# Chapter 27: Open Section Beams¶

## Example 27.2 Pg.No. 735¶

In [26]:
#reference Fig 27.20

from __future__ import division
import math
from sympy import integrate
from sympy import solve, symbols

# variable declaration
A_R=1.25*10**3         #from previous question
E=200000               #young's modulus (N/mm^2)
Gama_R=2.08*10**10     #torsion bending constant (mm^6)
mu=0.54*10**-3        #from previous question
A=400*5                #area of beam

#moment couple
M_Tau=-P*2*A_R
print "\nValue of moment couple at the top of column = %2.2e kN.mm^2"%(M_Tau)  #calculation mistake in book

d2tdz2 = M_Tau*10**3/E/Gama_R
# @z=3000 mm
D=0.04*10**-3
z=symbols('z')
F= -0.08*math.cosh(0)

def theta(z):
return 0.08*(math.cosh(0.54*10**(-3)*z))

print "\ntwist at the top of the column = %2.2f rad\n"%(theta(3000))

M_Tau=-E*Gama_R*0.02*10**-6
print "value of moment couple at bottom of column=%2.2e N.mm^2\n"%(M_Tau)

P=-100*10**3    # stress(N)
def sigma_z(A_R2):
return P/A+M_Tau*A_R2/Gama_R
print "sigma_z1=sigma_z4=%2.1f N/mm^2\n"%(sigma_z(-7.5*10**3))
print "sigma_z2=sigma_z3=%2.1f N/mm^2\n"%(sigma_z(2.5*10**3))

#please put the value of 2AR from Fig 27.21 in the equation of sigma_z
#these values in book need correction

Value of moment couple at the top of column = -2.50e+05 kN.mm^2

twist at the top of the column = 0.21 rad

value of moment couple at bottom of column=-8.32e+07 N.mm^2

sigma_z1=sigma_z4=-20.0 N/mm^2

sigma_z2=sigma_z3=-60.0 N/mm^2


In [48]: