ACES PSC Module:  Equations File   (Last modified: 29/04/21)

 This file contains a list of all equations used by the analysis routine.
 When performing an analysis calculations are performed in the strict
 order specified within this file.   New parameters can be defined and
 incorporated into this Equations file but they must first be defined
 in the Parameters List file.   

 EDITING INSTRUCTIONS

 The rules for editing this file and creating and defining equations are
 given below.

 GENERAL RULES

 Since this module mimics a "spreadsheet" equations must be inserted
 into the list in the strict order in which you require them to be
 executed when performing a design.  Consequently they must conform
 to the following rules:

  (1) Variables must first be defined in the Parameters List file.
  (2) Blank lines may be used anywhere to delineate equation blocks.
  (3) Comment lines must be prefaced with the exclamation symbol (!)
  (4) Each equation may be up to 120 characters long.
  (5) Allowable operands are ‘+’, ‘-‘, ‘*’, ‘/’ and ‘^’ (exponential)
  (6) Variables must appear in equations without curly braces.
  (7) Undefined variables will be allocated the value ‘1’.
  (8) Any number of bracket groups may be used in an equation.
  (9) Nested brackets are NOT permitted.
 (10) Spaces in the equation will be ignored.
 (11) Constants may be specified as decimal, integer or exponential
 (12) String (text) variables must contain the '$' symbol (e.g. Note$)
 (13) String variables can only be assigned a maximum of 44 characters
 (14) Comments on an IF statement line must not include the ( ) symbols
 (15) Only equations that lie within the **** boundaries will be used

 ________________________________________________________________________

 DISPLAYING EQUATIONS in the CALCULATION LOG

    .  Equations have been listed sequentially in the equation list to
       follow the logical order in which the design is usually performed.
       Blocks of equations therefore correspond to each tab in the 
       module.  The tabs have been internally numbered 1-9 and the 
       first block of equations in any tab is also given that same 
       number  e.g.   !4   PRESTRESS LOSSES TAB

    .  When the <Check calcs> button at the bottom of a tab is clicked 
       ACES will display the calculation log of all equations associated
       with that tab.

    .  Sub-groups of equations represent various frames and calculation
       buttons within a given tab.  They have been given a label and, 
       where applicable, a letter designating that sub-group  e.g.,
                !7b  SHEAR DESIGN - Flexure shear cracking

    .  Only the equations relating to this block will be displayed in the
       calculation log when the 'View calcs' button on that dialog box 
       (or in that frame) is clicked.

    .  When the <Full calcs> button at the bottom of a tab is clicked
       ACES will display the full calculation log i.e., all equations
       associated with the entire analysis.

    .  A block or sub-block is ended when another tab group number or
       sub-group number is encountered.

    .  !0 signifies that the equations in that block are not to be 
       associated with any button.

    .  !+ signifies that all equations in that block will always be 
       displayed in the log.

    .  !- signifies that equations in that block will not be displayed 
       in the log for subgroups.

 ________________________________________________________________________

 GENERAL FUNCTIONS

    .  The MAX and MIN functions 

       The MAXimising and MINimising functions operate on variables 
       and numbers only - no expressions are allowed.  Variables and
       numbers may be signed  (e.g.  -ve) and up to 20 values only are
       allowed within the brackets.  Note that the ABS and TAN 
       functions CANNOT be included in a MAX/MIN list.

    .  TAN (tangent) function.  This takes the form:
                              var = TAN (Angle)
       'Angle' must be specified in radians.  If it is not already in radians
       then convert it using one of the nine temporary work variables
       (WorkVarX) described in the Parameters List file and the two
       expressions:
                              WorkVarX = (Angle*3.14159/180.)
                              var = TAN (WorkVarX)
       Note that the ABS and TAN functions CANNOT be included together
       on the same line nor in a MAX/MIN list.  In such cases a
       temporary parameter (WorkVarX) must be used to calculate an
       intermediate value.

    .  ABS (absolute value) function.  This takes the form:
                              var = ABS (xxx)
       where 'var' is any parameter in the parameter list and 'xxx' is either
       an optionally signed variable or a number.  It MUST be included
       within normal brackets (as shown).   Note that the ABS and TAN
       functions CANNOT be included together on the same line nor in a
       MAX/MIN list.  In such cases a temporary parameter (WorkVarX)
       must be used to calculate an intermediate value.  Note also that in
       a statement such as var = -ABS (xxx)  var will always be negative.

    .  OUTPUT function

       The function is specified as:  OUTPUT a, b, c, d, .... etc  where a,
       b, c, etc  are parameters that have already been defined and used
       in the equation list.  ACES will simply display the specified values,
       separated by commas.   This can be very useful in LOOP and
       ITERATE functions to track the behaviour of one or more variables.
       A maximum of 20 parameters can be listed in OUTPUT ......

       Note that the display of values will occur even if the NOTRACK
       flag has been invoked (refer to the LOOP function below for a
       description of the NOTRACK flag).


    .  IF function.  There are two types of IF function:

       (1) Single line form:  The function can be expressed either as:
                       IF (xxx > yyy)  expression
                                       or as:
                       IF (xxx > yyy) THEN expression

       (2) Multiple line form.  This must be expressed as:
                       IF (xxx > yyy) THEN
                            expressions1
                       ELSE
                            expressions2
                       END IF

            Both expressions1 and expressions2 may contain up to 20
            statements (or none at all) and the operands can only be:
            ">", "<" or "=".   Values 'xxx' and 'yyy' can only be variables
            or numbers and must be included within normal brackets.
            Comments on an IF statement line must not include embedded
            quotation ( ) symbols.

       NOTE that only the Single line form can be used within a loop


    .  LOOP function.  This takes the form:

            LOOP  i = a, b NOTRACK
                  expression 1
                  function 2
	   ...... etc ......
            END LOOP

       NOTRACK is an optional attribute - it suppresses the tracking and
       display of intermediate results during the looping process.

       If any parameter name within 'expression' contains the character 'i'
       then the 'i' itself will be replaced with the number corresponding 
       to the loop variable 'i'.

       For example, in the calculation of tension forces in PS strands the
       general equation for setting the bar depth (Dpbari) of bars in row
       'i' is:  “Dpbari = D – Ybarri”.  Using the LOOP function, this can
       be performed for bar rows 1 to 8 using three lines of code  viz:

             LOOP  i = 1,8
                   Dpbarri = D - Ybarri
             END LOOP

       Internally ACES will create 8 equations of the form:
       Dpbarr1 = D - Ybarr1, Dpbarr2 = D - Ybarr2, etc.

       A maximum of 20 expressions and/or functions can be included in
       the loop and the loop variables 'a' and 'b' can only lie betweeb 0 
       and 20

      NOTE that only the Single line form of IF can be used within a loop

    .  ITERATE funtion.  This must take the form:

        ITERATE
          .........
        END ITERATE

              or

        ITERATE ON param IN STEPS OF xx  NOTRACK
            ......  (up to twenty statements allowed) .....
        END ITERATION WHEN (param ><= number) OR AFTER n CYCLES

        where:  'param' = any parameter in the parameter list

                         'xx' = the number to be added to 'param' at the
                                 beginning of each cycle. This may be zero 
                                 if the iteration is naturally convergent.

                         ' n' = maximum number of cycles to perform if the
                                 iteration is not converging quickly enough.

       The quantity evaluated, (param ><= number) must be enclosed in
       normal brackets.  Note that the tolerance for equality has been
       set to 1%.  That is, if two numbers are within 1% of each other,
       they are considered equal. 'number' may be a parameter or a 
       number.

       NOTRACK is optional and suppresses the tracking and display of
       intermediate results during the iteration process.

       Example:

         ITERATE ON WorkVar1 IN STEPS OF 5
                WorkVar2 = WorkVar1 * 2.
         END ITERATION WHEN (WorkVar1 = 25) OR AFTER 30 CYCLES

	For notes (TnoteXX) involving the Torsion equations, prepending 
        the string with a ? will display the note in red, prepending 
        with ^ will display in green.

 ________________________________________________________________________

SPECIAL FUNCTIONS

    .  SORT functions:
                       SORT_LOW_HIGH (p1i,p2i,r1i,r2i) NOTRACK
                       SORT_HIGH_LOW (p1i,p2i,r1i,r2i) NOTRACK

       These two functions sort a set of 8 values 'p1i' in ascending and/or
       descending order respectively and place the sorted results into the
       set labelled 'r1i'.  Values in set 'p2i' correspond to those in set 
       'p1i' and are placed into 'r2i' during the sort process.  In effect
       the function sorts the set 'p1i' and its corresponding values 'p2i' 
       and stores the results into 'r1i' and 'r2i'.  Note, however, that 
       'p1i' and 'p2i' must contain 8 values each.

       NOTRACK suppresses the tracking and display of sorted output.
       The functions have been set up specifically for sorting strand and
       passive reinforcement bars and their corresponding forces in order
       to determine if they lie in the tension zone of the section.

       Example:      SORT_LOW_HIGH (Ybarri, Fbari, Dsorti, Fsorti)


    .  COMBINE and SORT functions:

              COMBINE_SORT_LOW_HIGH (p1i, p2i, p3i, p4i, r1i, r2i, r3i)
              COMBINE_SORT_HIGH_LOW (p1i, p2i, p3i, p4i, r1i, r2i, r3i)

       This is similar to the SORT function described above with the
       exception that the 'p1i' and 'p3i' data sets and their corresponding
      'p2i' and 'p4i' sets are first combined before sorting.  The 8 values 
       in each of the individual 'p1i' and 'p3i' sets then appear as 16 
       sorted values in the final 'r1i' set.  

       This function is used to combine the strand table ('p1i'/'p3i') and 
       the passive reinforcement tables into one consolidated table which 
       is then sorted by bar distance ('r1i') and the corresponding bar 
       forces ('r2i').

       The values in 'r3i' are flags that indicate which set the 'r1i' values
       originally came from (either 'p1i' or 'p3i').  A value of 1 indicates 
       'p1i' and 2 indicates 'p3i'.  This information is required by the 
       strain compatibility routine to differentiate a PS strand from a 
       reinforcing bar when calculating the yield strain.

       Example:

       COMBINE_SORT_HIGH_LOW (Dbari,Fbari,Dpfi,Fbfi,Dsti,Fsti,Typei)


    .  LOCATE Ultimate Neutral Axis Depth (dn) Functions:

                     LOCATE_DN_USING_SIMPLIFIED
                                           and
                     LOCATE_DN_USING_STRAIN_COMPATIBILITY

       Both functions use the values returned by the COMBINE_SORT
       functions.  They locate the neutral axis depth (Dcb) and populate
       the bar force table automatically.  Although these functions could
       have been replaced by inserting relevant equations directly into the
       equations file it has been found that the hard-coded routines
       implemented here-in execute much faster.

       The '_SIMPLIFIED' method assumes:  (1) a concrete stress block of
       0.85f'c; and (2) that all bars and strands have yielded (except 
       those in the compression zone, which are excluded from the analysis).

       The '_STRAIN _COMPATIBILITY' method derives the concrete 
       ultimate strain from the parameter 'ucu' which is editable on the
       'Ult M Check' tab but which defaults to 0.003.  The function 
       incrementally adjusts the depth Dcb until the concrete force 
       balances the steel forces.  Bars and strands in the compression 
       zone are excluded and the bar/strand forces are reduced if the
       bar/strand strain is below yield.  (This is commonly refered to as
       'Partial Prestressing').

    .  Select critical combination function:

	      SELECT_CRITICAL_COMBINATIONS

       This function will calculate the results of all SLS and ULS load
       combinations flagged as to be included in the design, determine the 
       critical case, set the indicator flags indicsls and indiculs and copy the
       load factors into LfSLSDL ,LfSLSPS ,LfSLSSDL,LfSLSDSh,LfSLSRcr,LfSLSDSt,
                         LfSLSL,L LfSLSDTe,LfSLSUTr,
                         LfULSDL ,LfULSPS ,LfULSSDL,LfULSDSh,LfULSRcr,LfULSDSt,
                         LfULSL,L LfULSDTe,LfULSUTr,

KNOWN INCONSISTENCIES

    .  Problem with negative sign in front of bracket:


         WorkVar2 = (st-WorkVar1)^2 - (WorkVar1*WorkVar1)   --  will not work,
use:     WorkVar2 = (st-WorkVar1)^2 - WorkVar1*WorkVar1 or
         WorkVar2 = (st-WorkVar1)^2 - 1. * (WorkVar1*WorkVar1)


***************************** Start of Equations *****************************

!-  CALCULATION OF DEFAULT VALUES

IF (f`cg = 0.) THEN f`cg = 50.
IF (Eg = 0.) THEN Eg = 0.043 * (2500.^1.5) * (f`cg^0.5)
IF (f`cs = 0.) THEN f`cs = 40.
IF (Es = 0.) THEN Es = 0.043 * (2400.^1.5) * (f`cs^0.5)
IF (f`cmi = 0.) THEN f`cmi = 40.
IF (Egmi = 0.) THEN Egmi = 0.043 * (2500.^1.5) * (f`cmi^0.5)
IF (f`cmt = 0.) THEN f`cmt = 30.

IF (fcrack = 0.) fcrack = 200.
IF (Cover = 0.) Cover = 30.
IF (Sw = 0.) Sw = 10.547

CODE$ = AS5100-2017

IF (Egmt = 0.) THEN 
    WorkVar1 = 0.8 * f`cg
    Egmt = 0.043 * (2500.^1.5) * (WorkVar1^0.5)
END IF

IF (Esr = 0.) THEN Esr = Ep
IF (ø = 0.) THEN ø = 0.9
IF (O = 0.) THEN O = 0.9
IF (øm= 0.) THEN øm= 0.9
IF (Om= 0.) THEN Om= 0.9
IF (ucu = 0.) THEN ucu = 0.003

!2   SECTION PROPERTIES TAB - Section property calculations

IF (Ws = 0.) THEN Ws = Wtf
IF (Ts = 0.) THEN Ts = 200.
IF (bef = 0.) THEN bef = Ws
IF (Es = 0.) THEN Es = n * Eg

IF (n = 0.) THEN n  =  Es/Eg
Bw2 = 2*bw
bv = Bw2

!  Check auto-recalculate option on composite properties panel (Properties tab)

IF (Zt = 0.) THEN Zt = Ig / (Dg - Yb)
IF (Zb = 0.) THEN Zb = Ig / Yb

IF (CalcProp = 1) THEN
   CalcPrp$ = Composite section properties recalculated by ACES
!  Zt = Ig / (Dg - Yb)
!  Zb = Ig / Yb
   D = Dg + Ts
   As = Ws * Ts
   Ys = Dg + Ts/2.
   Ac = Ag + As*n
   Yc = (Ag * Yb + As*n*Ys) / (Ag + As*n)
   WorkVar1 = Yc - Yb
   WorkVar2 = Ys - Yc
   Ic = Ig + Ag*WorkVar1^2 + n*Ws*Ts^3/12. + n*As*WorkVar2^2
   WorkVar1 = D - Yc
   Zst = Ic / (WorkVar1*n)
   WorkVar1 = Dg - Yc
   Zsb = Ic / (WorkVar1*n)
   Zgt = Ic / (WorkVar1)
   Zgb = Ic / Yc
ELSE
   CalcPrp$ = Composite props NOT recalculated by ACES 
END IF

!  Set overall depth of section to depth of girder if it has not been set yet

 IF (D = 0.) THEN D = Dg

!  Calculation of shear flow at centroid and web/flange

Ybflan = (Yc - Ybf)                                   ! Bottom flange to composite centroid
WorkVar1 = (Yc - Dwf)                                 ! Height of web block
Areac = Abf + WorkVar1 * Bw2                          ! Shear area below composite centroid
Ymomsc = Abf * Ybflan + WorkVar1 * Bw2* WorkVar1 / 2. ! MOI below composite centroid
Ybarc = Ymomsc / Areac                                ! Centroidal offset of section below centroid

IF (CalcProp = 1) THEN 
   Qna = Areac * Ybarc                                   ! Shear flow at centroid point x2
END IF

!  Shear at BD03 point X1

Ybflang = (Yb - Ybf)                                    ! Bottom flange to girder centroid 
WorkVar1 = (Yb - Dwf)                                   ! Height of web block
Areac = Abf + WorkVar1 * Bw2                            ! Shear area below composite centroid
Ymomsc = Abf * Ybflang + WorkVar1 * Bw2* WorkVar1 / 2.  ! MOI below composite centroid
Ybarc = Ymomsc / Areac                                  ! Centroidal offset of section below centroid
!Qnagx1 = Areac * Ybarc                                  ! girder shear flow at girder point x1
!Qnacx1 = Areac * (Ybarc + Yc - Yb)                      ! composite shear flow at girder point x1    

!  Shear at BD03 point X2

Ybflang2 = (Yc - Ybf)                                    ! Bottom flange to girder centroid 
WorkVar1 = (Yc - Dwf)                                    ! Height of web block
Areac = Abf + WorkVar1 * Bw2                             ! Shear area below composite centroid
Ymomsc = Abf * Ybflang2 + WorkVar1 * Bw2* WorkVar1 / 2.  ! MOI below composite centroid
Ybarc = Ymomsc / Areac                                   ! Centroidal offset of section below centroid
WorkVar1 = Yc-Yb                                        
!Qnagx2 = Areac * (Ybarc - WorkVar1)                      ! girder shear flow at girder point x1
!Qnacx2 = Areac * Ybarc                                   ! composite shear flow at girder point x1    

!  Calculations for Web/flange joint (BD03 point Y)

Hwebfl = Dwf - Tbf                                    ! Height of web block
Ywebfl = Yc - Tbf - Hwebfl / 2.                       ! Centroidal offset of web block
Areac = Abf + Hwebfl*Bw2                              ! Area of bottom flange + web block
Ymomsc = Abf*Ybflan + Hwebfl*Bw2*Ywebfl               ! Moment of area of section below centroid
Ybarc = Ymomsc / Areac                                ! Centroidal offset of section below centroid

IF (Qfw = 0) THEN
   Qfw = Areac * (Yc-Dwf)                             ! Shear flow at web/flange interface 
END IF

IF (Qwfg = 0) THEN
   Qfwg= Areac * (Yb-Dwf)                             ! Shear flow at web/flange interface girder only
END IF

IF (Qna < 0.) THEN Qna = -Qna
IF (Qfw < 0.) THEN Qfw = -Qfw


!2a   SECTION PROPERTIES TAB - Non-prestressed reinforcement
!
!     (Zero out total)

Nrfbarst = 0
  Arft     = 0
Ynbarsrf = 0

LOOP  i = 1,20
  Nrfbarst = Nrfbarst + Nrfbrsi               ! Total number of non-ps bars
END LOOP

LOOP  i = 1,20
  WorkVar1 = 3.14159 * BarDtri * BarDtri / 4
  Arfi = WorkVar1 * Nrfbrsi                   ! Area of non-ps bars in each row
END LOOP

LOOP  i = 1,20
  Arft = Arft + Arfi ! Total area of non-ps bars
END LOOP

Arl = Arft                                    ! Total area of passive reinforcement

LOOP  i = 1,20
  YbxNrfi = Yrfi * Arfi                       ! Bar moment of area
END LOOP

LOOP i = 1,20
  Ynbarsrf = Ynbarsrf + YbxNrfi               ! Total of bar moment of area
END LOOP

!
!*************************************************************************
!

!3a  PS ESTIMATES TAB - Differential Shrinkage

!     The calculation of parameters u1 and u2 has been hard-coded into the PSC module.
!     To view these calculations click the <View Calcs> button on the <Shrinkage forces> 
!     dialog box or the <Check Calcs> button on the PS Estimates tab.

At = Ag + Ws * Ts
th = 2*At/(Gp + 0.5*Vp)

IF (th > 2000.) THEN th = 2000.                   ! limit in case GP and Vp are zero

th1 = 2*Ag/Per                                      ! Girder before made composite

IF (th1 > 2000.) THEN th1 = 2000.                 ! limit in case Per is zero

u = u2 - u1
IF (n = 0.) THEN n = Es/Eg
ec = Ys-Yc


!     The calculation of parameter Rcf has been hard-coded into the PSC module.
!     To view these calculations click the <View Calcs> button on the <Shrinkage forces> 
!     dialog box or the <Check Calcs> button on the PS Estimates tab.

Fshr = u*Es*As*1E-9*(1 - 2.71828^-Rcf)/Rcf   ! Calculation of shrinkage force
Mshr = Fshr*ec/1000
SumNA = n*As + Ag
Fsus = Fshr*1000*(1/As - n/SumNA)
Fsug = -Fshr*1000/SumNA

IF (ManLosCa = 0.) THEN 
   fts = Fsus - Mshr*1E6/Zst
   fbs = Fsus - Mshr*1E6/Zsb
   ftg = Fsug - Mshr*1E6/Zgt
   fbg = Fsug + Mshr*1E6/Zgb
END IF


!3b  PS ESTIMATES TAB - Prestress Forces
!
!    Remove debonded bars from the analysis

 Nbarb1 = Nbart1 - Nbard1
 Nbarb2 = Nbart2 - Nbard2
 Nbarb3 = Nbart3 - Nbard3
 Nbarb4 = Nbart4 - Nbard4
 Nbarb5 = Nbart5 - Nbard5
 Nbarb6 = Nbart6 - Nbard6
 Nbarb7 = Nbart7 - Nbard7
 Nbarb8 = Nbart8 - Nbard8
 IncDBar$ = Debonded bars are NOT included in analysis

! Moment of number of bars
YbxNb1 = Ybarr1 * Nbarb1
YbxNb2 = Ybarr2 * Nbarb2
YbxNb3 = Ybarr3 * Nbarb3
YbxNb4 = Ybarr4 * Nbarb4
YbxNb5 = Ybarr5 * Nbarb5
YbxNb6 = Ybarr6 * Nbarb6
YbxNb7 = Ybarr7 * Nbarb7
YbxNb8 = Ybarr8 * Nbarb8

Nbars = 0

LOOP  i = 1,8
  Nbars = Nbars + Nbarti   ! Total number of bars in layers 1 to 8 (Nbart1 to Nbart8)
END LOOP

Ndbars = 0

LOOP  i = 1,8
  Ndbars= Ndbars+ Nbardi   ! Total number of debonded bars in layers 1 to 8
END LOOP

IF (Nbars = 0) THEN
   Ntubbars = 0.
ELSE
   Ntubbars = 100. * Ndbars / Nbars
END IF

Nbbars = 0

LOOP  i = 1,8
  Nbbars= Nbbars+ Nbarbi   ! Find total number of bars (not including debonded bars)
END LOOP

Ynbars = 0

LOOP  i = 1,8
  Ynbars= Ynbars+ YbxNbi   ! Find total moment of area of bars in each layer
END LOOP

!    Calculate Pj; Centroid of bar group (Ycgs); Eccentricity of group (e)

Pj = Nbbars*Pult*Jf

IF (Nbbars = 0) THEN
   Ycgs = 0.
   e = 0.  
ELSE
   Ycgs = Ynbars / Nbbars
   e = Yb - Ycgs
END IF

!
!*************************************************************************
!

!4   PRESTRESS LOSSES TAB - Steam Relaxation Losses

k5a = 1 + (Jf-0.7)*0.5/0.1
k5b = (Jf-0.4)/0.3
WorkVar3 = 0.
k5 = MAX (k5a,k5b,WorkVar3)
Lsrl = 0.1*k5/1.5

IF (Lsr = 0.) THEN Lsr = 100*Lsrl

IF (ManLosCa = 0.) THEN
   Prl = -Lsr*Pj/100.
   Pjr = Pj + Prl
END IF

IF (ManLosCa = 1.0) THEN
   Prl = -Lsr*Pj/100.
   Pjr = Pj + Prl
END IF

IF (ManLosCa = 2.0) THEN
   Lsr = 0.
   Prl = 0.
END IF


!    PRESTRESS LOSSES TAB - Elastic Deformation Losses

Ap = Nbbars * Aps
Apt= Ap
fcgs = -Pjr*1000*(1/Ag + e*e/Ig) + Msw*1E6*e/Ig

IF (ManLosCa = 0.) THEN 
   Pelastic = fcgs*Ep*Ap/(Egmt*1000)
   Ledl = -Pelastic*100/Pj
   Pt = Pjr + Pelastic
   Ltr = Pt*100/Pj
END IF

IF (ManLosCa = 1.0) THEN
   Pelastic = -Ledl*Pj/100.
   Pt = Pjr + Pelastic
   Ltr = Pt*100/Pj
END IF

IF (ManLosCa = 2.0) THEN
   Pelastic = 0.
   Ledl = 0.
   Pt = 0.
   Ltr = 0.
END IF
   

!    PRESTRESS LOSSES TAB - Shrinkage Losses

!    The calculation of parameter us has been hard-coded into the PSC module.
!    To view these calculations click the <Check Calcs> button on the PS 
!    Losses tab.


IF (ManLosCa = 0.) THEN 
   Pshr = -us*Ep*Ap*1E-9/(1 + 15*Arl/Ac)   ! Clause 3.4.3.2
   Lshr = -Pshr*100/Pj
   Prs = Pt + Pshr
END IF

IF (u5 = 0.) THEN u5 = us

IF (ManLosCa = 1.0) THEN
   Pshr = -Lshr*Pj/100.
   Prs = Pt + Pshr
END IF

IF (ManLosCa = 2.0) THEN
   Pshr = 0.
   Lshr = 0.
   Prs = 0.
END IF

!    PRESTRESS LOSSES TAB - Creep loss parameters

Fratio = f`cmt/f`cg

!4e  PRESTRESS LOSSES TAB - Creep losses due to PS + SW

!    The calculation of parameter øcc has been hard-coded into the PSC module.
!    To view these calculations click the <View Calcs> button on the <Creep Losses:
!    Prestress and self weight> dialog box or the <Check Calcs> button on the 
!    PS Losses tab.


Occ = øcc                                            ! HTML Reports cannot handle ø symbol
Occb = øccb                                          ! HTML Reports cannot handle ø symbol
O = ø                                                ! HTML Reports cannot handle ø symbol
fcscgs = -Pt*1000/Ag - Pt*1000*e*e/Ig + Msw*1E6*e/Ig
ucc1 = 1.E6*0.8*fcscgs*øcc/Eg                      !  Eqn 3.4.3.3


!4f  PRESTRESS LOSSES TAB - Creep losses due to Deck + SDL

Fdeck = Mslab*1E6*(Yb-Ycgs)/Ig
Fsdl  = Msdl * 1E6*(Yc-Ycgs)/Ic

!    The calculation of parameter øcc2 has been hard-coded into the PSC module.
!    To view these calculations click the <View Calcs> button on the <Creep Losses:
!    Deck and Superimposed DL> dialog box or the <Check Calcs> button on the 
!    PS Losses tab.

Occ2  = øcc2                                         ! HTML Reports cannot handle ø symbol
ucc2  = 0.8*øcc2*1E6*(Fdeck+Fsdl)/Eg                 !  Eqn 3.4.3.3


!    PRESTRESS LOSSES TAB - Total creep losses

ucc    =  ucc1 + ucc2
IF (ManLosCa = 0.) THEN 
   Pcreep = ucc*Ep*Ap/1E9
   Lcr    =  -Pcreep*100/Pj
   P =  Pt+Pshr+Pcreep
   Ltt    =  P*100/Pj
END IF

IF (ManLosCa = 1.0) THEN
   Pcreep = -Lcr*Pj/100.
   P = Pt+Pshr+Pcreep
   Ltt    =  P*100/Pj
END IF

IF (ManLosCa = 2.0) THEN
   Pcreep = 0.
   Lcr = 0.
   P = Ltt*Pj/100.
END IF
   
TotPSlos = 100. - Ltt
!
!*************************************************************************
!
!5   SERVICEABILITY CHECK - Girder stresses at transfer

     SELECT_CRITICAL_COMBINATIONS


!   Calculate factored moments from crtitical combination

Mswfact = Msw*LfSLSDL
Mslafact = Mslab*LfSLSDL
MSDLfact = Msdl*LfSLSSDL
MLLfact  = Mll*LfSLSLL
MPrefact = Msecpres*LfSLSPS
MDshfact = Mdiffshr*LfSLSDSh
MRCrfact = Mrescree*LfSLSRcr
MDThtfac = Mdiffteh*LfSLSDTe
MDTctfac = Mdifftec*LfSLSDTe
MDSefact = Mdiffset*LfSLSDSt
MUsTfact = Musertra*LfSLSUTr

!   Calculate basic stresses

WorkVar1 = SLScombu
WorkVar2 = ULScombu

f`csat = 0.5*f`cmt^0.5
f`csac = 0.6*f`cmt
f`at   = 0.25*f`cg^0.5
f`ac   = 0.4*f`cg
f`atsv   = 0.5*f`cg^0.5
f`acsv   = 0.6*f`cg
Mpte   = -Pt*e/1000

fgt1   = -Pt*1000/Ag
fgb1   =  fgt1
fgt2   = -Mpte*1E6/Zt
fgb2   =  Mpte*1E6/Zb
fgt3   = -Msw *1E6/Zt
fgb3   =  Msw*1E6/Zb
fgt4   =  fgt1+fgt2+fgt3
fgb4   =  fgb1+fgb2+fgb3


!5b  SERVICEABILITY CHECK - Design moment stresses

Mpe    = -P*e/1000

!  Calculate stresses at various locations on girder section

fgtss1 = -P*1000/Ag
fgbss1 =  fgtss1

fgtss2 = -Mpe*1E6/Zt
fgbss2 =  Mpe*1E6/Zb

fgtss3 = -Mswfact*1E6/Zt
fgbss3 =  Mswfact*1E6/Zb

fgtss4 = -Mslafact*1E6/Zt
fgbss4 =  Mslafact*1E6/Zb

fstss5 = -MSDLfact*1E6/Zst
fsbss5 = -MSDLfact*1E6/Zsb
fgtss5 = -MSDLfact*1E6*SDLf/Zgt
fgbss5 =  MSDLfact*1E6*SDLf/Zgb

fstss6 =  fts
fsbss6 =  fbs
fgtss6 =  ftg
fgbss6 =  fbg

fstss7 = -MLLfact*1E6/Zst
fsbss7 = -MLLfact*1E6/Zsb
fgtss7 = -MLLfact*1E6/Zgt
fgbss7 =  MLLfact*1E6/Zgb

fstmpre = -MPrefact*1E6/Zst
fsbmpre = -MPrefact*1E6/Zsb
fgtmpre = -MPrefact*1E6/Zgt
fgbmpre =  MPrefact*1E6/Zgb

fstmdsh = -MDshfact*1E6/Zst
fsbmdsh = -MDshfact*1E6/Zsb
fgtmdsh = -MDshfact*1E6/Zgt
fgbmdsh =  MDshfact*1E6/Zgb

fstmcre = -MRCrfact*1E6/Zst
fsbmcre = -MRCrfact*1E6/Zsb
fgtmcre = -MRCrfact*1E6/Zgt
fgbmcre =  MRCrfact*1E6/Zgb

!  Ignore input temp stresses if diff temp load case excluded

IF (LfSLSDTe = 0.) THEN
   fstmdth = 0.
   fsbmdth = 0.
   fgtmdth = 0.
   fgbmdth = 0.

   fstmdtc = 0.
   fsbmdtc = 0.
   fgtmdtc = 0.
   fgbmdtc = 0.

   ftemstma = 0.
   ftemsbma = 0.
   ftemgtma = 0.
   ftemgbma = 0.

   ftemstmi = 0.
   ftemsbmi = 0.
   ftemgtmi = 0.
   ftemgbmi = 0.

ELSE

   fstmdth = -MDThtfac*1E6/Zst + ftempsth
   fsbmdth = -MDThtfac*1E6/Zsb + ftempsbh
   fgtmdth = -MDThtfac*1E6/Zgt + ftempgth
   fgbmdth =  MDThtfac*1E6/Zgb + ftempgbh

   fstmdtc = -MDTctfac*1E6/Zst + ftempstc
   fsbmdtc = -MDTctfac*1E6/Zsb + ftempsbc
   fgtmdtc = -MDTctfac*1E6/Zgt + ftempgtc
   fgbmdtc =  MDTctfac*1E6/Zgb + ftempgbc

   ftemstma = MAX(fstmdth,fstmdtc)
   ftemsbma = MAX(fsbmdth,fsbmdtc)
   ftemgtma = MAX(fgtmdth,fgtmdtc)
   ftemgbma = MAX(fgbmdth,fgbmdtc)


   ftemstmi = MIN(fstmdth,fstmdtc)
   ftemsbmi = MIN(fsbmdth,fsbmdtc)
   ftemgtmi = MIN(fgtmdth,fgtmdtc)
   ftemgbmi = MIN(fgbmdth,fgbmdtc)

END IF

   IF (ftemstma < 0.) ftemstma = 0.
   IF (ftemsbma < 0.) ftemsbma = 0.
   IF (ftemgtma < 0.) ftemgtma = 0.
   IF (ftemgbma < 0.) ftemgbma = 0.
   IF (ftemstmi > 0.) ftemstmi = 0.
   IF (ftemsbmi > 0.) ftemsbmi = 0.
   IF (ftemgtmi > 0.) ftemgtmi = 0.
   IF (ftemgbmi > 0.) ftemgbmi = 0.


fstdset = -MDSefact*1E6/Zst
fsbdset = -MDSefact*1E6/Zsb
fgtdset = -MDSefact*1E6/Zgt
fgbdset =  MDSefact*1E6/Zgb

fstmutr = -MUsTfact*1E6/Zst
fsbmutr = -MUsTfact*1E6/Zsb
fgtmutr = -MUsTfact*1E6/Zgt
fgbmutr =  MUsTfact*1E6/Zgb


!    SERVICEABILITY CHECK - Final design DL+SDL+LL+other stresses
!
!    Only add in temperature if it materially increases the stress value


fstll  =  fstss5+fstss6+fstss7+fstmpre+fstmdsh+fstmcre+fstdset+fstmutr

IF (fstll > 0.) THEN
   fstll = fstll + ftemstma
ELSE
   fstll = fstll + ftemstmi
END IF
                             
fsbll  =  fsbss5+fsbss6+fsbss7+fsbmpre+fsbmdsh+fsbmcre+fsbdset+fsbmutr 

IF (fsbll > 0.) THEN
   fsbll = fsbll + ftemsbma
ELSE
   fsbll = fsbll + ftemsbmi
END IF
                            
fgtll  =  fgtss1+fgtss2+fgtss3+fgtss4+fgtss5+fgtss6+fgtss7+fgtmpre+fgtmdsh+fgtmcre+fgtdset+fgtmutr

IF (fgtll > 0.) THEN
    fgtll = fgtll + ftemgtma
ELSE
    fgtll = fgtll + ftemgtmi
END IF


fgbll  =  fgbss1+fgbss2+fgbss3+fgbss4+fgbss5+fgbss6+fgbss7+fgbmpre+fgbmdsh+fgbmcre+fgbdset+fgbmutr 

IF (fgbll > 0.) THEN
    fgbll = fgbll + ftemgbma
ELSE
    fgbll = fgbll + ftemgbmi
END IF


!    SERVICEABILITY CHECK - Determine maximum values

Msdlf = Msdl*LfSLSSDL


!    Calculate maximum stresses

fmaxsllt = MAX (fstll,fsbll,fgtll,fgbll)
IF (fmaxsllt < 0.) THEN fmaxsllt = 0.

fmaxsllc = MIN (fstll,fsbll,fgtll,fgbll)
IF (fmaxsllc > 0.) THEN fmaxsllc = 0.

fmaxssvt = MAX (fstsv,fsbsv,fgtsv,fgbsv)
IF (fmaxssvt < 0.) THEN fmaxssvt = 0.

fmaxssvc = MIN (fstsv,fsbsv,fgtsv,fgbsv)
IF (fmaxssvc > 0.) THEN fmaxssvc = 0.


!5c  SERVICEABILITY CHECK - Cracking Check
!
!   Perform the SLS check using the linear-elastic strain compatibility method
!  
!   Four conditions are analysed:
!
!   - Cracking of PC girder only
!   - PC girder under self weight + slab
!   - Cracking of composite girder (incl selfwt+slab strains in PC girder)
!   - Composite girder serviceability design moment (incl strains from non-comp PC girder)
!
!  This module creates the following parameters
!
!  curvco  , Composite girder curvature
!  curvpc  , Precast curvature
!  fcocrps , Composite cracking strand stress
!  fcocrreo, Composite cracking reinf. stress
!  fcodlps , Composite moment strand stress
!  fcodlreo, Composite moment reinf. stress
!  fcoincps, Composite strand stress increment
!  fcoincre, Composite reinf. stress increment
!  fpccrps , Precast cracking strand stress
!  fpccrreo, Precast cracking reinf. stress
!  fpcdlps , Precast strand stress
!  fpcdlreo, Precast reinf. stress
!  fpcincps, Precast strand stress increment
!  fpcincrf, Precast reinf. stress increment
!  Mcocrack, Composite cracking (decompression) moment
!  Mcodesig, Composite moment
!  Mcoincr , Composite moment increment,
!  Mpccrack, Precast cracking (decompression) moment
!  Mpcdlsla, Precast moment - SW + deck
!  Mpcincr , Precast moment increment
!  ucocrbot, Composite cracking strain at bottom
!  ucocrtop, Composite cracking strain at top
!  ucodlbot, Composite strain at bottom
!  ucodltop, Composite strain at top
!  uconeutr, Composite neutral axis depth
!  upccrbot, Precast cracking strain at bottom
!  upccrtop, Precast cracking strain at top
!  upcdlbot, Precast strain at bottom
!  upcdltop, Precast strain at top
!  upcneutr, Precast neutral axis depth
!
!  Call the routine that performs the SLS analysis using strain compatibility
!  (There is no direct access to this check - it is hard coded into the module)

   ANALYSE_SLS_BY_LINEAR_ELASTIC_STRAIN

 fslscrck = MAX (fcoincps,fcoincre)                 ! Determine max stress increment

!  Set up messages

IF (fslscrck > fcrack) THEN
   CrkNote$ = Crack limit exceeded (fslscrck > fcrack)
ELSE
   CrkNote$ = Crack check OK (fslscrck < fcrack)
END IF
                    
IF (Mcodesig > Mcocrack) THEN
   MslNote$ = SLS design moment exceeds capacity
ELSE
   MslNote$ = SLS moment capacity OK
END IF

IF (SLScase = 0) THEN
   SLScase$ = SLS Crack Check for Live Load
ELSE
   SLScase$ = SLS Crack Check for Special Vehicle Load
END IF


!5d  SERVICEABILITY CHECK - Fatigue (AS5100.5 Cl 2.5)

IF (NumVftge = 0.) NumVftge = 40000
IF (Rfactor = 0) Rfactor = 1

FtgeFact = 1.
IF (Rfactor = 2) FtgeFact = 0.7
IF (Rfactor = 3) FtgeFact = 0.5
IF (Rfactor = 4) FtgeFact = 0.3

Ncycftge = NumVftge * 20000 * FtgeFact / Span^0.5 

IF (SLSok = 1.) THEN  WorkVar1 = 0.

IF (Ncycftge < 500000.) THEN
   Ftgeck$ = ^Fatigue check not needed for road bridges
   FtgueRqd = 0
ELSE
   Ftgeck$ = ?Fatigue check required for road and rail bridges
   FtgueRqd = 1.
END IF

fftgeps = 100.
fftgere = 150.
f`cftge = -0.45 * f`cs
IF (f`cftge < -18.) f`cftge = -18.


!   Calculate the distance from the extreme compression fibre to the centroid
!   of the outermost layer of tensile R/F or tendons.
!   (There is no access to this routine.  It is hard-coded into the programme).

SORT_LOW_HIGH (Ybarri, Fbari, Dsorti, Fsorti)

Ybarmin = Dsort1
do = D - Ybarmin

!  Calculate allowable shear in web limited by compressive strength (Cl 2.5.3)

WorkVar1 = 0.2*f`cg*Bw2*do/1000 + Pv

Vucftge = 0.6 * WorkVar1
Vfatigue = Vftge + Vsw + Vslab + Vsdl

y2 = Yc - Dwf
Mfatigue = Mftge + Msw + Mslab + Msdl
                 
fcslabf = -Mfatigue *1E6 /Zst
fcwebf  = -Mfatigue *y2*1E6/Ic

!  Calculate the stress range in steel
!
Ybarrmax = 0.

LOOP i = 1,8 
   WorkVar2 = 0. 
   IF (Ybarri > 1.) THEN WorkVar2 = Yc - Ybarri 
   IF (WorkVar2 > Ybarrmax) THEN Ybarrmax = WorkVar2 !  Max distance of PS strand from centroid
END LOOP

IF (Ybarrmax > 1.) THEN
   fsrangps = Mftge * 1E6 * Ybarrmax / Ic
ELSE
   fsrangps = 0.
END IF

Yrfmmax = 0.

LOOP i = 1,20 
   WorkVar2 = 0.
   IF (Yrfi > 1.) THEN WorkVar2 = Yc - Yrfi
   IF (WorkVar2 > Yrfmmax) THEN Yrfmmax = WorkVar2 ! Max distance of passive R/F from centroid
END LOOP

IF (Yrfmmax > 1.) THEN
   fsrangre = Mftge * 1E6 * Yrfmmax / Ic
ELSE
   fsrangre = 0.
END IF

Ftgcheck = 0

!  Check all fatigue criteria

IF (fcslabf  < f`cftge) THEN Ftgcheck = 1.
IF (fcwebf   < f`cftge) THEN Ftgcheck = 1.
IF (Vfatigue > Vucftge) THEN Ftgcheck = 1.
IF (fsrangps > fftgeps) THEN Ftgcheck = 1.
IF (fsrangre > fftgere) THEN Ftgcheck = 1.

IF (Ftgcheck = 0.) THEN
   FtgeOK$ = ^Fatigue check OK
ELSE
   FtgeOK$ = ?Fatigue check failed
END IF

!
!*************************************************************************
!
!6b  ULTIMATE MOMENT CHECK - Input data & constants 


Dp = D - Ycgs
IF (fp = 0.) THEN fp = 1000.*Pult/Aps

!   Set parameters to generate stress-strain curve for strain compatibility

IF (fpus = 0.) fpus = 1750.
IF (epus = 0.) epus = 0.035
IF (epyf = 0.) epyf = 0.85
IF (epy  = 0.) epy = epyf*fpus/Ep

fpy = Ep*epy
epe = P/(Nbbars*Aps*Ep)

WorkVar1 = Ap * fp
WorkVar2 = (Ast-Asc) * fsy
k2u = (WorkVar1 + WorkVar2) / (Ws*Dp*f`cs)

v = Srf - 0.007 * (f`cs-28)
fpu = fp * (1-k1u*k2u/v)
fuc = Srf * f`cs

!   Tension forces in steel

LOOP i = 1,8                       
   Dpbari = D - Ybarri             ! Strand depths
END LOOP

LOOP i = 1,20                     
   Dprfi = D - Yrfi                ! Passive reinforcement depths
END LOOP

LOOP i = 1,8                   
   Apbari = Nbarbi * Aps           ! Strand areas
END LOOP

!   Passive reinforcement areas (Arfi) are already calculated

LOOP i = 1,8    NOTRACK            
   Fbari = Apbari * fpu/1000.      ! Forces in strand (for simplified method)
   IF (Fbari = 0.) THEN Dpbari = 0.
END LOOP

LOOP i = 1,20  NOTRACK             
   Fbrfi = Arfi * fsy / 1000.      ! Forces in passive R/F (for simplified method)
   IF (Fbrfi = 0.) THEN Dprfi = 0.
END LOOP

!   LOCATE POSITION of NA (dn) & STEEL/CONCRETE CAPACITIES
!
!   Combine and sort prestressed and non-prestressed R/F in descending order of 
!   distance from the top fibre.  There is no access to this routine (hard-coded).

    COMBINE_SORT_HIGH_LOW (Dpbari,Fbari,Dprfi,Fbrfi,Dsorti,Fsorti,Typei)
!
    NOTRACK

!   Calculate depth to neutral axis (dn) & steel/concrete capacities.
!   Use values stored in Dsorti and Fsorti and base capacity
!   calculations on the type of method selected (see below).
!
!  SIMPLIFIED METHOD - Assumptions
!
!  1. The ultimate concrete stress state is assumed to be
!     rectangular down to a distance of:  gamma*neutral axis depth
!     (viz  gammaDn = v*dn  where v = gamma  and dn = depth to NA)
!
!  2. The ultimate concrete compressive stress Fuc = 0.85F’c
!
!  3. All steel (including passive reinforcement) below the neutral
!     axis is at yield.  Steel in compression is ignored.
!
!  4. The ultimate condition occurs when the compressive force in
!     the concrete balances the tensile forces in the steel.  
!
!
!  STRAIN-COMPATIBILITY METHOD - Assumptions
!
!  1. The ultimate concrete stress state is assumed to be
!     rectangular down to the depth of the equivalent concrete
!     compression block (gamma * Dcb).  Dcb is increased in increments
!     of 0.1mm from an initial value of 0.1mm.
!
!  2. The ultimate concrete strain at the top surface is given by
!     'ucu' (usually 0.003 microstrain).  The strain at each steel level
!     is determined by linear interpolation of a straight line running
!     from 'ucu' and through the neutral axis.  The strain in the compression
!     reinforcement is limited to the maximum allowed for the concrete.
!
!  3. If the interpolated strain exceeds the rupture strain the strand is
!     assumed to be ruptured.  If the interpolated strain exceeds the yield
!     strain for its particular grade of steel, the full yield force for
!     that bar is included.
!
!  4. If the interpolated strain is less that the yield strain, the
!     elastic force at that strain is used.
!
!  5. The total concrete force may include contributions from the slab, 
!     flanges and web depending on the location of gamma*dn.  Ultimate
!     strand stresses are based on the stress-strain interaction diagram.
!
!  6. The ultimate condition occurs when the compressive force in
!     the concrete balances the tensile forces in the steel.  If not,
!     increase the value of Dcb and iterate.
!
!  7. For legacy reasons, two parameters are used to represent the
!     neutral axis depth - Dcb and dn.
!   
!  8. Note that the concrete forces (Fultcs, Fultcf, Fultcw) and their
!     correpsonding moments (Multcs, Multcf, Multcw) are calculated
!     within the LOCATE_DN_.... functions, as is the value of 'gammaDn'.
!     (There is no access to this routine.  It is hard-coded into the module).



IF (CalcDcb = 0) THEN
   DcbNote$ = Based on simplified method
   CalcDcb$ = dn calculated using simplified method
   LOCATE_DN_USING_SIMPLIFIED_METHOD
ELSE
   DcbNote$ = Based on strain compatibility method
   CalcDcb$ = dn calc'd using strain compatibility method
   LOCATE_DN_USING_STRAIN_COMPATIBILITY
END IF

WorkVar1 = Ts + Ttf
DnNote$ = NA in slab

IF (dn > Ts)       THEN DnNote$ = Na in flange
IF (dn > WorkVar1) THEN DnNote$ = NA in Web
IF (CalcDcb = 0)   THEN DnNote$ = Simplified method assumes dn in slab

Ast = 0.

LOOP i = 1,20
   WorkVar1 = Arfi                           
   IF (Dprfi > Dcb) Ast = Ast + WorkVar1   !  Area of passive reinforcement in tension zone
END LOOP

Ftstrand = 0.
Aptensn  = 0.

LOOP i = 1,8
   IF (Fbari = 0.)  Yelds$i =
   IF (Ybarri > Yc) THEN
      Ftstrand = Ftstrand + Fbari  !  Total force in strand
      Aptensn  = Aptensn + Apbari
   END IF
END LOOP

LOOP i = 1,8
   ubari = 0.
   IF (Apbari > 0.) ubari = 1E9 * Fbari / (Ep*Apbari) ! Strain in strand
END LOOP

LOOP i = 1,20
   IF (Fbrfi = 0.)  Yeldr$i =                 ! Blank out yield message
END LOOP

LOOP i = 1,20
   ubrfi = 0.
   IF (Arfi > 0.) ubrfi = 1E9 * Fbrfi / (Esr*Arfi) !  Strain in non-ps bars
END LOOP

!   Calculate area of non-P/S steel in compression

Asc = Arft - Ast
Dcbnok  = Dcb
Dcbnok1 = Dcb
Dcbnok2 = Dcb

!   Sum strand and R/F forces in WorkVar1 and Moment in WorkVar2

Fsteel = 0.
Msteel = 0.

LOOP i = 1,8 NOTRACK
   Fsteel = Fsteel + Fbari  ! Total forces in strand
   Msteel = Msteel + Mbari  ! Total moment due to strand forces
END LOOP

LOOP i = 1,20 NOTRACK
   Fsteel = Fsteel + Fbrfi   ! Add forces in non-ps bars
   Msteel = Msteel + Mbrfi   ! Add moments in non-ps bars
END LOOP

!   Calculate Ku

IF (Fsteel = 0) THEN
   Ku = 0.
   WorkVar3 = 0.
ELSE
   WorkVar3 = 1000.*Msteel/Fsteel
END IF

IF (WorkVar3 = 0) THEN
   Ku = 0
ELSE
   Ku = dn/WorkVar3
END IF

IF (Ku > 0.4) THEN
   KuNote$ = ? Section is over-reinforced (Ku > 0.4)
ELSE
   KuNote$ = ^ Passive reinforcement OK (Ku < 0.4)
END IF

!-----------------------------------------------------------------------------

!6c  ULTIMATE MOMENT CHECK - Final Ultimate Design Moments

! Find maximum of the temperature secondaries

Mdifftma = MAX (Mdiffteh,Mdifftec)

! Apply load factors to moments

UMswfact=Msw*LfULSDL
UMslafac=Mslab*LfULSDL
UMSDLfac=Msdl*LfULSSDL 
UMLLfact=Mll*LfULSLL
UMPrefac=Msecpres*LfULSPS
UMDshfac=Mdiffshr*LfULSDSh
UMRCrfac=Mrescree*LfULSRcr
UMDTmafa=Mdifftma*LfULSDTe
UMDSefac=Mdiffset*LfULSDSt
UMUsTfac=Musertra*LfULSUTr

!  Legacy

Musw = UMswfact
Muslab = UMslafac
Musdl = UMSDLfac
Mull = UMLLfact
Muhvl = UMLLfact

!  Find total sum of moments

Mu1 = UMswfact+UMslafac+UMSDLfac+UMLLfact+UMPrefac+UMDshfac+UMRCrfac+UMDTmafa+UMDSefac+UMUsTfac
Mdesmax = Mu1
Mu2 = Mu1
Mu = Mcs + Mc

øMu =  øm * Mu
Om = øm                          ! HTML report can`t handle ø symbol
OMu  = øMu                       ! HTML report can`t handle ø symbol
Mmax = MAX (Mu1,Mu2)
Mllcap = øMu - Musw - Muslab - Musdl

!  Load rating check for moments  (limit set at 4 for graphing purposes)

IF (Mull = 0) THEN
   Muratll = 0.
ELSE
   Muratll = Mllcap / Mull
END IF

IF (Muratll > 4.) THEN Muratll = 4.

IF (Muhvl= 0) THEN
   Murathvl = 0.
ELSE
   Murathvl = Mllcap / Muhvl
END IF

IF (Murathvl > 4.) THEN Murathvl = 4.

Mrattarg = 1.0

!*******************************************************************************

!7   SHEAR DESIGN - Ultimate Design Parameters

!    (See deletedshear.txt for equations removed)

IF (s = 0.) THEN s = 300.


!7a   Clause 8.2.1.2 Consideration of torsion

Scp = P*1000/Ag 

IF (Ot = 0.) THEN Ot = 0.7  
IF (Os = 0.) THEN Os = 0.7  

pc = uc

WorkVar1 = 0.33 * f`cg^0.5
WorkVar2 = 1 + Scp / WorkVar1
Tcr = WorkVar1 * Acp * Acp * WorkVar2^0.5 * 1E-6 / uc
phiTcr = Tcr * Ot
Tcrmin = 0.25 * phiTcr 

IF (Tdesign > Tcrmin) THEN
   Torsflag = 1
   TorChck$ = ?T* > Tcrmin - torsional effects to be considered
ELSE
   Torsflag = 0
   TorChck$ = ^T* < Tcrmin - no need to check torsional effects
END IF


!   Check torsional requirements for cellular structure (eq. 8.2.1.2(3))
!        (Note that in all cases pc = uc)

Ao = 0.85 * Aoh
a1 = Acp * Acp * 1E-6 / uc
a2 = 2 * Ao * bv * 1E-6

IF (a1 < a2) THEN
   TrCheck$ = ^Torsional reqrmnts for cellular structure satisfied (a1<a2)
ELSE
   TrCheck$ = ?Torsional reqrmnts for cellular structure not satisfied (a1>a2)
END IF

IF (Mexmin < Mdesign) THEN
   MexChck$ = ^OK  (Mexmin < M*)
ELSE
   MexChck$ = ?Mexmin > M* Moment exceeds allowable
END IF


!7b   Vuc shear check (Cl 8.2.4.1 to 8.2.4.4)
!
!  Calculate equivalent shear due to combined shear + torsion (eq 8.2.1.4(5))

!  Calculate default for Dcfcnp if necessary

   WorkVar1 = 0.
   IF (Arft > 0.) WorkVar1 = D - Ynbarsrf / Arft
   IF (WorkVar1 = 0) WorkVar1 = D - Ycgs  
   IF (Dcfcnp < 1) Dcfcnp = WorkVar1

Veq = Vdesign + Tdesign * 1E3 * Dcfcnp / (2. * Ao)   


!  Calculate centroid of tensile steel

Atens = 0.
WorkVar2 = 0.    !  accumulator for area*depth

LOOP i = 1,8
   WorkVar1 = Apbari                           
   IF (Dpbari > Dcb) Atens = Atens + WorkVar1                  !  Area of strand in tension zone
   IF (Dpbari > Dcb) WorkVar2 = WorkVar2 + Dpbari * WorkVar1   !  MOI of strand in tension zone
END LOOP

AbarsFt = 0.                                                   !  AbarsFt gets re-calculated later looping 11->20

LOOP i = 1,20
   WorkVar1 = Arfi                           
   IF (Dprfi > Dcb) AbarsFt = AbarsFt + WorkVar1               !  Area of  all non-ps bars in tension zone
   IF (Dprfi > Dcb) WorkVar2 = WorkVar2 + Dprfi * WorkVar1     ! accumulate MOI of non-ps bars
END LOOP


!  Calculate dv (greater of .72D and .9 dcts)

dcts = WorkVar2 / (Atens + AbarsFt)
WorkVar2 = 0.9 * dcts
WorkVar3 = 0.72 * D
 
dv = MAX (WorkVar2,WorkVar3)
fpo = 0.7 * fp

Act = Areac


   CALCULATE_EX_VALUES 

!   Calculate concrete contribution to ultimate shear strength Vuc (Eq 8.2.4.1)

WorkVar1 = 1. + 1500. * ex
kv = 0.4 / WorkVar1                    				! Eq 8.2.4.2(4)

WorkVar1 = f`cg ^ 0.5
Vuc = kv *  WorkVar1 * bv * dv * 1E-03


!7c  Transverse shear requirements  (Cl 8.2.1.7)

!    Calculate angle of inclined compression

Ov = 29 + 7000 * ex
   				                         	!  Cl 8.2.1.6
Vucap = 0.5 * Os * Vuc

IF (Vucap > Vdesign) THEN
   ShearRF$ = ^V* < Vucap - transverse shear RF not required
ELSE
   ShearRF$ = ?V* > Vucap - transverse shear RF required
END IF

IF (fsysr = 0.) THEN fsysr = 500
IF (Dsr = 0) THEN Dsr = 16
IF (nVbars = 0) nVbars = 2

Asv = nVbars * 3.14 * Dsr * Dsr / 4

WorkVar1 = (Ov*3.14159/180.)
WorkVar2 = TAN (WorkVar1)
WorkVar3 = 1. / WorkVar2       !   cot(Ov)

Vus = (1E-3*Asv * fsysr * dv) /  (s * WorkVar2)


!    Calculate minimum transverse shear reinforcement  (Cl 8.2.1.7)

WorkVar1 = f`cg ^ 0.5

Asvmin = 0.08 * WorkVar1 * bv * s / fsysr

IF (Asv > Asvmin) THEN
   MinShRF$ = ^Asv > Asvmin - transverse shear RF OK
ELSE
   MinShRF$ = ?Asv > Asvmin - insufficient transverse shear RF
END IF

Vu = Vus + Vuc

phiVu = Os * Vu

IF (Veq < phiVu) THEN
   VuNote1$ = ^OK   (Veq < Øt*Vu)
ELSE
   VuNote1$ = ?Veq > Øt*Vu - Insufficient design shear strength
END IF


Vumax = 1E-3 * 0.55 * f`cg * bv * dv * WorkVar3 / (1. + WorkVar3*WorkVar3)

IF (Vumax < Vu) THEN
   VuNote2$ = ?Vu.max < Vu - Web crushing may occur
ELSE
   VuNote2$ = ^Vu < Vu.max  Web crushing will not occur
END IF


!7d   Combined shear and torsion check  (Cl 8.2.4.5)

twmin = Aoh / uh

tw = bv                                                 !  Set wall thickness to web thickness for shear

IF (tw > twmin) THEN
   WebCrsh$ = ^tw > twmin - Wall thickness OK
ELSE
   WebCrsh$ = ?tw < twmin - Insufficient wall thickness 
END IF

WorkVar1 = Vdesign * 1E3 / (bv * dv)
WorkVar2 = Tdesign * 1E6 / (1.7 * tw * Aoh)

Svt = WorkVar1 + WorkVar2

Svmaxx = Os * Vumax * 1E3 / (bv * dv)

IF (Svmaxx > Svt) THEN
   Crush$ =^OK - Web will not crush (Svmaxx > Svt)
ELSE
   Crush$ =?Web will crush (Svmaxx < Svt)
END IF


Asw = Asv / nVbars

Tus = 1E-6 * 2. * Ao * Asw * fsysr * WorkVar3 / s       !   WorkVar3 = cot(Ov)

IF (Tus > Tdesign) THEN
   TusNote$ = ^OK  (Tus > T*)
ELSE
   TusNote$ = ?Torsional reinforcement required  (Tus < T*)
END IF

IF (Tus > Tcr) THEN
   TcrNote$ = ^OK  (Tus > Tcr)
ELSE
   TcrNote$ = ?Tus < Tcr - Torsional reinforcement required
END IF

IF (y1 = 0.) y1 = D - 2.*Cover

ReoRatio = Asw / s
fsyRatio = 0.2 * y1 / fsysr

IF (ReoRatio > fsyRatio) THEN
   ReoRati$ = ^OK  (Asw/s > fsyRatio)
ELSE
   ReoRati$ = ?Asw/s < fsyRatio - Insufficient torsional reinforcement
END IF


!7e  Check transverse reinforcement for combined shear and torsion (Cl 8.2.5.3)

WorkVar1 = (Vdesign - Os*Vuc) * 1E3 * s
WorkVar2 = fsysr * dv * WorkVar3                       !  WorkVar3 = cot(Ov)

Aswsv = WorkVar1 / WorkVar2
IF (Aswsv < 0.) THEN Aswsv = 0.

WorkVar1 = Tdesign * 1E6 * s
WorkVar2 = 2. * Ao * fsysr * WorkVar3

Aswst = WorkVar1 / WorkVar2
IF (Aswst < 0.) THEN Aswst = 0.

Asvtotl = 0.5 * Aswsv + Aswst

IF (Asvtotl > Asvmin) THEN
   Asvmin$ = ^OK  (Asvtotl  > Asvmin)
ELSE
   Asvmin$ = ?Insufficient transverse RF
END IF


!7f   Longituidinal reinforcement on flexural tension side (Cl 8.2.7)

WorkVar1 = Vdesign * 1E3 - 0.5 * Os * 1E3 * Vus
WorkVar2 = 0.45 * Tdesign * 1E6 * uh / (2.*Ao)

WorkVar4 = WorkVar1*WorkVar1 + WorkVar2*WorkVar2

deltaFtd = WorkVar4^0.5 * WorkVar3 * 1E-3

DesignFt = deltaFtd / Os

AbarsFt = 0.

LOOP i = 11,20                                                 ! Loop 11->20 to include only special bars
   WorkVar1 = Arfi                           
   IF (Dprfi > Dcb) AbarsFt = AbarsFt + WorkVar1               ! Area of  extra non-ps bars in tension zone
END LOOP


ActualFt = 1E-3 * fsysr * AbarsFt 

IF (ActualFt = DesignFt) THEN AsNote1$ = ^OK (DesignFt <= ActualFt)

IF (ActualFt > DesignFt) THEN
   AsNote1$ = ^OK (DesignFt <= ActualFt)
ELSE
   AsNote1$ = ?Insufficient long. tensile reinforcement (DesignFt > ActualFt)
END IF


!7g   Longitudinal reinforcement on flexural compression side  (Cl 8.2.8)

Fclong =  deltaFtd

Fc = Fsteel

incFcd = Fclong - Fc

IF (incFcd < 0.) THEN
   AsNote2$ = ^incFcd < 0 - No additional longitudinal compression RF required
ELSE
   AsNote2$ = ?incFcd > 0 - Additional longitudinal compression RF required
END IF

AbarsFc = 0.

LOOP i = 11,20
   WorkVar1 = Arfi                           
   IF (Dprfi < Dcb) AbarsFc = AbarsFc + WorkVar1   	!  Area of  non-PS bars in compression zone
END LOOP


ActualFc = 1E-3 * fsysr * AbarsFc 

IF (ActualFc = incFcd) THEN AsNote3$ = ^Additional longitudinal compression RF OK

IF (ActualFc > incFcd) THEN
   AsNote3$ = ^Additional longitudinal compression RF OK
ELSE
   AsNote3$ = ?Insufficient longitudinal compression RF
END IF

!*******************************************************************
!
!8a   DEFORMATIONS - Axial shortening and transfer hog
!

!     The calculation of parameters øccsc and cu3 has been hard-coded into the PSC module.
!     To view these calculations click the <View Calcs> button on the <Axial shortening of
!     girder prior to erection> dialog box or the <Check Calcs> button on the 
!     Deformations tab.

IF (Lg = 0.) THEN Lg = Span
IF (Ptm = 0.) Ptm = Pt

Xe = Ptm*Lg*1E6/(Ag*Egmt)        ! Elastic shortening

Xs = cu3*Lg/1000                  ! Shortening due to shrinkage

øccsc = øcc

u4 = fcscgs*øccsc*1E6/Egmt
Xc = -u4*Lg/1000                 ! Shortening due to creep

Xa = Xe + Xs + Xc                ! Total axial shortening
Occsc = øccsc                    ! HTML reports can't handle ø symbol

Dsw = 40.*Mswx*Lg*Lg*1E12/(384.*Egmt*Ig)
Hps = -Ptm*1000*e*(Lg*1000)*(Lg*1000)/(8.*Egmt*Ig)
Htr = Dsw + Hps


!8b  DEFORMATIONS - Deflections

Ddeck = 40. * Mslabx * Lg*Lg * 1E12 / (384. * Eg * Ig)
Dsdl  = 40. * Msdlx * Lg*Lg * 1E12 / (384. * Eg * Ic)
Ddl = Ddeck + Dsdl
Dratio = Lg*1000/Dll
Dperm = Lg*1000/Drperm


!8c  DEFORMATIONS - Hog due to creep

!    The calculation of parameter øcc1 has been hard-coded into the PSC module.
!    To view these calculations click the <View Calcs> button on the <Girder hog
!    at installation> dialog box or the <Check Calcs> button on the Deformations tab.


WorkVar5 = Ti                    ! Number of days to installation of girder

Fratio3 = f`cmi/f`cg

Occ1 = øcc1                      ! HTML report can`t handle ø symbol
Occb1= øccb1                     ! HTML report can`t handle ø symbol
Ecc1 = fcgs * øcc1 * 1E6 / Egmi
Pc1 = Ecc1 * Ep * Ap / 1E9


!8d  DEFORMATIONS - Girder hog at installation

WorkVar5 = Ty                    ! Estimated life of girder after installation
Hgic = øcc1*Htr
Hgips = -(Ptm + Pc1)*e*Lg*Lg*1E9/(8*Egmi*Ig)
Hgi = Hgic + Hgips + Dsw


!8e  DEFORMATIONS - Final girder hog after installation

!    The calculation of parameter øcc3 has been hard-coded into the PSC module.
!    To view these calculations click the <View Calcs> button on the <Creep of
!    girder + slab after installation> dialog box or the <Check Calcs> button on
!    the Deformations tab.

th2 = th
Fratio4 = f`cg / f`cg

Occ3 = øcc3                      ! HTML report can`t handle ø symbol
Occb3 = øccb3                    ! HTML report can`t handle ø symbol

Hel = Hgips + Dsw + Ddl
Hgfps = -P*e*Lg*Lg*1E9/(8*Egmt*Ig)
Hgfc = øcc3*Hel
Hgf = Hgfps + Hgfc + Dsw + Ddl