protected override SecProp ShapeSecProp()
{
SecProp sp = new SecProp();
double cos = Math.Cos(alpha);
double sin = Math.Sin(alpha);
double E = Material.E;
double A = R * R / 2.0 * (2.0 * alpha - Math.Sin(2.0 * alpha));
double I_Y1 = A * R * R / 4.0 * (1.0 + (2.0 * Math.Pow(sin, 3.0) * cos) / (alpha - sin * cos));
double Ixx = A * R * R / 4.0 * (1.0 - (2.0 / 3.0) * (Math.Pow(sin, 3.0) * cos) / (alpha - sin * cos));
double Iyy = I_Y1 - 4.0 * Math.Pow(R, 6.0) * Math.Pow(sin, 6) / (9 * A);
double Ixy = 0.0;
sp.EA = E * A;
sp.EIxx = E * Ixx;
sp.EIyy = E * Iyy;
sp.EIxy = E * Ixy;
sp.Xcg = 4.0 * R * Math.Pow(sin, 3) / (3.0 * (2 * alpha - Math.Sin(2 * alpha)));
sp.Ycg = 0;
return(sp);
}
protected override SecProp ShapeSecProp()
{
SecProp sp = new SecProp();
double E = Material.E;
sp.EA = 1.0 / 2.0 * E * b * h;
sp.EIxx = E * 1.0 / 36.0 * b * Math.Pow(h, 3);
sp.EIyy = E * 1.0 / 36.0 * h * Math.Pow(b, 3);
sp.EIxy = E * -1.0 / 72.0 * Math.Pow(h, 2) * Math.Pow(b, 2);
sp.Xcg = b / 3.0;
sp.Ycg = h / 3.0;
return(sp);
}
protected override SecProp ShapeSecProp()
{
SecProp sp = new SecProp();
double E = Material.E;
sp.EA = E * b * t;
sp.EIxx = E * 1.0 / 12.0 * b * Math.Pow(t, 3);
sp.EIyy = E * 1.0 / 12.0 * t * Math.Pow(b, 3);
sp.EIxy = 0;
sp.Xcg = b / 2.0;
sp.Ycg = t / 2.0;
return(sp);
}
protected override SecProp ShapeSecProp()
{
SecProp sp = new SecProp();
double E = Material.E;
sp.EA = E * ((1 - Math.PI / 4) * r * r);
sp.EIxx = E * ((1 - 5 * Math.PI / 16) - (1 - Math.PI / 4) * Math.Pow((10 - 3 * Math.PI), 2) / (9 * Math.Pow((4 - Math.PI), 2))) * Math.Pow(r, 4);;
sp.EIyy = sp.EIxx;
sp.EIxy = E * (-0.00443868 * Math.Pow(r, 4));
sp.Xcg = ((10 - 3 * Math.PI) * r) / (3 * (4 - Math.PI));
sp.Ycg = ((10 - 3 * Math.PI) * r) / (3 * (4 - Math.PI));
return(sp);
}
protected override SecProp ShapeSecProp()
{
SecProp sp = new SecProp();
double E = Material.E;
double I_Y1 = alpha / 4 * (Math.Pow(_R, 4) - Math.Pow(r, 4)) * (1 + Math.Sin(alpha) * Math.Cos(alpha) / alpha);
sp.EA = E * (_R * _R - r * r) * alpha;
sp.EIxx = E * alpha / 4 * (Math.Pow(_R, 4) - Math.Pow(r, 4)) * (1 - Math.Sin(alpha) * Math.Cos(alpha) / alpha);
sp.EIyy = E * (I_Y1 - 1 / (alpha * (_R * _R - r * r)) * Math.Pow((2 * Math.Sin(alpha) * (Math.Pow(_R, 3) - Math.Pow(r, 3)) / 3), 2));
sp.EIxy = 0;
sp.Xcg = (2 * (Math.Pow(_R, 3) - Math.Pow(r, 3)) * Math.Sin(alpha)) / (3 * alpha * (_R * _R - r * r));
sp.Ycg = 0;
return(sp);
}
public static SecProp SecProp_Section(List <SecProp> SecPropList)
{
double sumEA = 0, sumXcgEA = 0, sumYcgEA = 0;
foreach (SecProp sp in SecPropList)
{
sumEA = sumEA + sp.EA;
sumXcgEA = sumXcgEA + sp.EA * sp.Xcg;
sumYcgEA = sumYcgEA + sp.EA * sp.Ycg;
}
double Xcg_global = sumXcgEA / sumEA;
double Ycg_global = sumYcgEA / sumEA;
double sumEIxx = 0, sumEIyy = 0, sumEIxy = 0;
foreach (SecProp sp in SecPropList)
{
sumEIxx = sumEIxx + sp.EIxx + sp.EA * Math.Pow(sp.Ycg - Ycg_global, 2);
sumEIyy = sumEIyy + sp.EIyy + sp.EA * Math.Pow(sp.Xcg - Xcg_global, 2);
sumEIxy = sumEIxy + sp.EIxy + sp.EA * (sp.Xcg - Xcg_global) * (sp.Ycg - Ycg_global);
}
double thetap = Theta_Principal(sumEIxx, sumEIyy, sumEIxy);
double[] EIPrincipal = RotatedAxesProperties(sumEIxx, sumEIyy, sumEIxy, thetap);
double sumEI1p = EIPrincipal[0];
double sumEI2p = EIPrincipal[1];
SecProp SPGlobal = new SecProp
{
Xcg = Xcg_global,
Ycg = Ycg_global,
EA = sumEA,
EIxx = sumEIxx,
EIyy = sumEIyy,
EIxy = sumEIxy,
EI1p = sumEI1p,
EI2p = sumEI2p,
thetap = thetap
};
return(SPGlobal);
}
protected override Coordinate LocalPointCoordinate(string PointID)
{
//Returns the coordinate of a defined point
//assumes zero rotation and translation
Coordinate point1_sh = new Coordinate();
SecProp sp = ShapeSecProp();
double x_cg = sp.Xcg;
double y_cg = sp.Ycg;
switch (PointID)
{
case "a":
point1_sh = ConvertXYtoCoordinate(0, 0);
break;
case "b":
point1_sh = ConvertXYtoCoordinate(-b / 2, 0);
break;
case "c":
point1_sh = ConvertXYtoCoordinate(-b / 4, h / 2);
break;
case "d":
point1_sh = ConvertXYtoCoordinate(0, h);
break;
case "e":
point1_sh = ConvertXYtoCoordinate(b / 4, h / 2);
break;
case "f":
point1_sh = ConvertXYtoCoordinate(b / 2, 0);
break;
case "cg":
point1_sh = ConvertXYtoCoordinate(x_cg, y_cg);
break;
}
return(point1_sh);
}
protected override Coordinate LocalPointCoordinate(string PointID)
{
//Returns the coordinate of a defined point
//assumes zero rotation and translation
Coordinate point1_sh = new Coordinate();
double cos = Math.Cos(alpha);
double sin = Math.Sin(alpha);
switch (PointID)
{
case "a":
point1_sh = ConvertXYtoCoordinate(0, 0);
break;
case "b":
point1_sh = ConvertXYtoCoordinate(R * cos, R * sin);
break;
case "c":
point1_sh = ConvertXYtoCoordinate(R, 0);
break;
case "d":
point1_sh = ConvertXYtoCoordinate(R * cos, -R * sin);
break;
case "e":
point1_sh = ConvertXYtoCoordinate(R * cos, 0);
break;
case "cg":
SecProp sp = ShapeSecProp();
double x_cg = sp.Xcg;
double y_cg = sp.Ycg;
point1_sh = ConvertXYtoCoordinate(x_cg, y_cg);
break;
}
return(point1_sh);
}
protected override Coordinate LocalPointCoordinate(string PointID)
{
//Returns the coordinate of a defined point
//assumes zero rotation and translation
Coordinate point1_sh = new Coordinate();
SecProp sp = ShapeSecProp();
double x_cg = sp.Xcg;
double y_cg = sp.Ycg;
switch (PointID)
{
case "a":
point1_sh = ConvertXYtoCoordinate(0, 0);
break;
case "b":
point1_sh = ConvertXYtoCoordinate(0, ((0) + (h - t2 - r2)) / 2);
break;
case "c":
point1_sh = ConvertXYtoCoordinate(0, h - t2 - r2);
break;
case "d":
point1_sh = ConvertXYtoCoordinate(-r2, h - t2);
break;
case "e":
point1_sh = ConvertXYtoCoordinate(((-r2) + (tw - b2)) / 2, h - t2);
break;
case "f":
point1_sh = ConvertXYtoCoordinate(-(b2 - tw), h - t2);
break;
case "g":
point1_sh = ConvertXYtoCoordinate(-(b2 - tw), h - t2 / 2);
break;
case "h":
point1_sh = ConvertXYtoCoordinate(-(b2 - tw), h);
break;
case "i":
point1_sh = ConvertXYtoCoordinate((-1 * (b2 - tw) + (tw)) / 2, h);
break;
case "j":
point1_sh = ConvertXYtoCoordinate(tw, h);
break;
case "k":
point1_sh = ConvertXYtoCoordinate(tw, ((h) + (t1 + r1)) / 2);
break;
case "l":
point1_sh = ConvertXYtoCoordinate(tw, t1 + r1);
break;
case "m":
point1_sh = ConvertXYtoCoordinate(tw + r1, t1);
break;
case "n":
point1_sh = ConvertXYtoCoordinate(((tw + r1) + (b1)) / 2, t1);
break;
case "o":
point1_sh = ConvertXYtoCoordinate(b1, t1);
break;
case "p":
point1_sh = ConvertXYtoCoordinate(b1, t1 / 2);
break;
case "q":
point1_sh = ConvertXYtoCoordinate(b1, 0);
break;
case "r":
point1_sh = ConvertXYtoCoordinate(b1 / 2, 0);
break;
case "cg":
point1_sh = ConvertXYtoCoordinate(x_cg, y_cg);
break;
}
return(point1_sh);
}
protected override Coordinate LocalPointCoordinate(string PointID)
{
//Returns the coordinate of a defined point
//assumes zero rotation and translation
Coordinate point1_sh = new Coordinate();
SecProp sp = ShapeSecProp();
double x_cg = sp.Xcg;
double y_cg = sp.Ycg;
switch (PointID)
{
case "a":
point1_sh = ConvertXYtoCoordinate(0, 0);
break;
case "b":
point1_sh = ConvertXYtoCoordinate(0, b2 / 2);
break;
case "c":
point1_sh = ConvertXYtoCoordinate(0, b2);
break;
case "d":
point1_sh = ConvertXYtoCoordinate(t2, b2);
break;
case "e":
point1_sh = ConvertXYtoCoordinate(t2, (b2 + t1 + r) / 2); //average of d and f
break;
case "f":
point1_sh = ConvertXYtoCoordinate(t2, t1 + r);
break;
case "g":
point1_sh = ConvertXYtoCoordinate(t2 + r, t1);
break;
case "h":
point1_sh = ConvertXYtoCoordinate((t2 + r + b1) / 2, t1); //average of g and i
break;
case "i":
point1_sh = ConvertXYtoCoordinate(b1, t1);
break;
case "j":
point1_sh = ConvertXYtoCoordinate(b1, 0);
break;
case "k":
point1_sh = ConvertXYtoCoordinate(b1 / 2, 0);
break;
case "cg":
point1_sh = ConvertXYtoCoordinate(x_cg, y_cg);
break;
}
return(point1_sh);
}
protected override Coordinate LocalPointCoordinate(string PointID)
{
//Returns the coordinate of a defined point
//assumes zero rotation and translation
Coordinate point1_sh = new Coordinate();
SecProp sp = ShapeSecProp();
double x_cg = sp.Xcg;
double y_cg = sp.Ycg;
switch (PointID)
{
case "a":
point1_sh = ConvertXYtoCoordinate(0, 0);
break;
case "b":
point1_sh = ConvertXYtoCoordinate(0, r1 + t);
break;
case "c":
point1_sh = ConvertXYtoCoordinate(0, ((r1 + t) + (h - r2 - t)) / 2);
break;
case "d":
point1_sh = ConvertXYtoCoordinate(0, h - r2 - t);
break;
case "e":
point1_sh = ConvertXYtoCoordinate(-r2, h - t);
break;
case "f":
point1_sh = ConvertXYtoCoordinate(((-r2) + (t - b2)) / 2, h - t);
break;
case "g":
point1_sh = ConvertXYtoCoordinate(t - b2, h - t);
break;
case "h":
point1_sh = ConvertXYtoCoordinate(t - b2, h - t / 2);
break;
case "i":
point1_sh = ConvertXYtoCoordinate(t - b2, h);
break;
case "j":
point1_sh = ConvertXYtoCoordinate(((t - b2) + (-r2)) / 2, h);
break;
case "k":
point1_sh = ConvertXYtoCoordinate(-r2, h);
break;
case "l":
point1_sh = ConvertXYtoCoordinate(t, h);
break;
case "m":
point1_sh = ConvertXYtoCoordinate(t, h - t - r2);
break;
case "n":
point1_sh = ConvertXYtoCoordinate(t, ((h - t - r2) + (t + r1)) / 2);
break;
case "o":
point1_sh = ConvertXYtoCoordinate(t, t + r1);
break;
case "p":
point1_sh = ConvertXYtoCoordinate(t + r1, t);
break;
case "q":
point1_sh = ConvertXYtoCoordinate(((t + r1) + (b1)) / 2, t);
break;
case "r":
point1_sh = ConvertXYtoCoordinate(b1, t);
break;
case "s":
point1_sh = ConvertXYtoCoordinate(b1, t / 2);
break;
case "t":
point1_sh = ConvertXYtoCoordinate(b1, 0);
break;
case "u":
point1_sh = ConvertXYtoCoordinate(((b1) + (t + r1)) / 2, 0);
break;
case "v":
point1_sh = ConvertXYtoCoordinate(t + r1, 0);
break;
case "cg":
point1_sh = ConvertXYtoCoordinate(x_cg, y_cg);
break;
}
return(point1_sh);
}
public virtual SecProp CalculateSecProp()
{
double E = Material.E;
double _E = E;
if (E == 0)
{
_E = 1E-10;
}
SecProp SP_shape = ShapeSecProp();
//find center of gravity
Coordinate cg_global = GetGlobalCGcoord();
double xcg = cg_global.x;
double ycg = cg_global.y;
//Shape Section Properties (before rotation)
double Ixx_sh = SP_shape.EIxx / _E;
double Iyy_sh = SP_shape.EIyy / _E;
double Ixy_sh = SP_shape.EIxy / _E;
//adjust for shape mirroring (if both are true then Ixy_l is positive again)
if (mirrorX)
{
Ixy_sh = -1 * Ixy_sh;
}
if (mirrorY)
{
Ixy_sh = -1 * Ixy_sh;
}
//Local Section Properties (after rotation)
double[] Irotated = SectionElements.RotatedElementProperties(Ixx_sh, Iyy_sh, Ixy_sh, theta);
double Ixx_l = Irotated[0];
double Iyy_l = Irotated[1];
double Ixy_l = Irotated[2];
double thetap = SectionElements.Theta_Principal(Ixx_l, Iyy_l, Ixy_l);
double[] Iprincipal = SectionElements.RotatedAxesProperties(Ixx_l, Iyy_l, Ixy_l, thetap);
double I1p = Iprincipal[0];
double I2p = Iprincipal[1];
double A = SP_shape.EA / _E;
SecProp sp = new SecProp
{
Xcg = xcg,
Ycg = ycg,
EA = E * A,
EIxx = E * Ixx_l,
EIyy = E * Iyy_l,
EIxy = E * Ixy_l,
EI1p = E * I1p,
EI2p = E * I2p,
thetap = thetap
};
return(sp);
}
