Chapter 7:Bending Stresses in Beams

Problem 7.1,page no.298

In [1]:
#Given
#Variable declaration
b=120             #Width of plate in mm
t=20              #Thickness of plate in mm
R=10*10**3        #Radius of curvature in mm
E=2e5             #Young's modulus in N/sq.mm

#Calculation
I=b*t**3/12                    #Moment of inertia in mm^4
y_max=t/2                      #Maximum distance in mm
sigma_max=int((E/R)*y_max)     #Maximum stress in N/sq.mm
M=round((E/R*I)*(10**-6),1)    #Bending moment in kNm

#Result
print "Maximum stress =",sigma_max,"N/mm^2"
print "Bending moment =",M,"kNm"

Maximum stress = 200 N/mm^2
Bending moment = 1.6 kNm

Problem 7.8,page no.305

In [3]:
from __future__ import division
import math

#Given
#Variable declaration
W=20*1000        #Total load in N
L=3.6            #Span in m
sigma_max=7      #Maximum stress in N/sq.mm

#Calculation
M1=W*L/8*1e3                                             #Maximum Bending moment in Nmm
b1=round((M1*3/(sigma_max*2))**(1/3),1)                  #Breadth of the beam in mm
d1=int(round(2*b1,0))                                    #depth of the beam in mm
M2=W*L/4*1e3                                             #Maximum Bending moment in Nmm
b2=float(str(round((M2*3/(sigma_max*2))**(1/3),4))[:6])  #Breadth of the beam in mm
d2=2*b2                                                  #depth of the beam in mm

#Result
print "Dimensions of the cross-section:"
print "Breadth of beam =",b1,"mm"
print "Depth of beam",d1,"mm"

print "Dimensions of the cross-section when the beam carries a point load at the centre:"
print "Breadth of beam =",b2,"mm"
print "Depth of beam",d2,"mm"

Dimensions of the cross-section:
Breadth of beam = 124.5 mm
Depth of beam 249 mm
Dimensions of the cross-section when the beam carries a point load at the centre:
Breadth of beam = 156.82 mm
Depth of beam 313.64 mm
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