Part 2 Problem 1

In [1]:

    

import pint
from math import pi


    

In [2]:

    

u = pint.UnitRegistry()


    

In [3]:

    

P = 13*u.kN


    

In [4]:

    

Fy = (-300/325)*P
Fz = (-125/325)*P


    

In [5]:

    

Fy


    

    
Out[5]:




-12.0 kilonewton

In [6]:

    

Fz


    

    
Out[6]:




-5.0 kilonewton

In [7]:

    

Mx = 0.2*u.m*Fz
My = 0.15*u.m*Fz
Mz = 0.15*u.m*Fy


    

In [8]:

    

Mx


    

    
Out[8]:




-1.0 kilonewton meter

In [9]:

    

My


    

    
Out[9]:




-0.75 kilonewton meter

In [10]:

    

Mz


    

    
Out[10]:




-1.7999999999999998 kilonewton meter

In [11]:

    

d = 50*u.mm
c = 0.5*d
A = pi*c**2


    

In [12]:

    

c


    

    
Out[12]:




25.0 millimeter

In [13]:

    

A


    

    
Out[13]:




1963.4954084936207 millimeter2

In [14]:

    

I = (pi/4)*c**4


    

In [15]:

    

I


    

    
Out[15]:




306796.1575771282 millimeter4

In [16]:

    

I.to(u.m**4)


    

    
Out[16]:




3.067961575771283e-07 meter4

In [17]:

    

I


    

    
Out[17]:




306796.1575771282 millimeter4

In [18]:

    

J = 2*I


    

In [19]:

    

J


    

    
Out[19]:




613592.3151542564 millimeter4

In [20]:

    

J.to(u.m**4)


    

    
Out[20]:




6.135923151542566e-07 meter4

In [21]:

    

A


    

    
Out[21]:




1963.4954084936207 millimeter2

In [22]:

    

A.to(u.m**2)


    

    
Out[22]:




0.001963495408493621 meter2

In [23]:

    

Q = (2/3)*c**3


    

In [24]:

    

Q


    

    
Out[24]:




10416.666666666666 millimeter3

In [25]:

    

Q.to(u.m**3)


    

    
Out[25]:




1.0416666666666666e-05 meter3

In [26]:

    

s_n = Fy/A
s_n


    

    
Out[26]:




-0.006111549814728781 kilonewton/millimeter2

In [27]:

    

s_b = Mz*c/I
s_b


    

    
Out[27]:




-0.00014667719555349072 kilonewton meter/millimeter3

In [28]:

    

s_h = s_n + s_b


    

In [29]:

    

s_h


    

    
Out[29]:




-0.15278874536821951 kilonewton/millimeter2

In [30]:

    

s_h.ito(u.N/u.mm**2)
s_h


    

    
Out[30]:




-152.7887453682195 newton/millimeter2

In [31]:

    

t = 50*u.mm
t_h = ((My*c)/J) + (Fz*Q)/(I*t)


    

In [32]:

    

t_h


    

    
Out[32]:




-3.395305452627101e-05 kilonewton meter/millimeter3

In [33]:

    

t_h.ito(u.N/u.mm**2)
t_h


    

    
Out[33]:




-33.95305452627101 newton/millimeter2

In [34]:

    

s_ave = s_h/2


    

In [35]:

    

s_ave


    

    
Out[35]:




-76.39437268410975 newton/millimeter2

In [36]:

    

from math import sqrt


    

In [37]:

    

R = sqrt( (s_h.m/2   )**2 + (t_h.m   )**2    )*(u.N/u.mm**2)
R


    

    
Out[37]:




83.59970149146818 newton/millimeter2

In [38]:

    

s_max = s_ave + R
s_min = s_ave - R
t_max = R


    

In [39]:

    

s_max


    

    
Out[39]:




7.205328807358427 newton/millimeter2

In [40]:

    

s_min


    

    
Out[40]:




-159.99407417557794 newton/millimeter2

In [41]:

    

print('s_m = {:P}'.format(s_h))
print('t_m = {:P}'.format(t_h))
print('s_max = {:P}'.format(s_max))
print('s_mim = {:P}'.format(s_min))
print('t_max = {:P}'.format(t_max))


    

    




s_m = -152.7887453682195 newton/millimeter²
t_m = -33.95305452627101 newton/millimeter²
s_max = 7.205328807358427 newton/millimeter²
s_mim = -159.99407417557794 newton/millimeter²
t_max = 83.59970149146818 newton/millimeter²

In [ ]: