//Finds the thinnest 4x4 angle that can handle an 8 kip shear force.
//The force is applied at the centroid so shear stresses are a 
//combination of flexural shear and torsional shear.

SetUnits("Kips & Inches");

ApplyCentroidLoad(0, 0, -8.0, 0, 0, 0);

var t = 0.0;
var extreme = 100.0;
var allowable = 0.9 * 0.6 * 36;
while(extreme > allowable)
{
    //remove the previous angle (if any)
    SelectAllShapes();
    DeleteSelected();
    
    //increment the thickness and add the shape
    t += 1/16.0;
    var angle = AddRolledAngle(4, 4, t, t, 0.8*t);
    SetMaterial(angle, "ASTM A36");
    MoveTo(angle, 0, 0);
    
    //extract the extreme shear stress (flexure + torsion)    
    //need to check the mesh refinement as we go
    var ratio = 0.0;
    var value = 0.0;
    var change = 100.0;
    while(change > 0.02)
    {    
        ratio += 1.0;
        SetMesh(ratio);
        await AdvancedAnalysis();
        var max = ResultantShear(true);
        var min = ResultantShear(false);
        var newValue = Math.Max(Math.Abs(max), Math.Abs(min));    
        change = Math.Abs((newValue - value)/value);
        value = newValue;
    }
    extreme = value;    
}

$"t_required = {t:f3} inches; extreme stress = {extreme:f2} ksi"