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Elastic Analysis of Reinforced and Prestresse
Contents:
Name Purpose
Elastic
Quartic Find the real roots of quartic equations
Cubic Find the real roots of cubic equations
Quadratic Find the real roots of quadratic equations
PlotXY Plot cross section diagram
Parameters:
Conc A 6 column range with concrete cross section details
Reo A 6 column range with reinforcement and prestress details
Momin The applied bending moment
Axin The applied axial load
Eccentric The eccentricity of the applied load
Out_Index An index number controlling the output data, see example
Units
Results are returned as single column arrays, depending on the value
To access the arrays either:
Enter the function as an array function (press ctrl-shift-ent
=INDEX(ELASTIC(Conc, Reo, Momin, Axin, Eccentric, 1),
Typical input and output is shown in the following sheets
www.interactiveds.com.au
http://newtonexcelbach.wordpress.com/
Find strain, stress, force and moment in prestressed andreinforced concrete beams with linear elastic materialproperties. Any section made up of rectangular ortrapezoidal layers
ELASTIC() is a User Defined Function (UDF) that carries out elastic aassuming zero tensile strength for the concrete, and linear elastic pro
Details of the analysis are provided in the file: DepthNA.pdf, which mhttp://newtonexcelbach.wordpress.com/
0 for loads and eccentricity in kN and metres, dimensions iconsistent units.
Or use the INDEX() function to return the required value.reinforcement enter:
Interactive Design Services
http://var/www/apps/conversion/tmp/scratch_4/www.interactiveds.com.auhttp://newtonexcelbach.wordpress.com/http://newtonexcelbach.wordpress.com/http://var/www/apps/conversion/tmp/scratch_4/www.interactiveds.com.au -
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Notes:1. The beam section may be made up of any arrangement of
2. Concrete and reinforcement are defined in layers, starting
3. Sign conventions:Bending causing compression on the top face is positive.
Compressive axial force is positive.
Eccentricity is the distance of the axial load from the top fa4. Datum for eccentricity of axial loads
5. Prestress forces
6. Plotting the cross section
If the eccentricity is omitted or blank the axial load is assuThis allows results of frame analysis programs to be enterhave been modelled on the concrete section centroid.
Where specified, the eccentricity is measured from the topeccentricity of zero will therefore be applied at the top faceunspecified eccentricity, which will be applied at the concr
Prestress forces may either be specified by entering a preentering the prestress force and eccentricity as an externa
Where the area of prestressing strand is included in the relosses deducted, since the strain in the strand is accounte
The "Redraw Section" button on the input sheet will draw treinforcement (in black) and prestressed reinforcement (in
Where voids are specified, B1 and B2 are the external coand B4 are the top and bottom width of the void.
The void dimensions are required for plotting purposes onlthe width of concrete for each layer, with void dimensions
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Tel +61 (0)2 9440 3414
Fax +61 (0)2 9940 6330
ABN 49 101 920 638
SectionsVer: 1.04 11-Oct-09
Usage
Quartic(A, B, C, D, E, Dt, Optional output index)
cubic(A, B, C)
Quadratic(A, B, C, Optional output index)
output.
of Out_Index.
r) after selecting the number of rows of output required.
3)
Elastic(conc, reo, momin, axin, Optional [eccentric,Out_Index, Units])
Creates diagram inside the range "PlotRange" on thecurrent sheet, using the data in "LayerRange", "ReoRange","Depth_NA", and "TFace".
nalysis of reinforced or prestressed concrete sections,erties for the reinforcement and concrete in compression.
y be downloaded from:
in mm, stresses in MPa (default), any other number for any
For instance to return the stress in the bottom layer of
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rectangular or trapezoidal layers
from the top or compressive face.
ce, positive upwards.
ed to be applied at the centroid of the concrete section.d without adjustment, assuming that the frame elements
face of the concrete. An axial load with a specified, and will give different results to the same axial load withte centroid.
tress force per strand for each layer of strand, or byl force.
inforcement list, the prestress force should not have elasticd for in the analysis.
he concrete section to scale, including passivered). The concrete compression zone is shaded blue.
crete dimensions (top and bottom of each layer), and B3
ly. The same numerical results may be obtained by enteringentered as zero or blank.
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Elastic Analysis of Reinforced and Prestressed Sections
Applied loads
Mom Axial Eccentricity
kN kN m
8.50E+03
Depth of Neutral Axis #NAME? mm
Tension face #NAME? #NAME?
Section Details (enter layers from top face, or compressive face for columns)
Concrete Void
Layer Depth B1(top) B2(bottom) B3(top) B4(bottom) Ec
25 2380.0 2380.0 866.3 866.3 32000
50 2380.0 2380.0 816.3 806.8
75 1212.6 1012.6 806.8 792.6
1305 1012.6 765.4 792.6 545.4
45 765.4 756.8 545.4 0.0
300 756.8 700.0 0.0 0.0
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Reinforcement and prestress
Depth Dia No Es Side Cover
50.00 16 10 200000 30
1635.00 15.2 12 180 100
1685.00 15.2 12 180 95
1735.00 15.2 12 180 90
Prestressforce/Strand
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Elastic Output
Elastic(conc, reo, momin, axin, Optional [eccentric, Out_Index, Units])
Ranges Concrete #NAME?
Reinforcement 'Elastic1 Input'.I21:N24
1 2
Stress, MPa Strain, m^-1 Force,
1 Compression face #NAME? #NAME? Concrete
2 Compression steel #NAME? #NAME? Passive Steel
3 Tension Steel #NAME? #NAME? Prestress
4 Tension face #NAME? #NAME? Applied axial
5 Location of tension face #NAME? #NAME?
6
78
910
1112
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output column index, Out
3 4
kN Moment, kNm
#NAME? Concrete #NAME?
#NAME? Passive Steel #NAME?
#NAME? Prestress #NAME?
#NAME? Moment due to axial #NAME?
Applied moment #NAME?
Prestress eccentricity #NAME?
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_index
5 6
Depth to NA etc Steel by layer Stress
Y #NAME? Compression laye #NAME?
Acomp #NAME? to #NAME?
QNA #NAME? Tension layer #NAME?
Ina #NAME? #NAME?
Eccentricity reaction force from comp. fa #NAME? Total passive forc #NAME?
Eccentricity applied force from comp. fac #NAME? Total prestress fo #NAME?
Depth centroid concrete section #NAME? #NAME?
Depth centroid reinforcement #NAME?
Depth centroid full composite section #NAME?
Depth centroid cracked composite sectio #NAME?
I reinforcement #NAME?
#NAME?
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7
Force
#NAME?
#NAME?
#NAME?
#NAME?
#NAME?
#NAME?
#NAME?
#NAME?
#NAME?
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RLayers
1: Es #NAME? #NAME?
2: Layer Area #NAME? #NAME?
3: Cumulative area #NAME? #NAME?
4: Transformed layer area in ten #NAME? #NAME?
5: Cumulative area in tension #NAME? #NAME?
6: Cumulative first MofA about to #NAME? #NAME?
' Find layer and adjusted total transformed 7: Transformed layer area in co #NAME? #NAME?' for NA down to current layer 8: Cumulative transformed area i #NAME? #NAME?
9: Cumulative transformed first #NAME? #NAME?
10: Layer Depth #NAME? #NAME?
11: Cumulative Centroid depth #NAME? #NAME?
12: Rsum1 tension #NAME? #NAME?
13: Rsum2 tension #NAME? #NAME?
14: Rsum1 compression to NA #NAME? #NAME?
15: Rsum2 compression to NA #NAME? #NAME?
16: I about steel centroid #NAME? #NAME?
Layers
1 Layer thickness #NAME? #NAME?
2 Transformed B1 #NAME? #NAME?
3 Transformed B2 #NAME? #NAME?
4 Transformed K #NAME? #NAME?
5 Transformed layer area #NAME? #NAME?
6 Cumulative area #NAME? #NAME?
7 Layer centroid height from botto #NAME? #NAME?
8 Composite conc. 1st moment of #NAME? #NAME?
9 Height of composite concrete ce #NAME? #NAME?
10 Depth of bottom of layer #NAME? #NAME?
11 Layer second moment of area a #NAME? #NAME?12 Layer second moment of area a #NAME? #NAME?
13 Composite concrete second mo #NAME? #NAME?
14-18: Composite transformed properties Area #NAME? #NAME?
15 First moment of area about top #NAME? #NAME?
16 Depth of centroid #NAME? #NAME?
17 First moment of area about botto #NAME? #NAME?
18 Second moment of area about b #NAME? #NAME?
19 I reinforcement in tension #NAME? #NAME?
XA
NA within section Full compression Full tension
1 Y Y Y2 Qna Qna Qna
3 Ina Ina Ina
4 Qstna Qstna Qstna
5 Qconcna Qconcna -
6 Istna Istna Istna
7 Icconc Icconc -
8 Depth centroid conc compression Dref -
9 Acomp Acomp Acomp
10 Dref Dref Dref
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11 DRefComp DRefComp DRefComp
12 a
13 b
14 c
15 d
16 e
17 Rsum1
18 Rsum2
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Public Function FindNA(reo, layers, rlayers, llayer, axin, momin, out2) As Variant
Dim SmallAx As Double, E_1 As Double, E_2 As Double
Dim Is1 As Double, Is0 As Double, Axs1 As Double, Axs0 As Double, numreo As Long
Dim Ar As Double, Dst As Double, Dbase As Double, Irt As Double, Art As Double, Drt As Double
Dim i As Long, j As Long, Firsti As Long, k As Long, XCoeff() As Double, out() As Double
Dim db As Double, Dt As Double, DL As Double, Bb As Double, B2b As Double, Kb As Double, Dct As DoubleDim At As Double, Ict As Double, Qa As Double, Qb As Double, Qc As Double, Qd As Double, Qe As Double
Dim X As Double, X0 As Double, Im(1 To 5) As Double, Fm(1 To 5) As Double
Dim Momx As Double, Axx As Double, Sigt As Double, Layer0 As Long, MAr As Double
Dim ap As Double, Acc As Double, Dcc As Double, Dcct As Double, Itb As Double
Dim A As Double, Dc As Double, Ip As Double, Dcg As Double
Dim Itbp As Double, Il As Double, dcp As Double, Ixs As Double, dsc As Double
numreo = UBound(reo) - LBound(reo) + 1
ReDim XCoeff(1 To 6, 1 To 5)
ReDim out(1 To llayer, 1 To 3)
Dbase = layers(llayer, 1)
'Axial load = 0 or very small
E_1 = 0
SmallAx = axin
If axin 0 Then E_1 = momin / axin
If (momin 0 And E_1 = 0) Or Abs(E_1) / layers(llayer, 1) > MaxERatio Then
SmallAx = 0
If E_1 0 Then
SmallAx = axin
axin = momin / (MaxERatio * layers(llayer, 1))
If SmallAx < 0 Then axin = axin * -1
End IfFor i = 1 To llayer
' Coefficients for x
' Reinforcement
Is1 = 0
Is0 = 0
Axs1 = 0
Axs0 = 0
For j = 1 To numreo
If reo(j, 1) >= layers(i, 1) Then Ar = rlayers(j, 1) Else Ar = rlayers(j, 2)
Axs1 = Ar + Axs1
Axs0 = -Ar * reo(j, 1) + Axs0
Next j
XCoeff(6, 3) = Axs1
XCoeff(6, 4) = Axs0
db = layers(i, 1)
Dt = layers(i, 12)
DL = layers(i, 2)
Bb = layers(i, 3)
B2b = layers(i, 4)
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Kb = (B2b - Bb) / DL
Dct = layers(i - 1, 9)
At = layers(i - 1, 8)
Ict = layers(i - 1, 11)
XCoeff(1, 1) = Kb / 12
XCoeff(1, 2) = Bb / 3 - Kb / 3 * Dt
XCoeff(1, 3) = (-Dt * Bb + Kb / 2 * Dt ^ 2)XCoeff(1, 4) = (Dt ^ 2 * Bb - Kb / 3 * Dt ^ 3)
XCoeff(1, 5) = -Dt ^ 3 / 3 * Bb + Kb / 12 * Dt ^ 4
'
'
'
XCoeff(2, 4) = -2 * Dct * At
XCoeff(2, 5) = (Ict + At * Dct ^ 2)
XCoeff(4, 1) = Kb / 6
XCoeff(4, 2) = Bb / 2 - Kb / 2 * Dt
XCoeff(4, 3) = Kb / 2 * Dt ^ 2 - Bb * Dt
XCoeff(4, 4) = (Bb / 2 * Dt ^ 2 - Kb / 6 * Dt ^ 3)XCoeff(5, 3) = At
XCoeff(5, 4) = -At * Dct
Qa = XCoeff(4, 1)
Qb = XCoeff(4, 2)
Qc = 0
For j = 4 To 6
Qc = XCoeff(j, 3) + Qc
Next j
Qd = 0
For j = 4 To 6
Qd = XCoeff(j, 4) + Qd
Next j
If Qa = 0 And Qb = 0 Then
X0 = -Qd / Qc
Else
X0 = quartic(0, Qa, Qb, Qc, Qd, Dt)
End If
If X0 > Dt And X0
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E_1 = momin / axin
E_2 = E_1 - layers(llayer, 9)
'Find first section under NA
' If axin < 0 Then Firsti = 0 Else Firsti = 1
' For i = Firsti To llayer + 1
' Coefficients for x
' Reinforcement' ReDim XCoeff(1 To 6, 1 To 5)
' Is1 = 0
' Is0 = 0
' Axs1 = 0
' Axs0 = 0
' For j = 1 To numreo
' If i 0 ThenIf NALayer 0 Then
Kb = (B2b - Bb) / DLDct = layers(i - 1, 9)
At = layers(i - 1, 8)
Ict = layers(i - 1, 11)
End If
Irt = layers(i, 20)
Art = layers(i, 14)
Drt = layers(i, 16)
If i < 1 Or NALayer > llayer Then
Bb = 0
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Kb = 0
End If
Qa = -Kb / 12
Qb = -Bb / 6 + Kb / 6 * (Dt - E_2)
Qc = -Bb * E_2 / 2 + Kb * Dt * E_2 / 2
Qd = Bb * Dt ^ 2 / 2 - Kb * Dt ^ 3 / 6 - At * Dct + E_2 * _
(Bb * Dt - At - Kb * Dt ^ 2 / 2) - Art * (Drt + E_2)Qe = Ict + Irt + At * Dct * (Dct + E_2) - Bb * Dt ^ 2 * (Dt / 3 + E_2 / 2) _
+ Kb / 6 * Dt ^ 3 * (Dt / 2 + E_2) + Art * Drt * (Drt + E_2)
' XCoeff(2, 4) = -2 * Dct * At
' XCoeff(2, 5) = (Ict + At * Dct ^ 2)
' XCoeff(4, 1) = -Kb / 6
' XCoeff(4, 2) = -Bb / 2 - Kb / 6 * (E_2 - 3 * Dt)
' XCoeff(4, 3) = -Bb / 2 * (E_2 - 2 * Dt) - Kb / 2 * (Dt ^ 2 - E_2 * Dt)
' XCoeff(4, 4) = (-Bb / 2 * (Dt ^ 2 - 2 * Dt * E_2) - Kb / 6 * (3 * E_2 * Dt ^ 2 - Dt ^ 3))
' XCoeff(4, 5) = (-Bb / 2 * Dt ^ 2 * E_2 + Kb / 6 * E_2 * Dt ^ 3)
' XCoeff(5, 4) = -At * (E_2 - Dct)' XCoeff(5, 5) = At * Dct * E_2
' ElseIf i > llayer Then
' Dct = layers(i - 1, 9)
' At = layers(i - 1, 8)
' Ict = layers(i - 1, 11)
' For j = 1 To 5
' XCoeff(1, j) = 0
' Next j
''
' XCoeff(2, 4) = -2 * Dct * At
' XCoeff(2, 5) = (Ict + At * Dct ^ 2)
' For j = 1 To 5
' XCoeff(4, j) = 0
' Next j
' XCoeff(5, 4) = -At * (E_2 - Dct)
' XCoeff(5, 5) = At * Dct * E_2
' End If
' Qa = 0
' For j = 1 To 6
' Qa = XCoeff(j, 1) + Qa
' Next j
' Qb = 0
' For j = 1 To 6
' Qb = XCoeff(j, 2) + Qb
' Next j
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' Qc = 0
' For j = 1 To 6
' Qc = XCoeff(j, 3) + Qc
' Next j
' Qd = 0
' For j = 1 To 6' Qd = XCoeff(j, 4) + Qd
' Next j
' Qe = 0
' For j = 1 To 6
' Qe = XCoeff(j, 5) + Qe
' Next j
If Qa = 0 And Qb = 0 And Qc = 0 Then
If Qd 0 Then X = -Qe / Qd Else X = 10000000000#
Else
X = quartic(Qa, Qb, Qc, Qd, Qe, Dt)
End If
' If (X > Dt And X < db) Or i > llayer Or (i = 0 And (X < 0 Or X > Dbase)) Then
out2(18) = (Qa * X ^ 4 + Qb * X ^ 3 + Qc * X ^ 2 + Qd * X + Qe) / Qe
FindX:
If SmallAx = 0 Then
X = X0
i = Layer0
' GoTo endfunc
ElseIf Abs(SmallAx) < Abs(axin) Then
X = X0 + (X - X0) * SmallAx / axin
End If
' Find top face strain
' Factor on moment if E_1 > 1 or axin = 0, otherwise axial load
' Find steel transformed area and 1st and 2nd Moment of area
Axs1 = 0
Axs0 = 0
Ixs = 0For j = 1 To numreo
If reo(j, 1) >= X Then Ar = rlayers(j, 1) Else Ar = rlayers(j, 2)
Axs1 = Ar + Axs1
Axs0 = Ar * reo(j, 1) + Axs0
Next j
dsc = Axs0 / Axs1
For j = 1 To numreo
If reo(j, 1) >= X Then Ar = rlayers(j, 1) Else Ar = rlayers(j, 2)
Ixs = Ar * (dsc - reo(j, 1)) ^ 2 + Ixs
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Next j
out2(17) = Ixs
'Find area and centroid of concrete compression zone
If X = Dbase ThenAcc = At
Dcc = Dct
Dcct = (Acc * Dcc + Axs1 * dsc) / (Acc + Axs1)
out2(16) = layers(llayer, 11) ' Concrete I about concrete centroid
Itb = layers(llayer, 11) + Acc * (Dcct - Dct) ^ 2
Ixs = Ixs + Axs1 * (Dcct - dsc) ^ 2
Else
DL = X - Dt
' B1 = Bb
B2b = Bb + Kb * DL
A = (Bb + B2b) / 2 * DLAcc = At + A
Dc = DL / 3 * (2 * B2b + Bb) / (B2b + Bb)
Dcc = (At * Dct + A * (Dc + Dt)) / Acc
Ip = layers(i - 1, 11) ' I to previous layer
Il = DL ^ 3 / 12 * (3 * Bb + B2b) ' Layer I about base
Il = Il - A * (DL - Dc) ^ 2 ' Layer I about layer centroid
out2(16) = Ip + At * ((Dcc - Dct) ^ 2) + Il + A * ((Dcc - (Dt + Dc)) ^ 2) ' Concrete I about concrete centroidDcct = (Acc * Dcc + Axs1 * dsc) / (Acc + Axs1)
Itb = Ip + At * ((Dcct - Dct) ^ 2) + Il + A * ((Dcct - (Dt + Dc)) 2) ' Total I about composite centroid
Ixs = Ixs + Axs1 * (Dcct - dsc) ^ 2
End If
' Exit For
' End If
' Next i
out2(3) = Acc
out2(5) = Axs1
out2(6) = Acc + Axs1out2(7) = Dcc
out2(9) = dsc
out2(10) = Dcct
out2(13) = Itb
out2(14) = Ixs
out2(15) = Itb + Ixs
out2(18) = Kb
out2(19) = Qb
out2(20) = Qc
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out2(21) = Qd
out2(22) = Qe
endfunc:
out2(1) = X
FindNA = X
End Function
Private Function CompFace(reo, layers, rlayers, llayer, axin, momin, CFOut)
Dim numreo As Long, Dcr As Double, Dcrt As Double, CompDrct As Double, Eut As Double, Euc As Double
Dim Dcg As Double, E_1 As Double, E_2 As Double, Depth As Double
numreo = UBound(rlayers) - LBound(rlayers) + 1
Dcr = rlayers(numreo, 5) / rlayers(numreo, 4)Dcrt = rlayers(numreo, 7) / rlayers(numreo, 6)
CompDrct = (rlayers(numreo, 7) + layers(llayer, 8) * layers(llayer, 9)) / (rlayers(numreo, 6) + layers(llayer, 8))
Dcg = layers(llayer, 9)
Depth = layers(llayer, 1)
'Load eccentricity for uniform tension
Eut = -Dcr
'Load eccentricity for uniform compression
Euc = -CompDrct
If axin 0 Then
E_1 = momin / axinE_2 = E_1 - (layers(llayer, 9) - CompDrct)
End If
' If top face is compression face then CompFace = 1, else CompFace = 0
If axin = 0 Then
If momin > 0 Then CompFace = 1 Else CompFace = 0
Else
If axin < 0 Then
If E_2 < Eut Then CompFace = 1 Else CompFace = 0
ElseIf E_2 > Euc Then CompFace = 1 Else CompFace = 0
End If
End If
If CompFace = 0 Then
Dcg = Depth - Dcg
Dcr = Depth - Dcr
CompDrct = Depth - CompDrct
Dcr = Depth - Dcr
End If
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CFOut(8) = Dcg
CFOut(9) = Dcr
CFOut(11) = CompDrct
CFOut(12) = Dcr
End Function
Private Sub SwapFace(layers, llayer, reo, rlayers, numreo)
Dim TempLayers() As Double, TempReo() As Double, Depth As Double
Dim i As Long, j As Long
ReDim TempLayers(0 To llayer, 1 To 22)
ReDim TempReo(1 To numreo, 1 To 4)
Depth = layers(llayer, 1)
For i = 1 To llayer
'For j = 1 To 13
TempLayers(i, 1) = Depth - layers(llayer - i + 1, 1)TempLayers(i, 2) = layers(llayer - i + 1, 2)
TempLayers(i, 3) = layers(llayer - i + 1, 4)
TempLayers(i, 4) = layers(llayer - i + 1, 3)
TempLayers(i, 5) = layers(llayer - i + 1, 5)
TempLayers(i, 6) = layers(llayer - i + 1, 6)
TempLayers(i, 7) = layers(llayer - i + 1, 7)
TempLayers(i, 8) = layers(llayer - i + 1, 8)
TempLayers(i, 9) = Depth - layers(llayer - i + 1, 9)
TempLayers(i, 10) = layers(llayer - i + 1, 10)
TempLayers(i, 11) = layers(llayer - i + 1, 11)
TempLayers(i, 12) = Depth - layers(llayer - i + 1, 12)
Next i
For i = 1 To numreo
TempReo(i, 1) = Depth - reo(numreo - i + 1, 1)
For j = 2 To 4
TempReo(i, j) = reo(numreo - i + 1, j)
Next j
Next i
layers = TempLayers
reo = TempReo
End Sub
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Public Sub Elastic3()
' Get mom, ax, e_1, concrete and reo arrays and number layers
' Concrete and steel properties' Adjust concrete widyhs for concrete modular ratio
' Split concrete layers at reinforcement layers
' Form layers array, columns 1 to 6:
' 1: Level of bottom of layer
' 2: Thickness of layer
' 3: Top width
' 4: Bottom width
' 5: Concrete E
' 6: Rate of change of width, K
' Form rlayers array, columns 8, 10, 1 to 3, 4 to 7, 9:' 1: Transformed area in tension
' 2: Transformed area in compression
' 3: Es
' 4: Cumulative area in tension
' 5: Cumulative first MofA about top fibre in tension
' 6: Cumulative area in compression
' 7: Cumulative first MofA about top fibre in compression
' 8: Area
' 9: Cumulative area
' 10: Depth
' CumLayers layers, numLayers, llayer'Find composite Q and Dc for full section in compression and tension and I/Q about base
' of layer for each layer
' Calc E_1, E_2
' Cface = CompFace(reo, layers, Rlayers, llayer, axin, momin, XA)
' Swap faces ic Cface = 0
' X = FindNA(reo, layers, Rlayers, llayer, axin, momin, XA)
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End Sub
Private Sub CumLayers2(layers, numLayers, llayer)
'Form rest of layers array,columns 6 to 13
' 6: Layer area, A (writes over K)' 7: Layer centrod depth from top of layer
' 8: Total area to layer
' 9: Total concrete centroid depth to current layer
' 10: Total I about base
' 11: Total I about centroid
' 12: Depth of top of layer
' 13: Total Q about base
End Sub
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Public Function FindNALayer(reo, layers, rlayers, llayer, E_2) As Variant
End Function
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#NAME? #NAME? #NAME?
#NAME? #NAME? #NAME?
#NAME? #NAME? #NAME?
#NAME? #NAME? #NAME?
#NAME? #NAME? #NAME?
#NAME? #NAME? #NAME?
#NAME? #NAME? #NAME?#NAME? #NAME? #NAME?
#NAME? #NAME? #NAME?
#NAME? #NAME? #NAME?
#NAME? #NAME? #NAME?
#NAME? #NAME? #NAME?
#NAME? #NAME? #NAME?
#NAME? #NAME? #NAME?
#NAME? #NAME? #NAME?
#NAME? #NAME? #NAME?
#NAME? #NAME? #NAME? #NAME?
#NAME? #NAME? #NAME? #NAME?
#NAME? #NAME? #NAME? #NAME?
#NAME? #NAME? #NAME? #NAME?
#NAME? #NAME? #NAME? #NAME?
#NAME? #NAME? #NAME? #NAME?
#NAME? #NAME? #NAME? #NAME?
#NAME? #NAME? #NAME? #NAME?
#NAME? #NAME? #NAME? #NAME?
#NAME? #NAME? #NAME? #NAME?
#NAME? #NAME? #NAME? #NAME?#NAME? #NAME? #NAME? #NAME?
#NAME? #NAME? #NAME? #NAME?
#NAME? #NAME? #NAME? #NAME?
#NAME? #NAME? #NAME? #NAME?
#NAME? #NAME? #NAME? #NAME?
#NAME? #NAME? #NAME? #NAME?
#NAME? #NAME? #NAME? #NAME?
#NAME? #NAME? #NAME? #NAME?
#VALUE!#VALUE!
#VALUE!
#VALUE!
#VALUE!
#VALUE!
#VALUE!
#VALUE!
#VALUE!
#VALUE!
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#VALUE!
#VALUE!
#VALUE!
#VALUE!
#VALUE!
#VALUE!
#VALUE!
#VALUE!
Renumber
1 1 1: Depth of bottom of l
2 2 2: Layer area
3 3 3: Layer centrod dept
4 4 4: Total area to layer
5 5 5: Centroid depth to l
6 6 6: Cumulative I about
7 7 7: Cumulative I about
8 8 8: Depth of top of laye
9 9 9: Cumulative First m10 10 10: Cumulative transf
11 11 11: Total transformed
12 12 12: I/Q
13 13 13: Ir about base of la
14 14 14: Reaction centroid
15 15 15: Total transformed
16 16 16: Transformed centr
17 17 17: Total Transformed
18
19
20
2122
23
24
25
constant
constant
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constant
constant
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ayer
from top of layer
yer
base to layer
centroid to layer
r
nemt of area about baseormed reinforcement Q about base
Q about base
er, Irt
eccentricity - applied load eccentricity, from base of layer
area
oid height above base of layer
I about transformed centroid
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Examples - copy data to Input sheet
Circular section - 600 dia.
Concrete Void
Depth B1 B2 B3 B4 Ec
10 0.0 153.6 33330
15 153.6 239.820 239.8 316.1
25 316.1 385.2
30 385.2 447.2
50 447.2 519.6
50 519.6 565.7
50 565.7 591.6
50 591.6 600.0
50 600.0 591.6
50 591.6 565.7
50 565.7 519.6
50 519.6 447.2
30 447.2 385.225 385.2 316.1
20 316.1 239.8
15 239.8 153.6
10 153.6 0
Super T pretensioned bridge girder
Concrete Void
Depth B1 B2 B3 B4 Ec25 2380.0 2380.0 866.3 866.3 32000
50 2380.0 2380.0 816.3 806.8
75 1212.6 1012.6 806.8 792.6
1305 1012.6 765.4 792.6 545.4
45 765.4 756.8 545.4 0.0
300 756.8 700.0 0.0 0.0
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Reinforcement and prestress
Depth Dia No Es Side Cover
50.00 20 1 200000 30
83.49 20 2 30175.00 20 2 30
300.00 20 2 30
425.00 20 2 30
516.51 20 2 30
550.00 20 1 30
Reinforcement and prestress
Depth Dia No Es Side Cover 50.00 20 10 200000 30
1600.00 20 12 100 30
1750.00 20 12 100 30
Prestressforce/Strand
Prestress
force/Strand
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About Beam Design Functions
Disclaimer
This program is distributed in the hope that it will be useful,
but without any warranty; without even the implied warranty of
merchantability or fitness for a particular purpose.
Copyright 2008 Interactive Design Services Pty Ltd. all rights reserved
Revision History
Current Version 1.04 11-Oct-09
Rev Date By Description
1 5/29/2008 DAJ First release
1.01 11/3/2008 DAJ Corrected for 0 axial load with NA above top reinforcement layer
1.02 2-Jun-08 DAJ Dim statement added for rlayers. Minor revisions to code.
1.03 5-Jun-08 DAJ Check of referenced DLLs added. Removed because of problems if acce
1.04 11-Oct-09 DAJ Dim statement added for NumPointA
This program is free software; you can redistribute it and/or modify it under the termsof the GNU General Public Licenseas published by the Free Software Foundation;either version 2 of the License, or (at your option) any later version.
www.interactiveds.com.au
http://newtonexcelbach.wordpress.com/
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s to VBA project not allowed