Chapter 07:Statically Indeterminate Beams

Example 7.7.3, Page No:251

import math
import numpy as np

#Variable Decleration
P=5000 #Load in N
L=2 #Half span in m

#Calculations
#After carrying put the variable computation 
#We obtain three equations which can be solved simultaneously
A=np.array([[1,1,0],[-L*2,0,1],[32,0,-24]]) #Array of the unknowns
B=np.array([P,-P*L,2000]) #Array of RHS
C=np.linalg.solve(A,B)

#Result
print "The values are as follows"
print "Ra=",C[0],"N  Rb=",C[1],"N and Ma=",C[2],"N.m"

#Answer in the textbook is incorrect

 The values are as follows
Ra= 3718.75 N  Rb= 1281.25 N and Ma= 4875.0 N.m

Example 7.7.4, Page No:252

import math
import numpy as np

#Variable Decleration
w=60 #Continous Load in lb/ft
L1=3 #Length in ft
L2=9 #Length in ft

#Calculations
#After carrying out the variable computations we get
A=np.array([[1,1,0,0],[(L1+L2),0,1,1],[0.5*(L1+L2)**2,0,-(L1+L2),0],[6**-1*(L1+L2)**3,0,-0.5*(L1+L2)**2,0]])
B=np.array([w*L2,w*L2*0.5*L2,L2**3*10,L2**4*2.5])
C=np.linalg.solve(A,B)

#Result
print "The values are as follows"
print "Ra=",round(C[0]),"lb Ma=",round(C[2]),"lb.ft Rb=",round(C[1]),"lb and Mb=",round(C[3]),"lb.ft"

#NOTE:The answer for Mb in the textbook is incorrect

The values are as follows
Ra= 190.0 lb Ma= 532.0 lb.ft Rb= 350.0 lb and Mb= -380.0 lb.ft