Part 2 Problem 2

In [113]:

    

import pint


    

In [114]:

    

u = pint.UnitRegistry()


    

In [115]:

    

P = 1*u.kilopound
w = 1*u.kilopound/u.foot
AB = 2*u.foot
BC = 3*u.foot
AC = AB + BC
Lp = AC
Ld = BC
b = 2*u.inch
h= 4*u.inch
E = 29e6*(u.pound/u.inch**2)
I = (1/12)*b*h**3


    

In [116]:

    

t_Ap = (-P*Lp**2)/(2*E*I)
t_Ap = t_Ap.to_base_units().to_compact()
t_Ap


    

    
Out[116]:




-0.00581896551724138 dimensionless

In [117]:

    

y_Ap = (-P*Lp**3)/(3*E*I)
y_Ap.ito(u.inch)
y_Ap


    

    
Out[117]:




-0.23275862068965514 inch

In [130]:

    

t_Bd = -(w*Ld**3)/(6*E*I)
#t_Bd = t_Ad.to_base_units().to_compact()
t_Bd = t_Bd.to_base_units()
t_Bd


    

    
Out[130]:




-0.0020948275862068965 dimensionless

In [131]:

    

t_Ad = t_Bd
t_Ad


    

    
Out[131]:




-0.0020948275862068965 dimensionless

In [133]:

    

t_At = t_Ap + t_Ad
t_At


    

    
Out[133]:




-0.007913793103448277 dimensionless

In [134]:

    

y_Bd = (-w*Ld**4)/(8*E*I)
y_Bd.ito(u.inch)
y_Bd


    

    
Out[134]:




-0.056560344827586206 inch

In [135]:

    

y_Ad = y_Bd + t_Bd*AB
y_Ad


    

    
Out[135]:




-0.10683620689655172 inch

In [136]:

    

y_At = y_Ap + y_Ad
y_At


    

    
Out[136]:




-0.33959482758620685 inch

In [54]:

    

E*I


    

    
Out[54]:




309333333.3333333 inch2 pound

In [58]:

    

I


    

    
Out[58]:




10.666666666666666 inch4

In [64]:

    

I_ft = I.to(u.foot**4)


    

In [65]:

    

E


    

    
Out[65]:




29000000.0 pound/inch2

In [66]:

    

E_ft = E.to(u.lb/u.ft**2)


    

In [67]:

    

E_ft*I_ft


    

    
Out[67]:




2148148.1481481483 foot2 pound

In [68]:

    

y_Ap


    

    
Out[68]:




-0.23275862068965514 inch

In [69]:

    

y_Ap.to(u.ft)


    

    
Out[69]:




-0.019396551724137928 foot

In [70]:

    

y_Bd


    

    
Out[70]:




-0.056560344827586206 inch

In [71]:

    

y_Bd.to(u.ft)


    

    
Out[71]:




-0.004713362068965517 foot

In [72]:

    

y_At


    

    
Out[72]:




-0.23904310344827584 inch

In [73]:

    

y_At.to(u.ft)


    

    
Out[73]:




-0.019920258620689652 foot

In [ ]: