Beam Elastic Analysis of Reinforced and Prestressed Sections

7/29/2019 Beam Elastic Analysis of Reinforced and Prestressed Sections

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Elastic Analysis of Reinforced and Prestressed

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 o

Units

Results are returned as single column arrays, depending on the value o

To access the arrays either:

Enter the function as an array function (press ctrl-shift-enter

=INDEX(ELASTIC(Conc, Reo, Momin, Axin, Eccentric, 1),3)

Typical input and output is shown in the following sheets

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 anassuming zero tensile strength for the concrete, and linear elastic prope

Details of the analysis are provided in the file: DepthNA.pdf, which mayhttp://newtonexcelbach.wordpress.com/

0 for loads and eccentricity in kN and metres, dimensions inconsistent units.

Or use the INDEX() function to return the required value. Freinforcement enter:


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Notes:1. The beam section may be made up of any arrangement of r

2. Concrete and reinforcement are defined in layers, starting fr

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 fac

4. 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 assumallows results of frame analysis programs to be entered withbeen modelled on the concrete section centroid.

Where specified, the eccentricity is measured from the top feccentricity of zero will therefore be applied at the top face,unspecified eccentricity, which will be applied at the concret

Prestress forces may either be specified by entering a prestthe prestress force and eccentricity as an external force.

Where the area of prestressing strand is included in the reinlosses deducted, since the strain in the strand is accounted

The "Redraw Section" button on the input sheet will draw th(in black) and prestressed reinforcement (in red). The conc

Where voids are specified, B1 and B2 are the external concB4 are the top and bottom width of the void.

The void dimensions are required for plotting purposes only.the width of concrete for each layer, with void dimensions e


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SectionsVer: 1.04 29-May-08

Usage

Quartic(A, B, C, D, E, Dt, Optional output index)

cubic(A, B, C)

Quadratic(A, B, C, Optional output index)

utput.

f Out_Index.

after selecting the number of rows of output required.

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".

lysis of reinforced or prestressed concrete sections,rties for the reinforcement and concrete in compression.

be downloaded from:

mm, stresses in MPa (default), any other number for any

r instance to return the stress in the bottom layer of


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ectangular or trapezoidal layers

om the top or compressive face.

, positive upwards.

d to be applied at the centroid of the concrete section. Thisout adjustment, assuming that the frame elements have

ace of the concrete. An axial load with a specifiednd will give different results to the same axial load withcentroid.

ess force per strand for each layer of strand, or by entering

forcement list, the prestress force should not have elasticfor in the analysis.

concrete section to scale, including passive reinforcementete compression zone is shaded blue.

rete dimensions (top and bottom of each layer), and B3 and

The same numerical results may be obtained by enteringtered as zero or blank.


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Elastic Analysis of Reinforced and Prestressed Sections

Applied loads

Mom Axial Eccentricity

kN kN m

3.00E+03

Depth of Neutral Axis #MACRO? mm

Tension face #MACRO? #MACRO?

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

100 100.0 100.0 32000


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Reinforcement and prestress

Depth Dia No Es Side Cover

75.00 20 10 200000 30

1600.00 20 12 100 30

1750.00 20 12 100 30

Prestressforce/Strand


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Elastic OutputElastic(conc, reo, momin, axin, Optional [eccentric, Out_Index, Units])

Ranges Concrete 'Elastic1 Input'.A21:G21Reinforcement 'Elastic1 Input'.I21:N23

1 2Stress, MPa Strain, m^-1 Force,1 Compression face #MACRO? #MACRO? Concrete2 Compression steel #MACRO? #MACRO? Passive Steel3 Tension Steel #MACRO? #MACRO?Prestress4 Tension face #MACRO? #MACRO? Applied axial

5 Location of tension face #MACRO? #MACRO?6

78

9

101112


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output column index, Out

3 4kN Moment, kNm#MACRO? Concrete #MACRO?#MACRO? Passive Steel #MACRO?#MACRO? Prestress #MACRO?#MACRO? Moment due to axial #MACRO?

Applied moment #MACRO?Prestress eccentricity #MACRO?


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_index

5 6Depth to NA etc Steel by layer StressY #MACRO?Compression laye #MACRO?Acomp #MACRO? to #MACRO?QNA #MACRO? Tension layer #MACRO?Ina #MACRO? #MACRO?Eccentricity reaction force from comp. fa #MACRO?Total passive forc #MACRO?Eccentricity applied force from comp. fac #MACRO?Total prestress fo #MACRO?Depth centroid concrete section #MACRO? #MACRO?Depth centroid reinforcement #MACRO?Depth centroid full composite section #MACRO?

Depth centroid cracked composite sectio #MACRO?I reinforcement #MACRO?#MACRO?


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7Force#MACRO?#MACRO?#MACRO?#MACRO?#MACRO?#MACRO?#MACRO?#MACRO?#MACRO?


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RLayers

1: Es #MACRO? #MACRO?

2: Layer Area #MACRO? #MACRO?

3: Cumulative area #MACRO? #MACRO?

4: Transformed layer area in ten #MACRO? #MACRO?

5: Cumulative area in tension #MACRO? #MACRO?

6: Cumulative first MofA about to #MACRO? #MACRO?

' Find layer and adjusted total transformed 7: Transformed layer area in co #MACRO? #MACRO?

' for NA down to current layer 8: Cumulative transformed area i #MACRO? #MACRO?

9: Cumulative transformed first #MACRO? #MACRO?

10: Layer Depth #MACRO? #MACRO?

11: Cumulative Centroid depth #MACRO? #MACRO?

12: Rsum1 tension #MACRO? #MACRO?

13: Rsum2 tension #MACRO? #MACRO?

14: Rsum1 compression to NA #MACRO? #MACRO?

15: Rsum2 compression to NA #MACRO? #MACRO?

16: I about steel centroid #MACRO? #MACRO?

Layers1 Layer thickness #MACRO? #MACRO?

2 Transformed B1 #MACRO? #MACRO?

3 Transformed B2 #MACRO? #MACRO?

4 Transformed K #MACRO? #MACRO?

5 Transformed layer area #MACRO? #MACRO?

6 Cumulative area #MACRO? #MACRO?

7 Layer centroid height from botto #MACRO? #MACRO?

8 Composite conc. 1st moment of #MACRO? #MACRO?

9 Height of composite concrete ce #MACRO? #MACRO?

10 Depth of bottom of layer #MACRO? #MACRO?

11 Layer second moment of area a #MACRO? #MACRO?

12 Layer second moment of area a #MACRO? #MACRO?13 Composite concrete second mo #MACRO? #MACRO?

14-18: Composite transformed properties Area #MACRO? #MACRO?

15 First moment of area about top #MACRO? #MACRO?

16 Depth of centroid #MACRO? #MACRO?

17 First moment of area about botto #MACRO? #MACRO?

18 Second moment of area about b #MACRO? #MACRO?

19 I reinforcement in tension #MACRO? #MACRO?

XA

NA within section Full compression Full tension

1 Y Y Y

2 Qna Qna Qna

3 Ina Ina Ina4 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

11 DRefComp DRefComp DRefComp

12 a


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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 Double

Dim 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 DoubleDim 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


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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 If

For 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) + Axs0Next 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)

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)


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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 = layers(i, 1) Then Ar = Rlayers(j, 1) Else Ar = Rlayers(j, 2)

' Else' Ar = Rlayers(j, 2)

' End If

' Is1 = reo(j, 1) * Ar * 2 + Is1

' Is0 = reo(j, 1) ^ 2 * Ar + Is0

' Axs1 = Ar * (E_2 - reo(j, 1)) + Axs1

' Axs0 = Ar * reo(j, 1) + Axs0

' Next j

' XCoeff(3, 4) = -Is1


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' XCoeff(3, 5) = Is0

' XCoeff(6, 4) = -Axs1

' XCoeff(6, 5) = Axs0 * E_2

' If i > 0 Then

If NALayer 0 Then

Kb = (B2b - Bb) / DL

Dct = 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

Kb = 0

End If

Qa = -Kb / 12

Qb = -Bb / 6 + Kb / 6 * (Dt - E_2)

Qc = -Bb * E_2 / 2 + Kb * Dt * E_2 / 2Qd = 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)


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' 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

' 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


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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 = 0

For 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 numreoIf reo(j, 1) >= X Then Ar = rlayers(j, 1) Else Ar = rlayers(j, 2)

Ixs = Ar * (dsc - reo(j, 1)) ^ 2 + Ixs

Next j

out2(17) = Ixs

'Find area and centroid of concrete compression zone

If X = Dbase Then

Acc = At

Dcc = DctDcct = (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 * DL

Acc = 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 centroid


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Dcct = (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 + Axs1

out2(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) = Qcout2(21) = Qd

out2(22) = Qe

endfunc:

out2(1) = X

FindNA = XEnd 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 tensionEut = -Dcr

'Load eccentricity for uniform compression

Euc = -CompDrct

If axin 0 Then

E_1 = momin / axin

E_2 = E_1 - (layers(llayer, 9) - CompDrct)

End If


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' 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

Else

If 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

CFOut(8) = DcgCFOut(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, 8) = layers(llayer - i + 1, 8)TempLayers(i, 9) = Depth - layers(llayer - i + 1, 9)



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


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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


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' 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)

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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#MACRO? #MACRO? #MACRO?
















#MACRO? #MACRO? #MACRO? #MACRO?











#MACRO? #MACRO? #MACRO? #MACRO?#MACRO? #MACRO? #MACRO? #MACRO?







#MACRO?

#MACRO?

#MACRO?#MACRO?

#MACRO?

#MACRO?

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#MACRO?

#MACRO?


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#MACRO?

#MACRO?

#MACRO?

#MACRO?

#MACRO?

#MACRO?

Renumber1 1 1: Depth of bottom of l

2 2 2: Layer area

3 3 3: Layer centrod depth

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 m

10 10 10: Cumulative transf

11 11 11: Total transformed

12 12 12: I/Q13 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

21

22

23

24

25

constant

constant

constant


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ayer

from top of layer

yer

base to layer

centroid to layer

r

onemt of area about base

ormed 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

15 153.6 239.8

20 239.8 316.1

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

30 447.2 385.2

25 385.2 316.120 316.1 239.8

15 239.8 153.6

10 153.6 0

Super T pretensioned bridge girder

Concrete Void

Depth B1 B2 B3 B4 Ec

25 2380.0 2380.0 866.3 866.3 3200050 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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50.00 20 1 200000 30

83.49 20 2 30

175.00 20 2 30

300.00 20 2 30

425.00 20 2 30

516.51 20 2 30

550.00 20 1 30



50.00 20 10 200000 301600.00 20 12 100 30

1750.00 20 12 100 30




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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

Required references:

Visual BasiC:\Program Files\Common Files\Microsoft Shared\VBA\VBA6\VBE6.DLL

Microsoft EC:\Program Files\Microsoft Office\Office12\EXCEL.EXE

Microsoft FC:\Windows\system32\FM20.DLL

Microsoft C:\Program Files\Common Files\Microsoft Shared\OFFICE12\MSO.DLL

Revision History

Current Version 1.04 29-May-08

Rev Date By Description

1.00 29-May-08 DAJ First release

1.01 31-May-08 DAJ Plot routine modified to work with Release 2000 - 2003

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.

1.04 7-Jun-08 DAJ DLL check removed (required "trust access to VBA project" to be set)

This program is free software provided for demonstration purposes only; you can copit provided that it is not changed in any way, other than the entry of data in unprotected


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and redistributedata input cells.

Documents

Beam Elastic Analysis of Reinforced and Prestressed Sections