SMTL301
Buckling
Problem 1. Determine the maximum magnitude of the concentrated load W that can
be applied to the the pinned truss structure without causing the compressive members to
buckle. The members of the truss are made of steel tubes having 60 mm outside diameter
and 5 mm thickness. The modulus of elasticity of steel is 210 GPa. Use a factor of safety
2 against buckling.
Answer: 31.56 kN
B
3m
D
W
3m
C
A
2.5 m
2m
Problem 2. A long slender structural aluminium (E = 70 GPa) flanged shape is used as
a 7-m long column. The column is supported in the x-direction at base A and pinned at
ends A and C against translation in the y and z directions. A lateral support is provided
to the column so that deflection in x − z plane is restrained at mid-height B; however, the
column is free to deflect in x − y plane at B. Determine the maximum compressive load
P the column can support if a factor of safety is 2.5 is required. In your analysis, consider
the possibility that buckling could occur about either the strong axis (i.e., the z-axis) or
the weak axis (i.e., the y-axis) of the aluminium column.
Answer: 31.56 kN
x
100
3.5 m
C
[mm]
z
B
3.5 m
152
z
9
5
A
y
DUT: Mech. Eng.
1
SMTL301
Buckling
Problem 3. Columns AB and CD have pinned ends, are made of an aluminium alloy
(E = 72.0 GPa), and have equal rectangular cross sections of 20 mm by 30 mm. Determine
the magnitude of P that will first cause one of the columns to buckle. Assume elastic
conditions.
Answer: 9.47 kN.
F
A
B
G
[mm]
600
500
P
C
1000
1000
500
D
Problem 4. Determine the maximum intensity w of the uniform distributed load that
can be applied on the beam without causing the compressive members of the supporting
truss to buckle. The members of the truss are made of steel tubes having 60 mm outside
diameter and 5 mm thickness. The modulus of elasticity of steel is 210 GP a. Use a factor
of safety 2 against buckling.
Answer: 2.52 kN.
w
A
D
C
2m
DUT: Mech. Eng.
3.6m
2
1.5m
B
SMTL301
Buckling
Problem 5. A pin-jointed steel truss (E = 200GP a) is constructed of rectangular steel
tubes of 40mm × 20mm and thickness 3mm. Using a safety factor Sf = 2 determine the
maximum load Pallow that can be applied without buckling of any bar.
Answer: 6.67 kN.
P
C
2m
11
00
00
11
00
11
00
11
00
11
00
11
00
11
00
11
40mm
3mm
20mm
B
A
D
1m
1m
Problem 6. The plane truss shown in the figure supports a load W . Each member is a
slender circular pipe (E = 180 GPa) with an outside diameter of 60 mm and wall thickness
of 4 mm. The truss is restrained against displacement perpendicular to the plane of the
truss. Determine the allowable value of load Wallow which can be safely applied without
buckling of any member. A safety factor of 1.5 is to be used. Assume that all joints are
pinned.
Answer: 14.72 kN.
W
D
2m
E
B
C
A
3m
DUT: Mech. Eng.
2m
3
3m
SMTL301
Buckling
Problem 7. The figure below shows two (E = 200GP a) bars of a diameter d = 10mm
on which a force F = 6kN is applied. Bars AP and BP have lengths LAP = 400mm and
LBP = 600mm. The joint P can only move vertically. Determine the factor of safety for
the assembly if the buckling to be avoided in the structure. Answer: 1.
B
60◦
P
30◦
A
F=6kN
Problem 8. A pin-jointed truss (E = 200 GPa) is constructed of circular tubes of 50 mm
external diameter and thickness 4 mm. Determine the maximum load Wallow that can be
applied without buckling of any member. Use a safety factor of 2.5. Answer: 8.78 kN.
4m
4m
D
30◦
4m
E
W
60◦
F
C
4m
A
B
G
DUT: Mech. Eng.
4