protected override double GetElementForce(ILocationArrayElement el, Point2D Center, ILocationArrayElement furthestBolt, double angle)
{
double Delta_u = furthestBolt.LimitDeformation;
double LiMax = furthestBolt.GetDistanceToPoint(Center);
double xi = el.Location.X - Center.X;
double yi = el.Location.Y - Center.Y;
double ri = Math.Sqrt(xi * xi + yi * yi); //radial distance from center to this element
double Delta = Delta_u * ri / LiMax; //this bolt deformation
double iRn = Math.Pow(1 - Math.Exp(-10.0 * Delta), 0.55); //force developed by this element
return iRn;
}
protected override double GetElementForce(ILocationArrayElement el, Point2D Center, ILocationArrayElement furthestBolt, double angle)
{
double Delta_u = furthestBolt.LimitDeformation;
double LiMax = furthestBolt.GetDistanceToPoint(Center);
double xi = el.Location.X - Center.X;
double yi = el.Location.Y - Center.Y;
double ri = Math.Sqrt(xi * xi + yi * yi); //radial distance from center to this element
double Delta = Delta_u * ri / LiMax; //this bolt deformation
double iRn = Math.Pow(1 - Math.Exp(-10.0 * Delta), 0.55); //force developed by this element
return(iRn);
}
/// <summary>
/// Returns a unit vector of the resultant force in the element. Which is perpendicular to
/// the ray from center of rotation to the element.
/// </summary>
/// <param name="e">Element</param>
/// <param name="c">Center of rotation</param>
/// <returns></returns>
protected Vector2d GetElementForceUnitVector(ILocationArrayElement e, Point2D c)
{
double BX = e.Location.X - c.X;
double BY = e.Location.Y - c.Y;
//Normal vector:
// cross product definition
//AXB=(AyBz -AzBy)i -(AxBz -AzBx)j +(AxBy -AyBx)k
//assuming AZ = 1, AX =AY =0;
if (BX == 0 && BY == 0)
{
return(new Vector2d(0, 0));
}
else
{
Vector2d perpVector = new Vector2d(-BY, BX);
return(perpVector.GetUnit());
}
}
public double GetPureMomentCoefficient()
{
Point2D centerOfGravity = GetGroupCenterOfGravity();
ILocationArrayElement furthestBolt = FindUltimateDeformationElement(centerOfGravity);
double LiMax = FindLargestElementDistanceFromCenter(centerOfGravity);
double C_prime = 0;
double Delta_Max = 0.34;
foreach (var bolt in Bolts)
{
double l_i = bolt.GetDistanceToPoint(centerOfGravity);
double C_primeThis = l_i * Math.Pow(1 - Math.Exp(-(10.0 * l_i * Delta_Max) / LiMax), 0.55);
//Manual Equation 7-21
C_prime = C_prime + C_primeThis;
}
return(C_prime);
}
protected override double GetElementForce(ILocationArrayElement element, Point2D center, ILocationArrayElement controllingWeld, double angle)
{
FilletWeldElement el = element as FilletWeldElement;
FilletWeldElement cp = controllingWeld as FilletWeldElement;
double elementForce = 0;
if (el != null && cp != null)
{
double theta = el.GetAngleTheta(center);
//this weld actual deformation
double Delta_r = el.DistanceFromCentroid * (cp.LimitDeformation / cp.DistanceFromCentroid);
//this weld ultimate deformation
double pi = Delta_r / el.UltimateLoadDeformation;
//double pi = Delta_r / el.LimitDeformation;
//calculate element force
elementForce = el.CalculateNominalShearStrength(pi, theta);
}
return(elementForce);
}
private void IterateThroughElements(ILocationArrayElement controllingElement, double AngleOfLoad)
{
M = 0;
Ry = 0;
Rx = 0;
J_ic = 0;
foreach (var el in elements)
{
// adjust coordinate
double xi = el.Location.X - Center.X; //delta X
double yi = el.Location.Y - Center.Y; //delta Y
double ri = Math.Sqrt(xi * xi + yi * yi); //radial distance from center to this element
double Rn_i = GetElementForce(el, Center, controllingElement, AngleOfLoad);
//Contribution of this bolt to the overall response of the group
M = M + (Rn_i) * ri; //Moment
Vector2d ForceUnitVector = GetElementForceUnitVector(el, Center);
Ry = Ry + Rn_i * ForceUnitVector.Y; //Vertical Force
Rx = Rx + Rn_i * ForceUnitVector.X; //Horizontal Force
J_ic = J_ic + Math.Pow(ri, 2);
}
}
/// <summary>
/// Finds bolt or weld group ultimate strength (force)
/// using instantaneous center of rotation method
/// </summary>
/// <param name="e_x">Horizontal component of eccentricity</param>
/// <param name="AngleOfLoad">Angle of load from vertical</param>
/// <returns></returns>
protected double FindUltimateEccentricForce(double e_x, double AngleOfLoad)
{
bool iterationYieldedResult = false;
int MaxNumberOfIterations = 1999;
//iteration variables
double P = 0.0;
M = 0.0;
J_ic = 0.0;
Ry = 0.0;
Rx = 0.0;
double Pprev = 0;
double Mapfunc = 0.0;
ILocationArrayElement controllingElement = null;
double Rot = AngleOfLoad.ToRadians();
double Ec = e_x;
int N = Elements.Count();
//Initial assumption of bolt center
Center = new Point2D(0, 0);
int iterationCount = 0;
while (iterationYieldedResult == false)
{
controllingElement = FindUltimateDeformationElement(Center);
//Iterate through all bolts/welds and using force-displacement
//relationship find the force in each element
//then find the contribution of this element to overall
//Force and Moment of the group.
//Calculate M and J for all elements
IterateThroughElements(controllingElement, AngleOfLoad);
//Define a force vector due to unit force
Vector2d UnitForce = new Vector2d(Math.Sin(Rot), Math.Cos(Rot));
//note: it is assumed that the force goes through the coordinate origin
//therefore for standard weld geometries the coordinates are by adding Ec to the
//IC location
Vector2d PositionVector;
PositionVector = new Vector2d(Ec - Center.X, -Center.Y);
//Distance between IC and and Force vector
double e = UnitForce.FindDistance(PositionVector); //Internal moment arm
P = M / e; //resolving the internal forces into a resultant at the given moment arm
double Py = P * Math.Cos(Rot);
double Px = P * Math.Sin(Rot);
double Fyy;
double Fxx = Px - Rx; //Horizontal Unbalanced Force
if (Ec >= 0)
{
Fyy = Py - Ry; //Vertical Unbalanced Force
}
else
{
Fyy = Py + Ry;
}
double Pp = Math.Sqrt(Fyy * Fyy + Fxx * Fxx); //Unbalanced force resultant
bool CovergedCriteria1 = Math.Abs(Fyy) <= 0.0001 && Math.Abs(Fxx) <= 0.0001 ? true : false; //reached convergence tolerance
bool CovergedCriteria2 = (iterationCount > MaxNumberOfIterations)? true :false;
bool CovergedCriteria3 = iterationCount > 200 && Pp > Pprev ? true : false;
if (CovergedCriteria1 == true)
{
break;
}
else
{
if (CovergedCriteria2 == true)
{
throw new Exception("Failed to find solution for bolt group coefficient. Maximum number of iterations in bolt group has been exceeded.");
}
else
{
if (CovergedCriteria3 == true)
{
break;
}
//throw new Exception(String.Format("Failed to find solution for bolt group coefficient.The resultant force increment increased after iteration {0}.", iterationCount ));
}
}
//if the solution hasn't converged update values for next iteration
Pprev = Pp;
Mapfunc = J_ic / (N * M); //Mapping function
//I.C. location on x-axis from bolt group C.G.
if (e_x >= 0)
{
Center.X = Center.X - Fyy * Mapfunc;
Center.Y = Center.Y + Fxx * Mapfunc;
}
else
{
Center.X = Center.X + Fyy * Mapfunc;
Center.Y = Center.Y - Fxx * Mapfunc;
}
iterationCount++;
}
#region Final run through elelents (for debug only)
IterateThroughElements(controllingElement, AngleOfLoad);
#endregion
return(P);
}
/// <summary>
/// Gets individual element force based on the response of the entire group
/// </summary>
/// <param name="element"> Bolt or weld element point</param>
/// <param name="Center">Instantaneous Center of rotation</param>
/// <param name="ControllingElement">Element in group the having the governing deformation.</param>
/// <param name="angle">Angle of force application, measured from Y-axis</param>
/// <returns></returns>
protected abstract double GetElementForce(ILocationArrayElement element, Point2D Center,
ILocationArrayElement ControllingElement, double angle);
protected override double GetElementForce(ILocationArrayElement element, Point2D center, ILocationArrayElement controllingWeld, double angle)
{
FilletWeldElement el = element as FilletWeldElement;
FilletWeldElement cp = controllingWeld as FilletWeldElement;
double elementForce =0;
if (el!=null && cp !=null)
{
double theta = el.GetAngleTheta(center);
//this weld actual deformation
double Delta_r = el.DistanceFromCentroid * (cp.LimitDeformation / cp.DistanceFromCentroid);
//this weld ultimate deformation
double pi = Delta_r / el.UltimateLoadDeformation;
//double pi = Delta_r / el.LimitDeformation;
//calculate element force
elementForce = el.CalculateNominalShearStrength(pi, theta);
}
return elementForce;
}
/// <summary>
/// Returns a unit vector of the resultant force in the element. Which is perpendicular to
/// the ray from center of rotation to the element.
/// </summary>
/// <param name="e">Element</param>
/// <param name="c">Center of rotation</param>
/// <returns></returns>
protected Vector2d GetElementForceUnitVector(ILocationArrayElement e, Point2D c)
{
double BX = e.Location.X - c.X;
double BY = e.Location.Y - c.Y;
//Normal vector:
// cross product definition
//AXB=(AyBz -AzBy)i -(AxBz -AzBx)j +(AxBy -AyBx)k
//assuming AZ = 1, AX =AY =0;
if (BX==0 && BY == 0)
{
return new Vector2d(0, 0);
}
else
{
Vector2d perpVector = new Vector2d(-BY, BX);
return perpVector.GetUnit();
}
}
/// <summary>
/// Gets individual element force based on the response of the entire group
/// </summary>
/// <param name="element"> Bolt or weld element point</param>
/// <param name="Center">Instantaneous Center of rotation</param>
/// <param name="ControllingElement">Element in group the having the governing deformation.</param>
/// <param name="angle">Angle of force application, measured from Y-axis</param>
/// <returns></returns>
protected abstract double GetElementForce(ILocationArrayElement element, Point2D Center,
ILocationArrayElement ControllingElement, double angle);
private void IterateThroughElements(ILocationArrayElement controllingElement, double AngleOfLoad)
{
M = 0;
Ry = 0;
Rx = 0;
J_ic = 0;
foreach (var el in elements)
{
// adjust coordinate
double xi = el.Location.X - Center.X; //delta X
double yi = el.Location.Y - Center.Y; //delta Y
double ri = Math.Sqrt(xi * xi + yi * yi); //radial distance from center to this element
double Rn_i = GetElementForce(el, Center, controllingElement, AngleOfLoad);
//Contribution of this bolt to the overall response of the group
M = M + (Rn_i) * ri; //Moment
Vector2d ForceUnitVector = GetElementForceUnitVector(el, Center);
Ry = Ry + Rn_i * ForceUnitVector.Y; //Vertical Force
Rx = Rx + Rn_i * ForceUnitVector.X; //Horizontal Force
J_ic = J_ic + Math.Pow(ri, 2);
}
}
