Simply Supported Beam Calculator

def simply_supported_beam(P, L, E, I, c=None):
    """
    Complete analysis of a simply supported beam
    with a central point load.

    P: Load (N)
    L: Beam length (mm)
    E: Elastic modulus (MPa)
    I: Area moment of inertia (mm⁴)
    c: Distance to extreme fiber (mm) – optional

    Returns dict with reaction, shear, moment, deflection, stress
    """

    if P <= 0 or L <= 0 or E <= 0 or I <= 0:
        raise ValueError("P, L, E, I must be greater than zero.")

    reaction = P / 2
    shear = P / 2
    moment = (P * L) / 4
    deflection = (P * L**3) / (48 * E * I)
    stress = (moment * c) / I if c and c > 0 else None

    return {
        "reaction_N": reaction,
        "shear_N": shear,
        "moment_Nmm": moment,
        "deflection_mm": deflection,
        "stress_MPa": stress
    }


# Example
P = 5000
L = 2000
E = 200000
I = 1500000
c = 50

results = simply_supported_beam(P, L, E, I, c)
for k, v in results.items():
    print(f"{k}: {v}")

function results = simply_supported_beam(P, L, E, I, c)
    % Complete analysis of a simply supported beam
    % with a central point load.
    %
    % P = Load (N)
    % L = Beam length (mm)
    % E = Elastic modulus (MPa)
    % I = Area moment of inertia (mm^4)
    % c = Distance to extreme fiber (mm) – optional

    if P <= 0 || L <= 0 || E <= 0 || I <= 0
        error('P, L, E, I must be greater than zero.');
    end

    results.reaction = P / 2;
    results.shear = P / 2;
    results.moment = (P * L) / 4;
    results.deflection = (P * L^3) / (48 * E * I);
    if nargin >= 5 && c > 0
        results.stress = (results.moment * c) / I;
    else
        results.stress = NaN;
    end
end

% Example
P = 5000;
L = 2000;
E = 200000;
I = 1500000;
c = 50;

r = simply_supported_beam(P, L, E, I, c);
disp(r);