beam.py

beam.py

"""
Beam calculations

My attempt at converting mathematical formulas
into Python code. 

Mu =1.35 G + 1.5 Q =1.35*0.5+1.5*0.15=0.9
µ=Mu / ( bw x d² x Fcd )=0.9/(0.3*(0.9*0.65)²*20)=0.438
Fcd=30/1.5=20
α =1.25 x ( 1 - ( 1 - ( 2 x µ ))^ 1/2)= 1.25 x ( 1 - ( 1 - ( 2 x0.438 ))^ 1/2)=0.81
Z= d x ( 1 - ( 0.4 x α ))= (0.9*0.65)*(1-(0.4*0.81))=0.395
As1=Mu / ( Z x Fsu )= 0.9/0.395*500=45.56cm²
"""

def calc_As1(Mu, Z):
	Fsu = 500
	return round((Mu / (Z * Fsu)) * 10000, 2)


def calc_a(u):
	val = 1.25 * (1 - (1 - (2 * u)) ** 0.5)
	return round(val, 3)


def calc_Fcd(y):
	return 30 / y


def calc_Mu(x, y):
	G = 0.5
	Q = 0.15
	return x * G + y * Q


def calc_u(Mu, Fcd):
	bw = 0.3
	d2 = (0.9 * 0.65) ** 2
	Fcd = 20
	return round(Mu / (bw * d2 * Fcd), 3)


def calc_Z(a):
	d = 0.9 * 0.65
	return round(d * (1 - (0.4 * a)), 3)


def main(x, y):
	Mu = calc_Mu(x, y)
	Fcd = calc_Fcd(y)
	u = calc_u(Mu, Fcd)
	a = calc_a(u)
	Z = calc_Z(a)
	As1 = calc_As1(Mu, Z)
	result = f"{As1}cm^2"
	
	assert Mu == 0.9
	assert Fcd == 20.0
	assert u == 0.438
	assert a == 0.81
	assert Z == 0.395
	assert As1 == 45.57
	assert result == "45.57cm^2"
	
	print(f" Mu: {Mu}")
	print(f"Fcd: {Fcd}")
	print(f"  u: {u}")
	print(f"  a: {a}")
	print(f"  Z: {Z}")
	print(f"As1: {As1}")
	print("-" * (len(result) + 4))
	print(f"  {As1}cm^2  ")
	print("-" * (len(result) + 4))


if __name__ == '__main__':
	x = 1.35
	y = 1.5
	main(x, y)