dimenzioniranje čelika
DESCRIPTION
PO starim propisima JUS U.E7.096 nizaTRANSCRIPT
CALCULATIONS
PROJECT PROJECT No.
PART OF STRUCTURE SHEET No. REVISION
BY DATE CHECKED BY
8-Apr-23
ELEMENT Glavni lučni nosač 1
Raspon cca 10.5 m
Slučaj opterećenja "NADOLJE"tj. Maksimalno vertikalno opterećenje
PODACI O Čelik Č0361 240 N/mm²PRESJEKU t≤40mm 92.9
Duljine izvijanja Lix = 10.00 mLiy = 2.50 m
Pretpostavljeni profil = IPB400Površina A = 198 cm²
Moment otpora Sx = 1620Moment otpora Wx = 2880 Wy = 721Moment inercije Ix = 57680 Iy = 10820
357
Radijus inercije ix = 17.1 cm iy = 7.4 cm
rezultat statičke Max. moment Mx = 6.3 kNmanalize My = 1.9 kNm
Max. uzdužno N = 32.5 kNMax. poprečna Vx = 8.0 kN
Vy = 4.0 kN
Koeficijenti oblika momentnog dijagrama
1.00
1.00
JUS U.E7.081 DOZVOLJENI NAPONI( 1986. g. )
= 240 = 180 N/mm²
n 1.33
= = 104 N/mm²
II slučaj opterećenja - osnovno+dopunsko
JUS U.E7.096 PROVJERA OSNOVNOG MATERIJALA:( 1986. g. )
s = N + Mx + MyA Wx Wy
= 32.5 + 6.3 + 1.9198.0 2880.0 2880.0
= 1.6 + 2.2 + 0.6
Čelik Č.0361 sv = lv =
cm3
cm3 cm3
cm4 cm4
Torzijski moment inercije ID = cm4
bx =
by =
s dop = sv
t dop = sv
n * Ö3
= 4.5 N/mm² < 180 N/mm² OK
JUS U.E7.081 PROVJERA IZVIJANJA( 1986. g. )
krivulja izvijanja presjeka : A
a = = 0.206
`s = = 0.009
= 058 / 093 = 0.629
= 015 / 093 = 0.157
= 1.485
= 0.880
JUS U.E7.096 = 1.089
( 1986. g. ) = 0.991
= 1.136
= 1.004
= 1.000
= 1.000
s = + +
= 1.8 + 2.2 + 0.6
= 4.6 N/mm² < 180 N/mm² OK
PROVJERA PROGIBA
Prema rezultatima statičkog proračuna
f max = 251 mmL = 10000 mm
f / L = 1 / 39.8 NE VALJA
g sN* / sV
`l x = lx / lV
`l y = ly / lV
b = 1+a (`l-0.2 ) +`l2
K = 2 / ( b + Ö (b2 - 4 `l2 ))
kN = 1+a (`lx-0.2 ) / (1-`lx2 `s)
1+a (`ly-0.2 ) / (1-`ly2 `s)
1/K
kMx = bx / (1-`lx2 `s)
kMy = by / (1-`ly2 `s)
J = sV / sD
kN s N J kMx sMx kMy sMy
ELEMENT Glavni lučni nosač 1
Raspon cca 10.5 m
Slučaj opterećenja "NADOLJE"tj. Maksimalno vertikalno opterećenje
PODACI O Čelik Č0361 240 N/mm²PRESJEKU t≤40mm 92.9
Duljine izvijanja Lix = 5.5 mLiy = 5.5 m
Pretpostavljeni profil = 108 diam x 4 debljinaPovršina A = 13.1 cm²
Moment otpora W = 32.8Moment inercije I = 177Radijus inercije i = 3.68 cm
rezultat statičke Max. uzdužno N = 23 kNanalize
JUS U.E7.081 DOZVOLJENI NAPONI( 1986. g. ) = 240 = 160 N/mm²
n 1.50
= = 92 N/mm²
I slučaj opterećenja - osnovno
JUS U.E7.096 PROVJERA OSNOVNOG MATERIJALA:( 1986. g. )
s = N = 23.0 = 17.6 N/mm²A 13.1
= 17.6 N/mm² < 160 N/mm² OK
JUS U.E7.081 PROVJERA IZVIJANJA( 1986. g. )
krivulja izvijanja presjeka : Da = = 0.756
= 1.609
= 1.609
= 4.653
= 0.250
s = = 17.6 =0.250
= 70.4 N/mm² < 160 N/mm² OK
sv = lv =
cm3
cm4
s dop = sv
t dop = sv
n * Ö3
`l x = lx / lV
`l y = ly / lV
b = 1+a ( `lx-0.2 ) + `lx2
K = 2 / ( b + Ö ( b2 - 4 `l2 ))
s N / K
ELEMENT Glavni lučni nosač 1
Raspon cca 10.5 m
Slučaj opterećenja "NADOLJE"tj. Maksimalno vertikalno opterećenje
PODACI O Čelik Č0361 240 N/mm²PRESJEKU t≤40mm 92.9
Duljine izvijanja Lix = 10.00 mLiy = 2.50 m
Pretpostavljeni profil = 139.7 dia x 4 deb.stij.Površina A = 17.1 cm²
Moment otpora W = 56.2Moment inercije I = 392.9Radijus inercije i = 4.79 cm
rezultat statičke Max. moment Mx = 6.3 kNmanalize My = 1.9 kNm
Max. uzdužno N = 32.5 kNMax. poprečna Vx = 8.0 kN
Vy = 4.0 kN
Koeficijenti oblika momentnog dijagrama
1.00
1.00
JUS U.E7.081 DOZVOLJENI NAPONI( 1986. g. )
= 240 = 180 N/mm²
n 1.33
= = 104 N/mm²
II slučaj opterećenja - osnovno+dopunsko
JUS U.E7.096 PROVJERA OSNOVNOG MATERIJALA:( 1986. g. )
s = N + Mx + MyA Wx Wy
= 32.5 + 6.3 + 1.917.1 56.2 56.2
= 19.0 + 112.4 + 32.9
= 164.3 N/mm² < 180 N/mm² OK
Čelik Č.0361 sv = lv =
cm3
cm4
bx =
by =
s dop = sv
t dop = sv
n * Ö3
JUS U.E7.081 PROVJERA IZVIJANJA( 1986. g. )
krivulja izvijanja presjeka : A
a = = 0.206
`s = = 0.106
= 209 / 093 = 2.247
= 052 / 093 = 0.562
= 6.472
= 0.180
JUS U.E7.096 = 1.904
( 1986. g. ) = 1.077
= 5.564
= 2.142
= 1.034
= 1.000
s = + +
= 36.2 + 240.7 + 34.0
= 310.9 N/mm² > 180 N/mm² NE VALJA
PROVJERA PROGIBA
Prema rezultatima statičkog proračuna
f max = 251 mmL = 10000 mm
f / L = 1 / 39.8 NE VALJA
g sN* / sV
`l x = lx / lV
`l y = ly / lV
b = 1+a (`l-0.2 ) +`l2
K = 2 / ( b + Ö (b2 - 4 `l2 ))
kN = 1+a (`lx-0.2 ) / (1-`lx2 `s)
1+a (`ly-0.2 ) / (1-`ly2 `s)
1/K
kMx = bx / (1-`lx2 `s)
kMy = by / (1-`ly2 `s)
J = sV / sD
kN s N J kMx sMx kMy sMy
ELEMENT Glavni lučni nosač 1
Raspon cca 10.5 m
Slučaj opterećenja "NADOLJE"tj. Maksimalno vertikalno opterećenje
PODACI O Čelik Č0361 240 N/mm²PRESJEKU t≤40mm 92.9
Duljine izvijanja Lix = 10.00 mLiy = 2.50 m
Pretpostavljeni profil = 139.7 dia x 4 deb.stij.Površina A = 17.1 cm²
Moment otpora W = 56.2Moment inercije I = 392.9Radijus inercije i = 4.79 cm
rezultat statičke Max. moment Mx = 6.3 kNmanalize Max. uzdužno N = 32.5 kN
Max. poprečna Vx = 8.0 kNVy = 4.0 kN
Koeficijenti oblika momentnog dijagrama
1.00
JUS U.E7.081 DOZVOLJENI NAPONI( 1986. g. )
= 240 = 200 N/mm²
n 1.20
= = 115 N/mm²
III slučaj opterećenja - izuzetno
JUS U.E7.096 PROVJERA OSNOVNOG MATERIJALA:( 1986. g. )
s = N + MxA Wx
= 32.5 + 6.317.1 56.2
= 19.0 + 112.4
= 131.4 N/mm² < 200 N/mm² OK
Čelik Č.0361 sv = lv =
cm3
cm4
bx =
s dop = sv
t dop = sv
n * Ö3
JUS U.E7.081 PROVJERA IZVIJANJA( 1986. g. )
krivulja izvijanja presjeka : A
a = = 0.206
`s = = 0.095
= 209 / 093 = 2.247
= 052 / 093 = 0.562
= 6.472
= 0.180
JUS U.E7.096 = 1.811
( 1986. g. ) = 1.077
= 5.564
= 1.923
= 1.000
s = +
= 34.4 + 216.0
= 250.4 N/mm² > 200 N/mm² NE VALJA
PROVJERA PROGIBA
Prema rezultatima statičkog proračuna
f max = 251 mmL = 10000 mm
f / L = 1 / 39.8 NE VALJA
g sN* / sV
`l x = lx / lV
`l y = ly / lV
b = 1+a (`l-0.2 ) +`l2
K = 2 / ( b + Ö (b2 - 4 `l2 ))
kN = 1+a (`lx-0.2 ) / (1-`lx2 `s)
1+a (`ly-0.2 ) / (1-`ly2 `s)
1/K
kMx = bx / (1-`lx2 `s)
J = sV / sD
kN s N J kMx sMx
REFERENCES - RAYTHEON DRAWING No.
- STAAD III STRUCTURAL ANALYSIS
Bowstring truss, restraint wires at 5m vertical centresfor latereral stability.
Main Column (Worst Case Moment)
DESIGN Steel Grade fyk = 240 N/mm²PARAMETERS Effective length Sk = 5 m
Assumed Section Size = 160 x 80 x 5.0 RHSArea A = 22.9 cm²
Elastic modulus zz = 62.9 (BS Notation Zy)Elastic modulus zx = 94.1
Second moment of area Izz = 251 (BS Notation Iyy)Second moment of area Ixx = 753
Radius of gyration rzz = 3.31 cm (Bs Notation ryy)Radius of gyration rxx = 5.74 cm
ref staad III Max. MomentMz max = 12.5 kNM load case 8 (Stad Notation My)Max. MomentMx max = 12.5 KNM load case 8 (Stad Notation Mz)
analysis results Max. Axial N max = 4 kN load case 8Max. Shear Vz max = 12.5 kN load case 8 (Stad Notation Vy)Max. Shear Vx max = 12.5 kN load case 8 (Stad Notation Vz)
Unity check based on elastic / elastic method
DIN 18800 Pt1 LIMIT STRESS[746]
= 240 = 218 N/mm²1.1
= = 126 N/mm²
DIN 18800 Pt1 CHECKS:[747]
Mz + NZz A
= 1E+07 + 4000 = 20062900 2290
Mx + NZx A
= 1E+07 + 4000 = 13594100 2290
= 200 = 0.92 < 1 OK218
= 135 = 0.62 < 1 OK= 218
= Vz = 10.90.5 A
= 10.92 = 0.09 < 1 OK126
= Vx = 10.90.5 A
= 10.92 = 0.09 < 1 OK1.26E+02
cm3
cm3
cm4
cm4
s R,D = fy,d = fyk
gm
tR,D fy,d
Ö3
sz =
N/mm2
sx =
N/mm2
sz s R,D
sx s R,D
txy N/mm2
txytR,D
tyz N/mm2
tyztR,D
DIN 18800 Pt1 FAILURE CRITERIA[748]
((200² +135²) -(200*135)+(357.6 = 179 N/mm²
= 179 = 0.820 < 1 OK218
DIN 18800 Pt2 OUT OF PLANE STABILITY CHECK[304] Stability check for design axial compression
Nki =Sk²
x 2.1E5 x 7.530E+06 = 624 KN5000²
Npl = A x fyk
= 2290 x 240 = 550 KN
=
(550 / 624) = 0.939
> 0.2
0.21 hot rolled RHS
k =
DIN 18800 Pt2 = 0.5 [ 1 + (0.939- 0.2) + 0.939²] = 1.018Table 4 & 5
x = 1
x = 1( 1.018² - 0.939² ) + 1.018 = 0.709
N = 4.0
0.709 x 2290 x 240/1.1 = 0.009 < 1 OK
160 x 80 x 5.0 RHSis aqequate
s v = Ö (sx²+sy²+sz²-sxsy-sxsz-sysz+3txy2+3txz2+3tyz2)
= Ö
s v
s R,D
p².E.I
= p²
lk Ö ( Npl / Nki )
= Ö
lk
where a =
0.5 [ 1 + a ( lk - 0.2 ) + lk² ]
lk (lk + a)
x. Npl/gm
CALCULATIONS
PROJECT PROJECT No.
PLIVA RESEARCH INSTITUTE , ZAGREB 393300PART OF STRUCTURE SHEET No. REVISION
Headblock Wall 3 of 8BY DATE CHECKED BY
RH 8-Apr-23
REFERENCES - RAYTHEON DRAWING No.
- STAAD III STRUCTURAL ANALYSIS
Bowstring truss, restraint wires at 5m vertical centresfor latereral stability.
Main Column (Worst Case Axial Force)
DESIGN Steel Grade fyk = 240 N/mm²PARAMETERS Effective length Sk = 5 m
Assumed Section Size = 160 x 80 x 5.0 RHSArea A = 22.9 cm²
Elastic modulus zz = 62.9 (BS Notation Zy)Elastic modulus zx = 94.1
Second moment of area Izz = 251 (BS Notation Iyy)Second moment of area Ixx = 753
Radius of gyration rzz = 3.31 cm (Bs Notation ryy)Radius of gyration rxx = 5.74 cm
ref staad III Max. MomentMz max = 1 kNM load case 8 (Stad Notation My)Max. MomentMx max = 1 KNM load case 8 (Stad Notation Mz)
analysis results Max. Axial N max = 110 kN load case 8Max. Shear Vz max = 5 kN load case 8 (Stad Notation Vy)Max. Shear Vx max = 5 kN load case 8 (Stad Notation Vz)
Unity check based on elastic / elastic method
DIN 18800 Pt1 LIMIT STRESS[746]
= 240 = 218 N/mm²1.1
= = 126 N/mm²
DIN 18800 Pt1 CHECKS:[747]
Mz + NZz A
= 1E+06 + 110000 = 6462900 2290
Mx + NZx A
= 1E+06 + 110000 = 5994100 2290
= 64 = 0.29 < 1 OK218
= 59 = 0.27 < 1 OK= 218
= Vz = 4.40.5 A
= 4.37 = 0.03 < 1 OK126
= Vx = 4.40.5 A
= 4.37 = 0.03 < 1 OK1.26E+02
cm3
cm3
cm4
cm4
s R,D = fy,d = fyk
gm
tR,D fy,d
Ö3
sz =
N/mm2
sx =
N/mm2
sz s R,D
sx s R,D
txy N/mm2
txytR,D
tyz N/mm2
tyztR,D
CALCULATIONS
PROJECT PROJECT No.
PLIVA RESEARCH INSTITUTE , ZAGREB 393300PART OF STRUCTURE SHEET No. REVISION
Headblock Wall 4 of 8 1of 8BY DATE CHECKED BY
RH 8-Apr-23
DIN 18800 Pt1 FAILURE CRITERIA[748]
((64² +59²) -(64*59)+(57.3+57.3) = 63 N/mm²
= 63 = 0.287 < 1 OK218
DIN 18800 Pt2 OUT OF PLANE STABILITY CHECK[304] Stability check for design axial compression
Nki =Sk²
x 2.1E5 x 7.530E+06 = 624 KN5000²
Npl = A x fyk
= 2290 x 240 = 550 KN
=
(550 / 624) = 0.939
> 0.2
0.21 hot rolled RHS
k =
DIN 18800 Pt2 = 0.5 [ 1 + (0.939- 0.2) + 0.939²] = 1.018Table 4 & 5
x = 1
x = 1( 1.018² - 0.939² ) + 1.018 = 0.709
N = 110.0
0.709 x 2290 x 240/1.1 = 0.257 < 1 OK
160 x 80 x 5.0 RHSis aqequate
s v = Ö (sx²+sy²+sz²-sxsy-sxsz-sysz+3txy2+3txz2+3tyz2)
= Ö
s v
s R,D
p².E.I
= p²
lk Ö ( Npl / Nki )
= Ö
lk
where a =
0.5 [ 1 + a ( lk - 0.2 ) + lk² ]
lk (lk + a)
x. Npl/gm
CALCULATIONS
PROJECT PROJECT No.
PLIVA RESEARCH INSTITUTE , ZAGREB 393300PART OF STRUCTURE SHEET No. REVISION
Headblock Wall 6 of 8BY DATE CHECKED BY
RH 8-Apr-23
DIN 18800 Pt1 FAILURE CRITERIA[748]
=
#REF! #REF! N/mm²
= #REF! = #REF! #REF! ###180
DIN 18800 Pt2 OUT OF PLANE STABILITY CHECK[304] Stability check for design axial compression
Nki = x 2.1E5 x 3.929E+06Sk² 10000²
= 81 kN
Npl = A x fyk = 1710 x 240
= 410 kN
= (410 / 81)
= 2.250
k = 0.21 hot rolled CHS
= 0.5 [ 1 + 0.21(2.25- 0.2) + 2.25²]
= 3.247 DIN 18800 Pt2Table 4 & 5
> 0.2
=> x = 1 = 0.179
Ö ( 3.247² - 2.25² ) + 3.247
N = 1.9
0.179 x 410/1.33333333333333
= 0.03 < 1 OK
=> 139.7x4 CHS###
s v Ö s² + 3 x t
= Ö
s v
s R,D
p².E.I = p²
lk Ö ( Npl / Nki ) = Ö
0.5 [ 1 + a ( lk - 0.2 ) + lk² ] where a =
lk
x. Npl/gm
CALCULATIONS
PROJECT PROJECT No.
PLIVA RESEARCH INSTITUTE , ZAGREB 393300PART OF STRUCTURE SHEET No. REVISION
Headblock Wall 7 of 8BY DATE CHECKED BY
RH 8-Apr-23
REFERENCES - RAYTHEON DRAWING No.
- STAAD III STRUCTURAL ANALYSIS
Bowstring truss, restraint at 2.5m vertical centres for lateral stability
Bowstring Strut (Worst possible Case)
DESIGN Steel Grade fyk = 240 N/mm²PARAMETERS Effective length Sk = 1.6 m
Assumed plate Size = 12.5 cm x 2 cm thkArea A = 25 cm²
Elastic modulus z = 52.08Second moment of area I = 325.52 cm4
Radius of gyration i = 3.61 cm
ref staad III Max. Moment M max = 2 kN load case 11analysis results Max. Axial N max = 13 kN load case 11
Max. Shear V max = 4 kN load case 11
Unity check based on elastic / elastic method
DIN 18800 Pt1 LIMIT STRESS[746]
= 240 = 218 N/mm²
1.1
= = 126 N/mm²
DIN 18800 Pt1 CHECKS:[747]
s = M + NZ A
= 2E+06 + 1300052080 2500
= 44 N/mm²
s = 44 = 0.20 < 1 OK218
t = V = 4000 = 3 N/mm²0.5 x A 0.5 x2500
t = 3.00 = 0.02 < 1 OK
126
cm3
s R,D = fy,d = fyk
gm
tR,D fy,d
Ö3
s R,D
tR,D
CALCULATIONS
PROJECT PROJECT No.
PLIVA RESEARCH INSTITUTE , ZAGREB 393300PART OF STRUCTURE SHEET No. REVISION
Headblock Wall 8 of 8BY DATE CHECKED BY
RH 8-Apr-23
DIN 18800 Pt1 FAILURE CRITERIA[748]
=
(44² + 3 x 3²) = 44 N/mm²
= 44 = 0.202 < 1 OK218
DIN 18800 Pt2 OUT OF PLANE STABILITY CHECK[304] Stability check for design axial compression
Nki = x 2.1E5 x 3.255E+06Sk² 1600²
= 2635 kN
Npl = A x fyk = 2500 x 240
= 600 kN
= (600 / 2635)
= 0.477
k = 0.49 solid sections
= 0.5 [ 1 + 0.49(0.477- 0.2) + 0.477²]
= 0.682 DIN 18800 Pt2Table 4 & 5
> 0.2
=> x = 1 = 0.855
Ö ( 0.682² - 0.477² ) + 0.682
N = 13.0
0.855 x 600/1.1
= 0.03 < 1 OK
=> 12.5x2 cm plateis aqequate
s v Ö s² + 3 x t
= Ö
s v
s R,D
p².E.I = p²
lk Ö ( Npl / Nki ) = Ö
0.5 [ 1 + a ( lk - 0.2 ) + lk² ] where a =
lk
x. Npl/gm