public void LoadInternalForce_concentratedLLoad_eulerbernoullybeam_dirZ_fy()
{
//internal force of 2 node beam beam with uniform load and both ends fixed
var w = 2.0;
var forceLocation = 0.5; //[m]
var L = 4; //[m]
//var model = new Model();
var nodes = new Node[2];
nodes[0] = (new Node(0, 0, 0)
{
Label = "n0"
});
nodes[1] = (new Node(4, 0, 0)
{
Label = "n1"
});
var elm = new BarElement(nodes[0], nodes[1])
{
Label = "e0"
};
var u1 = new Loads.ConcentratedLoad();
u1.Case = LoadCase.DefaultLoadCase;
u1.Force = new Force(0, -w, 0, 0, 0, 0);
u1.CoordinationSystem = CoordinationSystem.Global;
u1.ForceIsoLocation = new IsoPoint(elm.LocalCoordsToIsoCoords(forceLocation)[0]);
var hlpr = new EulerBernoulliBeamHelper(BeamDirection.Z, elm);
var length = (elm.Nodes[1].Location - elm.Nodes[0].Location).Length;
foreach (var x in CalcUtil.Divide(length, 10))
{
var xi = elm.LocalCoordsToIsoCoords(x);
//https://www.engineeringtoolbox.com/beams-fixed-both-ends-support-loads-deflection-d_809.html
var mi = 0.0;
var vi = 0.0;
{
var a = forceLocation;
var b = L - a;
var ma = -w * a * b * b / (L * L);
var mb = -w * a * a * b / (L * L);
var mf = 2 * w * a * a * b * b / (L * L * L);
double x0, x1, y0, y1;
if (x < forceLocation)
{
x0 = 0;
x1 = forceLocation;
y0 = ma;
y1 = mf;
}
else
{
x0 = forceLocation;
x1 = L;
y0 = mf;
y1 = mb;
}
var m = (y1 - y0) / (x1 - x0);
mi = m * (x - x0) + y0;
var ra = w * (3 * a + b) * b * b / (L * L * L); //1f
var rb = w * (a + 3 * b) * a * a / (L * L * L); //1g
if (x < forceLocation)
{
vi = ra;
}
else
{
vi = -rb;
}
}
var ends = hlpr.GetLocalEquivalentNodalLoads(elm, u1);
var testFrc = hlpr.GetLoadInternalForceAt(elm, u1, new double[] { xi[0] * (1 - 1e-9) }).ToForce();
var exactFrc = new Force(fx: 0, fy: vi, fz: 0, mx: 0, my: 0, mz: +mi);
var dm = Math.Abs(testFrc.Mz) - Math.Abs(exactFrc.Mz);
var df = Math.Abs(testFrc.Fy) - Math.Abs(exactFrc.Fy);
Assert.IsTrue(Math.Abs(dm) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(df) < 1e-5, "invalid value");
}
{
var end1 = hlpr.GetLocalEquivalentNodalLoads(elm, u1);
var f0 = hlpr.GetLoadInternalForceAt(elm, u1, new double[] { -1 + 1e-9 }).ToForce();;
var sum = end1[0] + f0;
Assert.IsTrue(Math.Abs(sum.Forces.Length) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(sum.Moments.Length) < 1e-5, "invalid value");
}
}
public void LoadInternalForce_concentratedLLoad_eulerbernoullybeam_dirY_My()
{
//internal force of 2 node beam beam with uniform load and both ends fixed
var w = 2.0;
var forceLocation = 2.123; //[m]
var L = 4; //[m]
//var model = new Model();
var nodes = new Node[2];
nodes[0] = (new Node(0, 0, 0)
{
Label = "n0"
});
nodes[1] = (new Node(4, 0, 0)
{
Label = "n1"
});
var elm = new BarElement(nodes[0], nodes[1])
{
Label = "e0"
};
var u1 = new Loads.ConcentratedLoad();
u1.Case = LoadCase.DefaultLoadCase;
u1.Force = new Force(0, 0, 0, 0, w, 0);
u1.CoordinationSystem = CoordinationSystem.Global;
u1.ForceIsoLocation = new IsoPoint(elm.LocalCoordsToIsoCoords(forceLocation)[0]);
var hlpr = new EulerBernoulliBeamHelper(BeamDirection.Y, elm);
var length = (elm.Nodes[1].Location - elm.Nodes[0].Location).Length;
//foreach (var x in CalcUtil.Divide(length, 10))
{
var x = 2.4;
var xi = elm.LocalCoordsToIsoCoords(x);
var mi = 0.0;
var vi = 0.0;
{
//https://www.amesweb.info/Beam/Fixed-Fixed-Beam-Bending-Moment.aspx
var a = forceLocation;
var b = L - a;
var ma = w / (L * L) * (L * L - 4 * a * L + 3 * a * a);
var mb = w / (L * L) * (3 * a * a - 2 * a * L);
var ra = -6 * w * a / (L * L * L) * (L - a); //R1
var rb = 6 * w * a / (L * L * L) * (L - a); //R1
mi = ma + ra * x - ((x > forceLocation) ? w : 0.0);
vi = ra;
}
var ends = hlpr.GetLocalEquivalentNodalLoads(elm, u1);
var testFrc = hlpr.GetLoadInternalForceAt(elm, u1, new double[] { xi[0] * (1 - 1e-9) }).ToForce();
var exactFrc = new Force(fx: 0, fy: 0, fz: vi, mx: 0, my: -mi, mz: 0);
var dm = Math.Abs(testFrc.My) - Math.Abs(exactFrc.My); //regarding value
var df = Math.Abs(testFrc.Fz) - Math.Abs(exactFrc.Fz); //regarding value
Assert.IsTrue(Math.Abs(dm) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(df) < 1e-5, "invalid value");
}
{
var end1 = hlpr.GetLocalEquivalentNodalLoads(elm, u1);
var f0 = hlpr.GetLoadInternalForceAt(elm, u1, new double[] { -1 + 1e-9 }).ToForce();;
var sum = end1[0] + f0;
Assert.IsTrue(Math.Abs(sum.Forces.Length) < 1e-5, "invalid value"); //regarding sign
Assert.IsTrue(Math.Abs(sum.Moments.Length) < 1e-5, "invalid value"); //regarding sign
}
}
public void LoadInternalForce_concentratedLLoad_eulerbernoullybeam_dirY_My()
{
//internal force of 2 node beam beam with uniform load and both ends fixed
var w = 2.0;
var forceLocation = 0.5; //[m]
var L = 4; //[m]
//var model = new Model();
var nodes = new Node[2];
nodes[0] = (new Node(0, 0, 0)
{
Label = "n0"
});
nodes[1] = (new Node(4, 0, 0)
{
Label = "n1"
});
var elm = new BarElement(nodes[0], nodes[1])
{
Label = "e0"
};
var u1 = new Loads.ConcentratedLoad();
u1.Case = LoadCase.DefaultLoadCase;
u1.Force = new Force(0, 0, 0, 0, w, 0);
u1.CoordinationSystem = CoordinationSystem.Global;
u1.ForceIsoLocation = new IsoPoint(elm.LocalCoordsToIsoCoords(forceLocation)[0]);
var hlpr = new EulerBernoulliBeamHelper(BeamDirection.Y);
var length = (elm.Nodes[1].Location - elm.Nodes[0].Location).Length;
foreach (var x in CalcUtil.Divide(length, 10))
{
var xi = elm.LocalCoordsToIsoCoords(x);
var mi = 0.0;
var vi = 0.0;
{
//https://www.amesweb.info/Beam/Fixed-Fixed-Beam-Bending-Moment.aspx
var a = forceLocation;
var b = L - a;
var ma = -w / (L * L) * (L * L - 4 * a * L + 3 * a * a);
var mb = -w / (L * L) * (3 * a * a - 2 * a * L);
//var m = (y1 - y0) / (x1 - x0);
var ra = -6 * w * a / (L * L * L) * (L - a); //R1
var rb = -ra; //R2
mi = ma + ra * x + ((x > forceLocation) ? w : 0.0);
vi = ra;
}
var ends = hlpr.GetLocalEquivalentNodalLoads(elm, u1);
var testFrc = hlpr.GetLoadInternalForceAt(elm, u1, new double[] { xi[0] * (1 - 1e-9) });
var exactFrc = new Force(fx: 0, fy: 0, fz: vi, mx: 0, my: -mi, mz: 0);
var dm = testFrc.FirstOrDefault(i => i.Item1 == DoF.Ry).Item2 - exactFrc.My;
var df = testFrc.FirstOrDefault(i => i.Item1 == DoF.Dz).Item2 + exactFrc.Fz;
Assert.IsTrue(Math.Abs(dm) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(df) < 1e-5, "invalid value");
}
}
