cm

1. SOPSTVENA TE@INA MONTA@NOG NOSA^A: Mkgo 552.02= kNm

2. KOLOVOZNA PLO^A I ISPUNA: Mkpl 164.63= kNm

Mu 1.6 Mkgo Mkpl+( )⋅= Mu 1146.64= kNm

kh

Mu 102⋅

b fb⋅

= k 2.642= ea / eb = 10.0 / 2.725 o/oo

μ' 16.175%=

Aa1 μ' b⋅ h⋅fbσv⋅= Aa1 46.58= cm2

KONTROLA PRESEKA PREMA GRANI^NIM UTICAJIMA TRANSVERZALNIH SILA

PRAVOUGAONI POPRE^NI PRESEK:

b 65.0= cm d 75.0= cm a 5.50= cm

h d a−= h 69.50= cm

z 0.9 h⋅= z 62.55= cm

6

Aap 0.20 Aa⋅= Aap 17.94= cm2

U MONTA@NOM NOSA^U: 13 RA ∅ 28 ( Aan 80.08= cm2 )

U ISPUNI: 3 RA ∅ 28 ( Aai 18.48= cm2 )

USVOJENO UKUPNO: 16 RA ∅ 28 ( Aan Aai+ 98.56= cm2 )

USVOJENA PODEONA ARMATURA: RA ∅ 14 / 7.5 cm ( Aap 20.53= cm2 )

PRORA^UN PRSLINA U FAZI MONTA@E

MB 40 ⇒ fbzm 2.90= MPa

RA 400/500-2 ⇒ Ea 210= GPa

∅ 2.8= cm k1 0.4= ( RA 400 / 500 - 2 )

eφ 7.8= cm k2 0.125= ( SAVIJAWE )

- ARMATURA U MONTA@NOM NOSA^U: 13 RA ∅ 28 ( Aan 80.08= cm2 )

d 75.0= cm a 6.9= cm ao 3.9= cm

- SREDWE RASTOJAWE PRSLINA:

hbzef min a 7.5 ∅⋅+d2

,⎛⎜⎝

⎞⎟⎠

= hbzef 27.90= cm

FAZA EKSPLOATACIJE - KONTINUALNA PLO^A•

- PRESEK U POQU

95

75

60

155

b 95.0= cm d 75.0= cm a 7.5= cm

h d a−= h 67.5= cm

1. DODATNO STALNO OPTERE]EWE: MkΔg 135.63= kNm

2. POKRETNO OPTERE]EWE: Mkp 478.54= kNm

Mu 1.6 MkΔg⋅ 1.8 Mkp⋅+= Mu 1078.38= kNm

kh

Mu 102⋅

b fb⋅

= k 3.199= ea / eb = 10.0 / 1.925 o/oo

μ' 10.552%=

Aa2 μ' b⋅ h⋅fbσv⋅= Aa2 43.14= cm2

UKUPNA ARMATURA U POQU - FAZA MONTA@E + FAZA EKSPLOATACIJE:

Aa Aa1 Aa2+= Aa 89.72= cm2

7

apk 0.16= mm < dop apk 0.20= mm

apk 0.016= cmapk 1.7 ξa⋅ εa1⋅ 10 3−⋅ lps⋅=

ξa 0.966=ξa 1 β1 β2⋅MprM

⎛⎜⎝

⎞⎟⎠

2⋅−=

( VI[E PUTA PONOVQENO OPTERE]EWE )β2 0.5=

( RA 400 / 500 - 2 )β1 1.0=

εa1 0.701= o/ooεa1

σa1 10⋅

Ea=

σa1 14.73= kN/cm2σa1M 102⋅

0.9 h⋅ Aan⋅=

M 716.65= kNmM Mkgo Mkpl+=

Mpr 186.19= kNmMpr fbzs Wb1⋅ 10 2−⋅=

Wb1 89062.50= cm3Wb1b d2⋅

6=

fbzs 0.209= kN/cm2fbzs fbz 0.60.4

4d 10 2−⋅

+⎛⎜⎜⎝

⎞⎟⎟⎠

⋅=

fbz 0.203= kN/cm2fbz 0.7 fbzm⋅ 10 1−⋅=

- KARAKTERISTI^NA [IRINA PRSLINA:

lps 13.99= cmlps 2 aoeφ10

+⎛⎜⎝

⎞⎟⎠

⋅ k1 k2⋅∅

μ1ef⋅+=

μ1ef 3.02%=μ1efAan

b hbzef⋅=

8

Aa' 5.09= cm2

minAa' 0.20b d⋅100⋅= minAa' 9.75= cm2

USVOJENA ARMATURA U GORWOJ ZONI: 7 RA ∅ 28 ( Aa' 43.12= cm2 )

SREDWE POQE - FAZA MONTA@E ( NOSA^I KAO PROSTE GREDE )•

65

95

6510

30 60

75

b 65.0= cm d 75.0= cm a 6.0= cm

h d a−= h 69.0= cm

DU@INA MONTA@NOG NOSA^A: maxL 16.32= m

RASPON MONTA@NOG NOSA^A: maxLo 15.72= m

1. SOPSTVENA TE@INA MONTA@NOG NOSA^A: Mkgo 476.28= kNm

2. KOLOVOZNA PLO^A I ISPUNA: Mkpl 149.35= kNm

Mu 1.6 Mkgo Mkpl+( )⋅= Mu 1001.01= kNm

SREDWE POQE - FAZA PODIZAWA NOSA^A•

( NOSA^I KAO GREDE SA PREPUSTIMA )

65

95

6510

30 6075

b 65.0= cm d 75.0= cm a 5.5= cm

h d a−= h 69.5= cm

DU@INA MONTA@NOG NOSA^A: maxL 16.32= m

RASPON MONTA@NOG NOSA^A: maxLo 9.35= m

- PRESEK NA MESTU HVATAWA

1. SOPSTVENA TE@INA MONTA@NOG NOSA^A: Mkgo' 82.06−= kNm

Mu 1.6 Mkgo'⋅= Mu 131.30−= kNm

kh

Mu 102⋅

b fb⋅

= k 7.809= ea / eb = 10.0 / 0.650 o/oo

μ' 1.769%=

Aa' μ' b⋅ h⋅fbσv⋅=

9

Tu 257.09= kN

τnTub z⋅

10⋅= τn 0.64= MPa < τr 1.30= MPa

NIJE POTREBNO OSIGURAWE OD TRANSVERZALNIH SILA.

PRORA^UN DEFORMACIJA

Ib 0.0343= m4

SOPSTVENA TE@INA NOSA^A:

gkn 15.56= kN/m

Ug5

384gkn maxLo4

⋅ 102⋅

Eb 106⋅ Ib⋅

⋅= Ug 1.06= cm

TE@INA KOLOVOZNE PLO^E I ISPUNE:

gplk 4.88= kN/m

Upl5

384gplk maxLo4

⋅ 102⋅

Eb 106⋅ Ib⋅

⋅= Upl 0.33= cm

UKUPNI UGIB KRAJWEG NOSA^A U FAZI MONTA@E:

Ukn Ug Upl+= Ukn 1.39= cm

kh

Mu 102⋅

b fb⋅

= k 2.808= ea / eb = 10.0 / 2.375 o/oo

μ' 13.805%=

Aa1 μ' b⋅ h⋅fbσv⋅= Aa1 39.47= cm2

KONTROLA PRESEKA PREMA GRANI^NIM UTICAJIMA TRANSVERZALNIH SILA

PRAVOUGAONI POPRE^NI PRESEK:

b 65.0= cm d 75.0= cm a 6.00= cm

h d a−= h 69.00= cm

z 0.9 h⋅= z 62.10= cm

Tkgo 122.32= kN Tkpl 38.36= kN

Tu 1.6 Tkgo Tkpl+( )⋅=

10

Aap 0.20 Aa⋅= Aap 13.94= cm2

U MONTA@NOM NOSA^U: 10 RA ∅ 28 ( Aan 61.60= cm2 )

U ISPUNI: 3 RA ∅ 28 ( Aai 18.48= cm2 )

USVOJENO UKUPNO: 13 RA ∅ 28 ( Aan Aai+ 80.08= cm2 )

USVOJENA PODEONA ARMATURA: RA ∅ 14 / 7.5 cm ( Aap 20.53= cm2 )

PRORA^UN PRSLINA U FAZI MONTA@E

MB 40 ⇒ fbzm 2.90= MPa

RA 400/500-2 ⇒ Ea 210= GPa

∅ 2.8= cm k1 0.4= ( RA 400 / 500 - 2 )

eφ 7.8= cm k2 0.125= ( SAVIJAWE )

- ARMATURA U MONTA@NOM NOSA^U: 10 RA ∅ 28 ( Aan 61.60= cm2 )

d 75.0= cm a 6.1= cm ao 3.9= cm

- SREDWE RASTOJAWE PRSLINA:

hbzef min a 7.5 ∅⋅+d2

,⎛⎜⎝

⎞⎟⎠

= hbzef 27.10= cm

FAZA EKSPLOATACIJE - KONTINUALNA PLO^A•

- PRESEK U POQU

95

75

60

155

b 95.0= cm d 75.0= cm a 7.0= cm

h d a−= h 68.0= cm

1. DODATNO STALNO OPTERE]EWE: MkΔg 62.27= kNm

2. POKRETNO OPTERE]EWE: Mkp 377.20= kNm

Mu 1.6 MkΔg⋅ 1.8 Mkp⋅+= Mu 778.59= kNm

kh

Mu 102⋅

b fb⋅

= k 3.793= ea / eb = 10.0 / 1.500 o/oo

μ' 7.337%=

Aa2 μ' b⋅ h⋅fbσv⋅= Aa2 30.22= cm2

UKUPNA ARMATURA U POQU - FAZA MONTA@E + FAZA EKSPLOATACIJE:

Aa Aa1 Aa2+= Aa 69.69= cm2

11

apk 0.20= mm = dop apk 0.20= mm

apk 0.020= cmapk 1.7 ξa⋅ εa1⋅ 10 3−⋅ lps⋅=

ξa 0.956=ξa 1 β1 β2⋅MprM

⎛⎜⎝

⎞⎟⎠

2⋅−=

( VI[E PUTA PONOVQENO OPTERE]EWE )β2 0.5=

( RA 400 / 500 - 2 )β1 1.0=

εa1 0.790= o/ooεa1

σa1 10⋅

Ea=

σa1 16.60= kN/cm2σa1M 102⋅

0.9 h⋅ Aan⋅=

M 625.63= kNmM Mkgo Mkpl+=

Mpr 186.19= kNmMpr fbzs Wb1⋅ 10 2−⋅=

Wb1 89062.50= cm3Wb1b d2⋅

6=

fbzs 0.209= kN/cm2fbzs fbz 0.60.4

4d 10 2−⋅

+⎛⎜⎜⎝

⎞⎟⎟⎠

⋅=

fbz 0.203= kN/cm2fbz 0.7 fbzm⋅ 10 1−⋅=

- KARAKTERISTI^NA [IRINA PRSLINA:

lps 15.21= cmlps 2 aoeφ10

+⎛⎜⎝

⎞⎟⎠

⋅ k1 k2⋅∅

μ1ef⋅+=

μ1ef 2.39%=μ1efAan

b hbzef⋅=

12

USVOJENA GLAVNA ARMATURA: RA ∅ 10 / 20 cm ( Aa 3.95= cm2 )

Aa 0.47= cm2Aa μ' b⋅ h⋅fbσv⋅=

ea / eb = 10.0 / 0.475 o/oo

μ' 0.992%=

k 10.308=kh

Mu 102⋅

b fb⋅

=

Mu 1.35= kNmMu 1.6 Mg Mgb+( )⋅=

Mgb 0.73= kNmMgbgb l2⋅

2=

Mg 0.11= kNmMgg l2⋅2

=

gb 16.25= kN/mgb 0.65 25.0⋅=2. TE@INA SVE@EG BETONA:

g 2.50= kN/mg 0.10 25.0⋅=1. SOPSTVENA TE@INA NO@ICE:

l 0.30= mh 7.5= cmh d a−=

a 2.5= cmd 10.0= cmb 100.0= cm

65

95

6510

30 6075

PRORA^UN NO@ICE MONTA@NOG ELEMENTA

13

Mu 92.00−= kNm

kh

Mu 102⋅

b fb⋅

= k 7.181= ea / eb = 10.0 / 0.700 o/oo

μ' 2.023%=

Aa' μ' b⋅ h⋅fbσv⋅= Aa' 4.48= cm2

minAa' 0.20b d⋅100⋅= minAa' 7.80= cm2

USVOJENA ARMATURA U GORWOJ ZONI: 7 RA ∅ 14 ( Aa' 10.78= cm2 )

KRAJWE POQE - FAZA MONTA@E ( NOSA^I KAO PROSTE GREDE )•

65

125

605010

60 b 65.0= cm d 60.0= cm a 6.5= cm

h d a−= h 53.5= cm

DU@INA MONTA@NOG NOSA^A: maxL 17.11= m

RASPON MONTA@NOG NOSA^A: maxLo 16.46= m

1.3. PRORA^UN SREDWIH NOSA^A

MB 40 ⇒ fb 25.50= MPa τr 1.30= MPa Eb 34= GPa

RA 400/500-2 ⇒ σv 400= MPa

KRAJWE POQE - FAZA PODIZAWA NOSA^A•

( NOSA^I KAO GREDE SA PREPUSTIMA )

65

1256050

1060

b 65.0= cm d 60.0= cm a 6.5= cm

h d a−= h 53.5= cm

DU@INA MONTA@NOG NOSA^A: maxL 17.11= m

RASPON MONTA@NOG NOSA^A: maxLo 9.88= m

- PRESEK NA MESTU HVATAWA

1. SOPSTVENA TE@INA MONTA@NOG NOSA^A: Msgo 57.50−= kNm

Mu 1.6 Msgo⋅=

14

Tsgo 92.94= kN Tspl 100.71= kN

Tu 1.6 Tsgo Tspl+( )⋅= Tu 309.84= kN

τnTub z⋅

10⋅= τn 0.99= MPa < τr 1.30= MPa

NIJE POTREBNO OSIGURAWE OD TRANSVERZALNIH SILA.

PRORA^UN DEFORMACIJA

Ib 0.0150= m4

SOPSTVENA TE@INA NOSA^A:

gsn 11.25= kN/m

Ug5

384gsn maxLo4

⋅ 102⋅

Eb 106⋅ Ib⋅

⋅= Ug 2.11= cm

TE@INA KOLOVOZNE PLO^E I ISPUNE:

gpls 12.19= kN/m

Upl5

384gpls maxLo4

⋅ 102⋅

Eb 106⋅ Ib⋅

⋅= Upl 2.28= cm

UKUPNI UGIB SREDWEG NOSA^A U FAZI MONTA@E:

Usn Ug Upl+= Usn 4.39= cm

1. SOPSTVENA TE@INA MONTA@NOG NOSA^A: Msgo 373.35= kNm

2. KOLOVOZNA PLO^A I ISPUNA: Mspl 404.54= kNm

Mu 1.6 Msgo Mspl+( )⋅= Mu 1244.62= kNm

kh

Mu 102⋅

b fb⋅

= k 1.952= ea / eb = 5.55 / 3.50 o/oo

μ' 31.307%=

Aa1 μ' b⋅ h⋅fbσv⋅= Aa1 69.40= cm2

KONTROLA PRESEKA PREMA GRANI^NIM UTICAJIMA TRANSVERZALNIH SILA

PRAVOUGAONI POPRE^NI PRESEK:

b 65.0= cm d 60.0= cm a 6.50= cm

h d a−= h 53.50= cm

z 0.9 h⋅= z 48.15= cm

15

Aap 0.20 Aa⋅= Aap 22.93= cm2

U MONTA@NOM NOSA^U: 14 RA ∅ 28 ( Aan 86.24= cm2 )

U ISPUNI: 6 RA ∅ 28 ( Aai 36.96= cm2 )

USVOJENO UKUPNO: 20 RA ∅ 28 ( Aan Aai+ 123.20= cm2 )

USVOJENA PODEONA ARMATURA: RA ∅ 14 / 7.5 cm ( Aap 20.53= cm2 )

PRORA^UN PRSLINA U FAZI MONTA@E

MB 40 ⇒ fbzm 2.90= MPa

RA 400/500-2 ⇒ Ea 210= GPa

∅ 2.8= cm k1 0.4= ( RA 400 / 500 - 2 )

eφ 7.8= cm k2 0.125= ( SAVIJAWE )

- ARMATURA U MONTA@NOM NOSA^U: 14 RA ∅ 28 ( Aan 86.24= cm2 )

d 60.0= cm a 7.1= cm ao 3.9= cm

- SREDWE RASTOJAWE PRSLINA:

hbzef min a 7.5 ∅⋅+d2

,⎛⎜⎝

⎞⎟⎠

= hbzef 28.10= cm

FAZA EKSPLOATACIJE - KONTINUALNA PLO^A•

- PRESEK U POQU

125

75

b 125.0= cm d 75.0= cm a 8.0= cm

h d a−= h 67.0= cm

1. DODATNO STALNO OPTERE]EWE: MsΔg 130.25= kNm

2. POKRETNO OPTERE]EWE: Msp 514.22= kNm

Mu 1.6 MsΔg⋅ 1.8 Msp⋅+= Mu 1134.00= kNm

kh

Mu 102⋅

b fb⋅

= k 3.552= ea / eb = 10.0 / 1.650 o/oo

μ' 8.471%=

Aa2 μ' b⋅ h⋅fbσv⋅= Aa2 45.23= cm2

UKUPNA ARMATURA U POQU - FAZA MONTA@E + FAZA EKSPLOATACIJE:

Aa Aa1 Aa2+= Aa 114.63= cm2

16

apk 0.18= mm < dop apk 0.20= mm

apk 0.018= cmapk 1.7 ξa⋅ εa1⋅ 10 3−⋅ lps⋅=

ξa 0.979=ξa 1 β1 β2⋅MprM

⎛⎜⎝

⎞⎟⎠

2⋅−=

( VI[E PUTA PONOVQENO OPTERE]EWE )β2 0.5=

( RA 400 / 500 - 2 )β1 1.0=

εa1 0.712= o/oo

εa1σa1 10⋅

Ea=

σa1 14.96= kN/cm2σa1M 102⋅

0.9 h⋅ Aan⋅=

M 777.89= kNmM Msgo Mspl+=

Mpr 160.55= kNmMpr fbzs Wb1⋅ 10 2−⋅=

Wb1 75000.00= cm3Wb1b d2⋅

6=

fbzs 0.214= kN/cm2fbzs fbz 0.60.4

4d 10 2−⋅

+⎛⎜⎜⎝

⎞⎟⎟⎠

⋅=

fbz 0.203= kN/cm2fbz 0.7 fbzm⋅ 10 1−⋅=

- KARAKTERISTI^NA [IRINA PRSLINA:

lps 15.06= cmlps 2 aoeφ10

+⎛⎜⎝

⎞⎟⎠

⋅ k1 k2⋅∅

μ1ef⋅+=

μ1ef 2.46%=μ1efAan

b hbzef⋅=

17

Aa' μ' b⋅ h⋅fbσv⋅= Aa' 4.48= cm2

minAa' 0.20b d⋅100⋅= minAa' 7.80= cm2

USVOJENA ARMATURA U GORWOJ ZONI: 7 RA ∅ 14 ( Aa' 10.78= cm2 )

SREDWE POQE - FAZA MONTA@E ( NOSA^I KAO PROSTE GREDE )•

65

125

605010

60

b 65.0= cm d 60.0= cm a 7.0= cm

h d a−= h 53.0= cm

DU@INA MONTA@NOG NOSA^A: maxL 16.17= m

RASPON MONTA@NOG NOSA^A: maxLo 15.57= m

1. SOPSTVENA TE@INA MONTA@NOG NOSA^A: Msgo 338.37= kNm

2. KOLOVOZNA PLO^A I ISPUNA: Mspl 366.64= kNm

SREDWE POQE - FAZA PODIZAWA NOSA^A•

( NOSA^I KAO GREDE SA PREPUSTIMA )

65

125

605010

60 b 65.0= cm d 60.0= cm a 6.5= cm

h d a−= h 53.5= cm

DU@INA MONTA@NOG NOSA^A: maxL 16.17= m

RASPON MONTA@NOG NOSA^A: maxLo 9.30= m

- PRESEK NA MESTU HVATAWA

1. SOPSTVENA TE@INA MONTA@NOG NOSA^A: Msgo 58.30−= kNm

Mu 1.6 Msgo⋅= Mu 93.28−= kNm

kh

Mu 102⋅

b fb⋅

= k 7.132= ea / eb = 10.0 / 0.700 o/oo

μ' 2.023%=

18

Tu 1.6 Tkgo Tkpl+( )⋅= Tu 257.09= kN

τnTub z⋅

10⋅= τn 0.83= MPa < τr 1.30= MPa

NIJE POTREBNO OSIGURAWE OD TRANSVERZALNIH SILA.

PRORA^UN DEFORMACIJA

Ib 0.0150= m4

SOPSTVENA TE@INA NOSA^A:

gsn 11.25= kN/m

Ug5

384gsn maxLo4

⋅ 102⋅

Eb 106⋅ Ib⋅

⋅= Ug 1.69= cm

TE@INA KOLOVOZNE PLO^E I ISPUNE:

gpls 12.19= kN/m

Upl5

384gpls maxLo4

⋅ 102⋅

Eb 106⋅ Ib⋅

⋅= Upl 1.83= cm

UKUPNI UGIB SREDWEG NOSA^A U FAZI MONTA@E:

Usn Ug Upl+= Usn 3.52= cm

Mu 1.6 Msgo Mspl+( )⋅= Mu 1128.02= kNm

kh

Mu 102⋅

b fb⋅

= k 2.032= ea / eb = 6.50 / 3.50 o/oo

μ' 28.333%=

Aa1 μ' b⋅ h⋅fbσv⋅= Aa1 62.22= cm2

KONTROLA PRESEKA PREMA GRANI^NIM UTICAJIMA TRANSVERZALNIH SILA

PRAVOUGAONI POPRE^NI PRESEK:

b 65.0= cm d 60.0= cm a 7.00= cm

h d a−= h 53.00= cm

z 0.9 h⋅= z 47.70= cm

Tsgo 87.66= kN Tspl 94.99= kN

19

Aap 0.20 Aa⋅= Aap 18.94= cm2

U MONTA@NOM NOSA^U: 11 RA ∅ 28 ( Aan 67.76= cm2 )

U ISPUNI: 6 RA ∅ 28 ( Aai 36.96= cm2 )

USVOJENO UKUPNO: 17 RA ∅ 28 ( Aan Aai+ 104.72= cm2 )

USVOJENA PODEONA ARMATURA: RA ∅ 14 / 7.5 cm ( Aap 20.53= cm2 )

PRORA^UN PRSLINA U FAZI MONTA@E

MB 40 ⇒ fbzm 2.90= MPa

RA 400/500-2 ⇒ Ea 210= GPa

∅ 2.8= cm k1 0.4= ( RA 400 / 500 - 2 )

eφ 7.8= cm k2 0.125= ( SAVIJAWE )

- ARMATURA U MONTA@NOM NOSA^U: 11 RA ∅ 28 ( Aan 67.76= cm2 )

d 60.0= cm a 6.4= cm ao 3.9= cm

- SREDWE RASTOJAWE PRSLINA:

hbzef min a 7.5 ∅⋅+d2

,⎛⎜⎝

⎞⎟⎠

= hbzef 27.40= cm

FAZA EKSPLOATACIJE - KONTINUALNA PLO^A•

- PRESEK U POQU

125

75

b 125.0= cm d 75.0= cm a 7.5= cm

h d a−= h 67.5= cm

1. DODATNO STALNO OPTERE]EWE: MsΔg 50.83= kNm

2. POKRETNO OPTERE]EWE: Msp 412.61= kNm

Mu 1.6 MsΔg⋅ 1.8 Msp⋅+= Mu 824.03= kNm

kh

Mu 102⋅

b fb⋅

= k 4.198= ea / eb = 10.0 / 1.325 o/oo

μ' 6.039%=

Aa2 μ' b⋅ h⋅fbσv⋅= Aa2 32.48= cm2

UKUPNA ARMATURA U POQU - FAZA MONTA@E + FAZA EKSPLOATACIJE:

Aa Aa1 Aa2+= Aa 94.71= cm2

20

apk 0.22= mm > dop apk 0.20= mm

apk 0.022= cmapk 1.7 ξa⋅ εa1⋅ 10 3−⋅ lps⋅=

ξa 0.974=ξa 1 β1 β2⋅MprM

⎛⎜⎝

⎞⎟⎠

2⋅−=

( VI[E PUTA PONOVQENO OPTERE]EWE )β2 0.5=

( RA 400 / 500 - 2 )β1 1.0=

εa1 0.816= o/ooεa1

σa1 10⋅

Ea=

σa1 17.13= kN/cm2σa1M 102⋅

0.9 h⋅ Aan⋅=

M 705.01= kNmM Msgo Mspl+=

Mpr 160.55= kNmMpr fbzs Wb1⋅ 10 2−⋅=

Wb1 75000.00= cm3Wb1b d2⋅

6=

fbzs 0.214= kN/cm2fbzs fbz 0.60.4

4d 10 2−⋅

+⎛⎜⎜⎝

⎞⎟⎟⎠

⋅=

fbz 0.203= kN/cm2fbz 0.7 fbzm⋅ 10 1−⋅=

- KARAKTERISTI^NA [IRINA PRSLINA:

lps 16.44= cmlps 2 aoeφ10

+⎛⎜⎝

⎞⎟⎠

⋅ k1 k2⋅∅

μ1ef⋅+=

μ1ef 1.98%=μ1efAan

b hbzef⋅=

21

USVOJENA GLAVNA ARMATURA: RA ∅ 28 / 10 cm ( Aa 61.60= cm2 )

USVOJENA PODEONA ARMATURA: RA ∅ 12 / 10 cm ( Aap 11.30= cm2 )

NAPOMENA:

SVI PRESECI IZNAD SREDWIH STUBOVA ARMIRAJU SE IDENTI^NO!

PRORA^UN PRSLINA

MB 40 ⇒ fbzm 2.90= MPa

RA 400/500-2 ⇒ Ea 210= GPa

b' 100.0= cm d 75.0= cm

- SREDWE RASTOJAWE PRSLINA:

∅ 2.8= cm k1 0.4= ( RA 400 / 500 - 2 )

eφ 10.0= cm k2 0.125= ( SAVIJAWE )

a 5.3= cm ao 3.9= cm

hbzef min a 7.5 ∅⋅+d2

,⎛⎜⎝

⎞⎟⎠

= hbzef 26.30= cm

μ1efAa

b' hbzef⋅= μ1ef 2.34%=

lps 2 aoeφ10

+⎛⎜⎝

⎞⎟⎠

⋅ k1 k2⋅∅

μ1ef⋅+= lps 15.78= cm

- PRESEK IZNAD SREDWIH STUBOVA

b 95.0= cm d 75.0= cm a 5.5= cm

h d a−= h 69.5= cm

1. DODATNO STALNO OPTERE]EWE: MkΔg 235.95−= kNm

2. POKRETNO OPTERE]EWE: Mkp 451.08−= kNm

Mu 1.6 MkΔg⋅ 1.8 Mkp⋅+= Mu 1189.46−= kNm

kh

Mu 102⋅

b fb⋅

= k 3.136= ea / eb = 10.0 / 1.975 o/oo

μ' 10.926%=

Aa μ' b⋅ h⋅fbσv⋅= Aa 45.99= cm2

SVEDENO NA 1 m. [IRINE KOLOVOZNE PLO^E:

AaAa

b 10 2−⋅

= Aa 48.41= cm2/m

Aap 0.20 Aa⋅= Aap 9.68= cm2/m

22

apk 0.22= mm > dop apk 0.20= mm

apk 0.022= cmapk 1.7 ξa⋅ εa1⋅ 10 3−⋅ lps⋅=

ξa 0.959=ξa 1 β1 β2⋅MprM

⎛⎜⎝

⎞⎟⎠

2⋅−=

( VI[E PUTA PONOVQENO OPTERE]EWE )β2 0.5=

( RA 400 / 500 - 2 )β1 1.0=

εa1 0.849= o/ooεa1

σa1 10⋅

Ea=

σa1 17.83= kN/cm2σa1M 102⋅

0.9 h⋅ Aa⋅=

M 687.03−= kNmM MkΔg Mkp+=

Mpr 195.99= kNmMpr fbzs Wb1⋅ 10 2−⋅=

Wb1 93750.00= cm3Wb1b' d2⋅

6=

fbzs 0.209= kN/cm2fbzs fbz 0.60.4

4d 10 2−⋅

+⎛⎜⎜⎝

⎞⎟⎟⎠

⋅=

fbz 0.203= kN/cm2fbz 0.7 fbzm⋅ 10 1−⋅=

- KARAKTERISTI^NA [IRINA PRSLINA:

23

MΔg2 Δg2 0.595⋅= MΔg2 0.18= kNm/m__________________________________________________________________

Δg Δg1 Δg2+= Δg 8.35= kN/m

MΔg MΔg1 MΔg2+= MΔg 3.57= kNm/m

3. POKRETNO OPTERE]EWE

PE[A^KA NAVALA p' 5.00= kN/m2

L 0.60= m

Kd 1.4 0.008 L⋅−= Kd 1.395=

p p' Kd⋅= p 6.98= kN/m2

Mp p0.502

2⋅= Mp 0.87= kNm/m

2. PRORA^UN KONZOLE

6095125 15

2842

70

3120

20140160

1520

2.1. ANALIZA OPTERE]EWA

NA 1m [IRINE KONZOLE:

1. SOPSTVENA TE@INA g 0.15 0.20+( ) 0.5⋅ 0.60⋅ 25.0⋅= g 2.63= kN/m

Mg g 0.2975⋅= Mg 0.78= kNm/m

2. DODATNO STALNO OPTERE]EWE

- PE[A^KA STAZA:Δg1 0.3365 π 0.06752

⋅−( ) 25.0⋅= Δg1 8.05= kN/m

MΔg1 Δg1 0.4208⋅= MΔg1 3.39= kNm/m

- ODBOJNA OGRADA: Δg2 0.30= kN/m

24

USVOJENA PODEONA ARMATURA: RA ∅ 10 / 20 cm ( Aap 3.95= cm2 )

USVOJENA GLAVNA ARMATURA: RA ∅ 12 / 20 cm ( Aa 5.65= cm2 )

minAap 1.70= cm2/mminAap 0.085b d⋅100⋅=

Aap 0.26= cm2/mAap 0.20 Aa⋅=

minAa 2.00= cm2/mminAa 0.10b d⋅100⋅=

Aa 1.30= cm2/mAa μ' b⋅ h⋅fbσv⋅=

ea / eb = 10.0 / 0.525 o/oo

μ' 1.195%=

k 9.296=kh

Mu 102⋅

b fb⋅

=

Mu 8.53= kNm

Mu 1.6 Mg MΔg+( )⋅ 1.8 Mp⋅+=

h 17.0= cmh d a−=

a 3.0= cmd 20.0= cmb 100.0= cm

RA 400/500-2 ⇒ σv 400= MPa

MB 40 ⇒ fb 25.50= MPa

2.2. DIMENZIONISAWE KONZOLE

25

maxMn2 94.25−= kNm Tn2 821.91= kNm

minMn2 767.85−= kNm Mtn2 19.90= kNm

- PRESEK U POQU

b 240.0= cm d 120.0= cm a 5.0= cm

h d a−= h 115.00= cm

Mu 1.6 maxMg maxMn2+( )⋅= Mu 141.66−= kNm

kh

Mu 102⋅

b fb⋅

= k 23.903=

Fb 240.0 70.0⋅ 240.0 140.0+( ) 0.5⋅ 50.0⋅+= Fb 26300.00= cm2

minAa 0.20Fb100⋅= minAa 52.60= cm2

3. PRORA^UN SREDWIH STUBOVA

3.1. PRORA^UN LE@I[NE GREDE IZNAD SREDWIH STUBOVA

5070

160 770 1601090

100100100185185100100100250235235250

970

240

140

5070

75

MB 40 ⇒ fb 25.50= MPa τr 1.30= MPa

RA 400/500-2 ⇒ σv 400= MPa

FAZA MONTA@E NOSA^A•

1. SOPSTVENA TE@INA LE@I[NE GREDE:

maxMg 5.71= kNm Tg1 131.42= kNm Mtg 0.00= kNm

minMg 131.79−= kNm Tg2 133.58= kNm

2. MONTA@NI NOSA^I MONTIRANI SAMO U JEDNOM POQU

maxMn1 108.74−= kNm Tn1 230.54= kNm

minMn1 256.82−= kNm Mtn1 207.49= kNm

3. MONTA@NI NOSA^I + KOLOVOZNA PLO^A + POPRE^NI NOSA^:

26

do d 2 a⋅−= do 110.0= cm dm do=

δodm8

= δo 13.8= cm

Obo 2 bo do+( )⋅= Obo 640.0= cm

Abo bo do⋅= Abo 23100.0= cm2

- NOSA^I MONTIRANI SAMO U JEDNOM POQU:

maxMtu 1.6 Mtg Mtn1+( )⋅= maxMtu 331.98= kNm

odgTu 1.6 Tg1 Tn1+( )⋅= odgTu 579.14= kN

τntodgTu

b z⋅10⋅= τnt 0.25= MPa

τnmtmaxMtu 103

⋅

2 Abo⋅ δo⋅= τnmt 0.52= MPa

τn τnt τnmt+=

τn 0.78= MPa < τr 1.30= MPa

- MONTA@NI NOSA^I + KOLOVOZNA PLO^A + POPRE^NI NOSA^:

maxTu1 1.6 Tg2 Tn2+( )⋅= maxTu1 1528.78= kN

odgMtu1 1.6 Mtg Mtn2+( )⋅= odgMtu1 31.84= kNm

τn1maxTu1

b z⋅10⋅= τn1 0.67= MPa

τn1 0.67= MPa < τr 1.30= MPa

- PRESEK IZNAD OSLONCA

b 140.0= cm d 120.0= cm a 5.0= cm

h d a−= h 115.00= cm

Mu 1.6− minMg minMn2+( )⋅= Mu 1439.42= kNm

kh

Mu 102⋅

b fb⋅

= k 5.727= ea / eb = 10.0 / 0.900 o/oo

μ' 3.158%=

Aa1 μ' b⋅ h⋅fbσv⋅= Aa1 32.41= cm2

minAa1 0.20Fb100⋅= minAa1 52.60= cm2

ARMATURA ]E BITI USVOJENA POSLE KONTROLE TRANSVERZALNIH SILA I

MOMENATA TORZIJE

KONTROLA PRESEKA PREMA GRANI^NIM UTICAJIMA

TRANSVERZALNIH SILA I MOMENATA TORZIJE

ZAMEWUJU]I PRAVOUGAONI PRESEK:

b 220.0= cm d 120.0= cm a 5.00= cm

h d a−= h 115.00= cm bo b 2 a⋅−= bo 210.0= cm

z 0.9 h⋅= z 103.50= cm

27

5. RAVNOMERNA PROMENA TEMPERATURE:

maxMt 28.08= kNm

minMt 1.77−= kNm minMt1 29.71−= kNm

6. VETAR - OPTERE]EN MOST:

maxMw 245.64= kNm

minMw 263.87−= kNm

7. SEIZMIKA - POPRE^NO:

maxMs 1552.73= kNm

minMs 1647.83−= kNm

1. STALNO + POKRETNO

maxMu1 1.6 maxMg maxMΔg+( )⋅ 1.8 maxMp⋅+=

maxMu1 2251.09−= kNm

minMu1 1.6 minMg minMΔg+( )⋅ 1.8 minMp⋅+=

minMu1 3503.13−= kNm

2. STALNO + POKRETNO + KO^EWE + TEMPERATURA

maxMu2 1.3 maxMg maxMΔg+( )⋅ 1.5 maxMp⋅+ 1.3 maxMk maxMt+( )⋅+=

maxMu2 1772.29−= kNm

minMu2 1.3 minMg minMΔg+( )⋅ 1.5 minMp⋅+ 1.3 minMk minMt+( )⋅+=

minMu2 2872.86−= kNm

ARMATURA IZNAD OSLONCA:

ZA MOMENTE SAVIJAWA POTREBNO Aa 52.60= cm2

USVOJENO: 12 RA ∅ 25 ( Aa 58.92= cm2 )

FAZA EKSPLOATACIJE•

1. SOPSTVENA TE@INA:

maxMg 850.41−= kNm

minMg 1012.43−= kNm minMg1 969.45−= kNm

2. DODATNO STALNO OPTERE]EWE:

maxMΔg 579.93−= kNm

minMΔg 565.26−= kNm minMΔg1 599.04−= kNm

3. POKRETNO OPTERE]EWE:

maxMp 20.81= kNm

minMp 543.79−= kNm minMp1 500.88−= kNm

4. ZAUSTAVQAWE I POKRETAWE VOZILA:

maxMk 14.95= kNm

minMk 2.98−= kNm minMk1 15.71−= kNm

28

Aa1 6.03= cm2

Fb 120.0 75.0⋅ 240.0 70.0⋅+ 240.0 140.0+( ) 0.5⋅ 50.0⋅+=

Fb 35300.00= cm2

minAa 0.20Fb100⋅= minAa 70.60= cm2

- PRESEK IZNAD OSLONCA

b 160.0= cm d 195.0= cm a 5.0= cm

h d a−= h 190.00= cm

Mu minMu4−= Mu 4181.22= kNm

kh

Mu 102⋅

b fb⋅

= k 5.935= ea / eb = 10.0 / 0.875 o/oo

μ' 3.007%=

Aa1 μ' b⋅ h⋅fbσv⋅= Aa1 58.28= cm2

minAa 0.20Fb100⋅= minAa 70.60= cm2

ARMATURA ]E BITI USVOJENA POSLE KONTROLE TRANSVERZALNIH SILA I

MOMENATA TORZIJE

3. STALNO + POKRETNO + KO^EWE + TEMPERATURA + VETAR

maxMu3 1.3 maxMg maxMΔg+( )⋅ 1.5 maxMp⋅+ 1.3 maxMk maxMt+ maxMw+( )⋅+=

maxMu3 1452.96−= kNm

minMu3 1.3 minMg1 minMΔg1+( )⋅ 1.5 minMp1⋅+ 1.3 minMk1 minMt1+ minMw+( )⋅+=

minMu3 3192.43−= kNm

4. STALNO + SEIZMIKA

maxMu4 1.3 maxMg maxMΔg+( )⋅ 1.3 maxMs⋅+=

maxMu4 159.11= kNm

minMu4 1.3 minMg1 minMΔg1+( )⋅ 1.3 minMs⋅+=

minMu4 4181.22−= kNm

- PRESEK U POQU

b 120.0= cm d 195.0= cm a 5.0= cm

h d a−= h 190.00= cm

Mu maxMu4= Mu 159.11= kNm

kh

Mu 102⋅

b fb⋅

= k 26.349= ea / eb = 10.0 / 0.300 o/oo

μ' 0.415%=

Aa1 μ' b⋅ h⋅fbσv⋅=

29

odgMtt1 136.80= kNm

5. VETAR - OPTERE]EN MOST:

maxTw 155.15= kN

odgMtw 40.54−= kNm

6. SEIZMIKA - POPRE^NO:

maxTz 811.31= kN

odgMtz 239.97−= kNm

1. STALNO + POKRETNO

Tu1 1.6 maxTΔg⋅ 1.8 maxTp⋅+=

Tu1 1606.26= kN

Mtu1 1.6 odgMtΔg⋅ 1.8 odgMtp⋅+( )−=

Mtu1 250.48= kNm

2. STALNO + POKRETNO + KO^EWE + TEMPERATURA

Tu2 1.3 maxTΔg⋅ 1.5 maxTp⋅+ 1.3 maxTk maxTt+( )⋅+=

Tu2 1336.61= kN

Mtu2 1.3 odgMtΔg⋅ 1.5 odgMtp⋅+ 1.3 odgMtk odgMtt+( )⋅+=

Mtu2 49.53= kNm

3. STALNO + POKRETNO + KO^EWE + TEMPERATURA + VETAR

Tu3 1.3 maxTΔg1⋅ 1.5 maxTp1⋅+ 1.3 maxTk1 maxTt1+ maxTw+( )⋅+=

Tu3 1467.86= kN

Mtu3 1.3 odgMtΔg1⋅ 1.5 odgMtp1⋅+ 1.3 odgMtk1 odgMtt1+ odgMtw+( )⋅+=

Mtu3 34.98= kNm

KONTROLA PRESEKA PREMA GRANI^NIM UTICAJIMA

TRANSVERZALNIH SILA I MOMENATA TORZIJE

- MAKSIMALNA TRANSVERZALNA SILA I ODGOVARAJU]I MOMENATAT TORZIJE

1. DODATNO STALNO OPTERE]EWE:

maxTΔg 322.76= kN maxTΔg1 165.16= kN

odgMtΔg 41.15−= kNm odgMtΔg1 16.84−= kNm

2. POKRETNO OPTERE]EWE:

maxTp 605.47= kN maxTp1 683.24= kN

odgMtp 102.58−= kNm odgMtp1 2.86−= kNm

3. ZAUSTAVQAWE I POKRETAWE VOZILA:

maxTk 3.42= kN maxTk1 6.56= kN

odgMtk 104.12= kNm odgMtk1 49.21−= kNm

4. RAVNOMERNA PROMENA TEMPERATURE:

maxTt 3.36= kN maxTt1 13.90= kN

odgMtt 93.49= kNm

30

maxMtΔg1 39.49= kNm maxMtΔg2 17.25= kNm

odgTΔg 322.76= kN odgTΔg1 321.85= kN odgTΔg2 167.53= kN

2. POKRETNO OPTERE]EWE:

maxMtp 597.56= kNm maxMtp1 598.08= kNm

odgTp 394.07= kN odgTp1 400.04= kN

3. ZAUSTAVQAWE I POKRETAWE VOZILA:

maxMtk 104.12= kNm maxMtk1 38.77= kNm

odgTk 3.42−= kN odgTk1 2.10−= kN

4. RAVNOMERNA PROMENA TEMPERATURE:

maxMtt 93.49= kNm maxMtt1 112.04= kNm

odgTt 3.36−= kN odgTt1 5.66−= kN

5. VETAR - OPTERE]EN MOST:

maxMtw 18.25= kNm

odgTw 3.19−= kN

6. SEIZMIKA - PODU@NO:

maxMtz 1330.60= kNm

odgTz 138.55−= kN

4. STALNO + SEIZMIKA

Tu4 1.3 maxTΔg1⋅ 1.3 maxTz⋅+=

Tu4 1269.41= kN

Mtu4 1.3 odgMtΔg1⋅ 1.3 odgMtz⋅+( )−=

Mtu4 333.85= kNm

b 120.0= cm d 195.0= cm a 5.00= cm

h d a−= h 190.00= cm

z 0.9 h⋅= z 171.00= cm δo 13.75= cm

Obo 640.00= cm maxTu Tu1=

Abo 23100.00= cm2 odgMtu Mtu1=

τntmaxTu

b z⋅10⋅= τnt 0.78= MPa

τnmtodgMtu 103

⋅

2 Abo⋅ δo⋅= τnmt 0.39= MPa

τn τn1 τnt+ τnmt+=

τr 1.30= MPa < τn 1.85= MPa < 3 τr⋅ 3.90= MPa

- MAKSIMALNI MOMENATAT TORZIJE I ODGOVARAJU]A TRANSVERZALNA SILA

1. DODATNO STALNO OPTERE]EWE:

maxMtΔg 41.15= kNm

31

h d a−= h 190.00= cm

z 0.9 h⋅= z 171.00= cm δo 13.75= cm

Obo 640.00= cm maxMtu Mtu4=

Abo 23100.00= cm2 odgTu Tu4=

τnmtmaxMtu 103

⋅

2 Abo⋅ δo⋅= τnmt 2.76= MPa

τntodgTu

b z⋅10⋅= τnt 0.02= MPa

τn τn1 τnt+ τnmt+=

τr 1.30= MPa < τn 3.45= MPa < 3 τr⋅ 3.90= MPa

DEO KOJI SE POVERAVA BETONU:

Tbuτn1 τnt+

τn12⋅ 3 τr⋅ τn−( )⋅ b⋅ z⋅ 10 1−

⋅= Tbu 92.76= kN

Mtbuτnmtτn

3 τr⋅ τn−( )⋅ Abo⋅ δo⋅ 10 3−⋅= Mtbu 114.83= kNm

Tru maxTu1 odgTu+ Tbu−= Tru 1473.70= kN

1. STALNO + POKRETNO

Mtu1 1.6 maxMtΔg⋅ 1.8 maxMtp⋅+=

Mtu1 1141.45= kNm

Tu1 1.6 odgTΔg⋅ 1.8 odgTp⋅+=

Tu1 1225.74= kN

2. STALNO + POKRETNO + KO^EWE + TEMPERATURA

Mtu2 1.3 maxMtΔg⋅ 1.5 maxMtp⋅+ 1.3 maxMtk maxMtt+( )⋅+=

Mtu2 1206.73= kNm

Tu2 1.3 odgTΔg⋅ 1.5 odgTp⋅+ 1.3 odgTk odgTt+( )⋅+=

Tu2 1001.88= kN

3. STALNO + POKRETNO + KO^EWE + TEMPERATURA + VETAR

Mtu3 1.3 maxMtΔg1⋅ 1.5 maxMtp1⋅+ 1.3 maxMtk1 maxMtt1+ maxMtw+( )⋅+=

Mtu3 1168.24= kNm

Tu3 1.3 odgTΔg1⋅ 1.5 odgTp1⋅+ 1.3 odgTk1 odgTt1+ odgTw+( )⋅+=

Tu3 1004.23= kN

4. STALNO + SEIZMIKA

Mtu4 1.3 maxMtΔg2⋅ 1.3 maxMtz⋅+=

Mtu4 1752.20= kNm

Tu4 1.3 odgTΔg2⋅ 1.3 odgTz⋅+=

Tu4 37.67= kN

b 120.0= cm d 195.0= cm a 5.00= cm

32

au1Mtru 102

⋅

2 Abo⋅ σv⋅eu⋅ tan θ( )⋅= au1 1.77= cm2

USVOJENE UZENGIJE: RA U∅ 16 / 20 cm ( au1 2.01= cm2 )

UKUPNA PODU@NA ARMATURA ZA PRIJEM TORZIJE, RAVNOMERNO

RASPORE\ENA PO OBIMU PRESEKA:

AatmaxMtu 102

⋅

2 Abo⋅ σv⋅Obo⋅ cot θ( )⋅= Aat 60.68= cm2

USVOJENO: 10+2 RA ∅ 25 ( Aa 58.92= cm2 )

UKUPNA ZATEGNUTA ARMATURA IZNAD OSLONCA:

ZA MOMENTE SAVIJAWA POTREBNO Aa 70.60= cm2

Aa Aa ΔAa+= Aa 90.18= cm2

USVOJENO: 22 RA ∅ 25 ( Aa 108.02= cm2 )

UKUPNA ZATEGNUTA ARMATURA U POQU:

ZA MOMENTE SAVIJAWA POTREBNO Aa 70.60= cm2

Aa Aa 2 4.91⋅+= Aa 80.42= cm2

USVOJENO: 20 RA ∅ 25 ( Aa 98.20= cm2 )

τruTrub z⋅

10⋅= τru 0.72= MPa

Mtru maxMtu Mtbu−= Mtru 1637.37= kNm

POTREBNA POVR[INA POPRE^NOG PRESEKA UZENGIJA ZA PRIHVATAWE UTICAJA

TRANSVERZALNIH SILA:

m 4= eu 20.0= cm θπ

4= α

π

2=

au1b τru⋅ 10 1−

⋅

m σv⋅ cos α( ) sin α( ) cot θ( )⋅+( )⋅eu⋅= au1 1.08= cm2

USVOJENE ^ETVOROSE^NE UZENGIJE: RA U∅ 14 / 20 cm ( au1 1.54= cm2 )

DODATNA ZATEGNUTA PODU@NA ARMATURA:

ΔAamaxTu1 odgTu+

2 σv⋅cot θ( ) cot α( )−( )⋅= ΔAa 19.58= cm2

POTREBNA POVR[INA POPRE^NOG PRESEKA UZENGIJA ZA PRIHVATAWE UTICAJA

MOMENTA TORZIJE:

eu 20.0= cm θπ

4=

33

maxMgz 222.72= kNm Mgy 6.33= kNm Ng 2063.15= kN

2. DODATNO STALNO OPTERE]EWE:

maxMΔgz 63.30= kNm MΔgy 16.38−= kNm NΔg 489.92= kN

3. POKRETNO OPTERE]EWE:

maxMpz 371.61= kNm Mpy 31.76= kNm Np 781.06= kN

4. ZAUSTAVQAWE I POKRETAWE VOZILA:

maxMkz 268.05= kNm Mky 36.40= kNm Nk 11.47−= kN

5. RAVNOMERNA PROMENA TEMPERATURE:

maxMtz 246.87= kNm Mty 14.53= kNm Nt 14.05−= kN

6. VETAR - OPTERE]EN MOST:

maxMwz 35.03= kNm Mwy 228.01−= kNm Nw 102.97−= kN

7. SEIZMIKA - PODU@NO:

maxMsz 2291.96= kNm Msy 108.67= kNm Ns 165.03−= kN

3.2. PRORA^UN SREDWIH STUBOVA

MB 30 ⇒ fb 20.50= MPa

RA 400/500-2 ⇒ σv 400= MPa

a 5.0= cm D 100.0= cmaD

0.05=

rD2

= r 50.0= cm

Ab π r2⋅= Ab 7853.98= cm2 Ibπ r4⋅

4=

Ob 2 π⋅ r⋅= Ob 314.16= cm Ib 4908738.52= cm4

dm 2AbOb⋅= dm 50.0= cm ρ 2.5=

DU@INA IZVIJAWA STUBA: hi 2 3.75⋅= hi 7.50= m

iIbAb

= i 25.00= cm

λihi 102⋅

i= 25 < λi 30= < 75

- PRESEK U GLAVI STUBA

1. STALNO OPTERE]EWE:

34

e1gMg1Ng1

= e1g 0.11= m

NE Eb Ib⋅π

2

hi2⋅ 10 2−

⋅= NE 292837.06= kN

αENg1NE

= αE 8.7184 10 3−×=

eρ e1g eo+( ) e

αE ρ⋅

1 αE− 1−

⎛⎜⎝

⎞⎟⎠⋅= eρ 0.003= m

- DODATNI EKSCENTRICITET II REDA:

0 < e1D

102⋅ 0.20= < 0.30

e2 D 10 2−⋅

λi 25−

100⋅ 0.1

e1D

+⋅= e2 0.02= m

- UKUPNI EKSCENTRICITET:

maxe1 e1 eo+ eρ+ e2+= maxe1 0.24= m

Nu1 1.0 Ng⋅ 1.8 Np⋅+= Nu1 3469.06= kN

Mu1 1.6 Ng⋅ 1.8 Np⋅+( ) maxe1⋅= Mu1 1136.09= kNm

nuNu1

π r2⋅ fb⋅= nu 0.22=

μ1 0.00=

muMu1 102

⋅

π r2⋅ D⋅ fb⋅= mu 0.07=

1. STALNO + POKRETNO

Mz1 maxMgz maxMΔgz+ maxMpz+= Mz1 657.63= kNm

My1 Mgy MΔgy+ Mpy+= My1 21.71= kNm

M1 Mz12 My12+( )= M1 657.99= kNm

N1 Ng NΔg+ Np+= N1 3334.13= kN

- EKSCENTRICITET USLED UTICAJA I REDA:

e1M1N1

= e1 0.20= m

- EKSCENTRICITET USLED NETA^NOSTI PRI IZVO\EWU:

eohi

300= 0.02 m < eo 0.03= m < 0.10 m

- DODATNI EKSCENTRICITET USLED TE^EWA BETONA:

Mgz1 maxMgz maxMΔgz+= Mgz1 286.02= kNm

Mgy1 Mgy MΔgy+= Mgy1 10.05−= kNm

Mg1 Mgz12 Mgy12+( )= Mg1 286.20= kNm

Ng1 Ng NΔg+= Ng1 2553.07= kN

35

e1g 0.11= m

NE Eb Ib⋅π

2

hi2⋅ 10 2−

⋅= NE 292837.06= kN

αENg2NE

= αE 8.7184 10 3−×=

eρ e1g eo+( ) e

αE ρ⋅

1 αE− 1−

⎛⎜⎝

⎞⎟⎠⋅= eρ 0.003= m

- DODATNI EKSCENTRICITET II REDA:

0.30 < e1D

102⋅ 0.36= < 2.50

e2 D 10 2−⋅

λi 25−

160⋅= e2 0.03= m

- UKUPNI EKSCENTRICITET:

maxe2 e1 eo+ eρ+ e2+= maxe2 0.41= m

Nu2 1.0 Ng2⋅ 1.5 Np⋅+ 1.3 Nk Nt+( )⋅+= Nu2 3691.48= kN

Mu2 1.3 Ng2⋅ 1.5 Np⋅+ 1.3 Nk Nt+( )⋅+[ ] maxe2⋅= Mu2 1847.02= kNm

nuNu2

π r2⋅ fb⋅= nu 0.23=

μ2 0.11=

muMu2 102

⋅

π r2⋅ D⋅ fb⋅= mu 0.11=

2. STALNO + POKRETNO + KO^EWE + TEMPERATURA

Mz2 maxMgz maxMΔgz+ maxMpz+ maxMkz+ maxMtz+= Mz2 1172.55= kNm

My2 Mgy MΔgy+ Mpy+ Mky+ Mty+= My2 72.64= kNm

M2 Mz22 My22+( )= M2 1174.80= kNm

N2 Ng NΔg+ Np+ Nk+ Nt+= N2 3308.61= kN

- EKSCENTRICITET USLED UTICAJA I REDA:

e1M2N2

= e1 0.36= m

- EKSCENTRICITET USLED NETA^NOSTI PRI IZVO\EWU:

eo 0.03= m

- DODATNI EKSCENTRICITET USLED TE^EWA BETONA:

Mgz2 maxMgz maxMΔgz+= Mgz2 286.02= kNm

Mgy2 Mgy MΔgy+= Mgy2 10.05−= kNm

Mg2 Mgz22 Mgy22+( )= Mg2 286.20= kNm

Ng2 Ng NΔg+= Ng2 2553.07= kN

e1gMg2Ng2

=

36

e1g 0.11= m

NE Eb Ib⋅π

2

hi2⋅ 10 2−

⋅= NE 292837.06= kN

αENg3NE

= αE 8.7184 10 3−×=

eρ e1g eo+( ) e

αE ρ⋅

1 αE− 1−

⎛⎜⎝

⎞⎟⎠⋅= eρ 0.003= m

- DODATNI EKSCENTRICITET II REDA:

0.30 < e1D

102⋅ 0.38= < 2.50

e2 D 10 2−⋅

λi 25−

160⋅= e2 0.03= m

- UKUPNI EKSCENTRICITET:

maxe3 e1 eo+ eρ+ e2+= maxe3 0.44= m

Nu3 1.0 Ng3⋅ 1.5 Np⋅+ 1.3 Nk Nt+ Nw+( )⋅+= Nu3 3557.62= kN

Mu3 1.3 Ng3⋅ 1.5 Np⋅+ 1.3 Nk Nt+ Nw+( )⋅+[ ] maxe3⋅= Mu3 1898.50= kNm

nuNu3

π r2⋅ fb⋅= nu 0.22=

μ3 0.13=

muMu3 102

⋅

π r2⋅ D⋅ fb⋅= mu 0.12=

3. STALNO + POKRETNO + KO^EWE + TEMPERATURA + VETAR

Mz3 maxMgz maxMΔgz+ maxMpz+ maxMkz+ maxMtz+ maxMwz+= Mz3 1207.58= kNm

My3 Mgy MΔgy+ Mpy+ Mky+ Mty+ Mwy+= My3 155.37−= kNm

M3 Mz32 My32+( )= M3 1217.53= kNm

N3 Ng NΔg+ Np+ Nk+ Nt+ Nw+= N3 3205.64= kN

- EKSCENTRICITET USLED UTICAJA I REDA:

e1M3N3

= e1 0.38= m

- EKSCENTRICITET USLED NETA^NOSTI PRI IZVO\EWU:

eo 0.03= m

- DODATNI EKSCENTRICITET USLED TE^EWA BETONA:

Mgz3 maxMgz maxMΔgz+= Mgz3 286.02= kNm

Mgy3 Mgy MΔgy+= Mgy3 10.05−= kNm

Mg3 Mgz32 Mgy32+( )= Mg3 286.20= kNm

Ng3 Ng NΔg+= Ng3 2553.07= kN

e1gMg3Ng3

=

37

e1g 0.11= m

NE Eb Ib⋅π

2

hi2⋅ 10 2−

⋅= NE 292837.06= kN

αENg4NE

= αE 8.7184 10 3−×=

eρ e1g eo+( ) e

αE ρ⋅

1 αE− 1−

⎛⎜⎝

⎞⎟⎠⋅= eρ 0.003= m

- DODATNI EKSCENTRICITET II REDA:

0.30 < e1D

102⋅ 1.08= < 2.50

e2 D 10 2−⋅

λi 25−

160⋅= e2 0.03= m

- UKUPNI EKSCENTRICITET:

maxe4 e1 eo+ eρ+ e2+= maxe4 1.14= m

Nu4 1.0 Ng4⋅ 1.3 Ns⋅+= Nu4 2338.53= kN

Mu4 1.3 Ng4⋅ 1.3 Ns⋅+( ) maxe3⋅= Mu4 1363.19= kNm

nuNu4

π r2⋅ fb⋅= nu 0.15=

μ4 0.10=

muMu4 102

⋅

π r2⋅ D⋅ fb⋅= mu 0.08=

4. STALNO + SEIZMIKA

Mz4 maxMgz maxMΔgz+ maxMsz+= Mz4 2577.98= kNm

My4 Mgy MΔgy+ Msy+= My4 98.62= kNm

M4 Mz42 My42+( )= M4 2579.87= kNm

N4 Ng NΔg+ Ns+= N4 2388.04= kN

- EKSCENTRICITET USLED UTICAJA I REDA:

e1M4N4

= e1 1.08= m

- EKSCENTRICITET USLED NETA^NOSTI PRI IZVO\EWU:

eo 0.03= m

- DODATNI EKSCENTRICITET USLED TE^EWA BETONA:

Mgz4 maxMgz maxMΔgz+= Mgz4 286.02= kNm

Mgy4 Mgy MΔgy+= Mgy4 10.05−= kNm

Mg4 Mgz42 Mgy42+( )= Mg4 286.20= kNm

Ng4 Ng NΔg+= Ng4 2553.07= kN

e1gMg4Ng4

=

38

maxMtz 279.86= kNm Mty 19.56−= kNm Nt 14.05−= kN

6. VETAR - OPTERE]EN MOST:

maxMwz 31.80= kNm Mwy 241.61= kNm Nw 102.97−= kN

7. SEIZMIKA - PODU@NO:

maxMsz 2566.62= kNm Msy 149.68−= kNm Ns 165.03−= kN

1. STALNO + POKRETNO

Muz 1.6 maxMgz1 maxMΔgz1+( )⋅ 1.8 maxMpz1⋅+= Muz 574.46= kNm

Muy 1.6 Mgy1 MΔgy1+( )⋅ 1.8 Mpy1⋅+= Muy 12.98= kNm

Mu Muz2 Muy2+( )= Mu 574.60= kNm

Nu 1.0 Ng1 NΔg1+( )⋅ 1.8 Np1⋅+= Nu 4184.06= kN

nuNu

D2 π

4⋅ fb⋅

= nu 0.26=

μ 0.00=

muMu 102

⋅

D2 π

4⋅ D⋅ fb⋅

= mu 0.04=

2. STALNO + POKRETNO + KO^EWE + TEMPERATURA

Muz 1.3 maxMgz maxMΔgz+( )⋅ 1.5 maxMpz⋅+ 1.3 maxMkz maxMtz+( )⋅+= Muz 1007.79= kNm

Muy 1.3 Mgy MΔgy+( )⋅ 1.5 Mpy⋅+ 1.3 Mky Mty+( )⋅+= Muy 39.79−= kNm

Aa μ3 π⋅ r2⋅fbσv⋅= Aa 52.33= cm2

minμ 0.8%=

minAa minμ π⋅ r2⋅= minAa 62.83= cm2

- PRESEK U NO@ICI STUBA

1. STALNO OPTERE]EWE:

maxMgz 56.40= kNm Mgy 23.11= kNm Ng 2210.41= kN

maxMgz1 122.19= kNm Mgy1 6.52= kNm Ng1 2326.93= kN

2. DODATNO STALNO OPTERE]EWE:

maxMΔgz 16.50= kNm MΔgy 12.27= kNm NΔg 489.92= kN

maxMΔgz1 34.11= kNm MΔgy1 7.04= kNm NΔg1 486.61= kN

3. POKRETNO OPTERE]EWE:

maxMpz 105.96= kNm Mpy 3.94−= kNm Np 39.81−= kN

maxMpz1 180.21= kNm Mpy1 4.84−= kNm Np1 761.40= kN

4. ZAUSTAVQAWE I POKRETAWE VOZILA:

maxMkz 300.20= kNm Mky 41.88−= kNm Nk 11.47−= kN

5. RAVNOMERNA PROMENA TEMPERATURE:

39

mu 0.07=

4. STALNO + SEIZMIKA

Muz 1.3 maxMgz maxMΔgz+( )⋅ 1.3 maxMsz⋅+= Muz 3431.38= kNmMuy 1.3 Mgy MΔgy+( )⋅ 1.3 Msy⋅+= Muy 148.59−= kNm

Mu Muz2 Muy2+( )= Mu 3434.59= kNm

Nu 1.0 Ng NΔg+( )⋅ 1.3 Ns⋅+= Nu 2485.79= kN

nuNu

D2 π

4⋅ fb⋅

= nu 0.15=

μ4 0.26=

muMu 102

⋅

D2 π

4⋅ D⋅ fb⋅

= mu 0.21=

Aa μ4 π⋅ r2⋅fbσv⋅= Aa 104.65= cm2

minμ 0.8%=

Aa minμ π⋅ r2⋅= Aa 62.83= cm2

USVOJENO: 24 RA ∅ 25 ( Aa 117.60= cm2 )

Mu Muz2 Muy2+( )= Mu 1008.57= kNm

Nu 1.0 Ng NΔg+( )⋅ 1.5 Np⋅+ 1.3 Nk Nt+( )⋅+= Nu 2607.44= kN

nuNu

D2 π

4⋅ fb⋅

= nu 0.16=

μ2 0.00=

muMu 102

⋅

D2 π

4⋅ D⋅ fb⋅

= mu 0.06=

3. STALNO + POKRETNO + KO^EWE + TEMPERATURA + VETAR

Muz 1.3 maxMgz maxMΔgz+( )⋅ 1.5 maxMpz⋅+ 1.3 maxMkz maxMtz+ maxMwz+( )⋅+=

Muz 1049.13= kNm

Muy 1.3 Mgy MΔgy+( )⋅ 1.5 Mpy⋅+ 1.3 Mky Mty+ Mwy+( )⋅+=

Muy 274.31= kNm

Mu Muz2 Muy2+( )= Mu 1084.40= kNm

Nu 1.0 Ng NΔg+( )⋅ 1.5 Np⋅+ 1.3 Nk Nt+ Nw+( )⋅+= Nu 2473.58= kN

nuNu

D2 π

4⋅ fb⋅

= nu 0.15=

μ3 0.04=

muMu 102

⋅

D2 π

4⋅ D⋅ fb⋅

=

40

Rkz1 11.47= kN

Rkx 12.47= kN Rkx1 75.87= kN

Mky 90.20= kNm Mky1 300.60= kNm

5. RAVNOMERNA PROMENA TEMPERATURE:

Rtz 19.54= kN Rtz1 14.05= kN

Rtx 37.61−= kN Rtx1 70.27= kN

Mty 272.66−= kNm Mty1 280.04= kNm

6. VETAR - OPTERE]EN MOST:

Rwz1 102.97= kNRwz 151.87= kNRwx1 8.28= kNRwx 0.60= kNMwy1 29.38= kNmMwy 5.36= kNm

7. SEIZMIKA - POPRE^NO:

Rzz1 500.69= kNRzz 789.86= kNRzx1 48.32= kNRzx 3.13= kNMzy1 170.39= kNmMzy 29.43= kNm

3.3. TEMEQ SREDWEG STUBA

- PRESEK U NO@ICI STUBA - max REAKCIJA Rz

1. SOPSTVENA TE@INA:

Rgz 2326.93= kN Rgz1 2210.41= kN

Rgx 23.95= kN Rgx1 37.19−= kN

Mgy 122.25= kNm Mgy1 56.17−= kNm

2. DODATNO STALNO OPTERE]EWE:

RΔgz 486.61= kN RΔgz1 489.92= kN

RΔgx 6.71= kN RΔgx1 10.60−= kN

MΔgy 34.18= kNm MΔgy1 16.38−= kNm

3. POKRETNO OPTERE]EWE:

maxRpz 1181.44= kN maxRpz1 1203.93= kN

Rpx 2.15= kN Rpx1 2.39= kN

Mpy 0.54−= kNm Mpy1 36.52= kNm

4. ZAUSTAVQAWE I POKRETAWE VOZILA:

Rkz 4.51= kN

41

1. STALNO OPTERE]EWE

Ng Rgz RΔgz+ Gj+ Gt+ Gz+= Ng 4492.00= kN

Hg Rgx RΔgx+= Hg 30.66= kN

Mg Mgy MΔgy+ Hg ht⋅+= Mg 233.08= kNm

σ1NgF

MgW

+= σ1 278.25= kN/m2

σ2NgF

MgW

−= σ2 238.07= kN/m2

2. STALNO + POKRETNO

N Ng maxRpz+= N 5673.44= kN

H Hg Rpx+= H 32.81= kN

M Mgy MΔgy+ Mpy+ H ht⋅+= M 237.92= kNm

σ1NF

MW

+= σ1 346.57= kN/m2

σ2NF

MW

−= σ2 305.55= kN/m2

KONTROLA NAPONA U TEMEQNOJ SPOJNICI

- ZA STUB S2

4001 2

MyRx

Rz 212

100

150

250

300

b 4.00= m d 4.35= m

ht 2.50= m

F b d⋅= F 17.40= m2

Wb2 d⋅

6= W 11.60= m3

- TE@INA JASTUKA

Gj 3.00 3.75⋅ 1.00⋅ 25.00⋅= Gj 281.25= kN

- TE@INA TEMEQNE STOPE

Gt 4.00 4.35⋅ 1.50⋅ 25.00⋅= Gt 652.50= kN

- TE@INA ZEMQE

Gz1 3.00 3.75⋅ π 0.502⋅−( ) 2.12⋅ 18.00⋅= Gz1 399.33= kN

Gz2 4.00 4.35⋅ 3.00 3.75⋅−( ) 3.12⋅ 18.00⋅= Gz2 345.38= kN

Gz Gz1 Gz2+= Gz 744.71= kN

42

- ZA STUB S5

4501 2

MyRx

Rz

335

100

150

250

300

b 4.50= m d 3.10= m

ht 2.50= m

F b d⋅= F 13.95= m2

Wb2 d⋅

6= W 10.46= m3

- TE@INA JASTUKA

Gj 3.00 2.00⋅ 1.00⋅ 25.00⋅= Gj 150.00= kN

- TE@INA TEMEQNE STOPE

Gt 4.50 3.10⋅ 1.50⋅ 25.00⋅= Gt 523.13= kN

- TE@INA ZEMQE

Gz1 3.00 2.00⋅ π 0.502⋅−( ) 3.35⋅ 18.00⋅= Gz1 314.44= kN

Gz2 4.50 3.10⋅ 3.00 2.00⋅−( ) 4.35⋅ 18.00⋅= Gz2 622.49= kN

Gz Gz1 Gz2+= Gz 936.93= kN

3. STALNO + POKRETNO + KO^EWE + TEMPERATURA + VETAR

N Ng maxRpz+ Rkz+ Rtz+ Rwz+= N 5849.36= kN

H Hg Rpx+ Rkx+ Rtx+ Rwx+= H 8.27= kN

M Mgy MΔgy+ Mpy+ Mky+ Mty+ Mwy+ H ht⋅+= M 0.53−= kNm

σ1NF

MW

+= σ1 336.12= kN/m2

σ2NF

MW

−= σ2 336.22= kN/m2

4. STALNO + SEIZMIKA

N Ng Rzz+= N 5281.86= kN

H Hg Rzx+= H 33.79= kN

M Mgy MΔgy+ Mzy+ H ht⋅+= M 270.34= kNm

σ1NF

MW

+= σ1 326.86= kN/m2

σ2NF

MW

−= σ2 280.25= kN/m2

43

N Ng maxRpz1+ Rkz1+ Rtz1+ Rwz1+= N 5642.80= kN

H Hg Rpx1+ Rkx1+ Rtx1+ Rwx1+= H 109.02= kN

M Mgy1 MΔgy1+ Mpy1+ Mky1+ Mty1+ Mwy1+ H ht⋅+= M 846.54= kNm

σ1NF

MW

+= σ1 485.41= kN/m2

σ2NF

MW

−= σ2 323.59= kN/m2

4. STALNO + SEIZMIKA

N Ng Rzz1+= N 4811.07= kN

H Hg Rzx1+= H 0.53= kN

M Mgy1 MΔgy1+ Mzy1+ H ht⋅+= M 99.16= kNm

σ1NF

MW

+= σ1 354.36= kN/m2

σ2NF

MW

−= σ2 335.40= kN/m2

1. STALNO OPTERE]EWE

Ng Rgz1 RΔgz1+ Gj+ Gt+ Gz+= Ng 4310.38= kN

Hg Rgx1 RΔgx1+= Hg 47.79−= kN

Mg Mgy1 MΔgy1+ Hg ht⋅+= Mg 192.02−= kNm

σ1NgF

MgW

+= σ1 290.63= kN/m2

σ2NgF

MgW

−= σ2 327.34= kN/m2

2. STALNO + POKRETNO

N Ng maxRpz1+= N 5514.31= kN

H Hg Rpx1+= H 45.40−= kN

M Mgy1 MΔgy1+ Mpy1+ H ht⋅+= M 149.53−= kNm

σ1NF

MW

+= σ1 381.00= kN/m2

σ2NF

MW

−= σ2 409.58= kN/m2

3. STALNO + POKRETNO + KO^EWE + TEMPERATURA + VETAR

44

maxMpy1 105.99−= kNm

maxMpy2 184.87= kNm

4. ZAUSTAVQAWE I POKRETAWE VOZILA:

Rkz 4.51= kN Rkz1 11.47= kN

Rkx 12.47= kN Rkx1 75.87= kN

Mky 90.20= kNm Mky1 300.60= kNm

5. RAVNOMERNA PROMENA TEMPERATURE:

Rtz 19.54= kN Rtz1 14.05= kN

Rtx 37.61−= kN Rtx1 70.27= kN

Mty 272.66−= kNm Mty1 280.04= kNm

6. VETAR - OPTERE]EN MOST:

Rwz1 102.97= kNRwz 151.87= kNRwx1 8.28= kNRwx 0.60= kNMwy1 29.38= kNmMwy 5.36= kNm

7. SEIZMIKA - PODU@NO:

Rzz1 500.69= kNRzz 789.86= kNRzx1 48.32= kNRzx 3.13= kNMzy1 170.39= kNmMzy 29.43= kNm

- PRESEK U NO@ICI STUBA - max MOMENAT My1. SOPSTVENA TE@INA:

Rgz 2326.93= kN Rgz1 2210.41= kN Rgz2 2055.98= kN

Rgx 23.95= kN Rgx1 37.19−= kN Rgx2 13.36= kN

Mgy 122.25= kNm Mgy1 56.17−= kNm Mgy2 71.43= kNm

2. DODATNO STALNO OPTERE]EWE:

RΔgz 486.61= kN RΔgz1 489.92= kN RΔgz2 415.31= kN

RΔgx 6.71= kN RΔgx1 10.60−= kN RΔgx2 3.41= kN

MΔgy 34.18= kNm MΔgy1 16.38−= kNm MΔgy2 18.47= kNm

3. POKRETNO OPTERE]EWE:

Rpz 761.40= kN Rpz1 39.81−= kN Rpz2 673.18= kN

Rpx 38.02= kN Rpx1 30.67−= kN Rpx2 37.99= kN

maxMpy 180.15= kNm

45

1. STALNO OPTERE]EWE

Ng Rgz RΔgz+ Gj+ Gt+ Gz+= Ng 4492.00= kN

Hg Rgx RΔgx+= Hg 30.66= kN

Mg Mgy MΔgy+ Hg ht⋅+= Mg 233.08= kNm

σ1NgF

MgW

+= σ1 278.25= kN/m2

σ2NgF

MgW

−= σ2 238.07= kN/m2

2. STALNO + POKRETNO

N Ng Rpz+= N 5253.40= kN

H Hg Rpx+= H 68.68= kN

M Mgy MΔgy+ maxMpy+ H ht⋅+= M 508.28= kNm

σ1NF

MW

+= σ1 345.74= kN/m2

σ2NF

MW

−= σ2 258.10= kN/m2

KONTROLA NAPONA U TEMEQNOJ SPOJNICI

- ZA STUB S2

4001 2

MyRx

Rz 212

100

150

250

300

b 4.00= m d 4.35= m

ht 2.50= m

F b d⋅= F 17.40= m2

Wb2 d⋅

6= W 11.60= m3

- TE@INA JASTUKA

Gj 3.00 3.75⋅ 1.00⋅ 25.00⋅= Gj 281.25= kN

- TE@INA TEMEQNE STOPE

Gt 4.00 4.35⋅ 1.50⋅ 25.00⋅= Gt 652.50= kN

- TE@INA ZEMQE

Gz1 3.00 3.75⋅ π 0.502⋅−( ) 2.12⋅ 18.00⋅= Gz1 399.33= kN

Gz2 4.00 4.35⋅ 3.00 3.75⋅−( ) 3.12⋅ 18.00⋅= Gz2 345.38= kN

Gz Gz1 Gz2+= Gz 744.71= kN

46

Gj 150.00= kN

- TE@INA TEMEQNE STOPE

Gt 4.00 3.10⋅ 1.50⋅ 25.00⋅= Gt 465.00= kN

- TE@INA ZEMQE

Gz1 3.00 2.00⋅ π 0.502⋅−( ) 3.35⋅ 18.00⋅= Gz1 314.44= kN

Gz2 4.00 3.10⋅ 3.00 2.00⋅−( ) 4.35⋅ 18.00⋅= Gz2 501.12= kN

Gz Gz1 Gz2+= Gz 815.56= kN

1. STALNO OPTERE]EWE

Ng Rgz1 RΔgz1+ Gj+ Gt+ Gz+= Ng 4130.89= kN

Hg Rgx1 RΔgx1+= Hg 47.79−= kN

Mg Mgy1 MΔgy1+ Hg ht⋅+= Mg 192.02−= kNm

σ1NgF

MgW

+= σ1 309.91= kN/m2

σ2NgF

MgW

−= σ2 356.37= kN/m2

3. STALNO + POKRETNO + KO^EWE + TEMPERATURA + VETAR

N Ng Rpz+ Rkz+ Rtz+ Rwz+= N 5429.32= kN

H Hg Rpx+ Rkx+ Rtx+ Rwx+= H 44.14= kN

M Mgy MΔgy+ maxMpy+ Mky+ Mty+ Mwy+ H ht⋅+= M 269.83= kNm

σ1NF

MW

+= σ1 335.29= kN/m2

σ2NF

MW

−= σ2 288.77= kN/m2

- ZA STUB S5

4501 2

MyRx

Rz

335

100

150

250

300

b 4.00= m d 3.10= m

ht 2.50= m

F b d⋅= F 12.40= m2

Wb2 d⋅

6= W 8.27= m3

- TE@INA JASTUKA

Gj 3.00 2.00⋅ 1.00⋅ 25.00⋅=

47

σ2 348.18= kN/m2σ2NF

MW

−=

σ1 533.00= kN/m2σ1NF

MW

+=

M 763.89= kNmM Mgy1 MΔgy1+ Mpy1+ Mky1+ Mty1+ Mwy1+ H ht⋅+=

H 75.96= kNH Hg Rpx1+ Rkx1+ Rtx1+ Rwx1+=

N 5463.31= kNN Ng maxRpz1+ Rkz1+ Rtz1+ Rwz1+=

3. STALNO + POKRETNO + KO^EWE + TEMPERATURA + VETAR

σ2 458.31= kN/m2σ2NF

MW

−=

σ1 402.14= kN/m2σ1NF

MW

+=

M 232.18−= kNmM Mgy1 MΔgy1+ Mpy1+ H ht⋅+=

H 78.46−= kNH Hg Rpx1+=

N 5334.82= kNN Ng maxRpz1+=

2. STALNO + POKRETNO

48

minM 515.00−= kNm

kh

minM 102⋅

b fb⋅

= k 10.381= ea / eb = 10.0 / 0.475 o/oo

μ' 0.992%=

Aa μ' b⋅ h⋅fbσv⋅= Aa 14.49= cm2

minAa 0.20b d⋅100⋅= minAa 60.00= cm2

USVOJENA GLAVNA ARMATURA: 30 RA ∅ 16 ( Aa 60.30= cm2 )

- PRESEK U POQU

maxM 1.7g2⋅

L2

4L12

−⎛⎜⎝

⎞⎟⎠

⋅= maxM 936.06= kNm

kh

maxM 102⋅

b fb⋅

= k 7.700= ea / eb = 10.0 / 0.650 o/oo

μ' 1.769%=

Aa μ' b⋅ h⋅fbσv⋅= Aa 25.84= cm2

minAa 0.20b d⋅100⋅= minAa 60.00= cm2

USVOJENA GLAVNA ARMATURA: 30 RA ∅ 16 ( Aa 60.30= cm2 )

PRORA^UN JASTUKA

MB 30 ⇒ fb 20.50= MPa τr 1.10= MPa

RA 400/500-2 ⇒ σv 400= MPa

b 300.0= cm d 100.0= cm a 5.0= cm

h d a−= h 95.0= cm

L 4.70= m L1 1.40= m

σ1 336.12= kN/m2 bt 4.00= m

σ2 336.22= kN/m2 dt 4.35= m

gσ1 σ2+

2 dt⋅bt⋅= g 309.12= kN/m

- PRESEK IZNAD OSLONCA

minM 1.7− g⋅L12

2⋅=

49

KONTROLA PRESEKA PREMA GRANI^NIM UTICAJIMA

TRANSVERZALNIH SILA

b 300.0= cm d 100.0= cm h 95.00= cm

z 0.9 h⋅= z 85.50= cm

Tl g L1⋅= Tl 432.77= kN

Td g L1L2

+⎛⎜⎝

⎞⎟⎠

⋅ Tl−= Td 726.44= kN

τn11.7 Td⋅

b z⋅10⋅= τn1 0.48= MPa

τn1 0.48= MPa < τr 1.10= MPa

USVAJAJU SE KONSTRUKTIVNE UZENGIJE: RA ∅ 12 / 20 cm

50

4. PRORA^UN KRAJWEG STUBA S1

51

g12 53.2163 0.50⋅ 25.0⋅=

- ^EONO PLATNO

e11 0.46−= mg11 561.24= kNg11 1.20 1.20⋅ 8.31 7.28+( )⋅ 25.0⋅=

- STUBOVI

e10 0.32−= mg10 25.90= kNg10 0.40 0.70⋅ 0.5⋅ 7.40⋅ 25.0⋅=

e9 0.45−= mg9 133.20= kNg9 0.60 1.20⋅ 7.40⋅ 25.0⋅=

- LE@I[NA GREDA

e8 0.06−= mg8 88.20= kNg8 0.40 0.90⋅ 9.80⋅ 25.0⋅=

- PARAPET

eΔg2 3.05= mΔg2 86.59= kNΔg2 14.93 5.80⋅=

eΔg1 4.32= mΔg1 124.67= kNΔg1 14.93 8.35⋅=

3. PE[A^KA STAZA NA KRILU

est 0.56= mgst 1452.03= kNgst 40.3341 1.50⋅ 24.0⋅=

- STOPA TEMEQA

ej 0.51−= mgj 600.81= kNgj 24.0325 1.00⋅ 25.0⋅=

- JASTUK

e12 0.81−= mg12 665.20= kN

e2 5.26= mg2 70.14= kNg2 3.35 3.35⋅ 0.5⋅ 0.50⋅ 25.0⋅=

e1 6.32= mg1 54.37= kNg1 1.00 4.35⋅ 0.50⋅ 25.0⋅=

- VISE]E KRILO

2. SOPSTVENA TE@INA STUBA

e 0.66−= mRp 865.02= kN

Rp 16.68 50.45+ 23.92− 292.51+ 403.19+ 126.11+=

RΔg 309.640= kN

RΔg 131.67 6.37− 22.19+ 22.61+ 12.66− 152.20+=

Rg 1520.520= kN

Rg 166.06 192.19+ 193.83+ 195.47+ 197.23+ 198.87+ 200.50+ 176.37+=

1. REAKCIJE SA KONSTRUKCIJE

4.1 PRORA^UN NAPONA U PRESECIMA

e7 3.05= mg7 29.51= kNg7 0.165 0.40⋅ 0.25 0.55⋅+( ) 5.80⋅ 25.0⋅=

e6 4.32= mg6 42.48= kNg6 0.165 0.40⋅ 0.25 0.55⋅+( ) 8.35⋅ 25.0⋅=

- KONZOLA PE[A^KE STAZE

e5 2.15= mg5 457.50= kNg5 4.00 9.15⋅ 0.50⋅ 25.0⋅=

- STOJE]E KRILO

e4 1.75= mg4 144.00= kNg4 4.80 4.80⋅ 0.5⋅ 0.50⋅ 25.0⋅=

e3 3.05= mg3 72.50= kNg3 1.00 5.80⋅ 0.50⋅ 25.0⋅=

52

PRESEK II - II PRESEK I - I

- KARAKTERISTIKE PRESEKA

Epv 78.53= kNEpv Ep sin ρ( )⋅=

ev 0.56−= mEzv 489.13= kNEzv Ez sin ρ( )⋅=

ephl 3.57−= mEph 249.07= kNEph Ep cos ρ( )⋅=

ephd 5.07−= mEzh 1551.32= kNEzh Ez cos ρ( )⋅=

ezhl 2.11−= mEp 261.15= kNEp ep F⋅=

ezhd 3.61−= mEz 1626.61= kNEz ezt F⋅=

ep 3.41= kN/m2

WII5 563.29= m3WII5I2

x25=WI5 105.66= m3WI5

I1x15

=

WII4 20.28= m3WII4I2

x24=WI4 3.69= m3WI4

I1x14

=

WII2 28.32= m3WII2I2

x22=WI3 14.49= m3WI3

I1x13

=

x25 0.1307= mx15 0.1447= m

x24 3.6307= mI2 73.6217= m4x14 4.1447= mI1 15.2895= m4

x22 2.60= mF2 24.0325= m2x13 1.0553= mF1 8.5805= m2

ez7 1.79= mz7 157.25= kNz7 2.40 3.64⋅ 18.0⋅=

ez6 2.23−= mz6 572.42= kNz6 4.90 1.90 4.59+( )⋅ 18.0⋅=

ez5 0.37−= mz5 179.10= kNz5 1.2516 7.95⋅ 18.0⋅=

ez4 1.44= mz4 1065.54= kNz4 6.3042 9.39⋅ 18.0⋅=

ez3 0.52−= mz3 75.82= kNz3 0.9728 4.33⋅ 18.0⋅=

ez2 1.23= mz2 171.12= kNz2 3.6010 2.64⋅ 18.0⋅=

ez1 2.00−= mz1 274.86= kNz1 3.00 1.24 3.85+( )⋅ 18.0⋅=

4. TE@INA ZEMQE

ep h1 γ⋅ tan β( )( )2⋅=

ezt 21.27= kN/m2ezt ht γ⋅ tan β( )( )2⋅=

ez 42.53= kN/m2ez h2 γ⋅ tan β( )( )2⋅=

ht 4.36= mF 76.4839= m2

h2 8.72= mh1 0.70= m

cos ρ( ) 0.954=sin ρ( ) 0.301=

γ 18.00= kN/m3,

φ 35= o,

ρ 17.5= o, β 45

φ

2−=

5. ZEMQANI PRITISAK

ez10 0.09= mz10 96.01= kNz10 0.60 8.89⋅ 18.0⋅=

ez9 1.84= mz9 439.92= kNz9 2.35 10.40⋅ 18.0⋅=

ez8 0.04= mz8 62.36= kNz8 0.65 5.33⋅ 18.0⋅=

53

M1 M' M''+= M1 2375.02= kNm

σ13N1F1

M1WI3

−= σ13 133.90= kN/m2

σ14N1F1

M1WI4

+= σ14 941.65= kN/m2

σ15N1F1

M1WI5

+= σ15 320.30= kN/m2

PRESEK II - II

N2 N1 gj+= N2 3156.32= kN

M2 M1 N1 ej⋅+= M2 1071.71= kNm

σ22N2F2

M2WII2

−= σ22 93.49= kN/m2

σ24N2F2

M2WII4

+= σ24 184.19= kN/m2

σ25N2F2

M2WII5

+= σ25 133.24= kN/m2

PRESEK III - III

F3 40.3341= m2 x31 3.0062= m

I3 158.4332= m4 x34 4.1938= m

x35 0.6938= m

WIII1I3

x31= WIII1 52.70= m3

WIII4I3

x34= WIII4 37.78= m3

WIII5I3

x35= WIII5 228.36= m3

1. SOPSTVENA TE@INA STUBA

PRESEK I - I

N1 g1 g2+ g3+ g4+ g5+ g6+ g7+ g8+ g9+ g10+ g11+ g12+ Δg1+ Δg2+=

N1 2555.51= kN

M' g1 e1⋅ g2 e2⋅+ g3 e3⋅+ g4 e4⋅+ g5 e5⋅+ g6 e6⋅+ g7 e7⋅+ g8 e8⋅+= M' 2437.56= kNm

M'' g9 e9⋅ g10 e10⋅+ g11 e11⋅+ g12 e12⋅+ Δg1 eΔg1⋅+ Δg2 eΔg2⋅+= M'' 62.55−= kNm

54

N2 N1 z1+ z2+ z3+ z4+ z5+= N2 4889.61= kN

M2d M1d N1 ej⋅+ z1 ez1⋅+ z2 ez2⋅+ z3 ez3⋅+ z4 ez4⋅+ z5 ez5⋅+= M2d 5309.29−= kNm

M2l M1l N1 ej⋅+ z1 ez1⋅+ z2 ez2⋅+ z3 ez3⋅+ z4 ez4⋅+ z5 ez5⋅+= M2l 2608.71−= kNm

σ22N2F2

M2dWII2

−= σ22 390.96= kN/m2

σ24N2F2

M2dWII4

+= σ24 58.37−= kN/m2

σ25N2F2

M2lWII5

+= σ25 198.83= kN/m2

PRESEK III - III

N3 N2 z6+ z7+ z8+ z9+ z10+= N3 6217.57= kN

M3d M2d N2 est⋅+ z6 ez6⋅+ z7 ez7⋅+ z8 ez8⋅+ z9 ez9⋅+ z10 ez10⋅+= M3d 2745.54−= kNm

M3l M2l N2 est⋅+ z6 ez6⋅+ z7 ez7⋅+ z8 ez8⋅+ z9 ez9⋅+ z10 ez10⋅+= M3l 44.96−= kNm

σ31N3F3

M3dWIII1

−= σ31 206.25= kN/m2

σ34N3F3

M3dWIII4

+= σ34 81.48= kN/m2

σ35N3F3

M3lWIII5

+= σ35 153.95= kN/m2

PRESEK III - III

N3 N2 gst+= N3 4608.35= kN

M3 M2 N2 est⋅+= M3 2839.25= kNm

σ31N3F3

M3WIII1

−= σ31 60.38= kN/m2

σ34N3F3

M3WIII4

+= σ34 189.41= kN/m2

σ35N3F3

M3WIII5

+= σ35 126.69= kN/m2

2. SOPSTVENA TE@INA STUBA, TE@INA ZEMQE I ZEMQANI PRITISAK

PRESEK I - I

N1 N1 Ezv+ Epv+= N1 3123.17= kN

M1d M1 Ezv Epv+( ) ev⋅+ Ezh ezhd⋅+ Eph ephd⋅+= M1d 4805.91−= kNm

M1l M1 Ezv Epv+( ) ev⋅+ Ezh ezhl⋅+ Eph ephl⋅+= M1l 2105.33−= kNm

σ13N1F1

M1dWI3

−= σ13 695.69= kN/m2

σ14N1F1

M1dWI4

+= σ14 938.81−= kN/m2

σ15N1F1

M1lWI5

+= σ15 344.06= kN/m2

PRESEK II - II

55

σ25 271.18= kN/m2

PRESEK III - III

N3 N3 Rg+ RΔg+= N3 8047.73= kN

M3d M3d Rg RΔg+( ) e ej+ est+( )⋅+= M3d 3861.94−= kNm

M3l M3l Rg RΔg+( ) e ej+ est+( )⋅+= M3l 1161.36−= kNm

σ31N3F3

M3dWIII1

−= σ31 272.81= kN/m2

σ34N3F3

M3dWIII4

+= σ34 97.30= kN/m2

σ35N3F3

M3lWIII5

+= σ35 194.44= kN/m2

4. SOPSTVENA TE@INA STUBA, TE@INA ZEMQE, ZEMQANI PRITISAK, REAKCIJASA KONSTRUKCIJE I POKRETNO OPTERE]EWE ( OSNOVNO )

PRESEK I - I

N1 N1 Rp+= N1 5818.35= kN

M1d M1d Rp e⋅+= M1d 6584.73−= kNm

M1l M1l Rp e⋅+= M1l 3884.15−= kNm

σ13N1F1

M1dWI3

−= σ13 1132.58= kN/m2

3. SOPSTVENA TE@INA STUBA, TE@INA ZEMQE, ZEMQANI PRITISAK IREAKCIJA SA KONSTRUKCIJE

PRESEK I - I

N1 N1 Rg+ RΔg+= N1 4953.33= kN

M1d M1d Rg RΔg+( ) e⋅+= M1d 6013.81−= kNm

M1l M1l Rg RΔg+( ) e⋅+= M1l 3313.23−= kNm

σ13N1F1

M1dWI3

−= σ13 992.36= kN/m2

σ14N1F1

M1dWI4

+= σ14 1052.96−= kN/m2

σ15N1F1

M1lWI5

+= σ15 545.92= kN/m2

PRESEK II - II

N2 N2 Rg+ RΔg+= N2 6719.77= kNM2d M2d Rg RΔg+( ) e ej+( )⋅+= M2d 7450.58−= kNmM2l M2l Rg RΔg+( ) e ej+( )⋅+= M2l 4750.00−= kNm

σ22N2F2

M2dWII2

−= σ22 542.73= kN/m2

σ24N2F2

M2dWII4

+= σ24 87.82−= kN/m2

σ25N2F2

M2lWII5

+=

56

σ31 304.26= kN/m2

σ34N3F3

M3dWIII4

+= σ34 104.78= kN/m2

σ35N3F3

M3lWIII5

+= σ35 213.58= kN/m2

5. SOPSTVENA TE@INA STUBA, TE@INA ZEMQE, ZEMQANI PRITISAK, REAKCIJASA KONSTRUKCIJE I POKRETNO OPTERE]EWE ( OSNOVNO I DOPUNSKO )

- HORIZONTALNA REAKCIJA KOJU PRIMAJU LE@I[TA

H 30.96 6⋅= H 185.76= kN

PRESEK I - I

N1 N1= N1 5818.35= kN

M1d M1d H 8.55⋅−= M1d 8172.97−= kNm

M1l M1l H 7.05⋅−= M1l 5193.75−= kNm

σ13N1F1

M1dWI3

−= σ13 1242.20= kN/m2

σ14N1F1

M1dWI4

+= σ14 1537.45−= kN/m2

σ15N1F1

M1lWI5

+= σ15 628.94= kN/m2

σ14N1F1

M1dWI4

+= σ14 1106.91−= kN/m2

σ15N1F1

M1lWI5

+= σ15 641.33= kN/m2

PRESEK II - II

N2 N2 Rp+= N2 7584.79= kN

M2d M2d Rp e ej+( )⋅+= M2d 8462.65−= kNm

M2l M2l Rp e ej+( )⋅+= M2l 5762.07−= kNm

σ22N2F2

M2dWII2

−= σ22 614.47= kN/m2

σ24N2F2

M2dWII4

+= σ24 101.74−= kN/m2

σ25N2F2

M2lWII5

+= σ25 305.38= kN/m2

PRESEK III - III

N3 N3 Rp+= N3 8912.75= kN

M3d M3d Rp e ej+ est+( )⋅+= M3d 4389.60−= kNm

M3l M3l Rp e ej+ est+( )⋅+= M3l 1689.02−= kNm

σ31N3F3

M3dWIII1

−=

57

PRESEK III III

USVOJENA ARMATURA: 3 RA ∅ 25 ( Aa 14.73= cm2 )

Aa 3.55= cm2AaZ 10⋅

dopσv=

- DOPU[TEN NAPON U ARMATURI RA 400 / 500 - 2: dopσv 240= MPa

Z 85.23= kNZ 225.77 1.51⋅ 0.5⋅ 0.50⋅=

σ25 302.72= kN/m2σ25N2F2

M2lWII5

+=

σ24 189.22−= kN/m2σ24N2F2

M2dWII4

+=

σ22 677.12= kN/m2σ22N2F2

M2dWII2

−=

M2l 7257.44−= kNmM2l M2l H 8.05⋅−=

M2d 10236.66−= kNmM2d M2d H 9.55⋅−=

N2 7584.79= kNN2 N2= PRESEK II - II

USVOJENA ARMATURA: 10 RA ∅ 25 ( Aa 49.10= cm2 )

Aa 46.12= cm2AaZ 10⋅

dopσv=

- DOPU[TEN NAPON U ARMATURI RA 400 / 500 - 2: dopσv 240= MPa

Z 1106.96= kNZ 1537.45 2.88⋅ 0.5⋅ 0.50⋅=

58

PRESEK III - III

N3 N3= N3 8912.75= kN

M3d M3d H 11.05⋅−= M3d 6442.25−= kNm

M3l M3l H 9.55⋅−= M3l 3463.03−= kNm

σ31N3F3

M3dWIII1

−= σ31 343.21= kN/m2

σ34N3F3

M3dWIII4

+= σ34 50.44= kN/m2

σ35N3F3

M3lWIII5

+= σ35 205.81= kN/m2

59

SA SPOQA[WE STRANE KRILA: RA ∅ 12 / 20 cm ( Aa 5.65= cm2/m )

USVOJENA ARMATURASA UNUTRA[WE STRANE KRILA: RA ∅ 16 / 20 cm

RA ∅ 14 / 20 cm ( Aa 17.22= cm2/m )

Aa 17.22= cm2/mAa μ' b⋅ h⋅fbσv⋅=

ea / eb = 10.0 / 1.475 o/oo

μ' 7.149%=

k 3.847=kh

Mu 102⋅

b fb⋅

=

Mu 306.02= kNm/mMu 1.6 Mg⋅ 1.8 Mp⋅+=

Mp 55.92= kNm/m

Mg 128.35= kNm/m

h 47.0= cmh d a−=

a 3.0= cmd 50.0= cmb 100.0= cm

HORIZONTALNA ARMATURA SA UNUTRA[WE STRANE KRILA•

4.2.1. KRILO NA DESNOJ STRANI MOSTA

RA 400/500-2 ⇒ σv 400= MPa

MB 30 ⇒ fb 20.50= MPa τr 1.10= MPa

4.2. PRORA^UN KRILA

60

g3 0.165 0.40⋅ 0.25 0.35⋅+( ) 4.35⋅ 25.0⋅= g3 16.69= kN

- PE[A^KA STAZA NA KRILU

Δg 1.05 13.58+ 0.30+( ) 4.35⋅= Δg 64.95= kN

- POKRETNO OPTERE]EWE

P 50.0= kN

Mg g1 g3+( ) 2.175⋅ g2 1.117⋅+= Mg 232.92= kNm

MΔg Δg 2.175⋅= MΔg 141.26= kNm

Mp P 4.35⋅= Mp 217.50= kNm

Mu 1.6 Mg MΔg+( )⋅ 1.8 Mp⋅+=

Mu 990.18= kNm

kh

Mu 102⋅

b fb⋅

= k 9.491= ea / eb = 10.0 / 0.325 o/oo

μ' 0.484%=

Aa μ' b⋅ h⋅fbσv⋅= Aa 3.66= cm2

USVOJENA ARMATURA: 3 RA ∅ 22 ( Aa 11.40= cm2 )

VERTIKALNA ARMATURA SA UNUTRA[WE STRANE KRILA•

Mg 151.98= kNm/m

Mp 31.73= kNm/m

Mu 1.6 Mg⋅ 1.8 Mp⋅+= Mu 300.28= kNm/m

kh

Mu 102⋅

b fb⋅

= k 3.883= ea / eb = 10.0 / 1.450 o/oo

μ' 6.962%=

Aa μ' b⋅ h⋅fbσv⋅= Aa 16.77= cm2/m

USVOJENA ARMATURASA UNUTRA[WE STRANE KRILA: RA ∅ 16 / 20 cm

RA ∅ 14 / 20 cm ( Aa 16.77= cm2/m )

SA SPOQA[WE STRANE KRILA: RA ∅ 12 / 20 cm ( Aa 5.65= cm2/m )

VEZA VISE]EG I STOJE]EG KRILA•

b 50.0= cm d 442.0= cm h 295.0= cm

- SOPSTVENA TE@INA KRILA

g1 1.00 4.35⋅ 0.50⋅ 25.0⋅= g1 54.37= kN

g2 3.35 3.35⋅ 0.5⋅ 0.50⋅ 25.0⋅= g2 70.14= kN

61

ea / eb = 10.0 / 1.050 o/oo

μ' 4.116%=

k 5.064=kh

Mu 102⋅

b fb⋅

=

Mu 176.57= kNmMu 1.7 MII⋅=

LAMELA II

Aa 6.53= cm2Aa μ' b⋅ h⋅fbσv⋅=

ea / eb = 10.0 / 0.825 o/oo

μ' 2.712%=

k 6.159=kh

Mu 102⋅

b fb⋅

=

Mu 119.39= kNmMu 1.7 MI⋅=

LAMELA I

MIV 59.01= kNm/mMIV 20.492.402

2⋅=

MIII 90.23= kNm/mMIII 15.613.402

2⋅=

MII 103.87= kNm/mMII 10.734.402

2⋅=

MI 70.23= kNm/mMI 5.854.902

2⋅=

h 47.0= cmh d a−=

a 3.0= cmd 50.0= cmb 100.0= cm

HORIZONTALNA ARMATURA SA UNUTRA[WE STRANE KRILA•

4.2.2. KRILO NA LEVOJ STRANI MOSTA

62

SA UNUTRA[WE STRANE KRILA: RA ∅ 12 / 20 cm ( Aa 5.65= cm2/m )

SA SPOQA[WE STRANE KRILA: RA ∅ 12 / 20 cm ( Aa 5.65= cm2/m )

VEZA VISE]EG I STOJE]EG KRILA•

b 50.0= cm d 590.0= cm h 384.0= cm

- SOPSTVENA TE@INA KRILA

g1 1.00 4.90⋅ 0.50⋅ 25.0⋅= g1 61.25= kN

g2 4.80 4.80⋅ 0.5⋅ 0.50⋅ 25.0⋅= g2 144.00= kN

g3 0.165 0.40⋅ 0.25 0.35⋅+( ) 4.90⋅ 25.0⋅= g3 18.80= kN

- PE[A^KA STAZA NA KRILU

Δg 1.05 13.58+ 0.30+( ) 4.90⋅= Δg 73.16= kN

- POKRETNO OPTERE]EWE

P 50.0= kN

Aa μ' b⋅ h⋅fbσv⋅= Aa 9.91= cm2

USVOJENA ARMATURASA UNUTRA[WE STRANE KRILA: RA ∅ 14 / 20 cm

RA ∅ 12 / 20 cm ( Aa 13.35= cm2/m )

LAMELA III

Mu 1.7 MIII⋅= Mu 153.38= kNm

kh

Mu 102⋅

b fb⋅

= k 5.434= ea / eb = 10.0 / 0.975 o/oo

μ' 3.627%=

Aa μ' b⋅ h⋅fbσv⋅= Aa 8.74= cm2

USVOJENA ARMATURASA UNUTRA[WE STRANE KRILA: RA ∅ 14 / 20 cm

RA ∅ 12 / 20 cm ( Aa 13.35= cm2/m )

LAMELA IV

Mu 1.7 MIV⋅= Mu 100.32= kNm

kh

Mu 102⋅

b fb⋅

= k 6.719= ea / eb = 10.0 / 0.750 o/oo

μ' 2.289%=

Aa μ' b⋅ h⋅fbσv⋅= Aa 5.51= cm2

USVOJENA ARMATURA

63

Mg g1 g3+( ) 2.45⋅ g2 1.60⋅+= Mg 426.53= kNm

MΔg Δg 2.45⋅= MΔg 179.23= kNm

Mp P 4.90⋅= Mp 245.00= kNm

Mu 1.6 Mg MΔg+( )⋅ 1.8 Mp⋅+=

Mu 1410.23= kNm

kh

Mu 102⋅

b fb⋅

= k 10.353= ea / eb = 10.0 / 0.475 o/oo

μ' 0.992%=

Aa μ' b⋅ h⋅fbσv⋅= Aa 9.76= cm2

USVOJENA ARMATURA: 3 RA ∅ 22 ( Aa 11.40= cm2 )

64

USVOJENA ARMATURASA UNUTRA[WE STRANE PLATNA: RA ∅ 16 / 20 cm

RA ∅ 12 / 20 cm ( Aa 15.70= cm2/m )

Aa 14.55= cm2/mAa μ' b⋅ h⋅fbσv⋅=

ea / eb = 10.0 / 1.325 o/oo

μ' 6.039%=

k 4.185=kh

Mu 102⋅

b fb⋅

=

Mu 258.57= kNm/mMu 1.6 Mg⋅ 1.8 Mp⋅+=

Mp 15.08= kNm/m

Mg 144.64= kNm/m

h 47.0= cmh d a−=

a 3.0= cmd 50.0= cmb 100.0= cm

HORIZONTALNA ARMATURA SA UNUTRA[WE STRANE PLATNA•

qp 3.41= kN/m

qg3 45.09= kN/mqg2 39.77= kN/mqg1 9.27= kN/m

- PLO^A JE UKQE[TENA SA TRI STRANE

h 47.0= cmh d a−=

a 3.0= cmd 50.0= cmb 100.0= cm

RA 400/500-2 ⇒ σv 400= MPa

MB 30 ⇒ fb 20.50= MPa

4.3. PRORA^UN ZIDNOG PLATNA

65

USVOJENA ARMATURA

SA SPOQA[WE STRANE PLATNA: RA ∅ 12 / 20 cm ( Aa 5.65= cm2/m )

USVOJENA ARMATURA

SA UNUTRA[WE STRANE PLATNA: RA ∅ 12 / 20 cm ( Aa 5.65= cm2/m )

Aa 5.51= cm2/mAa μ' b⋅ h⋅fbσv⋅=

ea / eb = 10.0 / 0.750 o/oo

μ' 2.289%=

k 6.726=kh

Mu 102⋅

b fb⋅

=

Mu 100.10= kNm/mMu 1.6 Mg⋅ 1.8 Mp⋅+=

Mp 7.84= kNm/m

Mg 53.74= kNm/m

VERTIKALNA ARMATURA SA UNUTRA[WE STRANE PLATNA•

USVOJENA ARMATURA

SA SPOQA[WE STRANE PLATNA: RA ∅ 14 / 20 cm ( Aa 7.70= cm2/m )

Aa 7.61= cm2/mAa μ' b⋅ h⋅fbσv⋅=

ea / eb = 10.0 / 0.900 o/oo

μ' 3.158%=

k 5.788=kh

Mu 102⋅

b fb⋅

=

Mu 135.17= kNm/mMu 1.6 Mg⋅ 1.8 Mp⋅+=

Mp 7.60= kNm/m

Mg 75.93= kNm/m

HORIZONTALNA ARMATURA SA SPOQA[WE STRANE PLATNA•

66

Ep 3.07= kN/m

U PRESEKU 1 - 1

Mg Ezhp3

⋅= Mg 0.59= kNm/m

Mp Ephp2

⋅= Mp 1.38= kNm/m

VERTIKALNA ARMATURA•

MB 30 ⇒ fb 20.50= MPa

RA 400/500-2 ⇒ σv 400= MPa

Mu 1.6 Mg⋅ 1.8 Mp⋅+= Mu 3.44= kNm/m

kh

Mu 102⋅

b fb⋅

= k 28.574= ea / eb = 10.0 / 0.175 o/oo

μ' 0.146%=

Aa μ' b⋅ h⋅fbσv⋅= Aa 0.28= cm2/m

minAa 0.20b d⋅100⋅= minAa 8.00= cm2/m

4.4. PRORA^UN PARAPETA

b 100.0= cm d 40.0= cm a 3.0= cm

h d a−= h 37.0= cm

hp 0.90= m lk 8.35= m

- STALNO OPTERE]EWE - ZEMQANI PRITISAK

γ 18.00= kN/m3,

φ 35= o,

β 45φ

2−=

ez hp γ⋅ tan β( )( )2⋅= ez 4.39= kN/m2

Ez ez hp⋅ 0.5⋅= Ez 1.98= kN/m

- POKRETNO OPTERE]EWE

ep 3.41= kN/m2

Ep ep hp⋅=

67

USVOJENA ARMATURA

PREMA NASIPU: RA ∅ 19 / 10 cm ( Aa1 28.40= cm2/m )

PREMA KONSTRUKCIJI: RA ∅ 12 / 20 cm ( Aa2 5.65= cm2/m )

Aa 25.58= cm2Aa μ' b⋅ h⋅fbσv⋅

Nuσv

−=

ea / eb = 10.0 / 2.375 o/oo

μ' 13.805%=

k 2.796=kh

Mau 102⋅

b fb⋅

=

Mau 322.98= kNm/m

Mau Mu Nud2

a−⎛⎜⎝

⎞⎟⎠

⋅ 10 2−⋅+=

Nu 80.65−= kNNu 1.6 Ng⋅ 1.8 Np⋅+=

Mu 336.69= kNmMu 1.6 Mg⋅ 1.8 Mp⋅+=

Np 28.51−= kNNp ep− lk⋅=

Ng 18.33−= kNNg ez− lk⋅ 0.5⋅=

- SILA ZATEZAWA OD ZEMQE

Mp 119.03= kNmMp eplk2

2⋅=

Mg 76.52= kNmMg ezlk2

2 2⋅⋅=

- UTICAJI SA VISE]EG KRILA DO PRESEKA 1 - 1

h 37.0= cmh d a−=

a 3.0= cmd 40.0= cmb 90.0= cm

HORIZONTALNA ARMATURA•

USVOJENA ARMATURA

PREMA NASIPU: RA ∅ 14 / 15 cm ( Aa1 10.27= cm2/m )

PREMA KONSTRUKCIJI: RA ∅ 12 / 15 cm ( Aa2 7.53= cm2/m )

68

5. PRORA^UN KRAJWEG STUBA S6

69

Δg 14.93 3.00⋅ 2⋅=

3. PE[A^KA STAZA NA KRILU

est 0.54= mgst 1319.54= kNgst 36.6538 1.50⋅ 24.0⋅=

- STOPA TEMEQA

ej 0.35−= mgj 533.67= kNgj 21.3469 1.00⋅ 25.0⋅=

- JASTUK

e9 0.58−= mg9 388.56= kNg9 31.0844 0.50⋅ 25.0⋅=

- ^EONO PLATNO

e8 0.23−= mg8 345.96= kNg8 1.20 1.20⋅ 5.82 3.79+( )⋅ 25.0⋅=

- STUBOVI

ez5 0.02= mz5 122.78= kNz5 1.2516 5.45⋅ 18.0⋅=

ez4 1.34= mz4 615.75= kNz4 4.8939 6.99⋅ 18.0⋅=

ez3 0.13−= mz3 97.53= kNz3 0.9728 5.57⋅ 18.0⋅=

ez2 1.12= mz2 113.29= kNz2 2.8351 2.22⋅ 18.0⋅=

ez1 1.61−= mz1 346.68= kNz1 3.00 1.47 4.95+( )⋅ 18.0⋅=

4. TE@INA ZEMQE

eΔg 1.87= mΔg 89.58= kN

- STOJE]E KRILO

e2 1.04= mg2 25.00= kNg2 2.00 2.00⋅ 0.5⋅ 0.50⋅ 25.0⋅=

e1 1.87= mg1 37.50= kNg1 1.00 3.00⋅ 0.50⋅ 25.0⋅=

- VISE]E KRILO

2. SOPSTVENA TE@INA STUBA

e 0.43−= mRp 899.70= kN

Rp 121.02 431.07+ 306.20+ 28.51− 50.47+ 19.45+=

RΔg 308.670= kN

RΔg 132.07 6.53− 22.15+ 22.38+ 12.75− 151.35+=

Rg 1520.520= kN

Rg 166.06 192.19+ 193.83+ 195.47+ 197.23+ 198.87+ 200.50+ 176.37+=

1. REAKCIJE SA KONSTRUKCIJE

5.1 PRORA^UN NAPONA U PRESECIMA

e7 0.10−= mg7 25.90= kNg7 0.40 0.70⋅ 0.5⋅ 7.40⋅ 25.0⋅=

e6 0.23−= mg6 133.20= kNg6 0.60 1.20⋅ 7.40⋅ 25.0⋅=

- LE@I[NA GREDA

e5 0.17= mg5 88.20= kNg5 0.40 0.90⋅ 9.80⋅ 25.0⋅=

- PARAPET

e4 1.87= mg4 30.53= kNg4 0.165 0.40⋅ 0.25 0.55⋅+( ) 3.00⋅ 25.0⋅ 2⋅=

- KONZOLA PE[A^KE STAZE

e3 1.87= mg3 251.63= kNg3 3.00 6.71⋅ 0.50⋅ 25.0⋅=

70

Ez 712.05= kN ezhd 3.08−= m

Ep ep F⋅= Ep 171.28= kN ezhl 0.58−= m

Ezh Ez cos ρ( )⋅= Ezh 679.09= kN ephd 4.05−= m

Eph Ep cos ρ( )⋅= Eph 163.36= kN ephl 1.55−= m

Ezv Ez sin ρ( )⋅= Ezv 214.12= kN ev 0.33−= m

Epv Ep sin ρ( )⋅= Epv 51.51= kN

- KARAKTERISTIKE PRESEKA

PRESEK I - I

F1 8.0785= m2 x13 0.8289= m

I1 8.1721= m4 x14 3.8330= m

x15 0.3711= m

WI3I1

x13= WI3 9.86= m3

WI4I1

x14= WI4 2.13= m3

WI5I1

x15= WI5 22.02= m3

z6 4.90 2.26 5.95+( )⋅ 18.0⋅= z6 724.12= kN ez6 1.86−= m

z7 1.8818 3.22⋅ 18.0⋅= z7 109.07= kN ez7 1.65= m

z8 0.65 6.37⋅ 18.0⋅= z8 74.53= kN ez8 0.42= m

z9 1.8739 7.99⋅ 18.0⋅= z9 269.50= kN ez9 1.74= m

z10 0.60 6.40⋅ 18.0⋅= z10 69.12= kN ez10 0.46= m

5. ZEMQANI PRITISAK

γ 18.00= kN/m3,

φ 35= o,

ρ 17.5= o, β 45

φ

2−=

sin ρ( ) 0.301= cos ρ( ) 0.954=

h1 0.70= m h2 5.83= m

F 50.1637= m2 ht 2.91= m

ez h2 γ⋅ tan β( )( )2⋅= ez 28.44= kN/m2

ezt ht γ⋅ tan β( )( )2⋅= ezt 14.19= kN/m2

ep h1 γ⋅ tan β( )( )2⋅= ep 3.41= kN/m2

Ez ezt F⋅=

71

M'' 170.64−= kNm

M1 M' M''+= M1 468.10= kNm

σ13N1F1

M1WI3

−= σ13 127.81= kN/m2

σ14N1F1

M1WI4

+= σ14 394.84= kN/m2

σ15N1F1

M1WI5

+= σ15 196.54= kN/m2

PRESEK II - II

N2 N1 gj+= N2 1949.72= kN

M2 M1 N1 ej⋅+= M2 27.52−= kNm

σ22N2F2

M2WII2

−= σ22 92.70= kN/m2

σ24N2F2

M2WII4

+= σ24 89.43= kN/m2

σ25N2F2

M2WII5

+= σ25 91.00= kN/m2

PRESEK III - III

N3 N2 gst+= N3 3269.25= kN

M3 M2 N2 est⋅+= M3 1025.33= kNm

σ31N3F3

M3WIII1

−= σ31 62.91= kN/m2

σ34N3F3

M3WIII4

+= σ34 124.81= kN/m2

σ35N3F3

M3WIII5

+= σ35 99.82= kN/m2

PRESEK III - III PRESEK II - II

F3 36.6538= m2 x31 2.6350= m F2 21.3469= m2 x22 2.1751= m

I3 102.7971= m4 x34 3.5708= m I2 43.7160= m4 x24 3.0307= m

x35 1.0650= m x25 0.5249= m

WIII1I3

x31= WIII1 39.01= m3 WII2

I2x22

= WII2 20.10= m3

WIII4I3

x34= WIII4 28.79= m3 WII4

I2x24

= WII4 14.42= m3

WIII5I3

x35= WIII5 96.52= m3 WII5

I2x25

= WII5 83.28= m3

1. SOPSTVENA TE@INA STUBA

PRESEK I - I

N1 g1 g2+ g3+ g4+ g5+ g6+ g7+ g8+ g9+ Δg+= N1 1416.05= kN

M' g1 e1⋅ g2 e2⋅+ g3 e3⋅+ g4 e4⋅+ g5 e5⋅+= M' 638.74= kNm

M'' g6 e6⋅ g7 e7⋅+ g8 e8⋅+ g9 e9⋅+ Δg eΔg⋅+=

72

σ25N2F2

M2lWII5

+= σ25 133.83= kN/m2

PRESEK III - III

N3 N2 z6+ z7+ z8+ z9+ z10+= N3 4224.05= kN

M3d M2d N2 est⋅+ z6 ez6⋅+ z7 ez7⋅+ z8 ez8⋅+ z9 ez9⋅+ z10 ez10⋅+= M3d 1604.63−= kNm

M3l M2l N2 est⋅+ z6 ez6⋅+ z7 ez7⋅+ z8 ez8⋅+ z9 ez9⋅+ z10 ez10⋅+= M3l 501.49= kNm

σ31N3F3

M3dWIII1

−= σ31 156.37= kN/m2

σ34N3F3

M3dWIII4

+= σ34 59.50= kN/m2

σ35N3F3

M3lWIII5

+= σ35 120.44= kN/m2

3. SOPSTVENA TE@INA STUBA, TE@INA ZEMQE, ZEMQANI PRITISAK IREAKCIJA SA KONSTRUKCIJE

PRESEK I - I

N1 N1 Rg+ RΔg+= N1 3510.86= kN

M1d M1d Rg RΔg+( ) e⋅+= M1d 3159.30−= kNm

M1l M1l Rg RΔg+( ) e⋅+= M1l 1053.18−= kNm

2. SOPSTVENA TE@INA STUBA, TE@INA ZEMQE I ZEMQANI PRITISAK

PRESEK I - I

N1 N1 Ezv+ Epv+= N1 1681.67= kN

M1d M1 Ezv Epv+( ) ev⋅+ Ezh ezhd⋅+ Eph ephd⋅+= M1d 2372.75−= kNm

M1l M1 Ezv Epv+( ) ev⋅+ Ezh ezhl⋅+ Eph ephl⋅+= M1l 266.63−= kNm

σ13N1F1

M1dWI3

−= σ13 448.83= kN/m2

σ14N1F1

M1dWI4

+= σ14 904.74−= kN/m2

σ15N1F1

M1lWI5

+= σ15 196.06= kN/m2

PRESEK II - II

N2 N1 z1+ z2+ z3+ z4+ z5+= N2 2977.70= kN

M2d M1d N1 ej⋅+ z1 ez1⋅+ z2 ez2⋅+ z3 ez3⋅+ z4 ez4⋅+ z5 ez5⋅+= M2d 2577.72−= kNm

M2l M1l N1 ej⋅+ z1 ez1⋅+ z2 ez2⋅+ z3 ez3⋅+ z4 ez4⋅+ z5 ez5⋅+= M2l 471.60−= kNm

σ22N2F2

M2dWII2

−= σ22 267.75= kN/m2

σ24N2F2

M2dWII4

+= σ24 39.21−= kN/m2

73

M3l M3l Rg RΔg+( ) e ej+ est+( )⋅+= M3l 62.48= kNm

σ31N3F3

M3dWIII1

−= σ31 217.53= kN/m2

σ34N3F3

M3dWIII4

+= σ34 94.16= kN/m2

σ35N3F3

M3lWIII5

+= σ35 165.79= kN/m2

4. SOPSTVENA TE@INA STUBA, TE@INA ZEMQE, ZEMQANI PRITISAK, REAKCIJASA KONSTRUKCIJE I POKRETNO OPTERE]EWE ( OSNOVNO )

PRESEK I - I

N1 N1 Rp+= N1 4410.56= kN

M1d M1d Rp e⋅+= M1d 3546.17−= kNm

M1l M1l Rp e⋅+= M1l 1440.06−= kNm

σ13N1F1

M1dWI3

−= σ13 905.65= kN/m2

σ14N1F1

M1dWI4

+= σ14 1117.32−= kN/m2

σ15N1F1

M1lWI5

+= σ15 480.57= kN/m2

σ13N1F1

M1dWI3

−= σ13 755.04= kN/m2

σ14N1F1

M1dWI4

+= σ14 1047.23−= kN/m2

σ15N1F1

M1lWI5

+= σ15 386.77= kN/m2

PRESEK II - II

N2 N2 Rg+ RΔg+= N2 4806.89= kNM2d M2d Rg RΔg+( ) e ej+( )⋅+= M2d 4004.49−= kNmM2l M2l Rg RΔg+( ) e ej+( )⋅+= M2l 1898.37−= kNm

σ22N2F2

M2dWII2

−= σ22 424.42= kN/m2

σ24N2F2

M2dWII4

+= σ24 52.44−= kN/m2

σ25N2F2

M2lWII5

+= σ25 202.39= kN/m2

PRESEK III - III

N3 N3 Rg+ RΔg+= N3 6053.24= kN

M3d M3d Rg RΔg+( ) e ej+ est+( )⋅+= M3d 2043.63−= kNm

74

σ34 111.20= kN/m2

σ35N3F3

M3lWIII5

+= σ35 188.10= kN/m2

5. SOPSTVENA TE@INA STUBA, TE@INA ZEMQE, ZEMQANI PRITISAK, REAKCIJASA KONSTRUKCIJE I POKRETNO OPTERE]EWE ( OSNOVNO I DOPUNSKO )

- HORIZONTALNA REAKCIJA KOJU PRIMAJU LE@I[TA

H 30.96 6⋅= H 185.76= kN

PRESEK I - I

N1 N1= N1 4410.56= kN

M1d M1d H 6.05⋅−= M1d 4670.02−= kNm

M1l M1l H 3.55⋅−= M1l 2099.50−= kNm

σ13N1F1

M1dWI3

−= σ13 1019.64= kN/m2

σ14N1F1

M1dWI4

+= σ14 1644.44−= kN/m2

σ15N1F1

M1lWI5

+= σ15 450.62= kN/m2

PRESEK II - II

N2 N2 Rp+= N2 5706.59= kN

M2d M2d Rp e ej+( )⋅+= M2d 4706.25−= kNm

M2l M2l Rp e ej+( )⋅+= M2l 2600.14−= kNm

σ22N2F2

M2dWII2

−= σ22 501.49= kN/m2

σ24N2F2

M2dWII4

+= σ24 58.94−= kN/m2

σ25N2F2

M2lWII5

+= σ25 236.11= kN/m2

PRESEK III - III

N3 N3 Rp+= N3 6952.94= kN

M3d M3d Rp e ej+ est+( )⋅+= M3d 2259.56−= kNm

M3l M3l Rp e ej+ est+( )⋅+= M3l 153.45−= kNm

σ31N3F3

M3dWIII1

−= σ31 247.61= kN/m2

σ34N3F3

M3dWIII4

+=

75

USVOJENA ARMATURA: 4 RA ∅ 25 ( Aa 19.64= cm2 )

Aa 2.03= cm2AaZ 10⋅

dopσv=

- DOPU[TEN NAPON U ARMATURI RA 400 / 500 - 2: dopσv 240= MPa

Z 48.67= kNZ 149.74 1.30⋅ 0.5⋅ 0.50⋅=

σ25 225.96= kN/m2σ25N2F2

M2lWII5

+=

σ24 149.74−= kN/m2σ24N2F2

M2dWII4

+=

σ22 566.65= kN/m2σ22N2F2

M2dWII2

−=

M2l 3445.35−= kNmM2l M2l H 4.55⋅−=

M2d 6015.86−= kNmM2d M2d H 7.05⋅−=

N2 5706.59= kNN2 N2= PRESEK II - II

USVOJENA ARMATURA: 12 RA ∅ 25 ( Aa 58.92= cm2 )

Aa 54.99= cm2AaZ 10⋅

dopσv=

- DOPU[TEN NAPON U ARMATURI RA 400 / 500 - 2: dopσv 240= MPa

Z 1319.66= kNZ 1644.44 3.21⋅ 0.5⋅ 0.50⋅=

76

PRESEK III - III

N3 N3= N3 6952.94= kN

M3d M3d H 8.55⋅−= M3d 3847.81−= kNm

M3l M3l H 6.05⋅−= M3l 1277.29−= kNm

σ31N3F3

M3dWIII1

−= σ31 288.32= kN/m2

σ34N3F3

M3dWIII4

+= σ34 56.03= kN/m2

σ35N3F3

M3lWIII5

+= σ35 176.46= kN/m2

77

SA SPOQA[WE STRANE KRILA: RA ∅ 12 / 20 cm ( Aa 5.65= cm2/m )

USVOJENA ARMATURA

SA UNUTRA[WE STRANE KRILA: RA ∅ 12 / 20 cm ( Aa 5.65= cm2/m )

minAa 5.00= cm2/mminAa 0.10b d⋅100⋅=

Aa 4.56= cm2/mAa μ' b⋅ h⋅fbσv⋅=

ea / eb = 10.0 / 0.675 o/oo

μ' 1.894%=

k 7.573=kh

Mu 102⋅

b fb⋅

=

Mu 78.97= kNm/mMu 1.6 Mg⋅ 1.8 Mp⋅+=

Mp 10.21= kNm/m

Mg 37.87= kNm/m

h 47.0= cmh d a−=

a 3.0= cmd 50.0= cmb 100.0= cm

HORIZONTALNA ARMATURA SA UNUTRA[WE STRANE KRILA•

RA 400/500-2 ⇒ σv 400= MPa

MB 30 ⇒ fb 20.50= MPa τr 1.10= MPa

5.2. PRORA^UN KRILA

78

VERTIKALNA ARMATURA SA UNUTRA[WE STRANE KRILA•

Mg 46.28= kNm/m

Mp 8.45= kNm/m

Mu 1.6 Mg⋅ 1.8 Mp⋅+= Mu 89.26= kNm/m

kh

Mu 102⋅

b fb⋅

= k 7.123= ea / eb = 10.0 / 0.700 o/oo

μ' 2.023%=

Aa μ' b⋅ h⋅fbσv⋅= Aa 4.87= cm2/m

minAa 0.10b d⋅100⋅= minAa 5.00= cm2/m

USVOJENA ARMATURA

SA UNUTRA[WE STRANE KRILA: RA ∅ 12 / 20 cm ( Aa 5.65= cm2/m )

SA SPOQA[WE STRANE KRILA: RA ∅ 12 / 20 cm ( Aa 5.65= cm2/m )

79

USVOJENA ARMATURASA UNUTRA[WE STRANE PLATNA: RA ∅ 14 / 20 cm

RA ∅ 12 / 20 cm ( Aa 13.35= cm2/m )

Aa 5.85= cm2/mAa μ' b⋅ h⋅fbσv⋅=

ea / eb = 10.0 / 0.775 o/oo

μ' 2.427%=

k 6.631=kh

Mu 102⋅

b fb⋅

=

Mu 102.99= kNm/mMu 1.6 Mg⋅ 1.8 Mp⋅+=

Mp 0.93= kNm/m

Mg 63.32= kNm/m

h 47.0= cmh d a−=

a 3.0= cmd 50.0= cmb 100.0= cm

HORIZONTALNA ARMATURA SA UNUTRA[WE STRANE PLATNA•

qp 3.41= kN/m

qg3 32.93= kN/mqg2 20.25= kN/mqg1 9.27= kN/m

- PLO^A JE UKQE[TENA SA TRI STRANE

h 47.0= cmh d a−=

a 3.0= cmd 50.0= cmb 100.0= cm

RA 400/500-2 ⇒ σv 400= MPa

MB 30 ⇒ fb 20.50= MPa

5.3. PRORA^UN ZIDNOG PLATNA

80

USVOJENA ARMATURA

SA SPOQA[WE STRANE PLATNA: RA ∅ 12 / 20 cm ( Aa 5.65= cm2/m )

USVOJENA ARMATURA

SA UNUTRA[WE STRANE PLATNA: RA ∅ 12 / 20 cm ( Aa 5.65= cm2/m )

minAa 5.00= cm2/mminAa 0.10b d⋅100⋅=

Aa 4.26= cm2/mAa μ' b⋅ h⋅fbσv⋅=

ea / eb = 10.0 / 0.650 o/oo

μ' 1.769%=

k 7.715=kh

Mu 102⋅

b fb⋅

=

Mu 76.07= kNm/mMu 1.6 Mg⋅ 1.8 Mp⋅+=

Mp 0.77= kNm/m

Mg 46.68= kNm/m

VERTIKALNA ARMATURA SA UNUTRA[WE STRANE PLATNA•

USVOJENA ARMATURA

SA SPOQA[WE STRANE PLATNA: RA ∅ 12 / 20 cm ( Aa 5.65= cm2/m )

minAa 5.00= cm2/mminAa 0.10b d⋅100⋅=

Aa 2.39= cm2/mAa μ' b⋅ h⋅fbσv⋅=

ea / eb = 10.0 / 0.475 o/oo

μ' 0.992%=

k 10.364=kh

Mu 102⋅

b fb⋅

=

Mu 42.16= kNm/mMu 1.6 Mg⋅ 1.8 Mp⋅+=

Mp 0.40= kNm/m

Mg 25.90= kNm/m

HORIZONTALNA ARMATURA SA SPOQA[WE STRANE PLATNA•

81

Ep ep hp⋅= Ep 3.07= kN/m

U PRESEKU 1 - 1

Mg Ezhp3

⋅= Mg 0.59= kNm/m

Mp Ephp2

⋅= Mp 1.38= kNm/m

VERTIKALNA ARMATURA•

MB 30 ⇒ fb 20.50= MPa

RA 400/500-2 ⇒ σv 400= MPa

Mu 1.6 Mg⋅ 1.8 Mp⋅+= Mu 3.44= kNm/m

kh

Mu 102⋅

b fb⋅

= k 28.574= ea / eb = 10.0 / 0.175 o/oo

μ' 0.146%=

Aa μ' b⋅ h⋅fbσv⋅= Aa 0.28= cm2/m

5.4. PRORA^UN PARAPETA

b 100.0= cm d 40.0= cm a 3.0= cm

h d a−= h 37.0= cm

hp 0.90= m lk 3.00= m

- STALNO OPTERE]EWE - ZEMQANI PRITISAK

γ 18.00= kN/m3,

φ 35= o,

β 45φ

2−=

ez hp γ⋅ tan β( )( )2⋅= ez 4.39= kN/m2

Ez ez hp⋅ 0.5⋅= Ez 1.98= kN/m

- POKRETNO OPTERE]EWE

ep 3.41= kN/m2

82

Np 10.24−= kN

Mu 1.6 Mg⋅ 1.8 Mp⋅+= Mu 43.46= kNm

Nu 1.6 Ng⋅ 1.8 Np⋅+= Nu 28.97−= kN

Mau Mu Nud2

a−⎛⎜⎝

⎞⎟⎠

⋅ 10 2−⋅+=

Mau 38.54= kNm/m

kh

Mau 102⋅

b fb⋅

= k 8.096= ea / eb = 10.0 / 0.650 o/oo

μ' 1.769%=

Aa μ' b⋅ h⋅fbσv⋅

Nuσv

−= Aa 3.74= cm2

minAa 0.20b d⋅100⋅= minAa 7.20= cm2/m

USVOJENA ARMATURA

PREMA NASIPU: RA ∅ 12 / 10 cm ( Aa 11.30= cm2/m )

PREMA KONSTRUKCIJI: RA ∅ 12 / 20 cm ( Aa 5.65= cm2/m )

minAa 0.20b d⋅100⋅= minAa 8.00= cm2/m

USVOJENA ARMATURA

PREMA NASIPU: RA ∅ 14 / 15 cm ( Aa1 10.27= cm2/m )

PREMA KONSTRUKCIJI: RA ∅ 12 / 15 cm ( Aa2 7.53= cm2/m )

HORIZONTALNA ARMATURA•

b 90.0= cm d 40.0= cm a 3.0= cm

h d a−= h 37.0= cm

- UTICAJI SA VISE]EG KRILA DO PRESEKA 1 - 1

Mg ezlk2

2 2⋅⋅= Mg 9.88= kNm

Mp eplk2

2⋅= Mp 15.37= kNm

- SILA ZATEZAWA OD ZEMQE

Ng ez− lk⋅ 0.5⋅= Ng 6.59−= kN

Np ep− lk⋅=

83

maxRt 2.28= kN Utx 8.83= mm αtx 0.03= o/oo

minRt 2.18−= kN Uty 1.89= mm αty 0.01−= o/oo

6. VETAR - OPTERE]EN MOST:

maxRw 41.77= kN Uwx 1.08= mm αwx 0.03= o/oo

minRw 2.18−= kN Uwy 9.79= mm αwy 0.01−= o/oo

7. SEIZMIKA - PODU@NO:

maxRs 19.13= kN Usx 17.19= mm αsx 0.12= o/oo

minRs 19.13−= kN Usy 3.58= mm αsy 0.04−= o/oo

max REAKCIJA NA LE@I[TU

maxR maxRg maxRΔg+ maxRp+ maxRk+ maxRt+ maxRw+=

maxR 713.38= kN

min REAKCIJA NA LE@I[TU

minR minRg minRΔg+ minRp+ minRk+ minRt+ minRw+=

minR 182.26= kN

DIMENZIONISAWE•

NAJMAWA POTREBNA POVR[INA LE@I[TA

PRETPOSTAVQA SE LE@I[TE: NAL ∅ 350 ( A 706.86= cm2, Vd 883= kN )

σdVdA

10⋅= σd 12.5= MPa

minσd 5.0= MPa

6. PRORA^UN LE@I[TA

STATI^KI UTICAJI•

- VERTIKALNO OPTERE]EWE

1. SOPSTVENA TE@INA:

maxRg 248.71= kN Ugx 0.66= mm αgx 1.72= o/oo

minRg 233.79= kN Ugy 0.28−= mm αgy 0.52−= o/oo

2. DODATNO STALNO OPTERE]EWE:

maxRΔg 12.75−= kN UΔgx 0.18= mm αΔgx 0.52= o/oo

minRΔg 22.15= kN

5. RAVNOMERNA PROMENA TEMPERATURE:

αky 0.00= o/ooUky 1.18= mmminRk 1.86−= kN

αkx 0.01= o/ooUkx 1.99= mmmaxRk 2.30= kN

4. ZAUSTAVQAWE I POKRETAWE VOZILA:

αpy 0.47−= o/ooUpy 0.45= mmminRp 67.46−= kN

αpx 1.58= o/ooUpx 1.87= mmmaxRp 431.07= kN

3. POKRETNO OPTERE]EWE:

αΔgy 0.17−= o/ooUΔgy 0.06−= mm

84

maxUx3 Ugx UΔgx+ Upx+ Ukx+ Utx+ Uwx+= maxUx3 14.61= mm

maxUy3 Ugy UΔgy+ Upy+ Uky+ Uty+ Uwy+= maxUy3 12.97= mm

maxU3 maxUx32 maxUy32+( )= maxU3 19.54= mm

4. STALNO + SEIZMIKA

maxUx4 Ugx UΔgx+ Usx+= maxUx4 18.03= mm

maxUy4 Ugy UΔgy+ Usy+= maxUy4 3.24= mm

maxU4 maxUx42 maxUy42+( )= maxU4 18.32= mm

e 1.20 max maxU1 maxU2, maxU3, maxU4,( )⋅=

e 23.44= mm

minTe

0.7=

minT 33.49= mm

- KAO FUNKCIJA ROTACIJE:

1. STALNO + POKRETNO

maxα1x αgx αΔgx+ αpx+= maxα1x 3.82= o/oo

maxα1y αgy αΔgy+ αpy+= maxα1y 1.16−= o/oo

maxα1 maxα1x2 maxα1y2+( )= maxα1 3.99= o/oo

maxR 713.38= kN

minR 182.26= kN

maxσmaxR

A10⋅= maxσ 10.1= MPa < σd 12.5= MPa

minσminR

A10⋅= minσ 2.6= MPa < minσd 5.0= MPa

USVAJAJU SE ANKEROVANA LE@I[TA NAL-p-3 ∅ 300

NAJMAWA POTREBNA VISINA LE@I[TA

- KAO FUNKCIJA POMERAWA:

1. STALNO + POKRETNO

maxUx1 Ugx UΔgx+ Upx+= maxUx1 2.71= mm

maxUy1 Ugy UΔgy+ Upy+= maxUy1 0.11= mm

maxU1 maxUx12 maxUy12+( )= maxU1 2.71= mm

2. STALNO + POKRETNO + KO^EWE + TEMPERATURA

maxUx2 Ugx UΔgx+ Upx+ Ukx+ Utx+= maxUx2 13.53= mm

maxUy2 Ugy UΔgy+ Upy+ Uky+ Uty+= maxUy2 3.18= mm

maxU2 maxUx22 maxUy22+( )= maxU2 13.90= mm

3. STALNO + POKRETNO + KO^EWE + TEMPERATURA + VETAR

85

ZAUSTAVQAWE I POKRETAWE VOZILA:

Ukx Ukx= Uky Uky=

Ukx 1.99= mm Uky 1.18= mm

Hkx0.1 A⋅ Ukx⋅ 10 1−

⋅

T= Hky

0.1 A⋅ Uky⋅ 10 1−⋅

T=

Hkx 3.52= kN Hky 2.09= kN

RAVNOMERNA PROMENA TEMPERATURE:

Utx Utx= Uty Uty=

Utx 8.83= mm Uty 1.89= mm

Htx0.1 A⋅ Utx⋅ 10 1−

⋅

T= Hty

0.1 A⋅ Uty⋅ 10 1−⋅

T=

Htx 15.60= kN Hty 3.34= kN

VETAR - OPTERE]EN MOST:

Uwx 1.08= mm Uwy 9.79= mm

Hwx0.1 A⋅ Uwx⋅ 10 1−

⋅

T= Hwy

0.1 A⋅ Uwy⋅ 10 1−⋅

T=

Hwx 1.91= kN Hwy 17.30= kN

2. STALNO + POKRETNO + KO^EWE + TEMPERATURA

maxα2x αgx αΔgx+ αpx+ αkx+ αtx+= maxα2x 3.86= o/oo

maxα2y αgy αΔgy+ αpy+ αky+ αty+= maxα2y 1.17−= o/oo

maxα2 maxα2x2 maxα2y2+( )= maxα2 4.03= o/oo

3. STALNO + POKRETNO + KO^EWE + TEMPERATURA + VETAR

maxα3x αgx αΔgx+ αpx+ αkx+ αtx+ αwx+= maxα3x 3.89= o/oo

maxα3y αgy αΔgy+ αpy+ αky+ αty+ αwy+= maxα3y 1.18−= o/oo

maxα3 maxα3x2 maxα3y2+( )= maxα3 4.07= o/oo

4. STALNO + SEIZMIKA

maxα4x αgx αΔgx+ αsx+= maxα4x 2.36= o/oo

maxα4y αgy αΔgy+ αsy+= maxα4y 0.73−= o/oo

maxα4 maxα4x2 maxα4y2+( )= maxα4 2.47= o/oo

α 1.20 max maxα1 maxα2, maxα3, maxα4,( )⋅=

α 4.88= o/oo

USVOJENA LE@I[TA: 2x6 NAL-p-3 ∅ 300, d = 72 mm, T = 40 mm

UKUPNA HORIZONTALNA SILA KOJA SE PRENOSI PREKO LE@I[TA

86

maxHx3 Hsx1= maxHy3 Hsy1=

maxHx3 30.38= kN maxHy3 6.33= kN

maxH3 maxHx32 maxHy32+( )= maxH3 31.03= kN

maxH max maxH1 maxH2, maxH3,( )=

maxH 31.03= kN

HORIZONTALNA SILA KOJU MO@E DA PRIMI LE@I[TE

T 4.0= cm < D5

6.0= cm ⇒ tanγ 0.7=

dopH A G⋅ tanγ⋅= dopH 49.48= kN

maxH 31.03= kN < dopH 49.48= kN

UKUPNA POMERAWA NA LE@I[TU

DOZVOQENO POMERAWE: dopU 28.0= mm

maxU 1.20 max maxU1 maxU2, maxU3, maxU4,( )⋅=

maxU 23.44= mm < dopU 28.00= mm

maxUx 1.20 max maxUx1 maxUx2, maxUx3, maxUx4,( )⋅=

maxUx 21.64= mm

USVOJENE DILATACIONE SPRAVE: MT(T) - 50

SRA^UNAO:

SEIZMIKA:

Usx 17.19= mm Usy 3.58= mm

Hsx10.1 A⋅ Usx⋅ 10 1−

⋅

T= Hsy1

0.1 A⋅ Usy⋅ 10 1−⋅

T=

Hsx1 30.38= kN Hsy1 6.33= kN

1. KO^EWE + TEMPERATURA

maxHx1 Hkx Htx+= maxHy1 Hky Hty+=

maxHx1 19.12= kN maxHy1 5.43= kN

maxH1 maxHx12 maxHy12+( )= maxH1 19.88= kN

2. KO^EWE + TEMPERATURA + VETAR

maxHx2 Hkx Htx+ Hwx+= maxHy2 Hky Hty+ Hwy+=

maxHx2 21.03= kN maxHy2 22.73= kN

maxH2 maxHx22 maxHy22+( )= maxH2 30.96= kN

3. SEIZMIKA - PODU@NO

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