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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