Chapter 10:Dams and Retaining Walls

Problem 10.19,page no.459

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from __future__ import division
import math
#Given
#Variable declaration
h=20              #height in m
D=4               #External diameter in m
d=2               #Internal diameter in m
p=1               #Horizontal wind pressure in kN/sq.m
w=22              #specific weight in kN/m^3            
K=2/3             #Co-efficient of wind resistance

#Calculation
A1=(math.pi/4)*(D**2-d**2)           #Area of cross-section
W=w*A1*h                             #Weigth of the chimney in kN
sigma0=W/A1                          #Direct stress in kN/sq.mm
A2=D*h                               #Projected area of the surface exposed to wind in sq.m
F=K*p*A2                             #Wind Force in kN
M=F*h/2                              #Bending moment in kNm
I=(math.pi/64)*(D**4-d**4)           #Moment of inertia
y=D/2                                #Distance between C.G. of the base section and extreme edge of the base
Z=I/y                                #Section modulus
sigmab=M/Z                           #Bending stress                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             
sigma_max=round(sigma0+sigmab,2)     #Maximum stress in kN/sq.m
sigma_min=round(sigma0-sigmab,2)     #Minimum stress in kN/sq.m

#Result
print"Maximum stress =",sigma_max,"kN/m^2"
print"Minimum stress =",sigma_min,"kN/m^2"
Maximum stress = 530.54 kN/m^2
Minimum stress = 349.46 kN/m^2
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