Prestressed Design.xls 2pk6e
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Prestressed Precast I-Girder Design for Intermediate Beams - CE767 Geometrical Properties Girder Span Length Girder Depth Spacing of Girders
L h S
24 90 0.85
m cm m
Deck Thickness
tdeck
20
cm
0 0
cm cm
Haunch Thickness Haunch Width
Please choose the type of the beam cross section (1/2) Please enter the dimensions of the section in "SectionComposer"
Material Properties of Concrete Elastic Modulus - AASHTO LRFD 5.4.2.4-1 Descrip. fc` Unit W (MPA) (kg/m3) CIP Deck 30 2500 Beam@transfer 40 2500 Beam@service 50 2500
Loads DW, Dead Load Placed on Structural Components Thickness of wearing surface 6 cm Unit weight of wearing surface 2200 kg/m3
1
Cross sectional Properties for a Single Beam Girder from LARSA Section Composer Area Istrong Iweak bw yb (cm2) (cm4) (cm4) (cm) (cm) 3037.5 3.18E+06 942070.31 15 50.22 Cross Diaphragms width height Quantity
25 94 3
Cross sectional Properties for the Composite Beam Descript. Area yb A.yb A(ycb-yb)2 (cm2) (cm) (cm3) (cm4) Beam 3037.50 50.2 152531 688500.94 Haunch 0.00 0 0 0 Deck 1316.81 100 131681 1588167.4 Sum 4354.31 2.84E+05 Section, ycb =
65.3
Ec (MPA) 29440 33994 38007
DC, Dead Load of Structural Components and non-structural elements Self Weight 0.759 t/m Deck Weight 0.425 t/m Haunch 0.000 t/m Sum 1.184 t/m
cm cm two at ends and one at mid-span
Istrong (cm4) 3.18E+06 0 43894
Istr+ADy2 (cm4) 3.87E+06 0.00E+00 1.63E+06 5.50E+06
Cross Diaphragms
0.499375 0.499375
tons per girder at mid-span tons per girder at each end
Barrier Wearing Surface Sum
0.100 0.112 0.212
t/m per beam t/m per beam t/m per beam
LL, Distrubution Factors for LiveLoad H30 truck Distribution Factor for Bending Moment - lane/beam
S= ts = L= Nb = Kg
cm
Effective Flange Width (AASHTO LRFD 4.6.2.6.1) 1/4 Span = 6 m 12ts + web 2.85 m Spacing = 0.85 m Use 0.85 m
Kg = DFM =
Distribution Factor for Shear - lane/beam
Spacing for prestressing strands
5
Layer 1 - # of strands Layer 2 - # of strands Layer 3 - # of strands Layer 4 - # of strands Layer 5 - # of strands Layer 6 - # of strands Layer 7 - # of strands Layer 8 - # of strands Layer 9 - # of strands
11 11 0 0 0 0 0 0 0
c.g of prestressing tendons from bottom
cm
Check for fitting x y,from bottom (cm) (cm) 60 5 60 10 5 15 5 20 5 25 5 30 5 35 5 40 5 45
7.50
cm
mm mm mm mm4
NOT OK OK OK OK OK
Table 4.6.2.2.3a-1
DFS =
(1/2 in. Dia. Seven wire, low relaxation) 22 Ab 98.71 mm2
850 200 24000 >=4 1.38E+11
1.38E+11 mm4 0.313 lanes/beam
Modular Ratio of Deck to Beam = 0.77 Span to Depth Ratio 27
Prestressing steel # of strands Area of 1 strand
Table 4.6.2.2.2b-1
Prestressing force Ultimate strength Yield strength Initially (=0.75 fpu) Initial loss Initial loss At Transfer after initial losses Total Prestressing Force
Reinforcing Bars Yield strength
fpy
fpu fpy fpi
1861.65 1675.485 1396.2 4.3 60.0 1336.2 2901.7
420
MPa
MPa MPa MPa % MPa MPa kN
0.430
lanes/beam
(LRFD Table 5.4.4.1-1) (LRFD Table 5.9.3-1)
STRESSES AT TRANSFER
Moment due to prestressing Moment due to SW of the beam
Mp at c/g of beam Mbeam at c.g of beam
1239.5 536.4
kN-m kN-m
Stress check at transfer - midspan Bottom Fiber - Compression
`=-P/A-Mp/Sb+Mb/Sb
-20.654
MPa
<
-24
MPa
OK
Top Fiber - Tension Check
`=-P/A+Mp/St-Mb/St
-0.758
MPa
<
1.581
MPa
OK
without bonded reinf. Check Total Loss due to Initial Prestressing Loss = n * elastic shortening stress n = Es/Ec 5.78 Elastic Shortening Stress
`=(-P/A)-(Mp*e)/I+(Mb*e)/I
Loss
iterate for loss
-109.80
-18.996 60.0 (estimated)
MPa
MPa
Check Stresses at Transfer Length Section Transfer Length =
60 dia =
mm
LRFD Art. 5.8.2.3
Mbeam @ end of Transfer Length =
65.96
kN-m
P= Mp at c.g of beam =
0.00 0.00
kN kN-m
Debonded strands =
762 22
Bottom Fiber Stresses =
`=-P/A-Mp/Sb+Mb/Sb
1.041
MPa
<
-24
MPa
OK
Top fiber Stresses =
`=-P/A+Mp/St-Mb/St
-0.825
MPa
<
1.581
MPa
OK
Not checked but say at every meter activate 8 strands from the end zone.
STRESSES AT SERVICE LOADS
Prestress Losses at Service Level Elastic Shortening
-109.80
MPa
fpi Aps Ag gamma-k gamma-st delta fpr
(see above comp.)
delta fpl
1396.24 MPa 2171.61 mm2 303750 mm2 0.8 0.74 17 MPa (AASHTO LRFD Section 5.9.5.3) 125.91 MPa
Total Prestress Loss at Service Total Prestress loss (%) Total Prestress Stress after losses
-235.72 16.9 1160.52
Total Prestress Force Mp Mdc Mdw Mll Mll+im Stresses at Mid-Span
Beam Top Fiber Stresses =
2520.2 1076.5 836.5 149.9 3464.6 1440.3
kN kN-m kN-m kN-m kN-m kN-m
Live Load Table H30-S24
MPa
Span m
MPa
(iterative) Finding the number of strands
Compute stresses using non-composite non-composite non-composite composite from the table in "live loads" sheet composite
Service I = P/A (MPa) -8.30
Mp term (MPa) 13.47
-8.30
13.47
Service III = -8.30
-17.00
-8.30
-17.00
fbc fpb ybs ec Ppe Final loss #
1.00(DC+DW) + 1.00 (LL+IM) Check compressive Stresses in prestressed comp. Mdc term Mdw term Mll+im term Total (MPa) (MPa) (MPa) (MPa) -10.46 -0.67 -5.97
28.66 25.12 4.5 45.72 2.39E+03 16.9 21
<
-22.50
OK
-0.67
-6.47
-12.44
<
-22.50
OK
-0.94
-9.07
-10.01
<
-13.5
OK
1.00(DC+DW) + 0.80 (LL+IM) Check tensile stresses in prestressed concrete comp. 13.21 1.78 -10.31
<
3.54
OK
<
3.54
OK
-10.46
Top of Deck Fiber Stresses
Beam Bottom Fiber Stresses =
from AASHTO Table
13.21
1.78
13.67
3.36
Mpa MPa cm cm Kn %
0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3 3.4 3.7 4 4.3 4.6 4.9 5.2 5.5 5.8 6.1 6.4 6.7 7 7.3 7.6 7.9 8.2 8.5 8.8
Moment kN-m 16.2 32.55 48.75 65.1 81.3 97.65 113.85 130.2 146.4 162.75 178.95 195.3 211.5 227.7 244.05 260.25 276.6 292.8 309.15 325.35 341.7 357.9 374.25 391.95 421.8 451.8 481.95 512.4 543
FATIGUE CHECK Fatigue is typically checked for one lane load instead of multiple lanes however for simplicity use above Mll+IM Distribution Factor for 1 lane loading Bottom Compressive Stress due to permanent loads and prestress = Bottom Tensile Stress due to( 0.75 Mll+IM) = Ratio comp/tension =
1.02
<
2
-10.31 10.08 check fatigue
MPa MPa LRFD 5.5.3.1
check of fatigue is not provided in this spreadsheet STRENGTH LIMIT STATE Mu1 = 1.25(DC)+1.5(DW)+1.75(LL+IM) Mu2 =0.9(DC)+0.65(DW)+1.75(LL+IM) Mu = 3791.0 kN-m Mu = 3370.8 kN-m dp
102.50
β 0.75
k 0.38
c=
22.77
cm
cm
>
20
Top flange thickness of the PC beam = c=
9.63
<
cm T-section behaviour
10
cm
30
cm
Average stress in prestressing tendons fps = 1704.4995 MPa Mn = 3435.8435 kN-m for rectangular Mn= 34533.072 kN-m for T-section Mr =Ø Mn Ø= 1 Mr =
LRFD 5.5.4.2.1
34533.07
>
3791.0
kN-m
OK
SHEAR DESIGN Vp =
0
kN
no draped tendons exist
Critical shear section approax. = de = h-ybs = Vdc = Vdw = Vll= Vll+im =
130.0 22.8 424.35 242.6
kN kN kN kN
Vu = Vc = Vu =
621.2 180.5 621.2
kN kN >
81.2
Vn >
Vu/phi =
690.3
kN
509.8
kN
Req'd Vs =
102.50
cm
from the live loads table
kN
provide stirrups
θ = 45 deg Av/s =
1.184
mm2/mm
Say S =
15
mm
Required Av =
17.8
mm2
Bar Dia =
8
mm
2 Bars, Av =
100.48
mm2
OK
Use
dia
@
15
8
mm
stirrups
Check minumum required reinforcement and maximum nominal capacity that can be provided by shear reinforcement Not done in this spreadsheet
DFS
0.246
lanes/beam
9.1 9.4 9.8 10.1 10.4 10.7 11 11.3 11.6 11.9 12.2 12.8 13.4 14
573.75 604.65 635.55 666.6 698.55 734.55 770.55 806.55 842.55 878.7 914.7 986.85 1059.3 1131.75
14.6 14.6 15.2 15.8 16.5 17.1 17.7 18.3 18.9 19.5 20.1 20.7 21.3 22.9 24.4 25.9 27.4 29 30.5 33.5 36.6 39.6 42.7 45.7 48.8 51.8 54.9 57.9 61 67.1 73.2 79.2 85.3 91.4
1204.05 1204.05 1276.05 1349.55 1422.15 1494.9 1567.5 1640.1 1713.15 1785.75 1858.8 1931.4 2004.3 2186.4 2368.95 2551.65 2734.05 2916.45 3099.3 3464.55 3829.95 4195.35 4561.05 5033.4 5629.05 6257.7 6918.6 7612.05 8337.9 9887.55 11567.25 13377.15 15317.25 17387.55
H30-S24 End shear and end reaction kN 213.45 213.45 213.45 213.45 213.45 213.45 213.45 213.45 213.45 213.45 213.45 213.45 213.45 213.45 227.55 240.15 251.55 260.85 269.55 277.5 284.85 290.85 296.85 302.25 307.65 312.3 316.2 320.25 325.65
330.9 335.55 340.2 344.25 348.3 352.35 355.65 358.95 362.25 365.7 368.25 373.65 378.3 382.35 387 387 390.3 394.35 397.65 400.35 403.05 405.6 408.3 410.4 412.95 414.3 416.4 421.05 424.35 427.65 430.35 433.05 435.75 439.65 442.95 451.05 472.35 493.8 515.1 536.4 557.85 579.15 600.45 643.2 685.95 728.55 771.3 814.05
GIRDER TYPE
1 Input lenghts (cm) X1 50 X2 90 X3 15 X4 0 Y1 15 Y2 7.5 Y3 50 Y4 0 Y5 7.5 Y6 10
Calculation of IXX A(cm2) 750 131.25 112.5 750 0 0 281.25 112.5 900
A1 A2 A3 A4 A5 A6 A7 A8 A9
XX --> Strong axis
yb (cm) 7.5 17.50 18.75 47.5 72.50 72.5 77.50 76.25 85
A yb'
3037.5 cm2 50.22 cm
IXX
3.181E+06 cm4
A*yb 5625 2296.875 2109.375 35625 0 0 21796.875 8578.125 76500 Σ 152531.25
Ix 14062.50 410.16 527.34 156250.00 0.00 0.00 878.91 527.34 7500.00 180156.25
A*(yb-yb')^2 1368495.66 140482.11 111387.63 5532.69 0.00 0.00 209366.43 76248.74 1088930.90 3000444.15509
A*yb 8437.5 5041.666667 4000 26812.5 12890.625 9187.5 52500 Σ 118869.7917
Ix 21093.75 1527.78 1666.67 57213.54 644.53 703.13 6250.00 89099.39
A*(yb-yb')^2 876806.55 80263.37 47539.51 22112.17 151277.14 100098.15 896964.96 2175061.85
7.641E+04 YY --> Weak Axis
GIRDER TYPE
A yl' IYY
3037.5 cm2 45.00 cm 9.421E+05 cm4
2 Required lenghts (cm)
Calculation of IXX
X1 X2 X3 Y1 Y2 Y3 Y4 Y5
A1 A2 A3 A4 A5 A6 A7
75 75 20 15 10 32.5 7.5 10
A(cm2) 1125 275 200 650 206.25 150 750
yb (cm) 7.5 18.33 20 41.25 62.5 61.25 70
XX --> Strong axis
A yb' IXX
3356.25 cm2 35.42 cm 2.264E+06 cm4
YY --> Weak Axis
A yl' IYY
3356.25 cm2 37.50 cm 1.109E+06 cm4
Calculation of IYY A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12
A 750 65.625 65.625 112.5 750 0 0 0 140.625 140.625 112.5 900
yl 45.00 31.67 58.33 45.00 45.00 37.50 52.50 45.00 25.00 65.00 45.00 45.00
A*yl 33750.00 2078.13 3828.13 5062.50 33750.00 0.00 0.00 0.00 3515.63 9140.63 5062.50 40500.00 Σ 136687.50
Iy 156250.00 1116.54 1116.54 2109.38 14062.50 0.00 0.00 0.00 10986.33 10986.33 2109.38 607500.00 806236.98
A*(yl-yl')^2 0.00 11666.67 11666.67 0.00 0.00 0.00 0.00 0.00 56250.00 56250.00 0.00 0.00 135833.33
yl 37.50 18.33 56.67 37.5 37.50 18.33 56.67 37.5 37.50
A*yl 42187.50 2520.83 7791.67 7500.00 24375.00 1890.63 5843.75 5625.00 28125.00 Σ 125859.38
Iy 527343.75 5776.91 5776.91 6666.666667 21666.67 4332.68 4332.68 5000 351562.50 932458.77
A*(yl-yl')^2 0.00 50512.15 50512.15 0.00 0.00 37884.11 37884.11 0.00 0.00 176792.53
Calculation of IYY A1 A2 A3 A4 A5 A6 A7 A8 A9
A 1125 137.5 137.5 200 650 103.125 103.125 150 750
L h S
24 90 0.85
m cm m
Deck Thickness
tdeck
20
cm
0 0
cm cm
Haunch Thickness Haunch Width
Please choose the type of the beam cross section (1/2) Please enter the dimensions of the section in "SectionComposer"
Material Properties of Concrete Elastic Modulus - AASHTO LRFD 5.4.2.4-1 Descrip. fc` Unit W (MPA) (kg/m3) CIP Deck 30 2500 Beam@transfer 40 2500 Beam@service 50 2500
Loads DW, Dead Load Placed on Structural Components Thickness of wearing surface 6 cm Unit weight of wearing surface 2200 kg/m3
1
Cross sectional Properties for a Single Beam Girder from LARSA Section Composer Area Istrong Iweak bw yb (cm2) (cm4) (cm4) (cm) (cm) 3037.5 3.18E+06 942070.31 15 50.22 Cross Diaphragms width height Quantity
25 94 3
Cross sectional Properties for the Composite Beam Descript. Area yb A.yb A(ycb-yb)2 (cm2) (cm) (cm3) (cm4) Beam 3037.50 50.2 152531 688500.94 Haunch 0.00 0 0 0 Deck 1316.81 100 131681 1588167.4 Sum 4354.31 2.84E+05 Section, ycb =
65.3
Ec (MPA) 29440 33994 38007
DC, Dead Load of Structural Components and non-structural elements Self Weight 0.759 t/m Deck Weight 0.425 t/m Haunch 0.000 t/m Sum 1.184 t/m
cm cm two at ends and one at mid-span
Istrong (cm4) 3.18E+06 0 43894
Istr+ADy2 (cm4) 3.87E+06 0.00E+00 1.63E+06 5.50E+06
Cross Diaphragms
0.499375 0.499375
tons per girder at mid-span tons per girder at each end
Barrier Wearing Surface Sum
0.100 0.112 0.212
t/m per beam t/m per beam t/m per beam
LL, Distrubution Factors for LiveLoad H30 truck Distribution Factor for Bending Moment - lane/beam
S= ts = L= Nb = Kg
cm
Effective Flange Width (AASHTO LRFD 4.6.2.6.1) 1/4 Span = 6 m 12ts + web 2.85 m Spacing = 0.85 m Use 0.85 m
Kg = DFM =
Distribution Factor for Shear - lane/beam
Spacing for prestressing strands
5
Layer 1 - # of strands Layer 2 - # of strands Layer 3 - # of strands Layer 4 - # of strands Layer 5 - # of strands Layer 6 - # of strands Layer 7 - # of strands Layer 8 - # of strands Layer 9 - # of strands
11 11 0 0 0 0 0 0 0
c.g of prestressing tendons from bottom
cm
Check for fitting x y,from bottom (cm) (cm) 60 5 60 10 5 15 5 20 5 25 5 30 5 35 5 40 5 45
7.50
cm
mm mm mm mm4
NOT OK OK OK OK OK
Table 4.6.2.2.3a-1
DFS =
(1/2 in. Dia. Seven wire, low relaxation) 22 Ab 98.71 mm2
850 200 24000 >=4 1.38E+11
1.38E+11 mm4 0.313 lanes/beam
Modular Ratio of Deck to Beam = 0.77 Span to Depth Ratio 27
Prestressing steel # of strands Area of 1 strand
Table 4.6.2.2.2b-1
Prestressing force Ultimate strength Yield strength Initially (=0.75 fpu) Initial loss Initial loss At Transfer after initial losses Total Prestressing Force
Reinforcing Bars Yield strength
fpy
fpu fpy fpi
1861.65 1675.485 1396.2 4.3 60.0 1336.2 2901.7
420
MPa
MPa MPa MPa % MPa MPa kN
0.430
lanes/beam
(LRFD Table 5.4.4.1-1) (LRFD Table 5.9.3-1)
STRESSES AT TRANSFER
Moment due to prestressing Moment due to SW of the beam
Mp at c/g of beam Mbeam at c.g of beam
1239.5 536.4
kN-m kN-m
Stress check at transfer - midspan Bottom Fiber - Compression
`=-P/A-Mp/Sb+Mb/Sb
-20.654
MPa
<
-24
MPa
OK
Top Fiber - Tension Check
`=-P/A+Mp/St-Mb/St
-0.758
MPa
<
1.581
MPa
OK
without bonded reinf. Check Total Loss due to Initial Prestressing Loss = n * elastic shortening stress n = Es/Ec 5.78 Elastic Shortening Stress
`=(-P/A)-(Mp*e)/I+(Mb*e)/I
Loss
iterate for loss
-109.80
-18.996 60.0 (estimated)
MPa
MPa
Check Stresses at Transfer Length Section Transfer Length =
60 dia =
mm
LRFD Art. 5.8.2.3
Mbeam @ end of Transfer Length =
65.96
kN-m
P= Mp at c.g of beam =
0.00 0.00
kN kN-m
Debonded strands =
762 22
Bottom Fiber Stresses =
`=-P/A-Mp/Sb+Mb/Sb
1.041
MPa
<
-24
MPa
OK
Top fiber Stresses =
`=-P/A+Mp/St-Mb/St
-0.825
MPa
<
1.581
MPa
OK
Not checked but say at every meter activate 8 strands from the end zone.
STRESSES AT SERVICE LOADS
Prestress Losses at Service Level Elastic Shortening
-109.80
MPa
fpi Aps Ag gamma-k gamma-st delta fpr
(see above comp.)
delta fpl
1396.24 MPa 2171.61 mm2 303750 mm2 0.8 0.74 17 MPa (AASHTO LRFD Section 5.9.5.3) 125.91 MPa
Total Prestress Loss at Service Total Prestress loss (%) Total Prestress Stress after losses
-235.72 16.9 1160.52
Total Prestress Force Mp Mdc Mdw Mll Mll+im Stresses at Mid-Span
Beam Top Fiber Stresses =
2520.2 1076.5 836.5 149.9 3464.6 1440.3
kN kN-m kN-m kN-m kN-m kN-m
Live Load Table H30-S24
MPa
Span m
MPa
(iterative) Finding the number of strands
Compute stresses using non-composite non-composite non-composite composite from the table in "live loads" sheet composite
Service I = P/A (MPa) -8.30
Mp term (MPa) 13.47
-8.30
13.47
Service III = -8.30
-17.00
-8.30
-17.00
fbc fpb ybs ec Ppe Final loss #
1.00(DC+DW) + 1.00 (LL+IM) Check compressive Stresses in prestressed comp. Mdc term Mdw term Mll+im term Total (MPa) (MPa) (MPa) (MPa) -10.46 -0.67 -5.97
28.66 25.12 4.5 45.72 2.39E+03 16.9 21
<
-22.50
OK
-0.67
-6.47
-12.44
<
-22.50
OK
-0.94
-9.07
-10.01
<
-13.5
OK
1.00(DC+DW) + 0.80 (LL+IM) Check tensile stresses in prestressed concrete comp. 13.21 1.78 -10.31
<
3.54
OK
<
3.54
OK
-10.46
Top of Deck Fiber Stresses
Beam Bottom Fiber Stresses =
from AASHTO Table
13.21
1.78
13.67
3.36
Mpa MPa cm cm Kn %
0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3 3.4 3.7 4 4.3 4.6 4.9 5.2 5.5 5.8 6.1 6.4 6.7 7 7.3 7.6 7.9 8.2 8.5 8.8
Moment kN-m 16.2 32.55 48.75 65.1 81.3 97.65 113.85 130.2 146.4 162.75 178.95 195.3 211.5 227.7 244.05 260.25 276.6 292.8 309.15 325.35 341.7 357.9 374.25 391.95 421.8 451.8 481.95 512.4 543
FATIGUE CHECK Fatigue is typically checked for one lane load instead of multiple lanes however for simplicity use above Mll+IM Distribution Factor for 1 lane loading Bottom Compressive Stress due to permanent loads and prestress = Bottom Tensile Stress due to( 0.75 Mll+IM) = Ratio comp/tension =
1.02
<
2
-10.31 10.08 check fatigue
MPa MPa LRFD 5.5.3.1
check of fatigue is not provided in this spreadsheet STRENGTH LIMIT STATE Mu1 = 1.25(DC)+1.5(DW)+1.75(LL+IM) Mu2 =0.9(DC)+0.65(DW)+1.75(LL+IM) Mu = 3791.0 kN-m Mu = 3370.8 kN-m dp
102.50
β 0.75
k 0.38
c=
22.77
cm
cm
>
20
Top flange thickness of the PC beam = c=
9.63
<
cm T-section behaviour
10
cm
30
cm
Average stress in prestressing tendons fps = 1704.4995 MPa Mn = 3435.8435 kN-m for rectangular Mn= 34533.072 kN-m for T-section Mr =Ø Mn Ø= 1 Mr =
LRFD 5.5.4.2.1
34533.07
>
3791.0
kN-m
OK
SHEAR DESIGN Vp =
0
kN
no draped tendons exist
Critical shear section approax. = de = h-ybs = Vdc = Vdw = Vll= Vll+im =
130.0 22.8 424.35 242.6
kN kN kN kN
Vu = Vc = Vu =
621.2 180.5 621.2
kN kN >
81.2
Vn >
Vu/phi =
690.3
kN
509.8
kN
Req'd Vs =
102.50
cm
from the live loads table
kN
provide stirrups
θ = 45 deg Av/s =
1.184
mm2/mm
Say S =
15
mm
Required Av =
17.8
mm2
Bar Dia =
8
mm
2 Bars, Av =
100.48
mm2
OK
Use
dia
@
15
8
mm
stirrups
Check minumum required reinforcement and maximum nominal capacity that can be provided by shear reinforcement Not done in this spreadsheet
DFS
0.246
lanes/beam
9.1 9.4 9.8 10.1 10.4 10.7 11 11.3 11.6 11.9 12.2 12.8 13.4 14
573.75 604.65 635.55 666.6 698.55 734.55 770.55 806.55 842.55 878.7 914.7 986.85 1059.3 1131.75
14.6 14.6 15.2 15.8 16.5 17.1 17.7 18.3 18.9 19.5 20.1 20.7 21.3 22.9 24.4 25.9 27.4 29 30.5 33.5 36.6 39.6 42.7 45.7 48.8 51.8 54.9 57.9 61 67.1 73.2 79.2 85.3 91.4
1204.05 1204.05 1276.05 1349.55 1422.15 1494.9 1567.5 1640.1 1713.15 1785.75 1858.8 1931.4 2004.3 2186.4 2368.95 2551.65 2734.05 2916.45 3099.3 3464.55 3829.95 4195.35 4561.05 5033.4 5629.05 6257.7 6918.6 7612.05 8337.9 9887.55 11567.25 13377.15 15317.25 17387.55
H30-S24 End shear and end reaction kN 213.45 213.45 213.45 213.45 213.45 213.45 213.45 213.45 213.45 213.45 213.45 213.45 213.45 213.45 227.55 240.15 251.55 260.85 269.55 277.5 284.85 290.85 296.85 302.25 307.65 312.3 316.2 320.25 325.65
330.9 335.55 340.2 344.25 348.3 352.35 355.65 358.95 362.25 365.7 368.25 373.65 378.3 382.35 387 387 390.3 394.35 397.65 400.35 403.05 405.6 408.3 410.4 412.95 414.3 416.4 421.05 424.35 427.65 430.35 433.05 435.75 439.65 442.95 451.05 472.35 493.8 515.1 536.4 557.85 579.15 600.45 643.2 685.95 728.55 771.3 814.05
GIRDER TYPE
1 Input lenghts (cm) X1 50 X2 90 X3 15 X4 0 Y1 15 Y2 7.5 Y3 50 Y4 0 Y5 7.5 Y6 10
Calculation of IXX A(cm2) 750 131.25 112.5 750 0 0 281.25 112.5 900
A1 A2 A3 A4 A5 A6 A7 A8 A9
XX --> Strong axis
yb (cm) 7.5 17.50 18.75 47.5 72.50 72.5 77.50 76.25 85
A yb'
3037.5 cm2 50.22 cm
IXX
3.181E+06 cm4
A*yb 5625 2296.875 2109.375 35625 0 0 21796.875 8578.125 76500 Σ 152531.25
Ix 14062.50 410.16 527.34 156250.00 0.00 0.00 878.91 527.34 7500.00 180156.25
A*(yb-yb')^2 1368495.66 140482.11 111387.63 5532.69 0.00 0.00 209366.43 76248.74 1088930.90 3000444.15509
A*yb 8437.5 5041.666667 4000 26812.5 12890.625 9187.5 52500 Σ 118869.7917
Ix 21093.75 1527.78 1666.67 57213.54 644.53 703.13 6250.00 89099.39
A*(yb-yb')^2 876806.55 80263.37 47539.51 22112.17 151277.14 100098.15 896964.96 2175061.85
7.641E+04 YY --> Weak Axis
GIRDER TYPE
A yl' IYY
3037.5 cm2 45.00 cm 9.421E+05 cm4
2 Required lenghts (cm)
Calculation of IXX
X1 X2 X3 Y1 Y2 Y3 Y4 Y5
A1 A2 A3 A4 A5 A6 A7
75 75 20 15 10 32.5 7.5 10
A(cm2) 1125 275 200 650 206.25 150 750
yb (cm) 7.5 18.33 20 41.25 62.5 61.25 70
XX --> Strong axis
A yb' IXX
3356.25 cm2 35.42 cm 2.264E+06 cm4
YY --> Weak Axis
A yl' IYY
3356.25 cm2 37.50 cm 1.109E+06 cm4
Calculation of IYY A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12
A 750 65.625 65.625 112.5 750 0 0 0 140.625 140.625 112.5 900
yl 45.00 31.67 58.33 45.00 45.00 37.50 52.50 45.00 25.00 65.00 45.00 45.00
A*yl 33750.00 2078.13 3828.13 5062.50 33750.00 0.00 0.00 0.00 3515.63 9140.63 5062.50 40500.00 Σ 136687.50
Iy 156250.00 1116.54 1116.54 2109.38 14062.50 0.00 0.00 0.00 10986.33 10986.33 2109.38 607500.00 806236.98
A*(yl-yl')^2 0.00 11666.67 11666.67 0.00 0.00 0.00 0.00 0.00 56250.00 56250.00 0.00 0.00 135833.33
yl 37.50 18.33 56.67 37.5 37.50 18.33 56.67 37.5 37.50
A*yl 42187.50 2520.83 7791.67 7500.00 24375.00 1890.63 5843.75 5625.00 28125.00 Σ 125859.38
Iy 527343.75 5776.91 5776.91 6666.666667 21666.67 4332.68 4332.68 5000 351562.50 932458.77
A*(yl-yl')^2 0.00 50512.15 50512.15 0.00 0.00 37884.11 37884.11 0.00 0.00 176792.53
Calculation of IYY A1 A2 A3 A4 A5 A6 A7 A8 A9
A 1125 137.5 137.5 200 650 103.125 103.125 150 750
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