Chapter 8:Shear Stresses in Beams

Problem 8.6,page no.355

In [1]:
from __future__ import division
import math
#Given
#Variable declaration
D=100           #Diameter in mm
R=D/2           #Radius in mm
F=5*10**3       #Shear force in N
y=40            #given distance from N.A. in mm

#Calculation
#case(i):Average shear stress 
A=math.pi*R**2
tau_avg=round(F/A,4)
#case(ii):Maximum shear stress for a circular section
tau_max=round(4/3*tau_avg,4)
#case(iii):Shear stress at a distance 40mm from N.A.
I=math.pi/64*D**4
tau=float(str(F/(3*I)*(R**2-y**2))[:6])

#Result
print "Average shear stress =",tau_avg,"N/mm^2"
print "Maximum shear stress =",tau_max,"N/mm^2"
print "Shear stress at a distance 40mm from N.A. =",tau,"N/mm^2"

Average shear stress = 0.6366 N/mm^2
Maximum shear stress = 0.8488 N/mm^2
Shear stress at a distance 40mm from N.A. = 0.3055 N/mm^2

Problem 8.12,page no.369

In [3]:
from __future__ import division
import math

#Given
#Variable declaration
F=50*10**3              #Shear force in N
b=250                   #Base width in mm
h=200                   #height in mm

#Calculation
tau_max=int((3*F)/(b*h))     #Maximum shear stress in N/sq.mm
tau=round((8*F)/(3*b*h),2)   #Shear stress at N.A. in N/sq.mm

#Result
print "Maximum shear stress =",tau_max,"N/mm^2"
print "Shear stress at N.A. =",tau,"N/mm^2"

Maximum shear stress = 3 N/mm^2
Shear stress at N.A. = 2.67 N/mm^2
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