private double DeltaTCCalculationFunction(double SteelStrain) { LinearStrainDistribution iteratedStrainDistribution = null; switch (currentCompressionFiberPosition) { case FlexuralCompressionFiberPosition.Top: iteratedStrainDistribution = new LinearStrainDistribution(StrainHeight, this.MaxConcreteStrain, SteelStrain); break; case FlexuralCompressionFiberPosition.Bottom: iteratedStrainDistribution = new LinearStrainDistribution(StrainHeight, SteelStrain, this.MaxConcreteStrain); break; default: throw new CompressionFiberPositionException(); } //2. Calculate result SectionAnalysisResult iteratedResult = GetSectionResult(iteratedStrainDistribution, currentCompressionFiberPosition); //3. calculate difference between T and C double T = iteratedResult.TForce; double C = iteratedResult.CForce; return(Math.Abs(T) - Math.Abs(C)); }
public virtual SectionAnalysisResult GetSectionResult(LinearStrainDistribution StrainDistribution, FlexuralCompressionFiberPosition compFiberPosition) { double CompressedBarCentroidCoordinate = 0; //Calculate the Coordinate of rebar resultant ForceMomentContribution CForceRebarResultant = GetCompressionForceRebarResultant(StrainDistribution, compFiberPosition); double CompressedRebarArea = GetCompressedRebarArea(CForceRebarResultant); ForceMomentContribution CForceConcreteResultant = GetCompressionForceConcreteResultant(StrainDistribution, compFiberPosition, CompressedRebarArea, CompressedBarCentroidCoordinate); ForceMomentContribution CForceResultant = CForceRebarResultant + CForceConcreteResultant; ForceMomentContribution TForceResultant = GetTensionForceResultant(StrainDistribution, compFiberPosition); SectionAnalysisResult result = new SectionAnalysisResult() { AxialForce = CForceResultant.Force + TForceResultant.Force, CForce = CForceResultant.Force, TForce = TForceResultant.Force, Moment = CForceResultant.Moment + TForceResultant.Moment, Rotation = 0, StrainDistribution = StrainDistribution, CompressionRebarResults = CForceRebarResultant.RebarResults, TensionRebarResults = TForceResultant.RebarResults }; return(result); }
protected override TCIterationBound GetSolutionBoundaries(SectionAnalysisResult result, LinearStrainDistribution ApproximationStrainDistribution) { double prestressForce = this.GetPrestressForceEffective(); if (prestressForce == 0) { //TODO: add check for prstressing if needed //throw new NotPrestressedBeamException(); } //prestressed beam strain iteration is different (from regular RC) from regular concrete because we are assuming that //the maximum depth of compression zone is 0.6d. Therefore this determines the start of iterations TCIterationBound bound = new TCIterationBound(); switch (currentCompressionFiberPosition) { case FlexuralCompressionFiberPosition.Top: bound.MinStrain = ApproximationStrainDistribution.BottomFiberStrain; break; case FlexuralCompressionFiberPosition.Bottom: bound.MinStrain = ApproximationStrainDistribution.TopFiberStrain; break; default: throw new CompressionFiberPositionException(); } bound.MaxStrain = CalculateMaximumSteelStrain(currentCompressionFiberPosition); return(bound); }
public ConcreteSectionIterationData(LinearStrainDistribution StrainDistribution, LinearStrainDistribution PreviousStrainDistribution, SectionAnalysisResult Result) { this.StrainDistribution = StrainDistribution; this.PreviousStrainDistribution = PreviousStrainDistribution; this.Result = Result; }
protected IStrainCompatibilityAnalysisResult GetResult(SectionAnalysisResult SectionResult) { RebarPointResult controllingBar = GetMaxSteelStrainPoint(SectionResult.TensionRebarResults); double MaxSteelTensionStrain = controllingBar.Strain; double Mn = SectionResult.Moment; IStrainCompatibilityAnalysisResult result = new ConcreteSectionFlexuralAnalysisResult(Mn, SectionResult.StrainDistribution, controllingBar); return(result); }
public IStrainCompatibilityAnalysisResult GetNominalMomentResult(double P_nominal, FlexuralCompressionFiberPosition CompressionFiberPosition) { double MaxSteelLimitingStrainInTension = CalculateMaximumSteelStrain(CompressionFiberPosition); SectionAnalysisResult IteratedResult = FindMomentResultInPresenceOfAxialForce(CompressionFiberPosition, P_nominal, MaxSteelLimitingStrainInTension); IStrainCompatibilityAnalysisResult result = GetResult(IteratedResult); return(result); }
protected virtual TCIterationBound GetSolutionBoundaries(SectionAnalysisResult result, LinearStrainDistribution ApproximationStrainDistribution) { double t = Math.Abs(result.TForce); double c = Math.Abs(result.CForce); SectionAnalysisResult secondResult = new SectionAnalysisResult(); TCIterationBound data = new TCIterationBound(); LinearStrainDistribution secondApproximationStrainDistribution = null; double MaxSteelStrain = CalculateMaximumSteelStrain(currentCompressionFiberPosition); //Step 1: create adjusted strain distribution if (t > c) { if (currentCompressionFiberPosition == FlexuralCompressionFiberPosition.Top) { secondApproximationStrainDistribution = new LinearStrainDistribution(ApproximationStrainDistribution.Height, ApproximationStrainDistribution.TopFiberStrain, this.MaxConcreteStrain); } else { secondApproximationStrainDistribution = new LinearStrainDistribution(ApproximationStrainDistribution.Height, this.MaxConcreteStrain, ApproximationStrainDistribution.BottomFiberStrain); } } else { if (currentCompressionFiberPosition == FlexuralCompressionFiberPosition.Top) { secondApproximationStrainDistribution = new LinearStrainDistribution(ApproximationStrainDistribution.Height, ApproximationStrainDistribution.TopFiberStrain, MaxSteelStrain); } else { secondApproximationStrainDistribution = new LinearStrainDistribution(ApproximationStrainDistribution.Height, MaxSteelStrain, ApproximationStrainDistribution.BottomFiberStrain); } } //Step 2: Fill in data for output if (currentCompressionFiberPosition == FlexuralCompressionFiberPosition.Top) { data.MinStrain = -Math.Max(Math.Abs(ApproximationStrainDistribution.BottomFiberStrain), Math.Abs(secondApproximationStrainDistribution.BottomFiberStrain)); data.MaxStrain = -Math.Min(Math.Abs(ApproximationStrainDistribution.BottomFiberStrain), Math.Abs(secondApproximationStrainDistribution.BottomFiberStrain)); } else { data.MinStrain = -Math.Max(Math.Abs(ApproximationStrainDistribution.TopFiberStrain), Math.Abs(secondApproximationStrainDistribution.TopFiberStrain)); data.MaxStrain = -Math.Min(Math.Abs(ApproximationStrainDistribution.TopFiberStrain), Math.Abs(secondApproximationStrainDistribution.TopFiberStrain)); } return(data); }
protected bool GetAnalysisResultConverged(SectionAnalysisResult sectionResult, double ConvergenceTolerance) { double C = Math.Abs(sectionResult.CForce); double T = Math.Abs(sectionResult.TForce); double MinForce = Math.Min(C, T); double ConvergenceToleranceDifference = ConvergenceTolerance * MinForce; if (Math.Abs(C - T) <= ConvergenceToleranceDifference) { return(true); } else { return(false); } }
protected virtual SectionAnalysisResult FindMomentResultInPresenceOfAxialForce(FlexuralCompressionFiberPosition CompressionFiberPosition, double P, double MaxSteelLimitingStrainInTension, double StrainConvergenceTolerance = 0.0000001) { currentCompressionFiberPosition = CompressionFiberPosition; //store this off because it will be necessary during iteration StrainHeight = GetStrainDistributionHeight(CompressionFiberPosition); //store this off because it will be necessary during iteration double StrainMin = MaxSteelLimitingStrainInTension; //double StrainMax = StrainUltimateConcrete.Value; double StrainMax = MaxConcreteStrain; double targetP = P; LinearStrainDistribution finalStrainDistribution = null; double SteelStrain = RootFinding.Brent(new FunctionOfOneVariable(SectionAxialForceResultantFunction), StrainMin, StrainMax, StrainConvergenceTolerance, targetP); switch (CompressionFiberPosition) { case FlexuralCompressionFiberPosition.Top: finalStrainDistribution = new LinearStrainDistribution(StrainHeight, this.MaxConcreteStrain, SteelStrain); break; case FlexuralCompressionFiberPosition.Bottom: finalStrainDistribution = new LinearStrainDistribution(StrainHeight, SteelStrain, this.MaxConcreteStrain); break; default: throw new CompressionFiberPositionException(); } SectionAnalysisResult finalResult = GetSectionResult(finalStrainDistribution, CompressionFiberPosition); return(finalResult); }
protected virtual SectionAnalysisResult FindPureMomentResult(FlexuralCompressionFiberPosition CompressionFiberPosition, TCIterationBound bound, double StrainConvergenceTolerance = 0.00001) { currentCompressionFiberPosition = CompressionFiberPosition; //store this off because it will be necessary during iteration StrainHeight = GetStrainDistributionHeight(CompressionFiberPosition); //store this off because it will be necessary during iteration double SteelStrain = 0; double StrainMax = bound.MaxStrain; double StrainMin = bound.MinStrain; double targetTCDelta = 0; LinearStrainDistribution finalStrainDistribution = null; //SteelStrain = RootFinding.Brent(new FunctionOfOneVariable(GetTandCDeltaForSteelStrainIteration), TCDeltaMin, TCDeltaMax, StrainConvergenceTolerance, targetTCDelta); SteelStrain = RootFinding.Brent(new FunctionOfOneVariable(DeltaTCCalculationFunction), StrainMin, StrainMax, StrainConvergenceTolerance, targetTCDelta); switch (CompressionFiberPosition) { case FlexuralCompressionFiberPosition.Top: finalStrainDistribution = new LinearStrainDistribution(StrainHeight, this.MaxConcreteStrain, SteelStrain); break; case FlexuralCompressionFiberPosition.Bottom: finalStrainDistribution = new LinearStrainDistribution(StrainHeight, SteelStrain, this.MaxConcreteStrain); break; default: throw new CompressionFiberPositionException(); } SectionAnalysisResult finalResult = GetSectionResult(finalStrainDistribution, CompressionFiberPosition); return(finalResult); }
public double SectionAxialForceResultantFunction(double SteelStrain) { //Create trial strain LinearStrainDistribution iteratedStrainDistribution = null; switch (currentCompressionFiberPosition) { case FlexuralCompressionFiberPosition.Top: iteratedStrainDistribution = new LinearStrainDistribution(StrainHeight, this.MaxConcreteStrain, SteelStrain); break; case FlexuralCompressionFiberPosition.Bottom: iteratedStrainDistribution = new LinearStrainDistribution(StrainHeight, SteelStrain, this.MaxConcreteStrain); break; default: throw new CompressionFiberPositionException(); } //Calculate result SectionAnalysisResult iteratedResult = GetSectionResult(iteratedStrainDistribution, currentCompressionFiberPosition); return(iteratedResult.AxialForce); }
public IStrainCompatibilityAnalysisResult GetNominalFlexuralCapacity (FlexuralCompressionFiberPosition CompressionFiberPosition) { currentCompressionFiberPosition = CompressionFiberPosition; //Step 1: Assume strain distribution with all bars below section centroid yielding LinearStrainDistribution TrialStrainDistribution = GetInitialStrainEstimate(CompressionFiberPosition); SectionAnalysisResult TrialSectionResult = GetSectionResult(TrialStrainDistribution, CompressionFiberPosition); double Mn = 0; //check id T and C force are equal //if T<>C if (GetAnalysisResultConverged(TrialSectionResult, ConvergenceToleranceStrain) == false) { SectionAnalysisResult IteratedResult = null; try { TCIterationBound bound = GetSolutionBoundaries(TrialSectionResult, TrialStrainDistribution); //make sure solution exists IteratedResult = FindPureMomentResult(CompressionFiberPosition, bound, ConvergenceToleranceStrain); RebarPointResult controllingBar = GetMaxSteelStrainPoint(TrialSectionResult.TensionRebarResults); Mn = IteratedResult.Moment; return(new ConcreteSectionFlexuralAnalysisResult(Mn, IteratedResult.StrainDistribution, controllingBar)); } catch (SectionAnalysisFailedToConvergeException) { throw new SectionFailedToConvergeException(); } } //if T=C else { IStrainCompatibilityAnalysisResult result = GetResult(TrialSectionResult); return(result); } }
protected List <SectionAnalysisResult> GetInteractionResults(FlexuralCompressionFiberPosition CompressionFiberPosition, int NumberOfSteps = 50) { List <SectionAnalysisResult> SectionResults = new List <SectionAnalysisResult>(); currentCompressionFiberPosition = CompressionFiberPosition; //store this off because it will be necessary during iteration StrainHeight = GetStrainDistributionHeight(CompressionFiberPosition); //store this off because it will be necessary during iteration double StrainMin = CalculateMaximumSteelStrain(CompressionFiberPosition); double StrainMax = MaxConcreteStrain; double TotalStrainVariation = StrainMax - StrainMin; double strainStep = TotalStrainVariation / NumberOfSteps; int NumberOfStartEndPoints = 10; int TotalSteps = NumberOfSteps + 2 * NumberOfStartEndPoints; for (int i = 0; i < TotalSteps; i++) { //double SteelStrain = StrainMax -i * strainStep; double SteelStrain = GetSteelStrain(NumberOfSteps, i, StrainMax, StrainMin, NumberOfStartEndPoints); LinearStrainDistribution currentStrainDistribution = null; switch (CompressionFiberPosition) { case FlexuralCompressionFiberPosition.Top: currentStrainDistribution = new LinearStrainDistribution(StrainHeight, this.MaxConcreteStrain, SteelStrain); break; case FlexuralCompressionFiberPosition.Bottom: currentStrainDistribution = new LinearStrainDistribution(StrainHeight, SteelStrain, this.MaxConcreteStrain); break; default: throw new CompressionFiberPositionException(); } if (i == 2) { } SectionAnalysisResult thisDistibutionResult = GetSectionResult(currentStrainDistribution, CompressionFiberPosition); #region Dubugging output StringBuilder sb = new StringBuilder(); sb.AppendLine(string.Format("AxialForce = {0}", Math.Round(thisDistibutionResult.AxialForce / 1000.0, 0))); sb.AppendLine(string.Format("Moment = {0}", Math.Round(thisDistibutionResult.Moment / 12.0 / 1000.0, 0))); sb.AppendLine(string.Format("CForce = {0}", Math.Round(thisDistibutionResult.CForce / 1000.0, 0))); sb.AppendLine(string.Format("TForce = {0}", Math.Round(thisDistibutionResult.TForce / 1000.0, 0))); sb.AppendLine(string.Format("SteelStrain = {0}", thisDistibutionResult.StrainDistribution.BottomFiberStrain, 0)); sb.AppendLine(string.Format("YNeutral = {0}", Math.Round(thisDistibutionResult.StrainDistribution.NeutralAxisTopDistance, 3))); #endregion SectionResults.Add(thisDistibutionResult); } //pure tension step LinearStrainDistribution pureTensionStrainDistribution = new LinearStrainDistribution(StrainHeight, StrainMin, StrainMin); SectionAnalysisResult pureTensionDistibutionResult = GetSectionResult(pureTensionStrainDistribution, CompressionFiberPosition); SectionResults.Add(pureTensionDistibutionResult); return(SectionResults); }