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

Comments: {COMMENT1}

Units:    mm, kN, kN.m, MPa

Design Code:   {CODE} (Section 8.3) {DEC 0}
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SECTION:   {Sectnum}

 

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

 

 

 

Strand segment number:  {SectSSeg}

 

Passive R/F segment number:  {SectPSeg}

SHEAR & TORSION DESIGN   

 

Note: Some parts of this design are also based on Chapter 13, "Concrete Structures" Warner et. al., (1998)

 

and "Design of Prestressed Concrete", Chapter 5, Gilbert & Mickleborough, 1990

 

 

 

 

 

 

 

Design parameters:

 

 

 

{DEC 1}

 

Ultimate design shear force  (V* = Vult)

=

{Vult}

  

kN

Moment corresponding to V*  (Mvcorr)

=

{Mvcorr}

 

kN.m

Torsion corresponding to V*  (Tvcorr)

=

{Tvcorr}

 

kN.m

 

 

 

 

 

 

 

Ultimate design torsion  (T* = Tult)

=

{Tult}

 

kN.m

 

Moment corresponding to T*  (Mtcorr)

=

{Mtcorr}

 

kN.m

 

Shear force corresponding to T*  (Vtcorr)

=

{Vtcorr}

 

kN

 

Flexural shear capacity  (Vuc)

=

{Vuc}

 

kN

Final design prestress force  (P)

=

{P}

 

kN

 

 

 

28 day girder concrete strength (f'cg)

=

{f'cg}

 

MPa

 

Yield stress of shear & torsion reinforcement (fsysr)

=

{fsysr}

 

MPa

 

 

 

 

 

{DEC 1} 

 

Overall depth of composite section (D)

=

{D}

 

mm

 

Distance of far compr fibre to outer RF bar in tension (do)   

=

{do}

 

mm

 

Web thickness (bw)

=

{bw}

 

mm

 

Effective width of both webs for shear (bv)

=

{bv}

 

mm {DEC 0}

 

 

Area enclosed by median lines of cell walls (Am)

=

  {Am}

 

mm^2

Area of precast girder  (Ag)

=

  {Ag}

 

mm^2 {DEC 2}

 

 

 

 

 

 

 

Capacity reduction factor for shear (Øs = Os in equation list)

=

{Os}

 

 

 

Capacity reduction factor for torsion (Øt = Ot in equation list)

=

{Ot}

 

{EXP 4}

 

 

 

 

 

 

 

Check section for web crushing failure:    ({CODE} - Clause 8.3.3)

 

 

 

 

 

 

 

Torsional modulus (for thin-walled sectns Jt = Am*2*bw)  

=

  {Jt}

 

mm^4 {DEC 1}

 

Ultimate torsional strength   (Tumax = 0.2*f`cg*Jt /10^6)

=

{Tumax}

 

kN.m ({CODE}- Eqn 8.3.3(2))

 

Ultimate shear strength (Vumax = .2*f’cg*2*bw*do/1000+Pv) 

=

{Vumax}

 

kN {DEC 3}

 

 

 

 

 

 

 

Check for web crushing under the combined action of max torsion and corresponding flexural shear

 

    Rtvt = Tult/(Øt*Tumax) + Vtcorr/(Øs*Vumax)

 =

{Rtvt}

 

({CODE}- Eqn 8.3.3(1))

 

Check for web crushing under the combined action of max shear and corresponding torsion

 

    Rtvv = Tvcorr/(Øt*Tumax) + Vult/(Øs*Vumax)

 =

{Rtvv}

 

({CODE}- Eqn 8.3.3(1))

Maximum value of Rtv   (Rtv must be < 1)

 =

{Rtv}

{Tnote1$}

 

 

 

 

 

 

 

Check if torsional reinforcement is required:   ({CODE} Clause 8.3.4)

 

 

 

 

 

{DEC 1}

 

Ultimate strength in pure torsion (Tuc)

 

 

 

 

 

   Tuc = 0.3*(f`cg^0.5)*Jt*(1+10*P*1000/(Ag*f`cg))^0.5/10^6  

=

{Tuc}

 

kN.m ({CODE}- Eqn 8.3.5(1))

 

 

 

 

 

 

 

Allowable unreinforced torsn strength (Tucmax = 0.25*Øt*Tuc)  

=

{Tucmax}

 

kN.m ({CODE}- Eqn 8.3.4(a))

 

Ultimate design torsion (T* = Tult)

=

{Tult}

 

kN.m {DEC 3}

 

                                                        Check if T* > Tucmax

 

 

 

Torsion R/F required if  T* >Tucmax

 

 

 

 

 

Combined torsional/shear ratio (Rtv1)

(Rtv1 = MAX of Rtv1tmax, Rtv1vmax)

 

   Rtv1tmax = Tult /(Øt*Tuc) + Vtcorr/(Øs*Vuc)

 =

{Rtv1tmax}

 

({CODE}- Eqn 8.3.4(2))

 

   Rtv1vmax = Tvcorr /(Øt*Tuc) + Vult/(Øs*Vuc)

 =

{Rtv1vmax}

 

 

Maximum value of Rtv1    (Rtv1 must be < 0.5)

 =

{Rtv1}

{Tnote2$}

 

 

 

 

 

 

Design for torsional reinforcement (combined torsion & shear):

 

 

 

 

 

 

 

(a) Determine required Asw/s ratio

 

 

 

 

 

 

 

 

 

{DEC 1} 

 

     Shear force corresponding to T* (Vtcorr)

=

{Vtcorr}

 

kN

 

     Required design shear strength (Vdesign = Vtcorr / Øs)

=

{Vdesign}

 

kN

 

     Min shear capacity (Vumin = Vuc + 0.6*bv*do/1000)

=

{Vumin}

 

kN ({CODE}- Eqn 8.2.9)

 

                          Check if Vumin > Vdesign

 

 

 

{Tnote4$}

 

{Asvmin$}

 

 

 

 

 

{DEC 2}

 

     Determine 'thetav' for both T* and V*.  Either:

 =

{thetav}

 

 

         30 + 15*(V - Øs*Vumin)/( Øs*Vumax - Øs*Vumin)

 

 (Warner, Eq 13.17)

 

                         or    30 < thetav < 45

 

 

 

 

         Value of thetavc where V = Vtcorr

 =

{thetavc}

         Value of thetavm where V = V*

 =

{thetavm}

   

 

     Determine 'thetat' for both T* and V*.  Either:

 =

{thetat}

 

 

 

         30 + 15*(T - Øt*Tuc)/(Øt*Tumax - Øt*Tuc)

 

(Warner, Eq 13.17)

 

                       or   30 < thetat < 45 

 

 

 

 

        Value of thetatm where T = T*

 =

{thetatm}

        Value of thetatc where T = Tvcorr

 =

{thetatc}

 

 

 

 

 

{DEC 0}

 

        Area of polygon with vertices at centre of bars (Atg)

=

  {Atg}

 

mm^2 ({CODE}- Eqn 8.3.5(b))

 

        Actual area of composite beam (At)

=

  {At}

 

mm^2

 

        Number of closed tie bars per leg (nclty)

 =

{nclty}

 

 

 

        Total number of bars per closed tie (nlegsh = 2*nclty)

 =

{nlegsh}

 

        Tie diameter (TieDiam)

=

{TieDiam}

 

mm

        Area of closed tie (Acltie = TieDaim^2*π/4)

=

  {Acltie}

 

mm^2

        Tie spacing adopted for design (Sdesign)

 =

{ Sdesign }

 

mm

  

 

     Steel area for torsional component (Aswst) is given by:

 

 

 

 

            T*10^6 / (Øt*2*fsysr*Atg/TAN(thetat*π/180) 

 

 

 (Warner, Eq 13.21) {DEC 3}

 

        where for T = T* and corresp ‘thetatm’ then Aswstm

 =

{Aswstm}

 

mm^2/mm 

 

        and for T = Tvcorr and corresp ‘thetatc’    then Aswstc

 =

{Aswstc}

 

mm^2/mm 

 

        Maximum steel area for torsional component Aswst

 =

{Aswst}

 

mm^2/mm per web

   

 

     Steel area for shear component (Aswsv) given by:

 

 

 

 

 

          V*1000/(Øs*nlegsh*fsysr*do/TAN(thetav*π/180)

 

(Warner, Eq 13.23)

 

        where for V = V* and maximum ‘thetav’ then Aswsvm

 =

{Aswsvm}

 

mm^2/mm 

 

        and for V = Vtcorr and corresp ‘thetav’     then Aswsvc

 =

{Aswsvc}

 

mm^2/mm 

 

        Maximum steel area for shear component Aswsv

 =

{Aswsv}

 

mm^2/mm per web

 

                           

 

 

 

 

 

      Total required steel area (Aswons = Aswst + Aswsv)

 =

{Aswons}

 

mm^2/mm  (Warner, Eq 13.26)

 

      Actual total area of torsional reinforcement (Asws)

 =

{Asws}

 

mm^2 / mm

          (Asws = Acltie * Sdesign)

 

 

 

 

 

 

 

(b) Check minimum amount of shear and torsional reinforcement

 

 

 

 

 

 

 

      Minimum ligs required for shear (Aswsmin1)

 

           Aswsmin1 = 0.35*bv/(nlegsh*fsysr)

 =

{Aswsmin1}

 

mm^2/mm  (Warner, Eq 13.32)

 

                           Check if Aswsmin1 > Asws

 

 

 

{Tnote6$}

 

 

 

 

 

 

 

      Larger dimension of closed tie (yt1)

 =

{yt1}

 

mm

 

      Minimum required for torsion (Aswsmin2 = 0.2*yt1/fsysr)

 =

{Aswsmin2}

 

mm^2/mm ({CODE}- Eqn 8.3.7)

 

                          Check if Aswsmin2 > Asws

 

 

 

{Tnote7$}

 

 

 

 

 

 

 

      Torsional strength (Tus) is given by:

 

 

 

{DEC 1}

 

              1E-6*2*fsysr*Asws*Atg / TAN(thetat*π/180)

 

({CODE}- Eqn 8.3.5(2))

 

                         For thetat = thetatm calculated Tus1

=

{Tus1}

 

kN.m

 

                         For thetat = thetatc calculated Tus2

=

{Tus2}

 

kN.m

 

                         and Tus = maximum of Tus1 and Tus2

=

{Tus}

 

kN.m

  

 

      Ultimate strength in pure torsion (Tuc)

=

{Tuc}

 

kN.m

 

                        Check if Tus > Tuc

 

 

 

{Tnote8$}

 

 

 

 

 

 

 

     Shear capacity of steel reinforcement (Vusteel) is:

 

 

 

({CODE}- Eqn 8.2.10) 

 

         nlegsh*Asws*fsysr*do/(TAN(theta*π/180)*1000)

             for theta = thetavm then Vusteel1

=

{Vusteel1}

 

kN

             for theta = thetavc then Vusteel2

=

{Vusteel2}

 

kN

 

             and Vusteel = maximum of Vusteel1 or Vusteel2

=

{Vusteel}

 

kN

  

 

     Vertical component of prestress force (Pv)

=

{Pv}

 

kN {DEC 3}

  

 

     Shear/torsion capacity ratio (Rtv2) is given by:

 

 

 

 

 

         Rtv2 = T/(Øt*Tus) + V/(Øs*Vusteel + Pv)

 

({CODE}- Eqn 8.3.4(b))

 

             for T = T* and V=Vtcorr then Rtv2t

=

{Rtv2t}

 

 

             for T = Tvcorr and V=V* then Rtv2c

=

{Rtv2c}

 

 

             and Rtv2 = maximum of Rtv2t and Rtv2c

=

{Rtv2}

 

 

         Check if combined shear/torsion ratio Rtv2 > 1

 

 

 

{Tnote9$}

 

 

 

 

 

 

 

Design of closed ties for combined shear and torsion:

 

 

 

 

 

 

 

{DEC 1} 

 

     Tie diameter (TieDiam)

=

{TieDiam}

 

mm {DEC 0}

 

     Area of closed ties (Acltie = TieDaim^2*π/4)

=

{Acltie}

 

mm^2 {DEC 1}

 

     Required tie spacing (Stiecalc = Acltie/Asws)

=

{Stiecalc}

 

mm {DEC 0}

 

 

 

 

 

 

 

     Perimeter of polygon associated with Atg (ut)

=

{ut}

 

mm {DEC 1}

 

     Calc'd maximum tie spacing (Sclmax1 = 0.12*ut)

=

{Sclmax1}

 

mm

 

     Max allowable tie spacing (Sclmax = Sclmax1 or 300)

=

{Sclmax}

 

mm

 

 

 

 

 

 

 

     Actual required tie spacing (Sclostie = Stiecalc or Sclmax)

=

{Sclostie}

 

mm

 

     Ratio of area of ties/tie spacing (Raswsy = Acltie/Sclostie)

=

{Raswsy}

 

mm^2/mm

 

 

 

 

 

 

 

Design for additional longitudinal torsional reinforcement:   ({CODE}- Clause 8.3.6)

 

 

 

 

 

 

 

(a) In flexural tensile zone

 

 

 

 

  

 

 

 

 

 

 

     Force additional to the design tensile flexural force is:

 

 

 

{DEC 1}

 

         Ftadd = 0.5*Asw*ut*(1/TAN(π*thetat/180))^2*fsysr/1000 

 

 

             For Asw = Aswstm and thetat = thetatm then Ftadd1

=

{Ftadd1}

 

kN

 

             For Asw = Aswstc and thetat = thetatc then Ftadd2

=

{Ftadd2}

 

kN

 

             and Ftadd = maximum of Ftadd1 and Ftadd2

=

{Ftadd}

 

kN

  

 

     Additional steel area is given by:

 

 

 

 

 

         Atadd = 0.5*Asw*ut*(1/TAN(π*thetat/180))^2

 

{DEC 1}

 

             For Asw = Aswstm and thetat = thetatm then Atadd1

=

{Atadd1}

 

mm^2

 

             For Asw = Aswstc and thetat = thetatc then Atadd2

=

{Atadd2}

 

mm^2

 

             and Atadd = maximum of Atadd1 and Atadd2

=

{Atadd}

 

mm^2

 

 

 

 

 

 

 

     Total tensile force of bars in flex. tensile zone (Ftcapbs)

=

{Ftcapbs}

 

kN

 

     Tensile force contributing to flexural bending (Ftmcorr)

=

{Ftmcorr}

 

kN

              where Ftmcorr = Mtcorr*1000/(0.8*0.9*do)

 

     Residual torsionl tensn force (Ftbdif = Ftcapbs-Ftmcorr)

=

{Ftbdif}

 

kN

 

                    Check if Ftbdif < Ftadd

 

 

 

{Tnote10$}

 

                                   Otherwise:

 

 

 

 

 

     The area of additional tension R/F (Aaddltr) is given by:

 

 

 

 

         Aaddltr = (Ftadd - Ftbdif)*1000/fsysr

=

{Aaddltr}

 

mm^2

 

 

     Bar diameter in tension zone (BarDtens)

=

{BarDtens}

 

mm {DEC 0}

 

     Number of bars in the tension zone (Ntbars)

=

{Ntbars}

 

 

  

 

     Area of bottom reinforcement (Abotreo) given by:

 

 

 

 

 

           Abotreo = π*(BarDtens^2/4)*Ntbars

=

{Abotreo}

 

mm^2 {DEC 1}

 

                    Check if Abotreo > Aaddltr

 

 

 

{Tnote11$}

 

 

 

 

 

 

 

(b) In flexural compression zone

 

 

 

 

 

 

 

 

 

 

 

     Additional force Fcadd in compressn zone  is given either by:

 

 

 

 

 

        Fcadd = Ftadd - Mtcorr*10^6/(0.8*fsysr*0.85*do)

=

{Fcadd0}

 

kN

 

              or = 0 if  Fcadd < 0

=

{Fcadd}

 

kN

 

 

 

 

 

 

 

     Sum of forces in bonded strands above NA (Ftstrand)

=

{Ftstrand}

 

kN {DEC 0}

 

     Area of additional RF in compression zone (Aaddlcr)

 

 

 

 

 

          Aaddlcr  = 0  if   Fcadd < Ftstrand;   OR

=

{Aaddlcr}

 

mm^2/mm

 

          Aaddlcr  =  (Fcadd - Ftstrand)*10^6/(fsysr*Wtf)

 

 

 

 

 

 

 

 

 

 

 

    Spacing of bars in compression zone (Scbars)

=

{Scbars}

 

mm {DEC 0}

 

    Bar diameter in flexural compression zone (BarDcomp)

=

{BarDcomp}

 

mm ({CODE}- Eqn 8.3.6)

 

 

    Area of additional RF in compression zone is given by:

 

 

 

 

 

        Atopreo = π*(BarDcomp^2/4)*(1000/Scbars)  OR

=

{Atopreo}

 

mm^2

 

        Atopreo = 0 if Scbars = 0

 

 

 

 

 

                    Check if Atopreo > Aaddlcr

 

 

 

{Tnote12$}

 

 

 

 

 

{ALRnote$}