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CFVR0908 - Shell reinforcement design according to Eurocode 2

Shell reinforcement design according to Eurocode 2 using the CEB-FIP method.

The model is made up of two square shell elements of 1.0m x 1.0m. The nodes of one side are completely restrained and one of the nodes between both element has its vertical movement restrained (perpendicular to the shells).
The applied loads are horizontal compression loads (-X direction) at the free side and a pressure of 30 kN/m2 on one of the elements.

The reinforcement design method is the CEB-FIP method.

Element types used in the model: SHELL63

Needed CivilFEM Modules:
Geotechnical Module
Bridges and Civil Non Linearities Module
Advanced Prestressed Concrete Module

The example can be launched on an educational license.
KEYWORDS
Shell
Shell Vertex
Reinforced Concrete
Eurocode 2

Model Statistics
Number of elements 2
Number of nodes 6
Number of civil materials 2
Number of cross sections 0
Number of shell vertices 1

Log file: CFVR0908.DAT


   FINISH
  ~CFCLEAR,,1
   NomFile='CFVR0908'
  /TITLE, %NomFile%, Shell reinforcement design according to EC2
! ---------------------------------------------------------------------------------
! Model definition and analysis
! ---------------------------------------------------------------------------------

! Setup
 ~UNITS,SI
 ~CODESEL,EC3-92,EC2-91,EC2-91,,EC8-94
 ~CFCONFG,PLRES   ,SHELL   ,EPSW 
 ~CFCONFG,RESULT,CFSHF,1

/PREP7
! Materials
 ~CFMP,5,LIB,CONCRETE,EC2,C40/50
 ~CFMP,2,LIB,REINF,EC2,S400
! Element types
  ET,2,SHELL63
! Shell Vertex
  t=0.12     ! Thickness
  r=0.03     ! Cover
  th = 0     ! Reinforcement angle
 ~SHLRNF,1,t,5,2,r,0.0,0.0,0.0,0.0,0,th,45
! Beam & Shell property
 ~BMSHPRO,10,SHELL,1,1,1,1,63,,,,Shell property

! Nodes
  N,10,0.0,0.0
  N,20,1.0,0.0
  N,30,2.0,0.0
  N,40,0.0,1.0
  N,50,1.0,1.0
  N,60,2.0,1.0
! Elements
  MAT,5
  REAL,10
  TYPE,2
  EN,100, 10, 20, 50, 40
  EN,200, 20, 30, 60, 50
! Boundary conditions
  D,10,ALL,0.0
  D,40,ALL,0.0
  D,50,UZ,0.0
! Solve
  /SOLU
  F,30,FX,-20000
  F,60,FX,-30000
  SFE,100,2,PRES, ,30000
  SOLVE

/POST1
! ---------------------------------------------------------------------------------
! Forces and moments calculation on nodes of element 100
! ---------------------------------------------------------------------------------
  *DIM,S  ,,6,3,4 ! Stresses(direction,layer,node)
  *DIM,ESF,,8,4   ! Forces & Moments(component,node)   (Tx,Ty,Txy,Mx,My,Mxy,Nx,Ny)
  ESEL,S,ELEM,,100
! Stresses
  SHELL,TOP
  *VGET,S(1,1,1),NODE,10,S,X,,,4
  *VGET,S(1,1,2),NODE,20,S,X,,,4
  *VGET,S(1,1,3),NODE,50,S,X,,,4
  *VGET,S(1,1,4),NODE,40,S,X,,,4
  SHELL,MID
  *VGET,S(1,2,1),NODE,10,S,X,,,4
  *VGET,S(1,2,2),NODE,20,S,X,,,4
  *VGET,S(1,2,3),NODE,50,S,X,,,4
  *VGET,S(1,2,4),NODE,40,S,X,,,4
  SHELL,BOT
  *VGET,S(1,3,1),NODE,10,S,X,,,4
  *VGET,S(1,3,2),NODE,20,S,X,,,4
  *VGET,S(1,3,3),NODE,50,S,X,,,4
  *VGET,S(1,3,4),NODE,40,S,X,,,4
! Forces & Moments
  *DO,I,1,4
    ESF(1,I)=t*(S(1,1,I)+4*S(1,2,I)+S(1,3,I))/6
    ESF(2,I)=t*(S(2,1,I)+4*S(2,2,I)+S(2,3,I))/6
    ESF(3,I)=t*(S(4,1,I)+4*S(4,2,I)+S(4,3,I))/6
    ESF(4,I)=-t**2*(S(1,1,I)-S(1,3,I))/12
    ESF(5,I)=-t**2*(S(2,1,I)-S(2,3,I))/12
    ESF(6,I)=-t**2*(S(4,1,I)-S(4,3,I))/12
    ESF(7,I)=t*(S(6,1,I)+4*S(6,2,I)+S(6,3,I))/6
    ESF(8,I)=t*(S(5,1,I)+4*S(5,2,I)+S(5,3,I))/6
  *ENDDO

! Designed reinforcement
  *DIM,Axi,,4
  *DIM,Ayi,,4
  *DIM,Axs,,4
  *DIM,Ays,,4

I=1
   Axi(I)= 0.000D+00
   Ayi(I)= 0.245D-03
   Axs(I)= 0.330D-03
   Ays(I)= 0.114D-03

I=2
   Axi(I)= 0.194D-03
   Ayi(I)= 0.100D-03
   Axs(I)= 0.000D+00
   Ays(I)= 0.160D-03

I=3
   Axi(I)= 0.000D+00
   Ayi(I)= 0.269D-03
   Axs(I)= 0.115D-03
   Ays(I)= 0.846D-04

I=4
   Axi(I)= 0.255D-04
   Ayi(I)= 0.636D-04
   Axs(I)= 0.000D+00
   Ays(I)= 0.163D-03
  ESEL,ALL

! ---------------------------------------------------------------------------------
! Design with CivilFEM
! ---------------------------------------------------------------------------------
 ~CFSET,,1,1
 ~DIMCON,SHELL,CEB

  ESEL,S,ELEM,,100
! Forces & Moments with CivilFEM
  *DIM,ESF_CF,,8,4   ! Forces & Moments(component,node)   (Tx,Ty,Txy,Mx,My,Mxy,Nx,Ny)
~PLSHFOR,TX
  *GET,ESF_CF(1,1),NODE,10,EPSW
  *GET,ESF_CF(1,2),NODE,20,EPSW
  *GET,ESF_CF(1,3),NODE,50,EPSW
  *GET,ESF_CF(1,4),NODE,40,EPSW
~PLSHFOR,TY
  *GET,ESF_CF(2,1),NODE,10,EPSW
  *GET,ESF_CF(2,2),NODE,20,EPSW
  *GET,ESF_CF(2,3),NODE,50,EPSW
  *GET,ESF_CF(2,4),NODE,40,EPSW
~PLSHFOR,TXY
  *GET,ESF_CF(3,1),NODE,10,EPSW
  *GET,ESF_CF(3,2),NODE,20,EPSW
  *GET,ESF_CF(3,3),NODE,50,EPSW
  *GET,ESF_CF(3,4),NODE,40,EPSW
~PLSHFOR,MX
  *GET,ESF_CF(4,1),NODE,10,EPSW
  *GET,ESF_CF(4,2),NODE,20,EPSW
  *GET,ESF_CF(4,3),NODE,50,EPSW
  *GET,ESF_CF(4,4),NODE,40,EPSW
~PLSHFOR,MY
  *GET,ESF_CF(5,1),NODE,10,EPSW
  *GET,ESF_CF(5,2),NODE,20,EPSW
  *GET,ESF_CF(5,3),NODE,50,EPSW
  *GET,ESF_CF(5,4),NODE,40,EPSW
~PLSHFOR,MXY
  *GET,ESF_CF(6,1),NODE,10,EPSW
  *GET,ESF_CF(6,2),NODE,20,EPSW
  *GET,ESF_CF(6,3),NODE,50,EPSW
  *GET,ESF_CF(6,4),NODE,40,EPSW
~PLSHFOR,NX
  *GET,ESF_CF(7,1),NODE,10,EPSW
  *GET,ESF_CF(7,2),NODE,20,EPSW
  *GET,ESF_CF(7,3),NODE,50,EPSW
  *GET,ESF_CF(7,4),NODE,40,EPSW
~PLSHFOR,NY
  *GET,ESF_CF(8,1),NODE,10,EPSW
  *GET,ESF_CF(8,2),NODE,20,EPSW
  *GET,ESF_CF(8,3),NODE,50,EPSW
  *GET,ESF_CF(8,4),NODE,40,EPSW

! Designed reinforcement obtained with CivilFEM
  *DIM,Axi_CF,,4
  *DIM,Ayi_CF,,4
  *DIM,Axs_CF,,4
  *DIM,Ays_CF,,4
~PLSHCON,ASBX
  *GET,Axi_CF(1),NODE,10,EPSW
  *GET,Axi_CF(2),NODE,20,EPSW
  *GET,Axi_CF(3),NODE,50,EPSW
  *GET,Axi_CF(4),NODE,40,EPSW
~PLSHCON,ASBY
  *GET,Ayi_CF(1),NODE,10,EPSW
  *GET,Ayi_CF(2),NODE,20,EPSW
  *GET,Ayi_CF(3),NODE,50,EPSW
  *GET,Ayi_CF(4),NODE,40,EPSW
~PLSHCON,ASTX
  *GET,Axs_CF(1),NODE,10,EPSW
  *GET,Axs_CF(2),NODE,20,EPSW
  *GET,Axs_CF(3),NODE,50,EPSW
  *GET,Axs_CF(4),NODE,40,EPSW
~PLSHCON,ASTY
  *GET,Ays_CF(1),NODE,10,EPSW
  *GET,Ays_CF(2),NODE,20,EPSW
  *GET,Ays_CF(3),NODE,50,EPSW
  *GET,Ays_CF(4),NODE,40,EPSW

!--------------------------------------------------------------------------------------
! DATA CHECK
!--------------------------------------------------------------------------------------
! Data comparison number
  NComp = 48
  NComp_ch = 0

! Matrix dim.
  *DIM,LABEL,CHAR,Ncomp,1
  *DIM,LABEL_CH,CHAR,Ncomp_ch,1
  *DIM,VALUE,,Ncomp,3
  *DIM,VALUE_CH,CHAR,Ncomp_ch,3
  *DIM,TOLER,,Ncomp,2

! Labels
!--------------------------------------------------------------------------------------
  LABEL( 1) ='TX_I'
  LABEL( 2) ='TX_J'
  LABEL( 3) ='TX_K'
  LABEL( 4) ='TX_L'
  LABEL( 5) ='TY_I'
  LABEL( 6) ='TY_J'
  LABEL( 7) ='TY_K'
  LABEL( 8) ='TY_L'
  LABEL( 9) ='TXY_I'
  LABEL(10) ='TXY_J'
  LABEL(11) ='TXY_K'
  LABEL(12) ='TXY_L'
  LABEL(13) ='MX_I'
  LABEL(14) ='MX_J'
  LABEL(15) ='MX_K'
  LABEL(16) ='MX_L'
  LABEL(17) ='MY_I'
  LABEL(18) ='MY_J'
  LABEL(19) ='MY_K'
  LABEL(20) ='MY_L'
  LABEL(21) ='MXY_I'
  LABEL(22) ='MXY_J'
  LABEL(23) ='MXY_K'
  LABEL(24) ='MXY_L'
  LABEL(25) ='NX_I'
  LABEL(26) ='NX_J'
  LABEL(27) ='NX_K'
  LABEL(28) ='NX_L'
  LABEL(29) ='NY_I'
  LABEL(30) ='NY_J'
  LABEL(31) ='NY_K'
  LABEL(32) ='NY_L'
  LABEL(33) ='ASxi_I'
  LABEL(34) ='ASxi_J'
  LABEL(35) ='ASxi_K'
  LABEL(36) ='ASxi_L'
  LABEL(37) ='ASyi_I'
  LABEL(38) ='ASyi_J'
  LABEL(39) ='ASyi_K'
  LABEL(40) ='ASyi_L'
  LABEL(41) ='ASxs_I'
  LABEL(42) ='ASxs_J'
  LABEL(43) ='ASxs_K'
  LABEL(44) ='ASxs_L'
  LABEL(45) ='ASys_I'
  LABEL(46) ='ASys_J'
  LABEL(47) ='ASys_K'
  LABEL(48) ='ASys_L'

! Correct values
!--------------------------------------------------------------------------------------
  ! Forces & Moments
    *DO,I,1,8
      *DO,J,1,4
        VALUE(4*(I-1)+J,1)= ESF(I,J)
      *ENDDO
    *ENDDO
  ! Reinforcement
    *DO,I,1,4
      VALUE(32+I,1)=Axi(I)
    *ENDDO
    *DO,I,1,4
      VALUE(36+I,1)=Ayi(I)
    *ENDDO
    *DO,I,1,4
      VALUE(40+I,1)=Axs(I)
    *ENDDO
    *DO,I,1,4
      VALUE(44+I,1)=Ays(I)
    *ENDDO

! Obtained values
!--------------------------------------------------------------------------------------
  ! Forces & Moments
    *DO,I,1,8
      *DO,J,1,4
        VALUE(4*(I-1)+J,2)= ESF_CF(I,J)
      *ENDDO
    *ENDDO
  ! Reinforcement
    *DO,I,1,4
      VALUE(32+I,2)=Axi_CF(I)
    *ENDDO
    *DO,I,1,4
      VALUE(36+I,2)=Ayi_CF(I)
    *ENDDO
    *DO,I,1,4
      VALUE(40+I,2)=Axs_CF(I)
    *ENDDO
    *DO,I,1,4
      VALUE(44+I,2)=Ays_CF(I)
    *ENDDO

! Warning and error tolerances
  TOLER( 1, 1)= 1E-01   $   TOLER( 1, 2)= 1E-00
  TOLER( 2, 1)= 1E-01   $   TOLER( 2, 2)= 1E-00
  TOLER( 3, 1)= 1E-02   $   TOLER( 3, 2)= 1E-01
  TOLER( 4, 1)= 1E-02   $   TOLER( 4, 2)= 1E-01
  TOLER( 5, 1)= 1E-02   $   TOLER( 5, 2)= 1E-01
  TOLER( 6, 1)= 1E-02   $   TOLER( 6, 2)= 1E-01
  TOLER( 7, 1)= 1E-02   $   TOLER( 7, 2)= 1E-01
  TOLER( 8, 1)= 1E-02   $   TOLER( 8, 2)= 1E-01
  TOLER( 9, 1)= 1E-11   $   TOLER( 9, 2)= 1E-10
  TOLER(10, 1)= 1E-11   $   TOLER(10, 2)= 1E-10
  TOLER(11, 1)= 1E-11   $   TOLER(11, 2)= 1E-10
  TOLER(12, 1)= 1E-11   $   TOLER(12, 2)= 1E-10
  TOLER(13, 1)= 1E-02   $   TOLER(13, 2)= 1E-01
  TOLER(14, 1)= 1E-03   $   TOLER(14, 2)= 1E-02
  TOLER(15, 1)= 1E-02   $   TOLER(15, 2)= 1E-01
  TOLER(16, 1)= 1E-03   $   TOLER(16, 2)= 1E-02
  TOLER(17, 1)= 1E-02   $   TOLER(17, 2)= 1E-01
  TOLER(18, 1)= 1E-04   $   TOLER(18, 2)= 1E-03
  TOLER(19, 1)= 1E-04   $   TOLER(19, 2)= 1E-03
  TOLER(20, 1)= 1E-03   $   TOLER(20, 2)= 1E-02
  TOLER(21, 1)= 1E-03   $   TOLER(21, 2)= 1E-02
  TOLER(22, 1)= 1E-03   $   TOLER(22, 2)= 1E-02
  TOLER(23, 1)= 1E-03   $   TOLER(23, 2)= 1E-02
  TOLER(24, 1)= 1E-03   $   TOLER(24, 2)= 1E-02
  TOLER(25, 1)= 1E-15   $   TOLER(25, 2)= 1E-14
  TOLER(26, 1)= 1E-15   $   TOLER(26, 2)= 1E-14
  TOLER(27, 1)= 1E-15   $   TOLER(27, 2)= 1E-14
  TOLER(28, 1)= 1E-15   $   TOLER(28, 2)= 1E-14
  TOLER(29, 1)= 1E-15   $   TOLER(29, 2)= 1E-14
  TOLER(30, 1)= 1E-15   $   TOLER(30, 2)= 1E-14
  TOLER(31, 1)= 1E-15   $   TOLER(31, 2)= 1E-14
  TOLER(32, 1)= 1E-15   $   TOLER(32, 2)= 1E-14
  TOLER(33, 1)= 1E-06   $   TOLER(33, 2)= 1E-05
  TOLER(34, 1)= 1E-06   $   TOLER(34, 2)= 1E-05
  TOLER(35, 1)= 1E-06   $   TOLER(35, 2)= 1E-05
  TOLER(36, 1)= 1E-06   $   TOLER(36, 2)= 1E-05
  TOLER(37, 1)= 1E-06   $   TOLER(37, 2)= 1E-05
  TOLER(38, 1)= 1E-06   $   TOLER(38, 2)= 1E-05
  TOLER(39, 1)= 1E-06   $   TOLER(39, 2)= 1E-05
  TOLER(40, 1)= 1E-06   $   TOLER(40, 2)= 1E-05
  TOLER(41, 1)= 1E-06   $   TOLER(41, 2)= 1E-05
  TOLER(42, 1)= 1E-06   $   TOLER(42, 2)= 1E-05
  TOLER(43, 1)= 1E-06   $   TOLER(43, 2)= 1E-05
  TOLER(44, 1)= 1E-06   $   TOLER(44, 2)= 1E-05
  TOLER(45, 1)= 1E-06   $   TOLER(45, 2)= 1E-05
  TOLER(46, 1)= 1E-06   $   TOLER(46, 2)= 1E-05
  TOLER(47, 1)= 1E-06   $   TOLER(47, 2)= 1E-05
  TOLER(48, 1)= 1E-06   $   TOLER(48, 2)= 1E-05

!--------------------------------------------------------------------------------------
! Results comparison
!--------------------------------------------------------------------------------------
  COMPARA.MAC

Results

LabelTargetCivilFEMRatioTolerance
TX_I -20000 -200001.000 1
TX_J -20000 -200001.000 1
TX_K -80000 -800001.000 0.1
TX_L -80000 -800001.000 0.1
TY_I -10000 -100001.000 0.1
TY_J 2857.1 2857.11.000 0.1
TY_K 2857.1 2857.11.000 0.1
TY_L -10000 -100001.000 0.1
TXY_I-7.9349e-009-7.9349e-0091.000 1e-010
TXY_J-7.9279e-009-7.9279e-0091.000 1e-010
TXY_K-7.9349e-009-7.9349e-0091.000 1e-010
TXY_L-7.9349e-009-7.9349e-0091.000 1e-010
MX_I -8639.6 -8639.61.000 0.1
MX_J 3859 38591.000 0.01
MX_K -4309.5 -4309.51.000 0.1
MX_L 2790.8 2790.81.000 0.01
MY_I -2220.4 -2220.41.000 0.1
MY_J 334.36 334.361.000 0.001
MY_K -142.61 -142.611.000 0.001
MY_L 1050.7 1050.71.000 0.01
MXY_I 1357.2 1357.21.000 0.01
MXY_J 2334.7 2334.71.000 0.01
MXY_K 2096.1 2096.11.000 0.01
MXY_L 1118.6 1118.61.000 0.01
NX_I 0 00.000 1e-014
NX_J 0 00.000 1e-014
NX_K 0 00.000 1e-014
NX_L 0 00.000 1e-014
NY_I 0 00.000 1e-014
NY_J 0 00.000 1e-014
NY_K 0 00.000 1e-014
NY_L 0 00.000 1e-014
ASxi_I 0 00.000 1e-005
ASxi_J 0.0001940.000193841.001 1e-005
ASxi_K 0 00.000 1e-005
ASxi_L 2.55e-0052.5494e-0051.000 1e-005
ASyi_I 0.0002450.000245061.000 1e-005
ASyi_J 0.00010.000100031.000 1e-005
ASyi_K 0.0002690.000268861.000 1e-005
ASyi_L 6.36e-0056.3584e-0051.000 1e-005
ASxs_I 0.000330.000330510.999 1e-005
ASxs_J 0 00.000 1e-005
ASxs_K 0.000115 0.00011520.998 1e-005
ASxs_L 0 00.000 1e-005
ASys_I 0.0001140.000114190.998 1e-005
ASys_J 0.000160.000159531.003 1e-005
ASys_K 8.46e-0058.4563e-0051.000 1e-005
ASys_L 0.0001630.000163160.999 1e-005

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