Function for simply supported beam

simply_supported_beam_function.py

import numpy as np
import matplotlib.pyplot as plt

def plot_beam_diagrams(length, w):
    """
    Plot the shear force and bending moment diagrams for a simply supported beam.

    Parameters:
    - length: Length of the beam (m)
    - w: Magnitude of the uniformly distributed load (kN/m)
    """

    # Functions for shear force and bending moment
    def shear_force(x):
        return w * (length / 2 - x)  # kN

    def bending_moment(x):
        return (w * x / 2) * (length - x)  # kNm

    # Maximum shear force and bending moment calculations
    V_max = w * length / 2
    M_max = w * length ** 2 / 8

    print(f"Maximum Shear Force: {V_max} kN")
    print(f"Maximum Bending Moment: {M_max} kNm")

    # Generating points for plotting
    x_values = np.linspace(0, length, 100)
    sf_values = [shear_force(x) for x in x_values]
    bm_values = [bending_moment(x) for x in x_values]

    # Plotting Shear Force Diagram (SFD) and Bending Moment Diagram (BMD)
    plt.figure(figsize=(12, 6))

    # Shear Force Diagram
    plt.subplot(1, 2, 1)
    plt.plot(x_values, sf_values, label='Shear Force (Vx)', lw=2, color='blue')
    plt.fill_between(x_values, 0, sf_values, color='skyblue', alpha=0.5)
    plt.axhline(0, color='black', lw=1)  # Beam axis
    plt.title('Shear Force Diagram (SFD)')
    plt.xlabel('Position along the beam (m)')
    plt.ylabel('Shear Force (kN)')
    plt.grid(True)
    plt.legend()

    # Bending Moment Diagram
    plt.subplot(1, 2, 2)
    plt.plot(x_values, bm_values, color='red', label='Bending Moment (Mx)', lw=2)
    plt.fill_between(x_values, 0, bm_values, color='salmon', alpha=0.5)
    plt.axhline(0, color='black', lw=1)  # Beam axis
    plt.title('Bending Moment Diagram (BMD)')
    plt.xlabel('Position along the beam (m)')
    plt.ylabel('Bending Moment (kNm)')
    plt.grid(True)
    plt.legend()

    plt.tight_layout()
    plt.show()

# Example usage
plot_beam_diagrams(length=10, w=10)