# Chapter8-Bending of beams¶

## Ex1-pg100¶

In [1]:
##Solutions to Problems In applied mechanics
##A N Gobby
import math
##initialisation of variables
h=12.##in
q=14.##in
w=12500.##in
p=2.5##in
m=0.067##in
t=2240.##in
n=2.5*10**-5##in
##CALCULATIONS
R=(p*h*q)/(w)##in
I=(1.*m**3/h)##in
M=((w*n)/(p*h)*t)##lbf in
##RESULTS
print'%s %.2f %s'%('the bending moment set up= ',M,' lbf in')

the bending moment set up=  23.33  lbf in


## Ex2-pg102¶

In [2]:
##Solutions to Problems In applied mechanics
##A N Gobby
import math
##initialisation of variables
E=14.*10**6##lbf/in^2
l=5.0##tonf/in^2
y=2.*(1/4.)##in
yc=4.*3./4.##in
n=2*1./2.##in
p=1*1./4.##in
q=2.25##in
I=55.25##in^4
m=10.56##tonf/in^2
a=(1*(yc**3))
b=6*(y**3)/3.
c=(n*p**3)/3.##in^4
##CALCULATIONS
INA=(a+b-2.*c)*2.##in^4
Fa=(l*yc)*(yc*y)/2.##tonf/in^2
M=(l*INA/q)##tonf in
##RESULTS
print'%s %.2f %s'%('Thesecound moment of area about its neutral axis= ',INA,' in^4')
print'%s %.2f %s'%('The maximum compressive stress on the section=',Fa	,' tonf/in^2')
print'%s %.2f %s'%('the bending moment is= ',M,' tonf in')

Thesecound moment of area about its neutral axis=  54.48  in^4
The maximum compressive stress on the section= 11.25  tonf/in^2
the bending moment is=  121.06  tonf in


## Ex3-pg104¶

In [3]:
##Solutions to Problems In applied mechanics
##A N Gobby
import math
##initialisation of variables
b=3.*6**3/12.##in^4
d=b+3*6*6**2##in^4
b2=math.pi*2**4/64.##in^4
h=b2+math.pi*1**2*6**2##in^4
##CALCULATIONS
P=d-h##in^4
##RESULTS
print'%s %.2f %s'%('the rectangular plate with circular hole= ',P,' in^4')

the rectangular plate with circular hole=  588.12  in^4


## Ex4-pg106¶

In [4]:
##Solutions to Problems In applied mechanics
##A N Gobby
import math
##initialisation of variables
h=12.##in
w=6.##in
x=375.77##in^4
y=28.28##in^4
p=7.##in
q=14.##in
##CALCULATIONS
Ix=x+(p*q**3/h)-(p*h**3/h)##in^4
Iy=y+2.*(1.*p**3/h)##in^4
Zx=x/w##in^3
Zy=Ix/p##in^3
X=(Zy-Zx)/(Zx)*100.##percent
##RESULTS
print'%s %.2f %s'%('the percentage increase in strength with respect to neutral= ',X,' percent')

the percentage increase in strength with respect to neutral=  120.90  percent