Question

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 the
diameter

(h) Poisson’s Ratio, v, may be determined by dividing the
negative value of the lateral strain by

the axial strain. What is Poisson’s Ratio for the rod material? Is
this an acceptable amount for

the rod?

(i) The Shear Modulus, G, of a material may be determined by the
following equation: G = E/

2(1 + ν), where E is the Modulus of Elasticity, and ν, is Poisson’s
Ratio. If the Modulus of

Elasticity for the rod material is E = 195 GPa, what is the value
of the Shear Modulus?

Answer #1

h)

lateral strain of the rod, lateral = change in diameter / diameter

as given, change in diameter, D = -0.0125 mm

Diameter of the rod, D = 70 mm

so, _{lateral}
= -0.0125 / 70 = -1.785 * 10^{-4}

Now, longitudinal strain, _{longitudinal}
= change in the length / length of the rod

change in the length , L = 0.5 mm

Actual length of the rod, L = 1.55 m = 1550 mm

so, _{longitudinal}
= 0.5 / 1550 = 3.2 * 10^{-4}

Now, poisson's Ratio of the rod material , V =
- _{lateral}
/ _{longitudinal}

= - -1.785 * 10^{-4} / 3.2 * 10^{-4}
= **0.553**

Value of poisson Ratio should be vary between 0.0 to 0.5, as here V = 0.553 , so it is not an acceptable amount.

**i)**

as G = E / 2(1+ 2V)

= 195 / 2(1+2*0.553)

so, Shear modulus, **G = 46.28 GPa**

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 solid steel shaft, 20 mm in diameter and 1 m long, is placed
concentrically inside a hollow
duralumin shaft with inside and outside diameters of 30 mm and
33 mm respectively and a
length of 500 mm. The ends of the hollow shaft are rigidly fixed
to the solid shaft. Determine
(a) the torsional stiffness of the composite shaft
(b) the maximum torque to which the composite shaft may be
subjected if the allowable
shear stresses for steel and...

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