public double GetRequiredShearReinforcementArea(double phiV_s)
{
double f_yt = rebarMaterial.YieldStress;
StrengthReductionFactorFactory f = new StrengthReductionFactorFactory();
double phi = f.Get_phi_ShearReinforced();
double A_v = ((phiV_s * s) / (f_yt * phi * d));
return(A_v);
}
public double GetSteelShearStrength()
{
double f_yt = rebarMaterial.YieldStress;
double V_s = ((A_v * f_yt * d) / (s));
StrengthReductionFactorFactory f = new StrengthReductionFactorFactory();
double phi = f.Get_phi_ShearReinforced();
return(phi * V_s);
}
public double GetMaximumShearStrength(double phiV_c)
{
StrengthReductionFactorFactory f = new StrengthReductionFactorFactory();
double phi = f.Get_phi_ShearReinforced();
//Section 22.5.1.2
double phiV_nMax = phiV_c + phi * 8 * Section.Material.Sqrt_f_c_prime * b_w * d;
return(phiV_nMax);
}
FlexuralCompressionFiberPosition FlexuralCompressionFiberPosition; //stored value for iteration
private double phiFactorDifferenceCalculation(double phi)
{
double P_nIter = phiP_n / phi;
IStrainCompatibilityAnalysisResult nominalResult = this.GetNominalMomentResult(P_nIter, FlexuralCompressionFiberPosition);
ConcreteCompressionStrengthResult result = new ConcreteCompressionStrengthResult(nominalResult, FlexuralCompressionFiberPosition, this.Section.Material.beta1);
StrengthReductionFactorFactory f = new StrengthReductionFactorFactory();
FlexuralFailureModeClassification failureMode = f.GetFlexuralFailureMode(result.epsilon_t, result.epsilon_ty);
double phiActual = f.Get_phiFlexureAndAxial(failureMode, ConfinementReinforcementType, result.epsilon_t, result.epsilon_ty);
return(phi - phiActual);
}
public double GetRequiredTorsionTransverseReinforcementArea(double T_u, double s, double f_yt,
double theta = 45.0)
{
double A_o = 0.85 * Shape.GetA_oh();
double thetaRad = theta.ToRadians();
StrengthReductionFactorFactory srf = new StrengthReductionFactorFactory();
double phi = srf.Get_phi_Torsion();
//(22.7.6.1a)
double A_tReq = ((T_u * s) / (phi * 2.0 * A_o * f_yt)) * 1.0 / (Math.Tan(thetaRad));
return(A_tReq);
}
public double GetRequiredTorsionLongitudinalReinforcementArea(double T_u, double f_y,
double theta = 45.0)
{
double A_o = 0.85 * Shape.GetA_oh();
double p_h = Shape.Get_p_h();
double thetaRad = theta.ToRadians();
StrengthReductionFactorFactory srf = new StrengthReductionFactorFactory();
double phi = srf.Get_phi_Torsion();
//(22.7.6.1b)
double A_lReq = ((T_u * p_h) / (phi * 2 * A_o * f_y)) * 1.0 / (Math.Tan(thetaRad));
return(A_lReq);
}
public double GetMaximumForceInteractionRatio(double V_u, double T_u, double phiV_c, double b, double d)
{
StrengthReductionFactorFactory srf = new StrengthReductionFactorFactory();
double phi = srf.Get_phi_Torsion();
double phi_shear = srf.Get_phi_ShearReinforced();
double V_c = phiV_c / phi_shear;
//(22.7.7.1a)
double Sqrt_f_c = Shape.Material.Sqrt_f_c_prime;
double p_h = Shape.Get_p_h();
double A_oh = Shape.GetA_oh();
double IR1 = Math.Sqrt(Math.Pow((((V_u) / (b * d))), 2) + Math.Pow((((T_u * p_h)) / (1.7 * Math.Pow(A_oh, 2))), 2));
double IR2 = phi * ((V_c) / (b * d) + 8 * Sqrt_f_c);
double IR = IR1 / IR2;
return(IR);
}
public ConcreteCompressionStrengthResult GetDesignMomentWithCompressionStrength(double phiP_n,
FlexuralCompressionFiberPosition FlexuralCompressionFiberPosition,
bool CapAxialForceAtMaximum = true)
{
this.phiP_n = phiP_n; //store value for iteration
this.FlexuralCompressionFiberPosition = FlexuralCompressionFiberPosition;
double P_o = GetMaximumForce();
StrengthReductionFactorFactory f = new StrengthReductionFactorFactory();
double phiAxial = f.Get_phiFlexureAndAxial(FlexuralFailureModeClassification.CompressionControlled, ConfinementReinforcementType, 0, 0);
double phiP_nMax = phiAxial * P_o;
if (phiP_n > phiP_nMax)
{
if (CapAxialForceAtMaximum == false)
{
throw new Exception("Axial forces exceeds maximum axial force.");
}
else
{
phiP_n = phiP_n;
}
}
//Estimate resistance factor to adjust from phiP_n to P_n
double phiMin = 0.65;
double phiMax = 0.9;
double ConvergenceTolerance = 0.0001;
double targetPhiFactorDifference = 0.0;
//Find P_n by guessing a phi-factor and calculating the result
double phiIterated = RootFinding.Brent(new FunctionOfOneVariable(phiFactorDifferenceCalculation), phiMax, phiMin, ConvergenceTolerance, targetPhiFactorDifference);
double P_nActual = phiP_n / phiIterated;
//Calculate final results using the estimated value of phi
IStrainCompatibilityAnalysisResult nominalResult = this.GetNominalMomentResult(P_nActual, FlexuralCompressionFiberPosition);
ConcreteCompressionStrengthResult result = new ConcreteCompressionStrengthResult(nominalResult, FlexuralCompressionFiberPosition, this.Section.Material.beta1);
FlexuralFailureModeClassification failureMode = f.GetFlexuralFailureMode(result.epsilon_t, result.epsilon_ty);
double phiFinal = f.Get_phiFlexureAndAxial(failureMode, ConfinementReinforcementType, result.epsilon_t, result.epsilon_ty);
double phiM_n = phiFinal * nominalResult.Moment;
result.phiM_n = phiM_n;
result.FlexuralFailureModeClassification = failureMode;
return(result);
}
public List <PMPair> GetPMPairs(FlexuralCompressionFiberPosition CompressionFiberPosition, int NumberOfSteps = 50, bool IncludeResistanceFactor = true)
{
List <PMPair> Pairs = new List <PMPair>();
List <SectionAnalysisResult> SectionResults = GetInteractionResults(CompressionFiberPosition, NumberOfSteps);
foreach (var thisDistibutionResult in SectionResults)
{
IStrainCompatibilityAnalysisResult nominalResult = GetResult(thisDistibutionResult);
ConcreteCompressionStrengthResult result = new ConcreteCompressionStrengthResult(nominalResult, CompressionFiberPosition, this.Section.Material.beta1);
StrengthReductionFactorFactory f = new StrengthReductionFactorFactory();
FlexuralFailureModeClassification failureMode = f.GetFlexuralFailureMode(result.epsilon_t, result.epsilon_ty);
double phi;
if (IncludeResistanceFactor == true)
{
phi = f.Get_phiFlexureAndAxial(failureMode, ConfinementReinforcementType, result.epsilon_t, result.epsilon_ty);
}
else
{
phi = 1.0;
}
double SignFactor = 1.0;
//if (CompressionFiberPosition == FlexuralCompressionFiberPosition.Bottom)
//{
// SignFactor = -1.0;
//}
double P = thisDistibutionResult.AxialForce * phi;
double M = thisDistibutionResult.Moment * phi * SignFactor;
PMPair thisPair = new PMPair(P, M);
Pairs.Add(thisPair);
}
if (IncludeResistanceFactor == true)
{
List <PMPair> TruncatedPairs = TruncateInteractionDiagram(Pairs, CompressionFiberPosition);
return(TruncatedPairs);
}
else
{
return(Pairs);
}
}
public double GetUpperLimitShearStrength(double phiV_c)
{
double h = Section.SliceableShape.YMax - Section.SliceableShape.YMin;
this.A_g = Section.SliceableShape.A;
this.N_u = N_u;
this.rho_w = rho_w;
double V_max;
double f_c = Section.Material.SpecifiedCompressiveStrength;
double lambda = Section.Material.lambda;
StrengthReductionFactorFactory f = new StrengthReductionFactorFactory();
double phi = f.Get_phi_ShearReinforced();
V_max = phiV_c + phi * (10.0 * lambda * Section.Material.Sqrt_f_c_prime * b_w * d); // (22.5.1.2)
return(V_max);
}
public double GetConcreteShearStrength(double N_u, double rho_w, double M_u, double V_u)
{
double h = Section.SliceableShape.YMax - Section.SliceableShape.YMin;
this.A_g = Section.SliceableShape.A;
this.N_u = N_u;
this.rho_w = rho_w;
double V_c;
double f_c = Section.Material.SpecifiedCompressiveStrength;
double lambda = Section.Material.lambda;
if (N_u == 0)
{
if (rho_w == 0 || M_u == 0 || V_u == 0)
{
V_c = 2 * lambda * Section.Material.Sqrt_f_c_prime * b_w * d; // (22.5.5.1)
}
else
{
//use detailed formula
//Table 22.5.5.1
double V_c_a = (1.9 * lambda * Section.Material.Sqrt_f_c_prime + 2500.0 * rho_w * ((V_u * d) / (M_u))) * b_w * d;
double V_c_b = (1.9 * lambda * Section.Material.Sqrt_f_c_prime + 2500.0 * rho_w) * b_w * d;
double V_c_c = 3.5 * lambda * Section.Material.Sqrt_f_c_prime * b_w * d;
List <double> V_cList = new List <double>()
{
V_c_a, V_c_b, V_c_c
};
V_c = V_cList.Min();
}
}
else
{
if (N_u > 0) //compression
{
if (rho_w == 0 || h == 0)
{
//Use simplified formula
V_c = 2.0 * (1 + ((N_u) / (2000.0 * A_g))) * lambda * Section.Material.Sqrt_f_c_prime * b_w * d;
}
else
{
//Table 22.5.6.1
double V_c_b = 3.5 * lambda * Section.Material.Sqrt_f_c_prime * b_w * d * Math.Sqrt(1 + ((N_u) / (500.0 * A_g)));
if (M_u - N_u * (((4.0 * h - d) / (8.0))) <= 0)
{
V_c = V_c_b;
}
else
{
double V_c_a = (1.9 * lambda * Section.Material.Sqrt_f_c_prime + 2500.0 * rho_w * ((V_u * d) / (M_u - N_u * (((4.0 * h - d) / (8.0)))))) * b_w * d;
V_c = Math.Min(V_c_a, V_c_b);
}
}
}
else //tension
{
V_c = 2.0 * (1.0 + ((N_u) / (500.0 * A_g))) * lambda * Section.Material.Sqrt_f_c_prime * b_w * d; //(22.5.7.1)
}
}
V_c = V_c < 0 ? 0 : V_c;
StrengthReductionFactorFactory f = new StrengthReductionFactorFactory();
double phi = f.Get_phi_ShearReinforced();
return(phi * V_c);
}