/// <summary>
/// Calculates plastic neutral axis (PNA) and plastic section modulus
/// in accordance with procedure in the foloowing paper:
/// "CALCULATION OF THE PLASTIC SECTION MODULUS USING THE COMPUTER"
/// DOMINIQUE BERNARD BAUER
/// AISC ENGINEERING JOURNAL / THIRD QUARTER /1997
/// </summary>
/// <param name="axis"></param>
/// <param name="rects"></param>
private void CalculatePlasticSectionModulus(AnalysisAxis axis,
List<CompoundShapePart> rects)
{
double Z = 0.0;
double Atar = A / 2;
double Sum_hi=0; //summation of height of previous rectangles
double Sum_Ai =0; //summation of areas of previous rectangles
double Sum_AiPreviousStep = 0;//summation of areas of previous rectangles in the step before this one
//find location of PNA
//and store the information in a list
List<plasticRectangle> pRects = new List<plasticRectangle>();
double PNACoordinate= 0;
#region Find PNA
foreach (var r in rects)
{
double bn = 0;
double hn = 0;
double hn_actual = 0; //actual height used for fillet areas
double yn = 0;
plasticRectangle pr = null;
switch (axis)
{
case AnalysisAxis.X:
pr = new plasticRectangle(r.b, r.h, r.InsertionPoint);
bn = pr.b;
hn = pr.h;
hn_actual = r.h_a;
break;
case AnalysisAxis.Y:
//pr = new plasticRectangle(r.h,r.b,new Point2D(r.InsertionPoint.Y,r.InsertionPoint.X));
pr = new plasticRectangle(r.b, r.h, r.InsertionPoint);
bn = pr.b;
hn = pr.h;
hn_actual = r.h_a;
break;
}
yn = pr.InsertionPoint.Y; //centroid of this rectangle
double An = bn * hn;
pr.An = An;
//distance from top of the rectangle to the PNA
//this number is meaningful only for one rectangle
double h_n_tilda;
if (An == 0 && Sum_Ai == Atar) // case when the rectangle represents a hole at the center of the section
{
h_n_tilda = hn / 2;
}
else //all other cases when rectangles are "stacked" on top of each other
{
h_n_tilda = (Atar - Sum_Ai) / bn;
}
double Y_n_tilda = 0;
//check if this rectangle is the one where
//PNA is located
if (h_n_tilda > 0 && h_n_tilda < hn) // remove equal?
{
//this condition is met only for one rectangle
Y_n_tilda = Sum_hi + h_n_tilda;
if (axis == AnalysisAxis.X)
{
PNACoordinate = Y_n_tilda - this.YMin; //PNA coordinate is meeasured from top
}
else
{
PNACoordinate = Y_n_tilda; //PNA coordinate is meeasured from left
}
pr.h_n_tilda = h_n_tilda;
}
else
{
pr.h_n_tilda = 0;
}
pr.Y_n_tilda = Y_n_tilda;
pRects.Add(pr);
Sum_AiPreviousStep = Sum_Ai;
Sum_Ai += An;
//Sum_hi +=hn;
Sum_hi += hn_actual;
}
double sectionHeight;
if (axis == AnalysisAxis.X)
{
sectionHeight= YMax - YMin;
}
else
{
sectionHeight= XMax - XMin;
}
double distanceFromBottomToPNA = sectionHeight - PNACoordinate;
#endregion
foreach (var pr in pRects)
{
double Zn;
if (pr.Y_n_tilda!=0) //special case when rectangle is cut by PNA
{
double ZnTop = pr.b*Math.Pow(pr.h_n_tilda,2)/2 ;
double ZnBot = pr.b * Math.Pow((pr.h - pr.h_n_tilda), 2) / 2;
Zn = ZnTop + ZnBot;
}
else
{
double dn = pr.InsertionPoint.Y - distanceFromBottomToPNA; //PNACoordinate ;
Zn = Math.Abs(dn) * pr.An;
}
Z += Zn;
}
switch (axis)
{
case AnalysisAxis.X:
this._Z_x = Z;
this.ypb = distanceFromBottomToPNA;
break;
case AnalysisAxis.Y:
this._Z_y = Z;
this.xpl = distanceFromBottomToPNA;
break;
}
}
/// <summary>
/// Calculates plastic neutral axis (PNA) and plastic section modulus
/// in accordance with procedure in the foloowing paper:
/// "CALCULATION OF THE PLASTIC SECTION MODULUS USING THE COMPUTER"
/// DOMINIQUE BERNARD BAUER
/// AISC ENGINEERING JOURNAL / THIRD QUARTER /1997
/// </summary>
/// <param name="axis"></param>
/// <param name="rects"></param>
private void CalculatePlasticSectionModulus(AnalysisAxis axis,
List <CompoundShapePart> rects)
{
double Z = 0.0;
double Atar = A / 2;
double Sum_hi = 0; //summation of height of previous rectangles
double Sum_Ai = 0; //summation of areas of previous rectangles
double Sum_AiPreviousStep = 0; //summation of areas of previous rectangles in the step before this one
//find location of PNA
//and store the information in a list
List <plasticRectangle> pRects = new List <plasticRectangle>();
double PNACoordinate = 0;
#region Find PNA
foreach (var r in rects)
{
double bn = 0;
double hn = 0;
double hn_actual = 0; //actual height used for fillet areas
double yn = 0;
plasticRectangle pr = null;
switch (axis)
{
case AnalysisAxis.X:
pr = new plasticRectangle(r.b, r.h, r.InsertionPoint);
bn = pr.b;
hn = pr.h;
hn_actual = r.h_a;
break;
case AnalysisAxis.Y:
//pr = new plasticRectangle(r.h,r.b,new Point2D(r.InsertionPoint.Y,r.InsertionPoint.X));
pr = new plasticRectangle(r.b, r.h, r.InsertionPoint);
bn = pr.b;
hn = pr.h;
hn_actual = r.h_a;
break;
}
yn = pr.InsertionPoint.Y; //centroid of this rectangle
double An = bn * hn;
pr.An = An;
//distance from top of the rectangle to the PNA
//this number is meaningful only for one rectangle
double h_n_tilda;
if (An == 0 && Sum_Ai == Atar) // case when the rectangle represents a hole at the center of the section
{
h_n_tilda = hn / 2;
}
else //all other cases when rectangles are "stacked" on top of each other
{
h_n_tilda = (Atar - Sum_Ai) / bn;
}
double Y_n_tilda = 0;
//check if this rectangle is the one where
//PNA is located
if (h_n_tilda > 0 && h_n_tilda < hn) // remove equal?
{
//this condition is met only for one rectangle
Y_n_tilda = Sum_hi + h_n_tilda;
if (axis == AnalysisAxis.X)
{
PNACoordinate = Y_n_tilda - this.YMin; //PNA coordinate is meeasured from top
}
else
{
PNACoordinate = Y_n_tilda; //PNA coordinate is meeasured from left
}
pr.h_n_tilda = h_n_tilda;
}
else
{
pr.h_n_tilda = 0;
}
pr.Y_n_tilda = Y_n_tilda;
pRects.Add(pr);
Sum_AiPreviousStep = Sum_Ai;
Sum_Ai += An;
//Sum_hi +=hn;
Sum_hi += hn_actual;
}
double sectionHeight;
if (axis == AnalysisAxis.X)
{
sectionHeight = YMax - YMin;
}
else
{
sectionHeight = XMax - XMin;
}
double distanceFromBottomToPNA = sectionHeight - PNACoordinate;
#endregion
foreach (var pr in pRects)
{
double Zn;
if (pr.Y_n_tilda != 0) //special case when rectangle is cut by PNA
{
double ZnTop = pr.b * Math.Pow(pr.h_n_tilda, 2) / 2;
double ZnBot = pr.b * Math.Pow((pr.h - pr.h_n_tilda), 2) / 2;
Zn = ZnTop + ZnBot;
}
else
{
double dn = pr.InsertionPoint.Y - distanceFromBottomToPNA; //PNACoordinate ;
Zn = Math.Abs(dn) * pr.An;
}
Z += Zn;
}
switch (axis)
{
case AnalysisAxis.X:
this._Z_x = Z;
this.ypb = distanceFromBottomToPNA;
break;
case AnalysisAxis.Y:
this._Z_y = Z;
this.xpl = distanceFromBottomToPNA;
break;
}
}
