Chapter12-Elastic And Inelastic Stability Of Columns

Ex3-pg448

In [2]:
import math
## initialization of variables
#calculate the buckling load P
b=25. ##mm
L=250. ##mm
E_T=31. ##GPa
Sigma_T=262. ##MPa ## From the curve
r=b/math.sqrt(12.)
Q=math.pi**2.*E_T/((L/r)**2)
## Since this is not close enough, increment E_T
E_T=31.6 ##GPa
Q=math.pi**2.*E_T/((L/r)**2)
P_T=Q*b**2
print'%s %.2f %s'%('Buckling load is ',P_T,' kN')
Buckling load is  162.44  kN

Ex5-pg449

In [3]:
import math
## initialization of variables
#calculate the  design load for buckling column based on safety factor 
L=1. ##m
b=40. ##mm
h=75. ##mm
SF=2.5
K=1.
L=L*10**3
Iy=b*h**3/12.
A=b*h
ry=math.sqrt(Iy/A)
K_y=K*L/ry
rz=b/math.sqrt(12.)
K=0.5
K_z=K*L/rz
S_cr=229. ##MPa
P_cr=S_cr*A
P=P_cr/SF
print'%s %.2f %s'%('P =',P/10**3,' kN')
P = 274.80  kN