Question

A
hollow right circular cylinder is made of cast iron and has an
outside diameter of 75 mm and an inside diameter of 60 mm. If the
cylinder is loaded by an axial compressive force of 50 KN,
determine the total shortening (in mm) in a 600-mm length. Take the
modulus of elasticity to be 100 GPa and neglect any possibility of
lateral buckling of the cylinder.

show the solution

Answer #1

the stress of cylinder is given by the hooke's law

where is a normal stress ( F is the axial force acting on the cylinder,and A is the cross-sectional area of the cylinder), E is the modulus of elasticity, and

is the strain of the cylinder.

the cross sectional area of the cylinder is given by

where, Do = outer circle diameter, Di = inner circle diameter

normal stress of the cylinder ,

=

= 31 Mpa

the strain of the cylinder,

i.e,

therefore the answer is 0.19 mm

A hollow circular steel column 2m long and outer diameter 200
mm carries an axial load of 325 kN. If the compressive stress is
150 MPa, lateral strain for external diameter is is 0.000325 and
Poisson’s ratio is 0.3, find the minimum wall thickness required
for the column. Also calculate the shear modulus for the material
of the column. Take E = 210 GPa.

A bar of hollow
circular cross section has an outer diameter of 50 mm, an inner
diameter of 40 mm, and a length of 3 m. The bar is used as a
structural member in a pin-jointed framework, and an analysis has
shown that it is subjected to a compressive axial force of 500 N.
As part of a buckling analysis, assuming the bar is pin-jointed at
each end, the effective slenderness ratio is then:
which option is
correct
133...

A composite member is made of a hollow steel pipe with an inner
diameter of 12” and wall thickness 1”. The hollow steel pipe is
filled with concrete and subjected to a compressive force of
120,000 lbs. The member length is 25’. The modulus of elasticity of
concrete and steel are Ec = 3,600,000 psi and
Es = 30,000,000 psi, respectively. Calculate the axial
and compressive loads resisted by the steel and concrete.
Fconcrete = 45000 lbs ; Fsteel =...

Question 2
(a) A steel pipe of length L =150 cm outside diameter d2 =
15cm, and inside diameter d1 = 11cm is compressed by an
axial force P = 600kN. The material has modulus of elasticity
E = 210GPa and Poisson's ratio V = 0.30.
Determine the following quantities for the pipe:
(i) The increase Δv in the volume of material, and
(ii) The dilatation (e).

During construction, field tests were conducted to
assess the suitability of the column to withstand a safe buckling
load of 2.5 kN assuming a factor of safety 4 using two different
hollow columns made up of steel and concrete. Both columns have
same cross section but varying length and different support
conditions. Steel column of length 3 m having external diameter 40
mm was tested with one end fixed and the other end hinged, when
subjected to a compressive stress...

Due to the operational conditions and temperature gradient, a 70
mm diameter, 1.55 m long
steel rod within a machine assembly is subjected to a combination
of tensile loading of 150 N and
thermal loading which imposes a longitudinal force of 230 N. The
total loading results in an even
distribution of forces on the body of the rod causing it to change
its dimensions by increasing 0.5
mm in length at both ends and decreasing by 0.0125 mm at...

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