singly_reinforced.m

% Name: Rembrant Oyangoren Albeos
% Singly Reinforced Rectangular Beam Calculator

% Inputs
fc = input('Compressive strength of concrete, fc (ksi): ');
fy = input('Yield strength of steel, fy (ksi): ');
b  = input('Width of the beam, b (in): ');
d  = input('Effective depth to centroid, d (in): ');
dt = input('Depth to extreme tension layer, dt (in): ');

As_choice = input('Input steel area: [1] Area [2] Bar Size: ');

if As_choice == 1
    As = input('Steel area, As (in^2): ');
else
    Asq = input('Number of bars: ');
    Asd = input('Bar size: ');
    As = Asq * (pi * (Asd/8)^2) / 4;
    fprintf('As: %.3f in^2\n', As);
end

Es = input('Modulus of Elasticity, Es (ksi): ');
Ecu = 0.003;

% Tension Force
T = As * fy;
fprintf('T: %.2f kips\n', T);

% Beta 1
if fc <= 4
    beta1 = 0.85;
elseif fc > 4 && fc <= 8
    beta1 = 0.85 - 0.05 * (fc - 4);
else
    beta1 = 0.65;
end

% Depth of compression block
a = T / (0.85 * fc * b);
c = a / beta1;
fprintf('a: %.3f in\n', a);
fprintf('c: %.3f in\n', c);

% Steel Strain
Strain_y = fy / Es;
Strain_s = Ecu * (d - c) / c;
fprintf('Ey: %.5f\n', Strain_y);
fprintf('Es: %.5f\n', Strain_s);

% Check yielding
if Strain_s >= Strain_y
    fprintf('Steel yielded. Assumption OK.\n');
    Mn = T * (d - a/2);
else
    fprintf('Steel did NOT yield. Recalculating c...\n');
    A_quad = 0.85 * fc * b * beta1;
    B_quad = As * Es * Ecu;
    C_quad = -As * Es * Ecu * d;
    c = (-B_quad + sqrt(B_quad^2 - 4 * A_quad * C_quad)) / (2 * A_quad);
    a = beta1 * c;
    Strain_s = Ecu * (d - c) / c;
    T = As * (Es * Strain_s);
    Mn = T * (d - a/2);
    fprintf('Exact c: %.3f in\n', c);
    fprintf('Exact T: %.2f kips\n', T);
end

% Nominal Moment
Mn_ft = Mn / 12;
fprintf('Mn: %.2f kip-in\n', Mn);
fprintf('Mn: %.2f kip-ft\n', Mn_ft);

% Minimum Steel Area
fc_psi = fc * 1000;
fy_psi = fy * 1000;
limit_check = 3 * sqrt(fc_psi);
if limit_check < 200
    As_min = (200 / fy_psi) * b * d;
else
    As_min = (limit_check / fy_psi) * b * d;
end
fprintf('As_min: %.3f in^2\n', As_min);

if As >= As_min
    fprintf('As >= As_min. OK.\n');
else
    fprintf('As < As_min. FAILED.\n');
end

% Strength Reduction Factor
Strain_t = Ecu * (dt - c) / c;
fprintf('Et: %.5f\n', Strain_t);

if Strain_t >= 0.005
    phi = 0.90;
elseif Strain_t < 0.002
    phi = 0.65;
else
    phi = 0.65 + (Strain_t - 0.002) * (250 / 3);
end
fprintf('phi: %.2f\n', phi);

% Design Strength
phi_Mn = phi * Mn_ft;
fprintf('M: %.2f kip-ft\n', phi_Mn);