Chapter 26: Closed Section Beams

Example 26.3 Pg.No.693

In [13]:
from __future__ import division
from sympy import solve, symbols
import math


G=20000               #shear modulus (N/mm^2)
E=G/0.36              #young's modulus
tau=20                #torque (Nm/mm)
t=1
b=200
a=500
L=2500
A=800

#torque at each support 
T=20*5000/2

mu=math.sqrt(8*G*t/(A*E*(b+a)))

z=2500
F=-1.95/mu*math.cosh(mu*z)+1.75*z**2

z=0                            # at mid-span z=0
theta=10**(-8)*(1.95/mu*math.cosh(mu*z)-1.75*z**2+F)
print "twist at mid-span = %1.3f rad = %1.2f degree"%(theta,theta*180/math.pi)
twist at mid-span = 0.108 rad = 6.20 degree
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