/// <summary>
/// Debug Code: Beam with simple supports at left and right ends that has two equal concentrated loads symmetrically placed.
/// Calculate results from User entered values and send output to Debug.
/// </summary>
/// <param name="loadConcentratedValuesLeft">Left concentrated load values.</param>
/// <param name="loadConcentratedValuesRight">Right concentrated load values.</param>
public static void CheckResultsSampleBeam02(LoadConcentratedValues loadConcentratedValuesLeft, LoadConcentratedValues loadConcentratedValuesRight)
{
Debug.WriteLine("\nBeam with simple supports at left and right ends that has two equal concentrated loads symmetrically placed:");
double E = CommonItems.doubleYoungsModulus;
double I = CommonItems.doubleInertia;
double l = CommonItems.doubleBeamLength;
double Pl = loadConcentratedValuesLeft.DoubleLoadConcentratedForce;
double a = loadConcentratedValuesLeft.DoubleLoadConcentratedPosition;
double Pr = loadConcentratedValuesRight.DoubleLoadConcentratedForce;
double b = l - loadConcentratedValuesRight.DoubleLoadConcentratedPosition;
Debug.WriteLine($"Inputs: E={E}, I={I}, l={l}, Pl={Pl}, a={a}, Pr={Pr}, b={b}");
if (Pl == Pr && a == b) //Check input.
{
// Reverse signs, upward forces are positive, downward forces are negative.
double Rleft = -(Pl);
double Rright = Rleft;
double Mmax = -(Pl * a); // Mmax occurs between loads.
double Dmax = Pl * a * (3d * l * l - 4d * a * a) / (24 * E * I);
double Da = Pl * a * (3d * l * a - 3d * a * a - a * a) / (6d * E * I);
Debug.WriteLine($"Reaction left={Rleft}, Reaction right={Rright}");
Debug.WriteLine($"Shear left={-Rleft}, Shear right={Rright}");
Debug.WriteLine($"Maximum moment occurs between loads is {Mmax}");
Debug.WriteLine($"Deflection @ a={a} is {Da}");
Debug.WriteLine($"Max deflection @ midpoint={l / 2d} is {Dmax}");
}
else
{
Debug.WriteLine($"Skipped results since entered load values not equal or not placed symmetrically.");
}
}
/// <summary>
/// Debug Code: Beam with simple supports at left and right ends that has single concentrated load at any point.
/// Calculate results from User entered values and send output to Debug.
/// </summary>
/// <param name="loadConcentratedValues">Concentrated load values.</param>
public static void CheckResultsSampleBeam01(LoadConcentratedValues loadConcentratedValues)
{
Debug.WriteLine("\nBeam with simple supports at left and right ends that has single concentrated load at any point:");
double E = CommonItems.doubleYoungsModulus;
double I = CommonItems.doubleInertia;
double l = CommonItems.doubleBeamLength;
double P = loadConcentratedValues.DoubleLoadConcentratedForce;
double a = loadConcentratedValues.DoubleLoadConcentratedPosition;
double b = l - a;
Debug.WriteLine($"Inputs: E={E}, I={I}, l={l}, P={P}, a={a}");
// Reverse signs, upward forces are positive, downward forces are negative.
double Rleft = -(P * b / l);
double Rright = -(P * a / l);
double Mmax = -(P * a * b / l); // Mmax occurs at point of load, 'a'.
double Da = P * a * a * b * b / (3d * E * I * l); // Deflection at 'a'
Debug.WriteLine($"Reaction left={Rleft}, Reaction right={Rright}");
Debug.WriteLine($"Shear left={-Rleft}, Shear right={Rright}");
Debug.WriteLine($"a={a}, Maximum moment is {Mmax}");
Debug.WriteLine($"a={a}, Maximum deflection is {Da}");
if (a > b) // Next values calculated and shown only if a > b.
{
double XDmax = Sqrt(a * (a + 2d * b) / 3d);
double Dmax = P * a * b * (a + 2d * b) * Sqrt(3d * a * (a + 2d * b)) / (27d * E * I * l);
Debug.WriteLine($"Max deflection occurs @ XDmax={XDmax}, Deflection @ XDmax={Dmax}");
}
}
/// <summary>
/// Debug Code: Beam with simple support at left end and fixed support at right end that has single concentrated load at any point.
/// Calculate results from User entered values and send output to Debug.
/// </summary>
/// <param name="loadConcentratedValues">Concentrated load values.</param>
public static void CheckResultsSampleBeam03(LoadConcentratedValues loadConcentratedValues)
{
Debug.WriteLine("\nBeam with simple support at left end and fixed support at right end that has single concentrated load at any point:");
double E = CommonItems.doubleYoungsModulus;
double I = CommonItems.doubleInertia;
double l = CommonItems.doubleBeamLength;
double P = loadConcentratedValues.DoubleLoadConcentratedForce;
double a = loadConcentratedValues.DoubleLoadConcentratedPosition;
double b = l - a;
Debug.WriteLine($"Inputs: E={E}, I={I}, l={l}, P={P}, a={a}");
// Reverse signs, upward forces are positive, downward forces are negative.
double Rleft = -(P * b * b * (a + 2d * l) / (2d * l * l * l));
double Rright = -(P * a * (3d * l * l - a * a) / (2d * l * l * l));
double Ma = -(Rleft * a); // Moment at 'a'.
double Da = (P * a * a * b * b * b) * (3d * l + a) / (12d * E * I * l * l * l); // Deflection at 'a'
double Ml = P * a * b * (a + l) / (2d * l * l); // Moment at left (fixed) end of beam.
// Not checking all available formula results since formulas are quite complex.
Debug.WriteLine($"Reaction left={Rleft}, Reaction right={Rright}");
Debug.WriteLine($"Shear left={-Rleft}, Shear right={Rright}");
Debug.WriteLine($"a={a}, Ma={Ma}");
Debug.WriteLine($"a={a}, Da={Da}");
Debug.WriteLine($"l={l}, Ml={Ml}");
}
/// <summary>
/// Debug Code: Cantilever beam with no support at left end and fixed support at right end that has single concentrated load at any point.
/// Calculate results from User entered values and send output to Debug.
/// </summary>
/// <param name="loadConcentratedValues">Concentrated load values.</param>
public static void CheckResultsSampleBeam04(LoadConcentratedValues loadConcentratedValues)
{
Debug.WriteLine("\nCantilever beam with no support at left end and fixed support at right end that has single concentrated load at any point:");
double E = CommonItems.doubleYoungsModulus;
double I = CommonItems.doubleInertia;
double l = CommonItems.doubleBeamLength;
double P = loadConcentratedValues.DoubleLoadConcentratedForce;
double a = loadConcentratedValues.DoubleLoadConcentratedPosition;
double b = l - a;
Debug.WriteLine($"Inputs: E={E}, I={I}, l={l}, P={P}, a={a}");
// Reverse signs, upward forces are positive, downward forces are negative.
double Rright = -(P);
double Ml = P * b; // Moment at left (fixed) end of beam.
double D0 = P * b * b * (3d * l - b) / (6d * E * I);
double Da = P * b * b * b / (3d * E * I);
Debug.WriteLine($"Reaction left={0d}, Reaction right={Rright}");
Debug.WriteLine($"Shear left={0d}, Shear right={Rright}");
Debug.WriteLine($"l={l}, Ml={Ml}");
Debug.WriteLine($"a={a}, Ma={0d}");
Debug.WriteLine($"a={a}, Da={Da}");
Debug.WriteLine($"At left end of beam, Dmax={D0}");
}
/*** private static methods follow *************************************************************************************/
/// <summary>
/// Calculate list of concentrated loads that simulate a uniform load. Concentrated loads are derived from segments of uniform load.
/// The area of each segment is calculated and an equivalent concentrated load is placed at centroid of each segment.
/// Parameters used to keep method independent from equivalent CommonItems values.
/// </summary>
/// <param name="loadUniformValues">Class used to save User entered uniform loads.</param>
/// <param name="doubleLoadUniformPositionLeft">Left uniform load position from left end of beam. Minimum value is 0d. Maximum value is doubleBeamLength.</param>
/// <param name="doubleLoadUniformPositionRight">Right uniform load position from left end of beam. Value must be > DoublePositionLeft and <= doubleBeamLength.</param>
/// <param name="doubleLoadUniformForceLeft">Left uniform load force. Uniform forces are distributed via straight line from left to right. Downward forces are negative.</param>
/// <param name="doubleLoadUniformForceRight">Right uniform load force. Uniform forces are distributed via straight line from left to right. Downward forces are negative.</param>
private static void UniformLoadSimulate(ref LoadUniformValues loadUniformValues, double doubleLoadUniformPositionLeft, double doubleLoadUniformPositionRight, double doubleLoadUniformForceLeft, double doubleLoadUniformForceRight)
{
loadUniformValues.DoublePositionLeft = doubleLoadUniformPositionLeft;
loadUniformValues.DoublePositionRight = doubleLoadUniformPositionRight;
loadUniformValues.DoubleForceLeft = doubleLoadUniformForceLeft;
loadUniformValues.DoubleForceRight = doubleLoadUniformForceRight;
loadUniformValues.DoubleLoadLength = doubleLoadUniformPositionRight - doubleLoadUniformPositionLeft;
if (doubleOutputSegmentLength == 0d)
{
// Case if doubleOutputSegmentLength was not entered or set to 0.
loadUniformValues.IntNumberOfSegments = 1;
loadUniformValues.DoubleSegmentLength = loadUniformValues.DoubleLoadLength;
}
else
{
// Calculate number of beam segments to spread uniform load across beam length.
int intBeamSegments = (int)Round(doubleBeamLength / doubleOutputSegmentLength, MidpointRounding.AwayFromZero);
double doubleBeamSegmentLength = doubleBeamLength / intBeamSegments;
//Debug.WriteLine($"CommonItems.UniformLoadSimulate(): doubleBeamLength={doubleBeamLength}, intBeamSegments={intBeamSegments}, doubleBeamSegmentLength={doubleBeamSegmentLength}");
// Use beam segment length as starting value to calculate load segment length.
if (doubleBeamSegmentLength >= loadUniformValues.DoubleLoadLength)
{
loadUniformValues.IntNumberOfSegments = 1;
loadUniformValues.DoubleSegmentLength = loadUniformValues.DoubleLoadLength;
}
else
{
loadUniformValues.IntNumberOfSegments = (int)Round(loadUniformValues.DoubleLoadLength / doubleBeamSegmentLength, MidpointRounding.AwayFromZero);
loadUniformValues.DoubleSegmentLength = loadUniformValues.DoubleLoadLength / loadUniformValues.IntNumberOfSegments;
}
}
//Debug.WriteLine($"CommonItems.UniformLoadSimulate(): loadUniformValues.IntNumberOfSegments={loadUniformValues.IntNumberOfSegments}, loadUniformValues.DoubleSegmentLength={loadUniformValues.DoubleSegmentLength}");
// Total uniform load force is area of uniform load. Absolute values need to be considered since forces can be positive or negative.
// Next two variables are used as 'ref' variables if uniform load is triangle or trapazoid. Therefore they need to be initialized to 0d.
double doubleArea = 0d; // Calculated segment area (force) of rectangle, triangle, or trapazoid.
double doubleCentroid = 0d; // Calculated segment centroid of rectangle, triangle, or trapazoid.
loadUniformValues.ListSimulatedLoads = new List <LoadConcentratedValues> {
};
// Case #1: Uniform load is a rectangle.
bool boolLoadIsRectangle = false;
if (loadUniformValues.DoubleForceLeft == loadUniformValues.DoubleForceRight)
{
//Debug.WriteLine($"EnterLoadsUniform.UniformLoadSimulate(): Uniform load is a rectangle.");
boolLoadIsRectangle = true;
doubleCentroid = loadUniformValues.DoublePositionLeft + loadUniformValues.DoubleSegmentLength / 2d;
doubleArea = loadUniformValues.DoubleForceLeft * loadUniformValues.DoubleLoadLength / loadUniformValues.IntNumberOfSegments;
if (loadUniformValues.IntNumberOfSegments == 1) // Applied single rectangle load.
{
//Debug.WriteLine($"CommonItems.UniformLoadSimulate(): Applied single rectangle load, doubleCentroid={doubleCentroid}, doubleArea={doubleArea}");
LoadConcentratedValues loadConcentratedValues = new LoadConcentratedValues
{
DoubleLoadConcentratedPosition = doubleCentroid,
DoubleLoadConcentratedForce = doubleArea,
DoubleLoadConcentratedMoment = 0d // Moment always zero if uniform load.
};
loadUniformValues.ListSimulatedLoads.Add(loadConcentratedValues);
}
else
{
doubleCentroid -= loadUniformValues.DoubleSegmentLength; // Initialize doubleCentroid value for first pass in next loop.
for (int i = 0; i < loadUniformValues.IntNumberOfSegments; i++)
{
doubleCentroid += loadUniformValues.DoubleSegmentLength;
//Debug.WriteLine($"CommonItems.UniformLoadSimulate(): Applied multiple rectangle loads, doubleCentroid={doubleCentroid}, doubleArea={doubleArea}");
LoadConcentratedValues loadConcentratedValues = new LoadConcentratedValues
{
DoubleLoadConcentratedPosition = doubleCentroid,
DoubleLoadConcentratedForce = doubleArea,
DoubleLoadConcentratedMoment = 0d // Moment always zero if uniform load.
};
loadUniformValues.ListSimulatedLoads.Add(loadConcentratedValues);
}
}
}
// Case #2: Uniform load is a triangle or trapazoid.
double doubleTriangleHeight; // Difference of ForceLeft and ForceRight is triangle height.
if (!boolLoadIsRectangle)
{
//Debug.WriteLine($"CommonItems.UniformLoadSimulate(): Uniform load is a triangle or trapazoid.");
if (loadUniformValues.IntNumberOfSegments == 1) // Applied single triangle or trapazoid uniform load.
{
doubleTriangleHeight = CalcTriangleHeight(loadUniformValues.DoubleForceLeft, loadUniformValues.DoubleForceRight);
if (Abs(loadUniformValues.DoubleForceLeft) > Abs(loadUniformValues.DoubleForceRight))
{
CalcCentroidValues(ref doubleArea, ref doubleCentroid, loadUniformValues.DoubleLoadLength, loadUniformValues.DoubleForceRight, doubleTriangleHeight, true);
//Debug.WriteLine($"CommonItems.UniformLoadSimulate(): Case: Abs(DoubleForceLeft) > Abs(DoubleForceRight), doubleArea={doubleArea}, doubleCentroid={doubleCentroid}");
}
else
{
CalcCentroidValues(ref doubleArea, ref doubleCentroid, loadUniformValues.DoubleLoadLength, loadUniformValues.DoubleForceLeft, doubleTriangleHeight, false);
//Debug.WriteLine($"CommonItems.UniformLoadSimulate(): Case: Abs(DoubleForceLeft) < Abs(DoubleForceRight), doubleArea={doubleArea}, doubleCentroid={doubleCentroid}");
}
doubleCentroid = loadUniformValues.DoublePositionLeft + doubleCentroid;
//Debug.WriteLine($"CommonItems.UniformLoadSimulate(): Case: Applied single triangle or trapazoid uniform load, doubleCentroid={doubleCentroid}, doubleArea={doubleArea}");
LoadConcentratedValues loadConcentratedValues = new LoadConcentratedValues
{
DoubleLoadConcentratedPosition = doubleCentroid,
DoubleLoadConcentratedForce = doubleArea,
DoubleLoadConcentratedMoment = 0d // Moment always zero if uniform load.
};
loadUniformValues.ListSimulatedLoads.Add(loadConcentratedValues);
}
else
{
// Equation of slope is m=(y2-y1)/(x2-x1) where m is the slope. More at: https://cls.syr.edu/mathtuneup/grapha/Unit4/Unit4a.html
double doubleSlope = (loadUniformValues.DoubleForceRight - loadUniformValues.DoubleForceLeft) / loadUniformValues.DoubleLoadLength;
// Equation of a line is y=mx+b where m is the slope and b is the y-intercept.
double doubleInterceptForce = loadUniformValues.DoubleForceLeft; // Save value for use below.
double doubleInterceptPosition = loadUniformValues.DoublePositionLeft; // Save value for use below.
double doubleLoadSegmentPositionLeft = loadUniformValues.DoublePositionLeft - loadUniformValues.DoubleSegmentLength; // Initialize value for first pass in next loop.
double doubleSegmentPositionLeft; // Initialize value for first pass in next loop.
double doubleSegmentForceLeft; // Initialize value for first pass in next loop.
double doubleSegmentPositionRight = loadUniformValues.DoublePositionLeft; // Initialize value for first pass in next loop.
double doubleSegmentForceRight = loadUniformValues.DoubleForceLeft; // Initialize value for first pass in next loop.
//Debug.WriteLine($"CommonItems.UniformLoadSimulate(): doubleSlope={doubleSlope}, doubleInterceptPosition={doubleInterceptPosition}, doubleInterceptForce={doubleInterceptForce}, loadUniformValues.DoubleSegmentLength={loadUniformValues.DoubleSegmentLength}");
for (int i = 0; i < loadUniformValues.IntNumberOfSegments; i++)
{
doubleSegmentPositionLeft = doubleSegmentPositionRight;
doubleSegmentPositionRight = doubleSegmentPositionLeft + loadUniformValues.DoubleSegmentLength;
doubleSegmentForceLeft = doubleSegmentForceRight;
doubleSegmentForceRight = doubleSlope * (doubleSegmentPositionRight - doubleInterceptPosition) + doubleInterceptForce;
//Debug.WriteLine($"CommonItems.UniformLoadSimulate(): Segment {i + 1} of {loadUniformValues.IntNumberOfSegments}: Line points are (doubleSegmentPositionLeft={doubleSegmentPositionLeft}, doubleSegmentForceLeft={doubleSegmentForceLeft}), (doubleSegmentPositionRight={doubleSegmentPositionRight}, doubleSegmentForceRight={doubleSegmentForceRight})");
doubleTriangleHeight = CalcTriangleHeight(doubleSegmentForceLeft, doubleSegmentForceRight);
if (Abs(doubleSegmentForceLeft) > Abs(doubleSegmentForceRight))
{
CalcCentroidValues(ref doubleArea, ref doubleCentroid, loadUniformValues.DoubleSegmentLength, doubleSegmentForceRight, doubleTriangleHeight, true);
//Debug.WriteLine($"CommonItems.UniformLoadSimulate(): Abs(doubleSegmentForceLeft) > Abs(doubleSegmentForceRight), doubleArea={doubleArea}, doubleCentroid={doubleCentroid}");
}
else
{
CalcCentroidValues(ref doubleArea, ref doubleCentroid, loadUniformValues.DoubleSegmentLength, doubleSegmentForceLeft, doubleTriangleHeight, false);
//Debug.WriteLine($"CommonItems.UniformLoadSimulate(): Abs(doubleSegmentForceLeft) < Abs(doubleSegmentForceRight), doubleArea={doubleArea}, doubleCentroid={doubleCentroid}");
}
doubleLoadSegmentPositionLeft += loadUniformValues.DoubleSegmentLength;
doubleCentroid = doubleLoadSegmentPositionLeft + doubleCentroid;
//Debug.WriteLine($"CommonItems.UniformLoadSimulate(): Applied sloping uniform loads {i + 1} of {loadUniformValues.IntNumberOfSegments}, doubleCentroid={doubleCentroid}, doubleArea={doubleArea}");
LoadConcentratedValues loadConcentratedValues = new LoadConcentratedValues
{
DoubleLoadConcentratedPosition = doubleCentroid,
DoubleLoadConcentratedForce = doubleArea,
DoubleLoadConcentratedMoment = 0d // Moment always zero if uniform load.
};
loadUniformValues.ListSimulatedLoads.Add(loadConcentratedValues);
}
}
}
}