Examples

Sectional Constant Calculation Example

H-Beam (HBeam-400x200x8x13.sec)

Separate calculation depending on whether there is a fillet or not.

Fig. 11. Sectional Constant Calculation for H-Beam

Fig. 11. Sectional Constant Calculation for H-Beam

Rectangular Section with a Hole (Hole.sec)

Fig. 12. Rectangular Section with a Hole

Fig. 12. Rectangular Section with a Hole

Tapered Section (IGrider.sec)

Fig. 13. Tapered Section

Fig. 13. Tapered Section

Composite Section (RCBeam.sec)

Fig. 14. Composite Section

Fig. 14. Composite Section

Singly Reinforced RC Beam

Performed flexural analysis of a rectangular singly reinforced beam with B=280, H=550. The compressive strength of the concrete is 24 MPa, and SD400, 3-D25 rebars were used. For the tensile zone of the concrete, the tensile strength was assumed to be 1/10 of the compressive strength, and a cut-off model was used, which neglects the strength after reaching the tensile strength. The secondary stiffness of the rebar was also ignored.

Fig. 15. Singly Reinforced RC Beam (from Udongyun et al., Reinforced Concrete, 3rd edition, Example 5-10)

Fig. 15. Singly Reinforced RC Beam (from Udongyun et al., Reinforced Concrete, 3rd edition, Example 5-10)

Fig. 16. Execution Overview

Fig. 16. Execution Overview

List. 3. RectRC.sec

*Function, TYPE=MPPCEnv, Name=MPP
 24, 23025, 0.002, 0.004, 24, 0.004

*Function, TYPE=MPPCIE, Name=MPPIE
 MPP, 0.002

*Function, TYPE=MultiLinear, Name=CutOff
 0, 0
 0.0001042, 2.4
 0.0001042, 0

*Material, TYPE=UConcrete, Name=conc
 MPP, MPPIE, 0, 0
 CutOff, Secant

*Material, TYPE=vonMises, Name=rebarByMises
 200000, 0, 0, 0  # E, nu, alpha, density
 400, 0, 0   # yield, H, theta 

*Material, TYPE=USteel, Name=rebar
 200000, 400, 0, 20,18.5,0.15, 0.01,7, 0.08, 0, 0
 # E0, yield, E1, R0, a1, a2, a3, a4, eu, alpha, density

*Section, Type=Beam, Name=RectRC-2D
*Cell, TYPE=Layer,Stack, Mat=conc
 -550/2, 280
 550/2, 280, 55
*Cell, TYPE=Point, Mat=rebar
 1, -225, 0, 1520

*SectionSignal
 conc, 0.0001042, "Concrete Tesile Failure"
 rebar, 0.002, "Rebar Yield"

*SectionAnalysis, Name=RectRC-2D, Section=RectRC-2D, Output=Preselect
 *SectionStep, ExtLoad=0,4e-05,NK, Inc=100

*SectionAnalysis, Name=RectRC-3D, Section=RectRC-3D, Ref=90,0,0, Output=Preselect
 *SectionStep, ExtLoad=0,4e-05,NK, Inc=100

Fig. 17. Moment-Curvature Curve (Unit: N-mm)

Fig. 17. Moment-Curvature Curve (Unit: N-mm)

Fig. 18. Stress-Strain Curve of the Outer Rebar (Unit: N-mm)

Fig. 18. Stress-Strain Curve of the Outer Rebar (Unit: N-mm)

Fig. 19. Stress-Strain Curve of Concrete at the Compressed Edge (Unit: N-mm)

Fig. 19. Stress-Strain Curve of Concrete at the Compressed Edge (Unit: N-mm)

RC Column with Seismic Details

This axial force and flexural analysis was performed for a column cross-section with seismic details. The concrete strength is 24 MPa, and 36-D25 SD300 rebars were used. The confinement pressure of the confined concrete was assumed to be 1.5 MPa, from which the maximum strength (fccp) is calculated to be 30 MPa, and the maximum strain is assumed to be 0.01. The tensile zone of the concrete assumed a strength of 1.826 MPa and a tension cut-off. The secondary stiffness of the rebar was assumed to be 0.01282 of the initial stiffness. The axial force for the analysis was 2000 kN.

Fig. 20. Cross-Section of a Column with Seismic Details (Lee Jaehun, "Seismic Design of Reinforced Concrete Piers", 2000.)

Fig. 20. Cross-Section of a Column with Seismic Details (Lee Jaehun, "Seismic Design of Reinforced Concrete Piers", 2000.)

Fig. 21. Execution Overview

Fig. 21. Execution Overview

List. 4. RCColumn.sec

*Function, TYPE=MPPCEnv, Name=MPPCore
 24, 23025, 0.002, 0.01, 33.07, 0.01

*Function, TYPE=MPPCIE, Name=MPPIECore
 MPPCore, 0.00577917

*Function, TYPE=MultiLinear, Name=CutOffCore
 0, 0
 0.0007926, 1.825
 0.0007926, 0

*Function, TYPE=MPPCEnv, Name=MPPCover
 24, 23025, 0.002, 0.003, 24, 0.006

*Function, TYPE=MPPCIE, Name=MPPIECover
 MPPCover, 0.002

*Function, TYPE=MultiLinear, Name=CutOffCover
 0, 0
 0.0007926, 1.825
 0.0007926, 0

*Material, TYPE=UConcrete, Name=CoreConc
 MPPCore, MPPIECore, 0, 0
 CutOffCore, Secant

*Material, TYPE=UConcrete, Name=CoverConc
 MPPCover, MPPIECover, 0, 0
 CutOffCover, Secant

*Material, TYPE=USteel, Name=Rebar
 200000, 400, 2564, 20,18.5,0.15, 0.01,7, 0.08, 0, 0
 # E0, yield, E1, R0, a1, a2, a3, a4, eu, alpha, density

*Section, Type=Beam, Name=ColSec
*Cell, TYPE=Layer,Circle, Mat=CoreConc
 500, 0, 0, 20
*Cell, TYPE=Layer,Circle, Mat=CoverConc
 600, 500, 0, 4, 20
*Cell, TYPE=Point,Circle, Mat=Rebar
 500, 506.7, 0, 0, 0, 36


*SectionStop
 CoreConc,-0.01,
 Rebar,,0.08

*SectionSignal
 CoreConc, 0.0007926, "Core concrete tensile failure"
 CoverConc, 0.0007926, "Cover concrete tensile failure"
 CoverConc, -0.003, "Cover concrete compressive failure"
 Rebar, 0.002, "Rebar Yield"

*SectionAnalysis, Name=E2, Section=ColSec, Output=Preselect
 *SectionStep, ExtLoad=-2e+06,0,NM, Inc=1
 *SectionStep, ExtLoad=-2e+06,5e-05,NK, Inc=100

*SectionAnalysis, Name=E2-PM, Section=ColSec, Output=Preselect
 *SectionStepPM, MaxDeform=-0.01,3.33333e-05  Inc=1000  PMPoints=50


 *SectionStepPM, MaxDeform=-0.01,0.02/600, Inc=1000, PMPoints=50

Fig. 22. Moment-Curvature Curve from Analysis E2

Fig. 22. Moment-Curvature Curve from Analysis E2

Fig. 23. Stress-Strain Curves at Key Material Points

Fig. 23. Stress-Strain Curves at Key Material Points

Fig. 24. PM Diagram

Fig. 24. PM Diagram

UHPC Beam

Flexural analysis was performed for a UHPC beam member with the shape shown in Fig. 25.

Fig. 25. SC120f Beam Member

Fig. 25. SC120f Beam Member

The material model for UHPC is as shown in Fig. 22, and the various material constants are as follows:

Design Strength: \(\small f_{ck}\) = 120 MPa
Allowable Tensile Strength: \(\small f_{tk}\) = 7 MPa
Modulus of Elasticity: \(\small E_c\) = 40,000 MPa
Characteristic Length: \(\small \frac{L_{eq}}{h_{beam}} = 0.8 \left[ 1 - \frac{1}{(1.05 + 6 \frac{h_{beam}}{l_{ch}})^3} \right]\)

Fig. 26. Stress-Strain Curve of UHPC

Fig. 26. Stress-Strain Curve of UHPC

Fig. 27. Execution Overview

Fig. 27. Execution Overview

List. 5. UL.sec

# UHPC beam
#
# Unit : N-mm
#
# fck = 120 MPa,  fcrk = 5 MPa, ftk = 7 MPa
# phic= 0.91(Compression), 0.8(Tension)
# Ec = 40000 MPa
# wu = 0.3 mm
# Leq = 465.8786 mm

*Function, TYPE=MultiLinear, Name=SC120f-C
 0., 0.
 0.85*0.91*120/40000, 0.85*0.91*120
 0.004, 0.85*0.91*120

*Function, TYPE=MultiLinear, Name=SC120f-T
 0., 0.
 0.8*5/40E3, 0.8*5
 0.8*5/40E3+0.3/465.8786, 0.8*7
 0.8*5/40E3+5.3/465.8786, 0.

*Material, Type=UConcrete, Name=SC120f   
 SC120f-C
 SC120f-T,Secant


# Yield = 400 MPa , zero 2nd moduls, 
*Material, Type=USteel, Name=rebar
 200E3, 400*0.9, 0, 20,18.5,0.15

*SectionStop
 SC120f,-0.004, 
 rebar,-0.12,0.12

# Et = 0. steel   assumed
*Section, TYPE=Beam, Name=section
*Cell, TYPE=Layer,Stack, Mat=SC120f
 -550, 220, ToDirectForm
    0, 220, 55
    0, 120, 0
  450, 120, 45
*Cell, TYPE=Point, Mat=rebar
 1, 450-860, 0, 3421.194 


*SectionAnalysis, Name=UL, Section=section
 *SectionOutput, TYPE=All   
 *SectionStep, ExtLoad=0.,0.00005,NK, Inc=100

Fig. 28. Moment-Curvature Curve of UHPC

Fig. 28. Moment-Curvature Curve of UHPC

RC Beams and Prestressed Beams under Axial Force

For program verification, the analysis of a prestressed beam under axial force, as presented in the textbook by Michael P. Collins et al. (1991), was performed.

Fig. 29. RC Beams and Prestressed Beams under Axial Force (Figure 4-4 from Collins et al.'s 1991 textbook)

Fig. 29. RC Beams and Prestressed Beams under Axial Force (Figure 4-4 from Collins et al.'s 1991 textbook)

Reference

Michael P. Collins, Denis Mitchell (1991), “Prestressed Concrete Structures,” Prentice Hall.

List. 6. P1.sec

# Unit: N-mm

# Verification sample: 
# Prestressed Concrete Structures by Michael P. Collins, and Denis Mitchell, Figure 4-4

## Concrete model
*Function, TYPE=MultiLinear, Name=concC
0.,     0
0.0005, 15.09375
0.001,  25.875
0.0015, 32.34375
0.002,  34.5
0.0025, 32.34375
0.003,  25.875
0.003,    0.

*Function, TYPE=MultiLinear, Name=concT
 0., 0.
 2*0.0005/15.09375, 2.
 2*0.0005/15.09375, 0.

*Material, Type=UConcrete, Name=conc   
 concC
 concT, Secant

## Rebar model   
*Material, Type=vonMises, Name=rebar
 200000. 
 400  # TYPE=Value, yield, H, theta, Kinf, K0, delta

## Tendon model 
*Material, Type=vonMises, Name=tendon
 200000. 
 1655  # TYPE=Value, yield, H, theta, Kinf, K0, delta

## Section A
*Section, TYPE=Beam, Name=memberA
*Cell, TYPE=Layer,Stack Mat=conc
 -254/2, 254
  254/2, 254, 2 
*Cell, TYPE=Point, Mat=rebar
 1, 0., 0., 1600.

## Section B
*Section, TYPE=Beam, Name=memberB
*Cell, TYPE=Layer,Stack, Mat=conc
 -254/2, 254
  254/2, 254, 2 
*Cell, TYPE=Point, Mat=tendon
 1, 0, 0, 395  # id, z, z, A

## Set stop strain 
*SectionStop
 conc,-0.003,
 rebar,-0.12,0.12
 tendon,-0.2,0.2

*SectionSignal
 conc, 0.0001042, "Concrete Tensile Failure"
 rebar, 0.002, "Rebar Yield"

*SectionAnalysis, Name=P1-A-T, Section=memberA
 *SectionStep, ExtLoad=0.003, 0., EM, Inc=100

*SectionAnalysis, Name=P1-A-C, Section=memberA
 *SectionStep, ExtLoad=-0.003, 0., EM, Inc=100

*SectionAnalysis, Name=P1-B-T, Section=memberB
 *SectionStep, ExtLoad=0., 0., NM, Inc=10
   InitialStress, 2, 1240  # pretension
 *SectionStep, ExtLoad=0.003, 0., EM, Inc=50

*SectionAnalysis, Name=P1-B-C, Section=memberB
 *SectionStep, ExtLoad=0., 0., NM, Inc=1
   InitialStress, 2, 1240  # pretension
 *SectionStep, ExtLoad=-0.003, 0., EM, Inc=50

## Section B - post 
#*SectionAnalysis, Name=P1-B-TPost, Section=memberB
# *SectionStep, ExtLoad=0., 0., NM, Inc=10
#   Stress, 2, 1240  # posttension
# *SectionStep, ExtLoad=0.003, 0., EM, Inc=50

PHC Pile

The PHC pile is a prestressed hollow circular member. In this case, an analysis was conducted on a member of type A with a diameter of 500 mm. According to the KS standard, it is required that the crack and failure moments must exceed a certain level through bending tests under no axial force and under three stages of applied axial force. Here, an analysis of the failure moment was conducted.

Name	Axial Force (kN)	Failure Moment (KS Standard, kN·m)	Failure Moment (Analysis, kN·m)
N0	0	155	169.4
N1	882.9	304.1	328
N2	1766	421.8	454.4
N3	2649	496.4	536.8

Fig. 31. PHC500A

Fig. 31. PHC500A

Fig. 32. PM Analysis Result of PHC500A

Fig. 32. PM Analysis Result of PHC500A

List. 7. PHC500A.sec

# K500E
# Unit : N-mm


#################################################
# Material model data (UNIT = N-mm)
#################################################
# KDS-C80        : KDS's 80 MPa concrete model for nonlinear analysis
# KDS-C80-LST-EX : KDS's 80 MPa concrete model for sectional analysis on extreme event state (phi=1., no tension)
# KDS-C80-LST-UL : KDS's 80 MPa concrete model for sectional analysis on ultimate state (phi=0.65, no tension)
# SD600L    : SD600 Rebar less than D22 for nonlinear analysis or extreme event state  (phi = 1.)
# SD600L-0.9 : SD600 Rebar less than D22 for nonlinear analysis or ultimate event state (phi = 0.9)
#################################################


#################################################
# KDS-C80N : KDS's 80 MPa concrete model for nonlinear analysis
*Function, Type=FIBCEnv, Name=KDS-C80-C
 86., 41270.9464, 0.00279  # fcm, Ec, eco

*Function, TYPE=MultiLinear, Name=KDS-C80-T
 0., 0.
 5.845031943/41270.9464, 5.845031943
 5.845031943/41270.9464, 0.

*Material, Type=UConcrete, Name=KDS-C80    
 KDS-C80-C,PlasticUnloading, ,KDS-C80-T,SecantUnloading


#################################################
# KDS-C80-LST-EX : KDS's 80 MPa concrete model for sectional analysis on extreme event state (phi=1., no tension)
*Function, TYPE=ParabolaCEnv, Name=KDS-C80-LST-EX-C
 0.85*80., 1.22, 0.0024, 0.0029  # fco, n, eco, ecu

*Material, Type=UConcrete, Name=KDS-C80-LST-EX
 KDS-C80-LST-EX-C,PlasticUnloading 


#################################################
# KDS-C80U : KDS's 80 MPa concrete model for sectional analysis on ultimate state (phi=0.65)
*Function, TYPE=ParabolaCEnv, Name=KDS-C80-LST-UL-C
 0.65*0.85*80., 1.22, 0.0024, 0.0029  # fco, n, eco, ecu

*Material, Type=UConcrete, Name=KDS-C80-LST-UL
 KDS-C80-LST-UL-C,PlasticUnloading


#################################################
# SD600H16E : SD600H16 Rebar for nonlinear analysis or extreme event state  (phi = 1.)
*Material, TYPE=vonMises, Name=SD600L
 200000. 
 600., 496.0727573,  # TYPE=Value, yield, H, theta, Kinf, K0, delta

#################################################
# SD600H16U : SD600H16 Rebar for nonlinear analysis or ultimate event state (phi = 0.9)
*Material, TYPE=vonMises, Name=SD600L-0.9
 200000. 
 600.*0.9, 496.0727573,  # TYPE=Value, yield, H, theta, Kinf, K0, delta


#################################################
# Ulbon
*Material, Type=vonMises, Name=ulbon74
 200000. 
 1335., 1391.373484,  # TYPE=Value, yield, H, theta, Kinf, K0, delta

*Material, Type=vonMises, Name=ulbon92
 200000. 
 1325., 1540.372671,  # TYPE=Value, yield, H, theta, Kinf, K0, delta

*Material, Type=vonMises, Name=ulbon110
 200000. 
 1325., 1540.372671,  # TYPE=Value, yield, H, theta, Kinf, K0, delta

*Material, Type=vonMises, Name=neturen71
 200000. 
 1275., 4407.294833,  # TYPE=Value, yield, H, theta, Kinf, K0, delta

#################################################
# Stop and signal strains
*SectionStop
 KDS-C80, -0.0029
 KDS-C80-LST-EX, -0.0029
 KDS-C80-LST-UL, -0.0029
 SD600L,-0.1,0.1
 SD600L-0.9,-0.1,0.1
 ulbon74,-0.04,0.04
 ulbon92,-0.04,0.04
 ulbon110,-0.04,0.04
 neturen71,-0.04,0.04

*SectionSignal
  KDS-C80, 5.845031943/41270.9464, "Concrete tensile failure"
  SD600L,-600/200000, "Rebar compressive yield"
  SD600L, 600/200000, "Rebar tesile yield"
  SD600L-0.9,-600*0.9/200000, "Rebar compressive yield"
  SD600L-0.9, 600*0.9/200000, "Rebar tensile yield"
  ulbon74, -1335/200000, "PS compressive yield"
  ulbon74, 1335/200000, "PS tensile yield"
  ulbon92, -1325/200000, "PS compressive yield"
  ulbon92, 1325/200000, "PS tensile yield"
  ulbon110, -1318.9/200000, "PS compressive yield"
  ulbon110,  1318.9/200000, "PS tensile yield"
  neturen71, -1275/200000, "PS compressive yield"
  neturen71,  1275/200000, "PS tensile yield"


### PHC500A section
*Section, TYPE=Beam, Name=PHC500A
*Cell, TYPE=Layer,Circle, Mat=KDS-C80, StartId=1, N=250,160
 250,170
*Cell, Type=Point,Circle, Mat=ulbon92, StartId=1001, N=9 
 220-9.2/2, 64

### Prention + N0 axial force flexure
*SectionAnalysis, Name=PHC500A-N0 Section=PHC500A
 *SectionStep, ExtLoad=0.,0.,NM, Inc=1
   InitialStress, 2, 994.625  # 0.7*fpu
 *SectionStep, ExtLoad=0,0.02/250,NK, Inc=1000  

### Prention + N1 axial force flexure
*SectionAnalysis, Name=PHC500A-N1 Section=PHC500A
 *SectionStep, ExtLoad=0.,0.,NM, Inc=1
   InitialStress, 2, 994.625  # 0.7*fpu
 *SectionStep, ExtLoad=-882900,0,NM, Inc=1  
 *SectionStep, ExtLoad=-882900,0.02/250,NK, Inc=1000   

### Prention + N2 axial force flexure
*SectionAnalysis, Name=PHC500A-N2 Section=PHC500A
 *SectionStep, ExtLoad=0.,0.,NM, Inc=1
   InitialStress, 2, 994.625  # 0.7*fpu
 *SectionStep, ExtLoad=-1766000,0,NM, Inc=1  
 *SectionStep, ExtLoad=-1766000,0.02/250,NK, Inc=1000   

### Prention + N3 axial force flexure
*SectionAnalysis, Name=PHC500A-N3 Section=PHC500A
 *SectionStep, ExtLoad=0.,0.,NM, Inc=1
   InitialStress, 2, 994.625  # 0.7*fpu
 *SectionStep, ExtLoad=-2649000,0,NM, Inc=1  
 *SectionStep, ExtLoad=-2649000,0.02/250,NK, Inc=1000   

### PM diaggram 
*SectionAnalysis, Name=PHC500A Section=PHC500A
 *SectionStep, ExtLoad=0.,0.,NM, Inc=1
   InitialStress, 2, 994.625  # 0.7*fpu
 *SectionStepPM, MaxDeform=-0.005,0.02/250, Inc=1000, PMPoints=20