```python
import sympy as sp
import numpy as np

eps_fu_d, eta, f_ck, K, M_Ed, b, h, d, f_cd = sp.symbols('eps_fu_d, eta, f_ck, K, M_Ed, b,h,  d, f_cd')

mu_Ed_ = M_Ed / (b*d**2*f_cd)
mu_Ed_I_ = 0.0926*(h/d)**2/(eta*f_ck**(1/3))
mu_Ed_bal_ = 0.8095 * (0.0035/(0.0035+eps_fu_d)) * (1-0.416 * (0.0035/(0.0035+eps_fu_d)))

sl_bal_ = K * ((50-f_ck/5)*mu_Ed_bal_ + (f_ck/200 - 0.75)*(17.7 * eta - 5.6))


ldr = sp.Piecewise(
     (K*(35+(sl_bal_-35)*()/()) , mu_Ed_ <= mu_Ed_bal_ ),
     (K , mu_Ed_ > mu_Ed_bal_)
)


```


```python
ldr = ldr.subs(rho_0, 0.001 * sp.sqrt(f_ck))
get_slenderness = sp.lambdify((rho, rho_p, K , f_ck), ldr, 'numpy')

rho_range = np.arange(0.0025, 0.025, 0.0001)
f_ck_range = (20, 30, 35, 40, 50, 70)

slenderness = []
for f_ck in f_ck_range:
    for rho in rho_range:
        slenderness.append(get_slenderness(rho, 0,  1, f_ck))
    plt.plot(rho_range*100, slenderness)
    slenderness = []

plt.ylim(10, 35)
plt.xlim(0.25, 2.5)
plt.ylabel('l/d')
plt.xlabel(r'$\rho$ %')
plt.title('7.16a & 7.16b curve')
plt.show()
```

5a9bdcb756d011a46e2ff95f47d2197c44364ebe
ipynb
Jupyter Notebook
notebooks/deflection/slenderness_curves/slenderness_curves_according_to_El Ghadioui2020_DRAFT.ipynb
bmcs-group/bmcs_beam
b53967d0d0461657ec914a3256ec40f9dcff80d5
MIT
2021-05-07T11:10:27.000Z
2021-05-07T11:10:27.000Z
notebooks/deflection/slenderness_curves/slenderness_curves_according_to_El Ghadioui2020_DRAFT.ipynb
bmcs-group/bmcs_beam
b53967d0d0461657ec914a3256ec40f9dcff80d5
MIT
notebooks/deflection/slenderness_curves/slenderness_curves_according_to_El Ghadioui2020_DRAFT.ipynb
bmcs-group/bmcs_beam
b53967d0d0461657ec914a3256ec40f9dcff80d5
MIT
Qwen/Qwen-72B
1. YES
2. YES