ex1.py

from matplotlib import pyplot


class Ex1:
    def __init__(self):
        self.message = "Exercice 1 initialized"

        #exercise parameters
        self.P = 400 #kN
        self.q = 25 #N/m

        self.M1 = -69.14 #Bending moment at each point [kNm]
        self.M2 = -238.27
        self.M3 = -218.52
        self.M4 = 0

        self.M1P = 0 #Abscisse of the M points are along the beam
        self.M2P = 4
        self.M3P = 10
        self.M4P = 14
        self.L = 14 #Length of the beam

        self.numberOfPoints = 100 #number of points to calculate bending moment

        print(self.message)
    
    def run(self):
        print("Running Exercice 1...")

        x_values = [i * self.L / self.numberOfPoints for i in range(self.numberOfPoints + 1)]
        y_values = [self.calculateBendingMomentAtAPoint(x) for x in x_values]

        pyplot.plot(x_values, y_values)
        pyplot.title('Bending Moment at each point')
        pyplot.xlabel('Position along beam (m)')
        pyplot.ylabel('Bending moment (kNm)')
        pyplot.show()
    
    def calculateBendingMomentAtAPoint(self, position):
        #determine the value of µ
        µ = 0
        x = position
        Mleft = 0
        Mright = 0

        if position < self.M1P or position > self.L: #verify if the position is valid
            print("Error: position out of bounds")
            return None

        if position < self.M2P:
            µ = (self.q * self.L * x) / 2 - (self.q * x**2) / 2
            Mleft = self.M1P
            Mright = self.M2P
        elif position < self.L/2:
            µ = (self.P * x) / 4
            Mleft = self.M2P
            Mright = self.M3P
        elif position < self.M3P:
            µ = (self.P * (self.L - x)) / 4
            Mleft = self.M2P
            Mright = self.M3P
        elif position > self.M3P:
            µ = (self.q * self.L * x) / 2 - (self.q * x**2) / 2
            Mleft = self.M3P
            Mright = self.M4P

        #calculate bending moments
        M = µ + Mleft * (self.L - x) / self.L + Mright * x / self.L

        return M