protected double GetCompressionBlockDepth(double RebarResultant, FlexuralCompressionFiberPosition CompressionFiberPosition)
{
//double fc = Section.Material.SpecifiedCompressiveStrength;
double RequiredConcreteArea = 0;
IMoveableSection compressedSection = null;
double WhitneyBlockStress = GetWhitneyBlockStress();
RequiredConcreteArea = RebarResultant / (WhitneyBlockStress);
if (RequiredConcreteArea > this.Section.SliceableShape.A)
{
//TODO: go directly to strain compatibility solution
}
switch (CompressionFiberPosition)
{
case FlexuralCompressionFiberPosition.Top:
compressedSection = this.Section.SliceableShape.GetTopSliceOfArea(RequiredConcreteArea);
break;
case FlexuralCompressionFiberPosition.Bottom:
compressedSection = this.Section.SliceableShape.GetBottomSliceOfArea(RequiredConcreteArea);
break;
default:
throw new CompressionFiberPositionException();
}
//Get corresponding strain
double a = compressedSection.YMax - compressedSection.YMin;
return(a);
}
protected double GetCompressionBlockDepth(double RebarResultant, FlexuralCompressionFiberPosition CompressionFiberPosition)
{
double fc = Section.Material.SpecifiedCompressiveStrength;
double RequiredConcreteArea = 0;
IMoveableSection compressedSection = null;
switch (CompressionFiberPosition)
{
case FlexuralCompressionFiberPosition.Top:
RequiredConcreteArea = RebarResultant / (0.85 * fc);
compressedSection = this.Section.SliceableShape.GetTopSliceOfArea(RequiredConcreteArea);
break;
case FlexuralCompressionFiberPosition.Bottom:
RequiredConcreteArea = RebarResultant / (0.85 * fc);
compressedSection = this.Section.SliceableShape.GetBottomSliceOfArea(RequiredConcreteArea);
break;
default:
throw new CompressionFiberPositionException();
}
//Get corresponding strain
double a = compressedSection.YMax - compressedSection.YMin;
return(a);
}
/// <summary>
/// Iterates the section until a top or bottom slice (as specified)
/// is of requested area.
/// </summary>
/// <param name="Area"></param>
/// <param name="sliceType"></param>
/// <returns></returns>
private IMoveableSection getSliceOfArea(double Area, SliceType sliceType)
{
double Atar = 0; //target area
double YOffsetTop = 0;
if (Area > this.A)
{
throw new Exception("Section analysis failed. Area of section sub-part exceeds the total area of cross section.");
}
else
{
if (sliceType == SliceType.Top) // need to return the TOP portion of given area
{
Atar = Area;
}
else // need to return the BOTTOM portion of given area
{
Atar = this.A - Area;
}
YOffsetTop = GetSlicePlaneTopOffset(Atar);
}
double SlicePlaneYCoordinte;
SlicePlaneYCoordinte = this.YMax - YOffsetTop;
IMoveableSection s = getSliceAtCoordinate(SlicePlaneYCoordinte, sliceType);
return(s);
}
private double BottomAreaDeltaCalculationFunction(double SliceAxisY)
{
cutSection = this.GetBottomSliceSection(SliceAxisY, SlicingPlaneOffsetType.Top);
double SliceArea = cutSection.A;
return(targetArea - SliceArea);
}
public void CompoundShapeReturnsTopSLiceAtOffset()
{
ArbitraryCompoundShape shape = GetCustomTeeShape();
IMoveableSection topSLice = shape.GetTopSliceSection(3.5, SlicingPlaneOffsetType.Top);
Assert.AreEqual(6.25, topSLice.A);
}
protected IMoveableSection GetCompressedConcreteSection(LinearStrainDistribution StrainDistribution,
FlexuralCompressionFiberPosition compFiberPos, double SlicingPlaneOffset)
{
IMoveableSection compressedPortion = null;
ISliceableSection sec = this.Section.SliceableShape as ISliceableSection;
//if (StrainDistribution.TopFiberStrain >= 0 && StrainDistribution.BottomFiberStrain >= 0)
//{
double SectionHeight = sec.YMax - sec.YMin;
if (SlicingPlaneOffset > SectionHeight)
{
compressedPortion = this.Section.SliceableShape;
}
else
{
switch (compFiberPos)
{
case FlexuralCompressionFiberPosition.Top:
compressedPortion = sec.GetTopSliceSection(SlicingPlaneOffset, SlicingPlaneOffsetType.Top);
break;
case FlexuralCompressionFiberPosition.Bottom:
compressedPortion = sec.GetBottomSliceSection(SlicingPlaneOffset, SlicingPlaneOffsetType.Bottom);
break;
default:
throw new CompressionFiberPositionException();
}
}
return(compressedPortion);
}
public void CompoundShapeReturnsBottomSliceAtCoordinate()
{
CompoundShape shape = GetRectangularShape();
IMoveableSection topSlice = shape.GetBottomSliceSection(2, SlicingPlaneOffsetType.Bottom);
Assert.AreEqual(24, topSlice.A);
Assert.AreEqual(-4, topSlice.YMax);
}
public void CompoundShapeReturnsBottomSliceOfArea()
{
CompoundShape shape = GetRectangularShape();
IMoveableSection bottomSlice = shape.GetBottomSliceOfArea(6);
Assert.AreEqual(6, bottomSlice.A);
Assert.AreEqual(-5.5, bottomSlice.YMax);
}
public void CompoundShapeReturnsTopSliceOfArea()
{
ArbitraryCompoundShape shape = GetCustomTeeShape();
IMoveableSection topSlice = shape.GetTopSliceOfArea(6.25);
Assert.AreEqual(6.25, topSlice.A);
Assert.AreEqual(3.5, topSlice.YMin);
}
private double GetZ_x()
{
IMoveableSection topSlice = this.GetTopSliceSection(YMax - PlasticCentroidCoordinate.Y, SlicingPlaneOffsetType.Top);
IMoveableSection botSlice = this.GetBottomSliceSection(YMax - PlasticCentroidCoordinate.Y, SlicingPlaneOffsetType.Top);
double Z = topSlice.A * (topSlice.PlasticCentroidCoordinate.Y - PlasticCentroidCoordinate.Y) +
botSlice.A * (PlasticCentroidCoordinate.Y - botSlice.PlasticCentroidCoordinate.Y);
return(Z);
}
private double GetZ_y()
{
PolygonShape NinetyDegreeShape = GetRotatedShape(90.0);
IMoveableSection topSlice = NinetyDegreeShape.GetTopSliceSection(XMax - PlasticCentroidCoordinate.X, SlicingPlaneOffsetType.Top);
IMoveableSection botSlice = NinetyDegreeShape.GetBottomSliceSection(XMax - PlasticCentroidCoordinate.X, SlicingPlaneOffsetType.Top);
double Z = topSlice.A * (topSlice.PlasticCentroidCoordinate.Y - PlasticCentroidCoordinate.Y) +
botSlice.A * (PlasticCentroidCoordinate.Y - botSlice.PlasticCentroidCoordinate.Y);
return(Z);
}
protected ForceMomentContribution GetConcreteWhitneyForceResultant(LinearStrainDistribution StrainDistribution, FlexuralCompressionFiberPosition compFiberPosition,
double CompressedRebarArea, double CompressedRebarCentroidCoordinate)
{
ForceMomentContribution ConcreteCompressionContribution = new ForceMomentContribution();
// CalculateBeta and compression block height
double c = GetDistanceToNeutralAxis(StrainDistribution, compFiberPosition);
double h = Section.SliceableShape.YMax - Section.SliceableShape.YMin;
double a;
if (c == double.PositiveInfinity || c == double.NegativeInfinity)
{
a = h;
}
else
{
a = GetCompressionBlockDepth(c);
if (a > h)
{
a = h;
}
}
//double CentroidYToTopEdge = (Section.SliceableShape.YMax-Section.SliceableShape.YMin)-Section.SliceableShape.y_Bar;
//double neutralAxisToBottomOfCompressedShapeOffset = CentroidYToTopEdge - a;
IMoveableSection compressedPortion = null;
ISliceableSection sec = this.Section.SliceableShape as ISliceableSection;
if (sec != null)
{
compressedPortion = GetCompressedConcreteSection(StrainDistribution, compFiberPosition, a);
}
//this analysis subtracts the area of bars from the section but the location of the centroid of the
//compressed section is not modified
double A = compressedPortion.A - CompressedRebarArea;
double fc = Section.Material.SpecifiedCompressiveStrength;
double WhitneyBlockStress = GetWhitneyBlockStress();
double ConcreteResultantForce = A * WhitneyBlockStress;
ConcreteCompressionContribution.Force = ConcreteResultantForce;
double concreteForceCentroidDistance = compressedPortion.GetElasticCentroidCoordinate().Y - Section.SliceableShape.GetElasticCentroidCoordinate().Y;
ConcreteCompressionContribution.Moment = concreteForceCentroidDistance * ConcreteResultantForce;
return(ConcreteCompressionContribution);
}
public void SliceTopReturnsPolygonForRectangle()
{
var Points = new List <Point2D>
{
new Point2D(-1, -1),
new Point2D(-1, 1),
new Point2D(1, 1),
new Point2D(1, -1)
};
var rect = new GenericShape(Points);
IMoveableSection sect = rect.GetTopSliceSection(1, SlicingPlaneOffsetType.Top);
Assert.AreEqual(1.0, sect.YMax);
}
protected ForceMomentContribution GetConcreteWhitneyForceResultant(LinearStrainDistribution StrainDistribution, FlexuralCompressionFiberPosition compFiberPosition)
{
ForceMomentContribution ConcreteCompressionContribution = new ForceMomentContribution();
// CalculateBeta and compression block height
double c = GetDistanceToNeutralAxis(StrainDistribution, compFiberPosition);
double h = Section.SliceableShape.YMax - Section.SliceableShape.YMin;
double a;
if (c == double.PositiveInfinity)
{
a = h;
}
else
{
a = GetCompressionBlockDepth(c);
if (a > h)
{
a = h;
}
}
double CentroidYToTopEdge = (Section.SliceableShape.YMax - Section.SliceableShape.YMin) - Section.SliceableShape.y_Bar;
double neutralAxisToBottomOfCompressedShapeOffset = CentroidYToTopEdge - a;
IMoveableSection compressedPortion = null;
ISliceableSection sec = this.Section.SliceableShape as ISliceableSection;
if (sec != null)
{
compressedPortion = GetCompressedConcreteSection(StrainDistribution, compFiberPosition, a);
}
double A = compressedPortion.A;
double fc = Section.Material.SpecifiedCompressiveStrength;
double ConcreteResultantForce = A * 0.85 * fc;
ConcreteCompressionContribution.Force = ConcreteResultantForce;
double concreteForceCentroidDistance = compressedPortion.GetElasticCentroidCoordinate().Y;
ConcreteCompressionContribution.Moment = concreteForceCentroidDistance * ConcreteResultantForce;
return(ConcreteCompressionContribution);
}
private void CalculateCrackedSectionTransformedShapes(double kd, FlexuralCompressionFiberPosition compFiber)
{
compressedConcretePortion = null;
CompShapeTransformed = new List <IMoveableSection>();
TensBarsTransformed = new List <IMoveableSection>();
CrackedMomentOfInertiaCompressedShapes = new List <IMoveableSection>();
CrackedMomentOfInertiaTensionShapes = new List <IMoveableSection>();
double YNeutral = GetYNeutral(kd);
switch (compFiber)
{
case FlexuralCompressionFiberPosition.Top:
//1. Concrete Shape (compression)
compressedConcretePortion = this.Section.SliceableShape.GetTopSliceSection(kd, SlicingPlaneOffsetType.Top);
//2. Steel bars (compression)
CompShapeTransformed = GetTransformedRebarShapes(this.Section.SliceableShape.YMax, YNeutral);
CompShapeTransformed.Add(compressedConcretePortion);
CrackedMomentOfInertiaCompressedShapes = CompShapeTransformed;
//3 Steel bars (tension)
TensBarsTransformed = GetTransformedRebarShapes(YNeutral, this.Section.SliceableShape.YMin);
CrackedMomentOfInertiaTensionShapes = TensBarsTransformed;
break;
case FlexuralCompressionFiberPosition.Bottom:
//1. Concrete Shape (compression)
compressedConcretePortion = this.Section.SliceableShape.GetBottomSliceSection(kd, SlicingPlaneOffsetType.Bottom);
//2. Steel bars (compression)
CompShapeTransformed = GetTransformedRebarShapes(YNeutral, this.Section.SliceableShape.YMin);
CompShapeTransformed.Add(compressedConcretePortion);
CrackedMomentOfInertiaCompressedShapes = CompShapeTransformed;
//3 Steel bars (tension)
TensBarsTransformed = GetTransformedRebarShapes(this.Section.SliceableShape.YMax, YNeutral);
CrackedMomentOfInertiaTensionShapes = TensBarsTransformed;
break;
break;
default:
throw new CompressionFiberPositionException();
}
}
private double TopAndBottomAreaDifferenceFunction(double Y)
{
double OffsetFromTop = YMax - Y;
if (OffsetFromTop == 0)
{
return(this.A);
}
else if (OffsetFromTop >= YMax - YMin)
{
return(-this.A);
}
else
{
IMoveableSection topSlice = this.GetTopSliceSection(OffsetFromTop, SlicingPlaneOffsetType.Top);
IMoveableSection botSlice = this.GetBottomSliceSection(OffsetFromTop, SlicingPlaneOffsetType.Top);
return(topSlice.A - botSlice.A);
}
}
private double BottomAreaDeltaCalculationFunction(double SliceAxisY)
{
cutSection = this.GetBottomSliceSection(SliceAxisY, SlicingPlaneOffsetType.Top);
double SliceArea = 0;
if (cutSection != null)
{
SliceArea = cutSection.A;
}
else
{
if (SliceAxisY == this.YMax - this.YMin)
{
SliceArea = this.A;
}
}
return(targetArea - SliceArea);
}
public virtual double GetCrackedMomentOfInertia(FlexuralCompressionFiberPosition compFiberPosition)
{
//Get LinearStrainDistribution from flexural result
double kd = FindCrackedSectionNeutralAxis(compFiberPosition);
IMoveableSection concreteShape = GetConcreteShape();
List <IMoveableSection> allShapes = GetRebarShapes();
//allShapes.Add(concreteShape);
double Ix = 0.0;
//Find centroid
double SumAreaDistance = allShapes.Sum(s => s.A * s.GetElasticCentroidCoordinate().Y);
double SumArea = allShapes.Sum(s => s.A);
double YCentr = SumAreaDistance / SumArea;
//Find moment of inertia
double I_cr = allShapes.Sum(s => s.A * Math.Pow(YCentr - s.GetElasticCentroidCoordinate().Y, 2.0) + s.I_x);
return(I_cr);
}
private double LeftAndRightAreaDifferenceFunction(double X)
{
double OffsetFromTop = X - XMin;
if (OffsetFromTop == 0)
{
return(this.A);
}
else if (OffsetFromTop >= XMax - XMin)
{
return(-this.A);
}
else
{
PolygonShape RotatedPoly = this.GetRotatedShape(90);
IMoveableSection topSlice = RotatedPoly.GetTopSliceSection(OffsetFromTop, SlicingPlaneOffsetType.Top);
IMoveableSection botSlice = RotatedPoly.GetBottomSliceSection(OffsetFromTop, SlicingPlaneOffsetType.Top);
return(botSlice.A - topSlice.A);
}
}
public double GetFlexuralStrength(double SumQ_n)
{
this.SumQ_n = SumQ_n;
double A_s = SteelSection.A;
double MaximumTForce = A_s * F_y;
//Equations (C-I3-7) and (C-I3-8)
this.C_Slab = GetCForce();
double SteelSectionHeight = (SteelSection.YMax - SteelSection.YMin);
double d_3 = SteelSectionHeight - SteelSection.y_pBar; // distance from Py to the top of the steel section
double d_1 = Get_d_1(); //distance from the centroid of the compression force, C, in the concrete to the top of the steel section
double d_2; //distance from the centroid of the compression force in the steel section to the top of the steel section
double C;
if (C_Slab >= MaximumTForce)
{
//Section is fully composite
C = MaximumTForce;
d_2 = 0;
DistanceFromTopOfSteelToPNY = 0;
}
else
{
//Section is partially composite
double C_steel = (MaximumTForce - C_Slab) / 2.0;
double A_sPrime = C_steel / F_y;
IMoveableSection compressedSteelSection = SteelSection.GetTopSliceOfArea(A_sPrime);
DistanceFromTopOfSteelToPNY = compressedSteelSection.YMax - compressedSteelSection.YMin;
var C_steelCoordinate = compressedSteelSection.GetElasticCentroidCoordinate();
d_2 = SteelSectionHeight - C_steelCoordinate.Y;
C = C_Slab + C_steel;
}
double P_y = MaximumTForce;
double phiM_n = 0.9 * (C * (d_1 + d_2) + P_y * (d_3 - d_2)); // (C-I3-10)
PNYCalculated = true;
return(phiM_n);
}
private void CalculateCrackedSectionTransformedShapes(double kd, FlexuralCompressionFiberPosition compFiber)
{
compressedConcretePortion = null;
CompShapeTransformed = new List<IMoveableSection>();
TensBarsTransformed = new List<IMoveableSection>();
CrackedMomentOfInertiaCompressedShapes = new List<IMoveableSection>();
CrackedMomentOfInertiaTensionShapes = new List<IMoveableSection>();
double YNeutral = GetYNeutral(kd);
switch (compFiber)
{
case FlexuralCompressionFiberPosition.Top:
//1. Concrete Shape (compression)
compressedConcretePortion = this.Section.SliceableShape.GetTopSliceSection(kd, SlicingPlaneOffsetType.Top);
//2. Steel bars (compression)
CompShapeTransformed= GetTransformedRebarShapes( this.Section.SliceableShape.YMax, YNeutral);
CompShapeTransformed.Add(compressedConcretePortion);
CrackedMomentOfInertiaCompressedShapes = CompShapeTransformed;
//3 Steel bars (tension)
TensBarsTransformed = GetTransformedRebarShapes(YNeutral, this.Section.SliceableShape.YMin);
CrackedMomentOfInertiaTensionShapes = TensBarsTransformed;
break;
case FlexuralCompressionFiberPosition.Bottom:
//1. Concrete Shape (compression)
compressedConcretePortion = this.Section.SliceableShape.GetBottomSliceSection(kd, SlicingPlaneOffsetType.Bottom);
//2. Steel bars (compression)
CompShapeTransformed = GetTransformedRebarShapes(YNeutral, this.Section.SliceableShape.YMin);
CompShapeTransformed.Add(compressedConcretePortion);
CrackedMomentOfInertiaCompressedShapes = CompShapeTransformed;
//3 Steel bars (tension)
TensBarsTransformed = GetTransformedRebarShapes(this.Section.SliceableShape.YMax, YNeutral);
CrackedMomentOfInertiaTensionShapes = TensBarsTransformed;
break;
break;
default:
throw new CompressionFiberPositionException();
}
}
private double BottomAreaDeltaCalculationFunction(double SliceAxisY)
{
cutSection = this.GetBottomSliceSection(SliceAxisY, SlicingPlaneOffsetType.Top);
double SliceArea = cutSection.A;
return targetArea - SliceArea;
}
