//[TestMethod]
public void LoadInternalForce_trapezoidload_eulerbernoullybeam_dirY()
{
//internal force of 2 node beam beam with uniform load and both ends fixed
var w = 2.0;
//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.(LoadCase.DefaultLoadCase, -Vector.K, w, CoordinationSystem.Global);
new Loads.PartialNonUniformLoad();
u1.CoordinationSystem = CoordinationSystem.Global;
u1.Direction = -Vector.K;
// u1.StartLocation = new double[] { };
// u1.EndLocation = new double[] { };
//u1.StartMagnitude
var hlpr = new ElementHelpers.EulerBernoulliBeamHelper(ElementHelpers.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 = w / 12 * (6 * length * x - 6 * x * x - length * length);
var vi = w * (length / 2 - x);
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 d = testFrc.FirstOrDefault(i => i.Item1 == DoF.Ry).Item2 + exactFrc.My;
Assert.IsTrue(d < 1e-5, "invalid value");
}
}
public void LoadInternalForce_uniformload_eulerbernoullybeam_endrelease()
{
//load internal force of beam with hinged ends should match the end releases
//if hinged then moment should be zero and so on
//added for issue#48
var w = 2.0;
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.UniformLoad(LoadCase.DefaultLoadCase, -Vector.K, w, CoordinationSystem.Global);
var hlpr = new ElementHelpers.EulerBernoulliBeamHelper(BeamDirection.Y, elm);
var length = (elm.Nodes[1].Location - elm.Nodes[0].Location).Length;
elm.NodalReleaseConditions[0] = Constraints.MovementFixed;
elm.NodalReleaseConditions[1] = Constraints.MovementFixed & Constraints.FixedRX;
foreach (var x in CalcUtil.Divide(length, 10))
{
var xi = elm.LocalCoordsToIsoCoords(x);
var vi = -w * (length / 2 - x);
var mi = -w / 2 * (length * x - x * x);
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 d = testFrc - exactFrc;
var dm = d.My;
var df = d.Fz;
Assert.IsTrue(dm.FEquals(0, 1e-5), "invalid value");
Assert.IsTrue(df.FEquals(0, 1e-5), "invalid value");
}
}
public static void TestFixedInternalForce2()
{
//internal force of 2 node beam beam with uniform load and both ends fixed
var w = 2.0;
//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.UniformLoad(LoadCase.DefaultLoadCase, -Vector.J, w, CoordinationSystem.Global);
var hlpr = new ElementHelpers.EulerBernoulliBeamHelper(ElementHelpers.BeamDirection.Z);
var length = (elm.Nodes[1].Location - elm.Nodes[0].Location).Length;
hlpr.GetLoadInternalForceAt(elm, u1, new double[] { -0.5774 });
foreach (var x in CalcUtil.Divide(length, 10))
{
var xi = elm.LocalCoordsToIsoCoords(x);
var mi = w / 12 * (6 * length * x - 6 * x * x - length * length);
var vi = w * (length / 2 - x);
var testFrc = hlpr.GetLoadInternalForceAt(elm, u1, new double[] { xi[0] * (1 - 1e-9) });
var exactFrc = new Force(fx: 0, fy: vi, fz: 0, mx: 0, my: 0, mz: mi);
var d = testFrc.FirstOrDefault(i => i.Item1 == DoF.Rz).Item2 + exactFrc.Mz;
if (Math.Abs(d) > 1e-5)
{
}
}
}
public void LoadEquivalentNodalLoads_partialnonuniformload_eulerbernoullybeam_dirY()
{
//internal force of 2 node beam beam with uniform load and both ends fixed
var w = 2.0;
var x1 = -1;
var x2 = 1;
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.PartialNonUniformLoad();
u1.Direction = -Vector.K;
u1.CoordinationSystem = CoordinationSystem.Global;
u1.SeverityFunction = Mathh.Polynomial.FromPoints(1.0, w);
u1.StartLocation = new IsoPoint(x1);
u1.EndLocation = new IsoPoint(x2);
var hlpr = new ElementHelpers.EulerBernoulliBeamHelper(ElementHelpers.BeamDirection.Y, elm);
var loads = hlpr.GetLocalEquivalentNodalLoads(elm, u1);
var L = (elm.Nodes[1].Location - elm.Nodes[0].Location).Length;
var m1 = w * L * L / 12;
var m2 = -w * L * L / 12;
var v1 = -w * L / 2;
var v2 = -w * L / 2;
Assert.IsTrue(Math.Abs(loads[0].Fz - v1) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(loads[0].My - m1) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(loads[1].Fz - v2) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(loads[1].My - m2) < 1e-5, "invalid value");
}
public void LoadEquivalentNodalLoads_uniformload_eulerbernoullybeam_dirZ()
{
//internal force of 2 node beam beam with uniform load and both ends fixed
var w = 2.0;
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.UniformLoad(LoadCase.DefaultLoadCase, -Vector.J, w, CoordinationSystem.Global);
var hlpr = new ElementHelpers.EulerBernoulliBeamHelper(ElementHelpers.BeamDirection.Z, elm);
var loads = hlpr.GetLocalEquivalentNodalLoads(elm, u1);
var L = (elm.Nodes[1].Location - elm.Nodes[0].Location).Length;
var m1 = -w * L * L / 12;
var m2 = w * L * L / 12;
var v1 = -w * L / 2;
var v2 = -w * L / 2;
Assert.IsTrue(Math.Abs(loads[0].Fy - v1) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(loads[0].Mz - m1) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(loads[1].Fy - v2) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(loads[1].Mz - m2) < 1e-5, "invalid value");
}
public void LoadEquivalentNodalLoads_ConcentratedLod_eulerbernoullybeam_dirY_My_End()
{
var l = 4.0;
var w = 2.0;
var a = l;
var nodes = new Node[2];
nodes[0] = (new Node(0, 0, 0)
{
Label = "n0"
});
nodes[1] = (new Node(l, 0, 0)
{
Label = "n1"
});
var elm = new BarElement(nodes[0], nodes[1])
{
Label = "e0"
};
var f = new Force(0, 0, 0, 0, w, 0);
var loc = new IsoPoint(elm.LocalCoordsToIsoCoords(a)[0]);
var u1 = new Loads.ConcentratedLoad(f, loc, CoordinationSystem.Global);
var hlpr = new ElementHelpers.EulerBernoulliBeamHelper(ElementHelpers.BeamDirection.Y, elm);
var loads = hlpr.GetLocalEquivalentNodalLoads(elm, u1);
var d0 = Force.Zero;
var d1 = loads[1] - f;
Assert.IsTrue(Math.Abs(d0.Forces.Length) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(d0.Moments.Length) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(d1.Forces.Length) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(d1.Moments.Length) < 1e-5, "invalid value");
}
public void LoadEquivalentNodalLoads_ConcentratedLod_eulerbernoullybeam_dirY_My_Start()
{
//equivalent nodal load of a concentrated load applied at start point is same as load itself!
var w = 2.0;
var a = 0;
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(new Force(0, 0, 0, 0, w, 0), new IsoPoint(elm.LocalCoordsToIsoCoords(a)[0]), CoordinationSystem.Global);
var hlpr = new ElementHelpers.EulerBernoulliBeamHelper(ElementHelpers.BeamDirection.Y, elm);
var loads = hlpr.GetLocalEquivalentNodalLoads(elm, u1);
var d0 = loads[0] - u1.Force;
var d1 = Force.Zero;
Assert.IsTrue(Math.Abs(d0.Forces.Length) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(d0.Moments.Length) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(d1.Forces.Length) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(d1.Moments.Length) < 1e-5, "invalid value");
}
public void LoadInternalForce_uniformload_eulerbernoullybeam_dirZ()
{
//internal force of 2 node beam beam with uniform load and both ends fixed
var w = 2.0;
//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.UniformLoad(LoadCase.DefaultLoadCase, -Vector.J, w, CoordinationSystem.Global);
var hlpr = new ElementHelpers.EulerBernoulliBeamHelper(ElementHelpers.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);
var mi = w / 12 * (6 * length * x - 6 * x * x - length * length);
var vi = -w * (length / 2 - x);
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 LoadEquivalentNodalLoads_ConcentratedLod_eulerbernoullybeam_dirZ_Fy()
{
//internal force of 2 node beam beam with uniform load and both ends fixed
// ^y w
// | ||
// | \/
// ====================================== --> x
// /
// /z
var w = 2.0;
var a = 2;
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(new Force(0, -w, 0, 0, 0, 0), new IsoPoint(elm.LocalCoordsToIsoCoords(a)[0]), CoordinationSystem.Global);
var hlpr = new ElementHelpers.EulerBernoulliBeamHelper(ElementHelpers.BeamDirection.Z, elm);
var loads = hlpr.GetLocalEquivalentNodalLoads(elm, u1);
var L = (elm.Nodes[1].Location - elm.Nodes[0].Location).Length;
var b = L - a;
var ma = w * a * b * b / (L * L);
var mb = w * a * a * b / (L * L);
var ra = w * (3 * a + b) * b * b / (L * L * L); //1f
var rb = w * (a + 3 * b) * a * a / (L * L * L); //1g
var expectedF0 = new Force(0, -ra, 0, 0, 0, -ma);
var expectedF1 = new Force(0, -rb, 0, 0, 0, mb);
/*
* var m1 = -w * L * L / 12;
* var m2 = w * L * L / 12;
*
* var v1 = -w * L / 2;
* var v2 = -w * L / 2;
*/
var d0 = loads[0] - expectedF0;
var d1 = loads[1] - expectedF1;
Assert.IsTrue(Math.Abs(d0.Forces.Length) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(d0.Moments.Length) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(d1.Forces.Length) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(d1.Moments.Length) < 1e-5, "invalid value");
}
public void LoadEquivalentNodalLoads_ConcentratedLod_eulerbernoullybeam_dirZ_Mz()
{
//internal force of 2 node beam beam with uniform load and both ends fixed
//https://www.amesweb.info/Beam/Fixed-Fixed-Beam-Bending-Moment.aspx
// ^
// ^m m0 ^
// | /z |
// | / |
// ====================================== --> x
//
var w = 2.0;
var a = 1.234560;
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(new Force(0, 0, 0, 0, 0, w), new IsoPoint(elm.LocalCoordsToIsoCoords(a)[0]), CoordinationSystem.Global);
var hlpr = new ElementHelpers.EulerBernoulliBeamHelper(ElementHelpers.BeamDirection.Z, elm);
var loads = hlpr.GetLocalEquivalentNodalLoads(elm, u1);
var L = (elm.Nodes[1].Location - elm.Nodes[0].Location).Length;
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
var expectedR1 = new Force(0, ra, 0, 0, 0, ma); //expected reaction 1
var expectedR2 = new Force(0, rb, 0, 0, 0, -mb); //expected reaction 2
/*
* var m1 = -w * L * L / 12;
* var m2 = w * L * L / 12;
*
* var v1 = -w * L / 2;
* var v2 = -w * L / 2;
*/
var d0 = loads[0] + expectedR1;
var d1 = loads[1] + expectedR2;
Assert.IsTrue(Math.Abs(d0.Forces.Length) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(d0.Moments.Length) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(d1.Forces.Length) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(d1.Moments.Length) < 1e-5, "invalid value");
}
