/// <summary>
/// Calculate diaphragm design forces
/// </summary>
/// <param name="F">List of the applied design forces at each Level</param>
/// <param name="w">List of the tributary weights at each Level</param>
/// <param name="w_px">The tributary weight of the diaphragm at Level x</param>
/// <returns></returns>
public static Force Eqn_12_10_1(Force w_px, List <Force> F, List <Force> w, int x, ref RecordedCalculation Calculation)
{
string equationNumber = "12.10-1";
string expression = @"\frac{\sum\limits_{i=x}^{n} F_i}{\sum\limits_{i=x}^{n} w_i} w_{px}";
string resultDisplay = @"F_{px}";
SubCalculation subCalc = new SubCalculation(_standard, $"Calculate the diaphragm design force", Chapter, SectionNumber, equationNumber, expression, resultDisplay);
Force sum_F = new Force(0, ForceUnit.Kip);
Force sum_w = new Force(0, ForceUnit.Kip);
subCalc.AddVariable(new LaTexVariable(@"w_{px}", w_px, ForceUnit.Kip));
for (var i = x; i >= 0; i--)
{
sum_F = (Force)(sum_F + F[i]);
sum_w = (Force)(sum_w + w[i]);
}
subCalc.AddVariable(@"\sum\limits_{i=x}^{n} F_i", sum_F, ForceUnit.Kip);
subCalc.AddVariable(@"\sum\limits_{i=x}^{n} w_i", sum_w, ForceUnit.Kip);
subCalc.Result = sum_F / sum_w * w_px;
Calculation.AddCalculation(subCalc);
return((Force)subCalc.Result);
}
/// <summary>
/// Calculate the torsional amplification factor
/// </summary>
/// <param name="delta_max">The maximum displacement at Level x computed assuming Ax = 1 (in)</param>
/// <param name="delta_avg">The average of the displacements at the extreme points of the structure at Level x computed assuming Ax = 1</param>
/// <param name="calc"></param>
/// <returns></returns>
public static Unitless Eqn_12_8_14(Length delta_max, Length delta_avg, ref RecordedCalculation calc)
{
string equationNumber = "12.8-14";
string expression = @"\left(\frac{\delta_{max}}{1.2 \delta_{avg}}\right)^2";
var subCalc = new SubCalculation(_standard, $"Calculate Torsional Amplification Factor",
Chapter, "12.8.4.3", equationNumber, expression, @"A_x");
subCalc.AddVariable(new LaTexVariable(@"\delta_{max}", delta_max, LengthUnit.Inch));
subCalc.AddVariable(new LaTexVariable(@"\delta_{avg}", delta_avg, LengthUnit.Inch));
subCalc.Result = (delta_max / (1.2 * delta_avg)) ^ 2;
if (subCalc.Result.Value < 1.0)
{
subCalc.Limit = new ResultLimit(new Unitless(1.0), ResultLimitType.Override);
}
else if (subCalc.Result.Value > 3.0)
{
subCalc.Limit = new ResultLimit(new Unitless(3.0), ResultLimitType.Override);
}
calc.AddCalculation(subCalc);
return((Unitless)subCalc.Result);
}
/// <summary>
/// Calculate the vertical distribution factor
/// </summary>
/// <param name="w_x">The portion of total effective seismic weight of the structure (W) located or assigned to Level x</param>
/// <param name="h_x">The height (ft) from the base to Level</param>
/// <param name="k">Exponent related to the structural period</param>
/// <param name="w">List of level seismic weights</param>
/// <param name="h">List of level heights</param>
/// <returns></returns>
public static Unitless Eqn_12_8_12(Force w_x, Length h_x, double k, int n, List <Force> w,
List <Length> h, ref RecordedCalculation calc)
{
string equationNumber = "12.8-12";
string expression = @"\frac{w_x h_x^k}{\sum\limits_{i=1}^{n} w_i h_i^k}";
string resultDisplay = @"C_{vx}";
SubCalculation subCalc = new SubCalculation(_standard, $"Calculate the vertical distribution factor", Chapter, SectionNumber, equationNumber, expression, resultDisplay);
var h_xTok = new Length(Math.Pow(h_x.ConvertTo(LengthUnit.Inch), k), LengthUnit.Inch);
subCalc.AddVariable("w_x", w_x, ForceUnit.Kip);
subCalc.AddVariable("h_x^k", h_xTok, LengthUnit.Foot);
var sum = new Moment(0, MomentUnit.KipInch);
for (var i = 0; i < n; i++)
{
double h_i = h[i].ConvertTo(LengthUnit.Inch);
Force w_i = w[i];
sum = (Moment)(sum + w_i * new Length(Math.Pow(h_i, k), LengthUnit.Inch));
}
subCalc.AddVariable(@"\sum\limits_{i=1}^{n} w_i h_i^k", sum, MomentUnit.KipFoot);
subCalc.Result = w_x * (h_x ^ new Unitless(k)) / sum;
calc.AddCalculation(subCalc);
return((Unitless)subCalc.Result);
}
/// <summary>
/// Calculates coeffiction for equation 12.8-9
/// </summary>
/// <param name="A_B">Area of base of structure, in ft2</param>
/// <param name="x">Number of shear walls in the building effective in resisting lateral forces in the direction under consideration</param>
/// <param name="h_n">Structural height of building</param>
/// <param name="h">List of shear wall heights</param>
/// <param name="A">List of shear wall areas</param>
/// <param name="D">List of shear wall lengths</param>
/// <returns></returns>
public static Unitless Eqn_12_8_10(Area A_B, int x, Length h_n, List <double> h, List <double> A, List <double> D, ref RecordedCalculation Calculation)
{
string equationNumber = "12.8-10";
string expression = @"\frac{100}{A_B} \sum\limits_{i=1}^{x} \left(\frac{h_n}{h_i}\right)^2 \frac{A_i}{\left[1+0.83 \left(\frac{h_i}{D_i}\right)^2\right]}";
string resultDisplay = @"C_w";
SubCalculation subCalc = new SubCalculation(_standard, @"Calculate the approximate fundamental period", Chapter, SectionNumber, equationNumber, expression, resultDisplay);
subCalc.AddVariable(new LaTexVariable("A_B", A_B, AreaUnit.SquareFoot));
Area sum = new Area(0, AreaUnit.SquareInch);
for (var i = 0; i < x; i++)
{
var h_i = new Length(h[i], LengthUnit.Inch);
var A_i = new Area(A[i], AreaUnit.SquareInch);
var D_i = new Length(D[i], LengthUnit.Inch);
sum = (Area)(sum + ((h_n / h_i) ^ 2) * A_i / (1 + 0.83 * ((h_i / D_i) ^ 2)));
}
subCalc.AddVariable(new LaTexVariable(@"\sum\limits_{i=1}^{x} \left(\frac{h_n}{h_i}\right)^2 \frac{A_i}{\left[1+0.83 \left(\frac{h_i}{D_i}\right)^2\right]}", sum, AreaUnit.SquareFoot));
subCalc.Result = 100 * sum / A_B;
Calculation.AddCalculation(subCalc);
return((Unitless)subCalc.Result);
}
/// <summary>
/// Returns the seismic base shear of the building
/// </summary>
/// <param name="C_s">Seismic response coefficient determined in accordance with Section 12.8.1.1</param>
/// <param name="W">Effective seismic weight per Section 12.7.2</param>
/// <returns></returns>
public static Force Eqn_12_8_1(Unitless C_s, Force W, ref RecordedCalculation calc)
{
string equationNumber = "12.8-1";
string expression = @"C_s W";
string resultDisplay = @"V";
SubCalculation subCalc = new SubCalculation(_standard, "Calculate seismic base shear of the building", Chapter, SectionNumber, equationNumber, expression, resultDisplay);
subCalc.AddVariable("C_s", C_s, UnitlessUnit.Unitless);
subCalc.AddVariable("W", W, ForceUnit.Kip);
subCalc.Result = C_s * W;
calc.AddCalculation(subCalc);
return((Force)subCalc.Result);
}
/// <summary>
/// Calculates approximate fundamental period (T_a) for masonry or concrete shear wall structures
/// </summary>
/// <param name="C_w"></param>
/// <param name="h_n"></param>
/// <returns></returns>
public static Time Eqn_12_8_9(Unitless C_w, Length h_n, ref RecordedCalculation Calculation)
{
string equationNumber = "12.8-9";
string expression = @"\frac{0.0019}{\sqrt{C_w}} h_n";
string resultDisplay = @"T_a";
SubCalculation subCalc = new SubCalculation(_standard, @"Calculate the approximate fundamental period", Chapter, SectionNumber, equationNumber, expression, resultDisplay);
subCalc.AddVariable(new LaTexVariable("C_w", C_w, UnitlessUnit.Unitless));
subCalc.AddVariable(new LaTexVariable("h_n", h_n, LengthUnit.Foot));
subCalc.Result = new Time(0.0019 / Math.Sqrt(C_w.Value) * h_n.ConvertTo(LengthUnit.Foot));
Calculation.AddCalculation(subCalc);
return((Time)subCalc.Result);
}
/// <summary>
/// Calculates the seismic response coefficient where S_1 >= 0.6g
/// </summary>
/// <param name="S_1">Mapped maximum considered earthquake spectral response aceleration parameter determined in accordance with Section 11.4.1 or 11.4.7</param>
/// <param name="R">Response modification factor in Table 12.2-1</param>
/// <param name="I_e">Importance factor determined in accordance with Section 11.5.1</param>
/// <returns></returns>
public static Unitless Eqn_12_8_6(double S_1, double R, double I_e, ref RecordedCalculation Calculation)
{
string equationNumber = "12.8-6";
string expression = @"0.5 S_1/(R/I_e)";
string resultDisplay = @"C_s";
SubCalculation subCalc = new SubCalculation(_standard, @"Calculate seismic response coefficient minimum where $S_1 \ge 0.6 g$", Chapter, SectionNumber, equationNumber, expression, resultDisplay);
subCalc.AddVariable("S_1", S_1);
subCalc.AddVariable("R", R);
subCalc.AddVariable("I_e", I_e);
subCalc.Result = new Unitless(0.5 * S_1 / (R / I_e));
Calculation.AddCalculation(subCalc);
return((Unitless)subCalc.Result);
}
/// <summary>
/// Calculate the lateral seismic force induced at any level
/// </summary>
/// <param name="C_vx">Vertical distribution factor</param>
/// <param name="V">Total design lateral force or shear at the base of the structure</param>
/// <returns></returns>
public static Force Eqn_12_8_11(Unitless C_vx, Force V, ref RecordedCalculation calc)
{
var equationNumber = "12.8-11";
var expression = @"C_{vx} V";
var resultDisplay = @"F_x";
SubCalculation subCalc = new SubCalculation(_standard, $"Calculate the lateral seismic force induced",
Chapter, SectionNumber, equationNumber, expression, resultDisplay);
subCalc.AddVariable(new LaTexVariable("C_{vx}", C_vx, UnitlessUnit.Unitless));
subCalc.AddVariable(new LaTexVariable("V", V, ForceUnit.Kip));
subCalc.Result = C_vx * V;
calc.AddCalculation(subCalc);
return((Force)subCalc.Result);
}
/// <summary>
/// Calculates approximate fundamental period (T_a), in s
/// </summary>
/// <param name="C_t">Coefficient determined from Table 12.8-2</param>
/// <param name="h_n">Structural height as defined in Section 11.2</param>
/// <param name="x">Coefficient determined from Table 12.8-2</param>
/// <returns></returns>
public static Time Eqn_12_8_7(Length h_n, double C_t, double x, ref RecordedCalculation Calculation)
{
string equationNumber = "12.8-7";
string expression = @"C_t h_n^{x}";
string resultDisplay = @"T_a";
SubCalculation subCalc = new SubCalculation(_standard, @"Calculate the approximate fundamental period", Chapter, SectionNumber, equationNumber, expression, resultDisplay);
subCalc.AddVariable(new LaTexVariable(@"C_t", C_t));
subCalc.AddVariable(new LaTexVariable("h_n", h_n, LengthUnit.Foot));
subCalc.AddVariable(new LaTexVariable("x", x));
subCalc.Result = new Time(C_t * Math.Pow(h_n.ConvertTo(LengthUnit.Foot), x));
Calculation.AddCalculation(subCalc);
return((Time)subCalc.Result);
}
/// <summary>
/// Calculates the seismic response coefficient
/// </summary>
/// <param name="S_DS">Design spectral response acceleration parameter in the short period range as determined from Section 11.4.4 or 11.4.7</param>
/// <param name="R">Response modification factor in Table 12.2-1</param>
/// <param name="I_e">Importance factor determined in accordance with Section 11.5.1</param>
/// <returns></returns>
public static Unitless Eqn_12_8_2(double S_DS, double R, double I_e, ref RecordedCalculation Calculation)
{
string equationNumber = "12.8-2";
string expression = @"\frac{S_{DS}}{\left({\frac{R}{I_e}}\right)}";
string resultDisplay = @"C_s";
SubCalculation subCalc = new SubCalculation(_standard, "Calculate seismic response coefficient", Chapter, SectionNumber, equationNumber, expression, resultDisplay);
subCalc.AddVariable(new LaTexVariable(@"S_{DS}", S_DS));
subCalc.AddVariable(new LaTexVariable("R", R));
subCalc.AddVariable(new LaTexVariable("I_e", I_e));
subCalc.Result = new Unitless(S_DS / (R / I_e));
Calculation.AddCalculation(subCalc);
return((Unitless)subCalc.Result);
}
/// <summary>
/// Calculates the seismic response coefficient minimum
/// </summary>
/// <param name="S_DS">Design spectral response acceleration parameter in the short period range as determined from Section 11.4.4 or 11.4.7</param>
/// <param name="I_e">Importance factor determined in accordance with Section 11.5.1</param>
/// <returns></returns>
public static Unitless Eqn_12_8_5(double S_DS, double I_e, ref RecordedCalculation Calculation)
{
string equationNumber = "12.8-5";
string expression = @"0.044 S_{DS} I_e";
string resultDisplay = @"C_s";
SubCalculation subCalc = new SubCalculation(_standard, @"Calculate seismic response coefficient minimum where $C_s \ge 0.01$", Chapter, SectionNumber, equationNumber, expression, resultDisplay);
subCalc.AddVariable(new LaTexVariable(@"S_{DS}", S_DS));
subCalc.AddVariable(new LaTexVariable("I_e", I_e));
subCalc.Result = new Unitless(0.044 * S_DS * I_e);
subCalc.Limit = new ResultLimit(new Unitless(0.01), ResultLimitType.MaximumOf);
Calculation.AddCalculation(subCalc);
return((Unitless)subCalc.Result);
}
/// <summary>
/// Calculates the seismic response coefficient limit where T <= T_L
/// </summary>
/// <param name="S_D1">Design spectral response acceleration parameter at a period of 1.0 s, as determined from Section 11.4.4 or 11.4.7</param>
/// <param name="T">Fundamental period of the structure(s) determined in Section 12.8.2</param>
/// <param name="R">Response modification factor in Table 12.2-1</param>
/// <param name="I_e">Importance factor determined in accordance with Section 11.5.1</param>
/// <returns></returns>
public static Unitless Eqn_12_8_3(double S_D1, Time T, double R, double I_e, ref RecordedCalculation Calculation)
{
string equationNumber = "12.8-3";
string expression = @"\frac{S_{D1}}{T \left({\frac{R}{I_e}}\right)}";
string resultDisplay = @"C_s";
SubCalculation subCalc = new SubCalculation(_standard, @"Calculate seismic response coefficient limit where $T \le T_L$", Chapter, SectionNumber, equationNumber, expression, resultDisplay);
subCalc.AddVariable(new LaTexVariable(@"S_{D1}", S_D1));
subCalc.AddVariable(new LaTexVariable("T", T, TimeUnit.Seconds));
subCalc.AddVariable(new LaTexVariable("R", R));
subCalc.AddVariable(new LaTexVariable("I_e", I_e));
subCalc.Result = new Unitless((S_D1 / (T * R / I_e)).Value);
Calculation.AddCalculation(subCalc);
return((Unitless)subCalc.Result);
}
/// <summary>
/// Calculate maximum diaphragm design forces
/// </summary>
/// <param name="S_DS">Design spectral response acceleration parameter in the short period range as determined from Section 11.4.4 or 11.4.7</param>
/// <param name="I_e">The importance factor determined in accordance with Section 11.5.1</param>
/// <param name="w_px">The tributary weight of the diaphragm at Level x</param>
/// <returns></returns>
public static Force Eqn_12_10_3(double S_DS, double I_e, Force w_px, ref RecordedCalculation calc)
{
string equationNumber = "12.10-3";
string expression = @"0.4 S_{DS} I_e w_{px}";
string resultDisplay = @"F_{px}";
SubCalculation subCalc = new SubCalculation(_standard, $"Calculate the maximum diaphragm design force",
Chapter, SectionNumber, equationNumber, expression, resultDisplay);
subCalc.AddVariable(new LaTexVariable(@"w_{px}", w_px, ForceUnit.Kip));
subCalc.AddVariable(new LaTexVariable(@"I_e", I_e));
subCalc.AddVariable(new LaTexVariable(@"S_{DS}", S_DS));
subCalc.Result = 0.4 * S_DS * I_e * w_px;
calc.AddCalculation(subCalc);
return((Force)subCalc.Result);
}
/// <summary>
/// Calculate the deflection at Level x
/// </summary>
/// <param name="C_d">The deflection amplification factor in Table 12.2-1</param>
/// <param name="d_xe">The deflection at the location required by this section determined by elastic analysis</param>
/// <param name="I_e">The importance factor determined in accordance with Section 11.5.1</param>
/// <returns></returns>
public static double Eqn_12_8_15(double C_d, double d_xe, double I_e, ref RecordedCalculation Calculation, string note = null)
{
string equationNumber = "12.8-15";
string expression = @"\frac{C_d \delta_{xe}}{I_e}";
string resultDisplay = @"\delta_x";
SubCalculation subCalc = new SubCalculation(_standard, $"Calculate the deflection", Chapter, SectionNumber, equationNumber, expression, resultDisplay);
subCalc.AddVariable(new LaTexVariable(@"C_d", C_d));
subCalc.AddVariable(new LaTexVariable(@"\delta_{xe}", new Length(d_xe, LengthUnit.Inch), LengthUnit.Inch));
subCalc.AddVariable(new LaTexVariable(@"I_e", I_e));
double result = C_d * d_xe / I_e;
subCalc.Result = new Length(result, LengthUnit.Inch);
Calculation.AddCalculation(subCalc);
return(result);
}
/// <summary>
/// Calculate the horizontal distribution of forces
/// </summary>
/// <param name="F">Ordered list of all story forces, with lowest level first</param>
/// <returns></returns>
public static Force Eqn_12_8_13(List <Force> F, int x, ref RecordedCalculation Calculation)
{
string equationNumber = "12.8-13";
string expression = @"\sum\limits_{i=x}^{n} F_i";
string resultDisplay = @"V_x";
SubCalculation subCalc = new SubCalculation(_standard, $"Calculate the horizontal distribution of forces",
Chapter, SectionNumber, equationNumber, expression, resultDisplay);
Force sum = new Force(0, ForceUnit.Kip);
for (var i = F.Count - 1; i >= x; i--)
{
sum = (Force)(sum + F[i]);
}
subCalc.Result = sum;
Calculation.AddCalculation(subCalc);
return((Force)subCalc.Result);
}
/// <summary>
/// Calculates approximate fundamental period (T_a) where the seismic force-resisting system consists entirely of concrete or steel moment resisting frames
/// </summary>
/// <param name="T_a">Approximate fundamental period, in s</param>
/// <param name="N">Number of stories above the base</param>
/// <param name="note"></param>
/// <returns></returns>
public static double Eqn_12_8_8(int N, ref RecordedCalculation Calculation, string note = null)
{
string equationNumber = "12.8-8";
string expression = @"0.1 N";
string resultDisplay = @"T_a";
SubCalculation subCalc = new SubCalculation(_standard, @"Calculate the approximate fundamental period", Chapter, SectionNumber, equationNumber, expression, resultDisplay);
subCalc.AddVariable(new LaTexVariable("N", N));
double result = 0.1 * N;
subCalc.Result = new Time(result);
if (note != null)
{
subCalc.AddNote(note);
}
Calculation.AddCalculation(subCalc);
return(result);
}
/// <summary>
/// Calculate the stability coefficient considered for P-Delta Effects
/// </summary>
/// <param name="P_x">The total vertical design load at and above Level x (kip); where computing Px, no individual load factor need exceed 1.0</param>
/// <param name="D">The design story drift as defined in Section 12.8.6 occurring simultaneously with Vx (in)</param>
/// <param name="I_e">The importance factor determined in accordance with Section 11.5.1</param>
/// <param name="V_x">The seismic shear force acting between Levels x and x-1 (kip)</param>
/// <param name="h_sx">The story height below Level x (in)</param>
/// <param name="C_d">The deflection amplification factor in Table 12.2-1</param>
/// <returns></returns>
public static double Eqn_12_8_16(double P_x, double D, double I_e, double V_x, double h_sx, double C_d, ref RecordedCalculation Calculation, string note = null)
{
string equationNumber = "12.8-16";
string expression = @"\frac{P_x \Delta I_e}{V_x h_{sx} C_d}";
string resultDisplay = @"\theta";
SubCalculation subCalc = new SubCalculation(_standard, $"Calculate the stability coefficient", Chapter, SectionNumber, equationNumber, expression, resultDisplay);
subCalc.AddVariable(new LaTexVariable(@"P_x", new Force(P_x, ForceUnit.Kip), ForceUnit.Kip));
subCalc.AddVariable(new LaTexVariable(@"\Delta", new Length(D, LengthUnit.Inch), LengthUnit.Inch));
subCalc.AddVariable(new LaTexVariable(@"I_e", I_e));
subCalc.AddVariable(new LaTexVariable(@"V_x", new Force(V_x, ForceUnit.Kip), ForceUnit.Kip));
subCalc.AddVariable(new LaTexVariable(@"h_{sx}", new Length(h_sx, LengthUnit.Inch), LengthUnit.Inch));
subCalc.AddVariable(new LaTexVariable(@"C_d", C_d));
double result = (P_x * D * I_e) / (V_x * h_sx * C_d);
subCalc.Result = new Unitless(result);
Calculation.AddCalculation(subCalc);
return(result);
}
/// <summary>
/// Calculate the maximum stability coefficient
/// </summary>
/// <param name="B">The ratio of shear demand to shear capacity for the story between levels x and x-1</param>
/// <param name="C_d">The deflection amplification factor in Table 12.2-1</param>
/// <returns></returns>
public static double Eqn_12_8_17(double B, double C_d, ref RecordedCalculation Calculation, string note = null)
{
string equationNumber = "12.8-17";
string expression = @"\frac{0.5}{\beta C_d}";
string resultDisplay = @"\theta_{max}";
SubCalculation subCalc = new SubCalculation(_standard, $"Calculate the maximum stability coefficient", Chapter, SectionNumber, equationNumber, expression, resultDisplay);
subCalc.AddVariable(new LaTexVariable(@"\beta", B));
subCalc.AddVariable(new LaTexVariable(@"C_d", C_d));
double result = 0.5 / (B * C_d);
if (result > 0.25)
{
result = 0.25;
}
subCalc.Result = new Unitless(result);
Calculation.AddCalculation(subCalc);
return(result);
}