beam design functions

7/27/2019 Beam Design Functions

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[email protected]

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, 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

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?








#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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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


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.

[email protected]

www.interactiveds.com.au

http://newtonexcelbach.wordpress.com/
mailto:[email protected]://www.interactiveds.com.au/http://newtonexcelbach.wordpress.com/http://newtonexcelbach.wordpress.com/http://www.interactiveds.com.au/mailto:[email protected]


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beam design functions

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