Chapter 10 : Method of virtual work

Example 10.3 Page No : 501

import math 

# Given Data
m = 1000.;			#kg, mass of krate
theta = 60.;			#degree
theta = theta*math.pi/180;			#radians, conversion into rad
a = 0.70;			#m
L = 3.20;			#m
g = 9.81;			#m/s**2

# Calculations
#From theory we get
W = m*g;			#N, Weight
W = W/1000;			#kN, conversion into kN
S = math.sqrt(a**2+L**2-2*a*L*math.cos(theta));			#m
F_DH = W*S/L/math.tan(theta);			#kN

# Results
print "Force exerted by each cylinder is F_DH = %.2f kN"%(F_DH);

Force exerted by each cylinder is F_DH = 5.16 kN

Example 10.4 Page No : 503

import math 
from numpy import arange

# Given Data
m = 10.;			#kg, mass of rim
r = 300.;			#mm, radius of disk
a = 0.08;			#m
b = 0.3;			#m
k = 4.;			#kN/m
g = 9.81;			#m/s**2  gravity

#From theory we get

# Calculations and Results
#math.sin(theta) = k*a**2/m/g/b*theta
dif = 1.;
for theta in arange(0,1+0.001,.001):
    dif = math.sin(math.radians(theta))-k*a**2/m/g/b*theta;
    if dif <= 0.001:
        print "theta =  %.3f rad or %.1f degrees"%(theta,theta/math.pi*180);

theta =  0.000 rad or 0.0 degrees
theta =  0.001 rad or 0.1 degrees
theta =  0.002 rad or 0.1 degrees
theta =  0.003 rad or 0.2 degrees
theta =  0.004 rad or 0.2 degrees
theta =  0.005 rad or 0.3 degrees
theta =  0.006 rad or 0.3 degrees
theta =  0.007 rad or 0.4 degrees
theta =  0.008 rad or 0.5 degrees
theta =  0.009 rad or 0.5 degrees
theta =  0.010 rad or 0.6 degrees
theta =  0.011 rad or 0.6 degrees
theta =  0.012 rad or 0.7 degrees
theta =  0.013 rad or 0.7 degrees
theta =  0.014 rad or 0.8 degrees
theta =  0.015 rad or 0.9 degrees
theta =  0.016 rad or 0.9 degrees
theta =  0.017 rad or 1.0 degrees
theta =  0.018 rad or 1.0 degrees
theta =  0.019 rad or 1.1 degrees
theta =  0.020 rad or 1.1 degrees
theta =  0.021 rad or 1.2 degrees
theta =  0.022 rad or 1.3 degrees
theta =  0.023 rad or 1.3 degrees
theta =  0.024 rad or 1.4 degrees
theta =  0.025 rad or 1.4 degrees
theta =  0.026 rad or 1.5 degrees
theta =  0.027 rad or 1.5 degrees
theta =  0.028 rad or 1.6 degrees
theta =  0.029 rad or 1.7 degrees
theta =  0.030 rad or 1.7 degrees
theta =  0.031 rad or 1.8 degrees
theta =  0.032 rad or 1.8 degrees
theta =  0.033 rad or 1.9 degrees
theta =  0.034 rad or 1.9 degrees
theta =  0.035 rad or 2.0 degrees
theta =  0.036 rad or 2.1 degrees
theta =  0.037 rad or 2.1 degrees
theta =  0.038 rad or 2.2 degrees
theta =  0.039 rad or 2.2 degrees
theta =  0.040 rad or 2.3 degrees
theta =  0.041 rad or 2.3 degrees
theta =  0.042 rad or 2.4 degrees
theta =  0.043 rad or 2.5 degrees
theta =  0.044 rad or 2.5 degrees
theta =  0.045 rad or 2.6 degrees
theta =  0.046 rad or 2.6 degrees
theta =  0.047 rad or 2.7 degrees
theta =  0.048 rad or 2.8 degrees
theta =  0.049 rad or 2.8 degrees
theta =  0.050 rad or 2.9 degrees
theta =  0.051 rad or 2.9 degrees
theta =  0.052 rad or 3.0 degrees
theta =  0.053 rad or 3.0 degrees
theta =  0.054 rad or 3.1 degrees
theta =  0.055 rad or 3.2 degrees
theta =  0.056 rad or 3.2 degrees
theta =  0.057 rad or 3.3 degrees
theta =  0.058 rad or 3.3 degrees
theta =  0.059 rad or 3.4 degrees
theta =  0.060 rad or 3.4 degrees