ACES PSC Design Module V{VERSION}:   Run date:  {DATE}
-------------------------------------------------------------------------------------------------
Heading:   {PROJECT}
Job Name: {JOBNAME}
Designer:  {DESIGNER}

Comments: {COMMENT1}

Units:    mm, microstrain, kN, kN.m, MPa

Design Code:   {CODE} {DEC 0}
-------------------------------------------------------------------------------------------------

SECTION:   {Sectnum} ({SecName$})

 

Distance (x) of section from the first node = {x}  mm

 

   

 

 

 

 

 

 

PRESTRESS LOSSES

 

Initial jacking force (Pj)

=

{Pj}

   

kN {DEC 3}

 

Jacking force factor (Jf)

=

{Jf}

 

 

 

 

 

 

 

 

Loss due to Steam Relaxation (default based on Transport SA method)

 

 

 

 

 

 

 

 

 

The steam relaxation factor (k5) is the larger of 0.0 or:

 

     The maximum of:  k5a = 1 + (Jf - 0.7)*0.5/0.1

=

{k5a}

 

 

     and:  k5b = (Jf-0.4)/0.3

=

{k5b}

 

 

 

 

 

 

 

 

Steam relaxation factor (k5)

=

{k5}

 

 

 

Loss due to relaxation  (Lsrl = 0.1*k5/1.5)

=

{Lsrl}

 

{DEC 1}

 

 

 

 

 

 

Loss in PS due to relaxation  (Prl = - Lsrl*Pj)

=

{Prl}

 

kN

 

Loss as a proportion of Pj  (Lsr = - 100*Lsrl)

=

{Lsr}

 

%   {DEC 0}

 

PS force remaining  (Pjr = Pj + Prl)

=

{Pjr}

 

kN

 

 

 

 

 

 

Elastic Deformation Loss

 

 

 

 

 

 

 

 

 

Area of a single strand (Aps)

=

{Aps}

 

mm^2

 

Area of bonded PS steel (Ap = Nbbars*Aps)

=

{Ap}

 

mm^2

 

 

 

 

 

 

Mean Young's Modulus of girder concrete (Egmt)

=

{Egmt}

 

MPa 

 

Young's Modulus of stressing steel (Ep)  

=

{Ep}

 

MPa

 

Area of girder (Ag)

=

{Ag}

 

mm^2  {EXP 4}

 

Moment of inertia of girder (Ig)

=

  {Ig}

 

mm^4 {DEC 0}

 

Dist between CG girder and CG of strands (e)

=

{e}

 

mm 

 

Moment due to girder self-weight (Msw)

=

{Msw}

 

kN.m 

 

 

 

 

 

 

Stress at CG of strand group:

 

 

{DEC 2}

 

 

 

 

 

 

 fcgs = - Pjr*1000*(1/Ag+e^2/Ig)+Msw*10^6*e/Ig  

=

{fcgs}

 

MPa {DEC 1}

 

 

 

 

 

 

Elastic deformation loss:

 

  Pelastic = fcgs*Ep*Ap/(Egmt*1000)

=

{Pelastic}

 

kN.m 

 

Loss as a proportion of Pj (Ledl = - Pelastic*100/Pj)

=

{Ledl}

 

%  {DEC 0}

 

 

 

 

 

 

PS force at transfer (Pt = Pjr + Pelastic)

=

{Pt}

 

kN {DEC 1}

 

PS at transfer as a proportion of Pj (Ltr = Pt*100/Pj)

=

{Ltr}

 

%

 

 

 

 

 

 

Shrinkage Loss

 

 

{DEC 0}

 

 

Aggregate source location:

 

    {AgSrce$}

 

Bridge environment:

 

    {Environ$}

 

 

 

 

 

 

 

Girder strength  (fcg)

=

{f`cg}

 

MPa

 

Hypothetical thickness  (th = At/(Gp + 0.5*Vp)))

=

{th}

 

mm 

 

 

 

 

{DEC 2}

 

Factor a1  (fctra1#4)

=

 {fctra1#4}

 

(Figure 3.1.7.2)  {DEC 0}

 

Basic drying shrinkage strain  (Ecsd.b)

=

{Ecsd.b}

 

{DEC 2}

 

Factor k4   (fctrk4#4)

=

{fctrk4#4}

 

[Clause 3.1.7.2(4)]

 

 

 

 

 

 

Final strain:

 

 

{DEC 0}

 

   Autogenous shrinkage strain  (Ecsc)

=

{E`csc}

 

{DEC 2}

 

   Factor  k1  (fctrk1#4)

=

{fctrk1#4}

 

{DEC 0}

 

   Drying shrinkage strain  (Ecsd4)

=

{Ecsd4}

 

 

 

   Total shrinkage strain  (us = Ecsc + Ecsd4)

=

{us}

 

 

 

 

 

 

 

 

Loss in PS due to shrinkage:

 

   Area of girder (Ag)

=

{Ag}

 

mm^2 

 

   Area of concrete slab (As)

=

{As}

 

mm^2  {DEC 2}

 

   Modular ratio (n = Es/Eg)

=

{n}

 

{DEC 0}

 

   Effective area of composite girder (Ac = n*As + Ag)

=

  {Ac}

 

mm^2

 

   Total area of longitudinal reinforcement (Arl)

=

{Arl}

 

mm^2

 

 

 

 

 

   Pshr = - us*Ep*Ap*10^-9/(1 + 15*Arl/Ac)

=

{Pshr}

 

kN {DEC 1}

 

   Loss as a proportion of Pj: (Lshr = - Pshr*100/Pj)

=

{Lshr}

 

%  {DEC 0}

 

   PS force remaining after shrinkage: (Prs=Pt+Pshr)

=

{Prs}

 

kN

 

 

 

 

 

 

Creep Loss due to Prestress & Self-Weight

 

 

 

 

 

 

 

 

 

Time between when the girder starts to dry and when it is made composite

=

{Tdrygc}

 

 Days

 

 

 

 

 

 

Time at which the girder is first loaded

=

{Tloadg}

 

 Days

 

 

 

 

 

 

28 day girder concrete strength (f'cg)

=

{f`cg}

 

MPa

 

Actual area of composite girder (At)

=

{At}

 

mm^2

 

Exposed girder perimeter (Gp)

=

{Gp}

 

mm

 

Void perimeter (Vp)

=

{Vp}

 

mm

 

Theoretical thickness girder only (th1 = 2*At/Gp)

=

{th1}

 

(Clause 6.1.7) {DEC 3}

 

 

 

 

 

 

Basic concrete creep coefficient  (Coefcr)

=

{Coefcr}

 

(Table 3.1.8.2)

 

Factor  a2  (fctra2#2)

=

{fctra2#2}

 

(Figure 3.1.8.3)

 

Factor  k2  (fctrk2#2)

=

{fctrk2#2}

 

(Clause 3.1.8.3)

 

Factor  k3  (fctrk3#2)

=

{fctrk3#2}

 

(Clause 3.1.8.3)

 

Factor  k4  (fctrk4#5)

=

{fctrk4#5}

 

(Clause 3.1.8.3)

 

Factor  k5  (fctrk5#2)

=

{fctrk5#2}

 

(Clause 3.1.8.3)

 

 

Design creep factor (cc = Coefcr*k2*k3*k4*k5)

=

{Occ}

 

(Clause 3.1.8.3) {DEC 0}

 

 

Moment due to girder self-weight (Msw)

=

{Msw}

 

kN.m

 

Young's Modulus of girder at 28 days (Eg)

=

{Eg}

 

MPa {DEC 1}

 

 

 

 

 

 

Creep stress at CG of strand group:

 

 

 

 

   fcscgs = -Pt*1000(1/Ag + e^2/Ig) + Msw*10^6*e/Ig

=

{fcscgs}

 

MPa

 

 

 

 

 

 

Creep strain at CG of strand group  (Eqn 3.4.3.3):

 

 

{DEC 0}

 

    ucc1 = (10^6*0.8*fcscgs*cc)/Eg

=

{ucc1}

 

 

 

 

 

 

 

Creep Loss due to Deck & Superimposed Loads

 

 

 

 

 

 

 

Deal load moment of concrete slab (Mslab)

=

{Mslab}

 

kN.m

 

Moment due to superimposed loads (Msdl)

=

{Msdl}

 

kN.m {EXP 4}

 

 

Moment of inertia of girder (Ig)

=

  {Ig}

 

mm^4

 

Moment of inertia of composite sectn (Ic)

=

{Ic}

 

mm^4 {DEC 0}

 

Height to centroid of girder (Yb)

=

{Yb}

 

mm

 

Height to centroid of composite sectn (Yc)

=

{Yc}

 

mm

 

Height to CG of strand group (Ycgs)

=

{Ycgs}

 

mm {DEC 2}

 

 

 

 

 

 

Stress at CG due to the concrete deck:

 

 

 

 

   Fdeck = Mslab*10^6*(Yb - Ycgs)/Ig

=

{Fdeck}

 

MPa

 

Stress at CG due to the superimposed DL:

 

   Fsdl = Msdl*10^6*(Yc - Ycgs)/Ic

=

{Fsdl}

 

MPa {DEC 0}

 

 

Time at which all girder creep has finished

=

{Tfinal}

 

 Days

 

Time at which the girder is first loaded

=

{Tloadg}

 

 Days

 

 

 

 

 

 

28 day slab concrete strength (f'cs)

=

{f`cs}

 

MPa {DEC 2}

 

 

 

 

 

 

Basic creep coefficient of slab (Coefcrs)

=

{Coefcrs}

 

[Table 3.1.8.2] {DEC 4}

 

Factor  a2  (fctra2#3)

=

{fctra2#2}

 

[Figure 3.1.8.3]

 

Factor  k2  (fctrk2#3)

=

{fctrk2#2}

 

(Clause 3.1.8.3)

 

Factor  k3  (fctrk3#3)

=

{fctrk3#2}

 

(Clause 3.1.8.3) {DEC 2}

 

Factor  k4  (fctrk4#6)

=

{fctrk4#5}

 

(Clause 3.1.8.3)

 

Factor  k5  (fctrk5#3)

=

{fctrk5#2}

 

(Clause 3.1.8.3)

 

 

Design creep factor  (cc2 = Coefcrs*k2*k3*k4*k5)

=

{Occ2}

 

[Clause 3.1.8.3] {DEC 0}

 

 

 

 

 

 

Creep strain at CG of strand group   (Eqn 3.4.3.3):

 

   ucc2 = cc2*0.8*10^6*(Fdeck+Fsdl)/Eg

=

{ucc2}

 

 

 

 

 

 

 

Total creep strain:

 

   ucc = ucc1 + ucc2

=

{ucc}

 

 

 

 

 

 

 

Summary of Creep Losses

 

 

{DEC 1}

 

 

 

 

 

 

Loss in PS due to creep (Pcreep = ucc*Ep*Ap/10^9)              =

{Pcreep}

 

kN

 

Loss as a proportion of Pj (Lcr = - Pcreep*100/Pj)                 =

{Lcr}

 

%  {DEC 0}

 

 

 

 

 

 

 

Summary of Prestress Losses

 

 

 

 

 

 

 

 

 

 

 

Total remaining prestress force (P = Pt + Pshr + Pcreep)     =

{P}

 

kN  {DEC 1}

 

Total loss of PS as a proportion of Pj (Ltt = P*100/Pj)           =

{Ltt}

 

%

 

 

 

 

 

 

 

 

Force (kN)

    %Pj    

JACKING FORCE (Pj)

{Pj}

100

Loss in PS due to relaxation

{Prl}

{Lsr}

Loss in PS due to elastic deformation

{Pelastic}

{Ledl}

 

 

 

TRANSFER FORCE (Pt)

{Pt}

{Ltr}

Loss in PS due to shrinkage

{Pshr}

{Lshr}

Loss in PS due to creep

{Pcreep}

{Lcr}

 

 

 

FINAL PS FORCE (P)

{P}

{Ltt} {DEC 0}