LEC – 15 MECHANICAL PROPERTIES TUTORIAL Q1 A PIECE

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Lec – 15

Mechanical Properties: Tutorial

Q1: A piece of copper originally 305 mm (12 in.) long is pulled in tension with a stress of 276 MPa . If the deformation is entirely elastic, and elastic modulus is 110 MPa , what will be the resultant elongation?

Solution:

LEC – 15 MECHANICAL PROPERTIES TUTORIAL Q1 A PIECE

Poisson's Ratio:

LEC – 15 MECHANICAL PROPERTIES TUTORIAL Q1 A PIECE

Q2:

LEC – 15 MECHANICAL PROPERTIES TUTORIAL Q1 A PIECE

Solution:

LEC – 15 MECHANICAL PROPERTIES TUTORIAL Q1 A PIECE

Q3:

LEC – 15 MECHANICAL PROPERTIES TUTORIAL Q1 A PIECE

Solution:

a -

LEC – 15 MECHANICAL PROPERTIES TUTORIAL Q1 A PIECE

Q4: A specimen of aluminum having a rectangular cross section(10mm x 12.7mm) is pulled in tension with 35,500 N force, producing only elastic deformation. Calculate the resulting strain.

( Note : E _Al = 69 GPa )

Solution :

A₀ = 10mm x 12.7mm = 127 mm² = 1.27 x 10^-4m²

LEC – 15 MECHANICAL PROPERTIES TUTORIAL Q1 A PIECE

Q5: A cylindrical specimen of a titanium alloy having an elastic modulus of 107 GPa and an original diameter of 3.8mm will experience only elastic deformation when a tensile load of 2000 N is applied.

Compute the maximum length of the specimen before deformation if the maximum allowable elongation is 0.42mm .

Solution :

LEC – 15 MECHANICAL PROPERTIES TUTORIAL Q1 A PIECE

Q6: A steel bar 100mm long and having a square cross section 20mm on an edge is pulled in tension with a load of 89,000 N , and experiences an elongation of 0.10mm. Assuming that the deformation is entirely elastic, calculate the elastic modulus of the steel.

Solution :

A₀ = b₀²

LEC – 15 MECHANICAL PROPERTIES TUTORIAL Q1 A PIECE

Q7: Consider a cylindrical titanium wire 3.0mm in diameter and 2.5x10⁴mm long. Calculate its elongation when a load of 500 N is applied. Assume that the deformation is totally elastic.

( Note : E _Ti = 107GPa )

Solution :

LEC – 15 MECHANICAL PROPERTIES TUTORIAL Q1 A PIECE

Q8: A cylindrical rod of copper (E = 110 GPa) having a yield strength of 240 MPa is to be subjected to a load of 6660 N . If the length of the rod is 380mm , what must be the diameter to allow an elongation of 0.50mm ?

Solution : Since, б = F/A₀ ……………(1)

and б = є E ……………(2)

LEC – 15 MECHANICAL PROPERTIES TUTORIAL Q1 A PIECE

Q9: Consider a cylindrical specimen of a steel alloy (Figure 1) 10mm in diameter and 75mm long that is pulled in tension. Determine its elongation when a load of 23,500 N is applied.

LEC – 15 MECHANICAL PROPERTIES TUTORIAL Q1 A PIECE

Figure 1: Tensile stress-strain behavior of a plain carbon steel

Solution :

LEC – 15 MECHANICAL PROPERTIES TUTORIAL Q1 A PIECE

Referring to fig.1: at this stress level , we are in the elastic region on the stress-strain curve, which corresponds to a stain of 0.0013 . Now:

LEC – 15 MECHANICAL PROPERTIES TUTORIAL Q1 A PIECE

Q10: A cylindrical specimen of aluminum having a diameter of 19mm and length of 200mm is deformed elastically in tension with a force of 48,800 N . ( Note : ν _Al = 0.33)

(a) The amount by which this specimen will elongate in the direction of the applied stress.

(b) The change in diameter of the specimen. Will the diameter increase or decrease?

Solution : (a):

LEC – 15 MECHANICAL PROPERTIES TUTORIAL Q1 A PIECE

(b):

LEC – 15 MECHANICAL PROPERTIES TUTORIAL Q1 A PIECE

The diameter will decrease

Q11: A cylindrical specimen of some alloy 8mm in diameter is stressed elastically in tension. A force of 15,700 N produces a reduction in specimen diameter of 5 x 10^-3mm . Compute Poisson’s ratio for this material if its modulus of elasticity is 140 GPa .

Solution :

LEC – 15 MECHANICAL PROPERTIES TUTORIAL Q1 A PIECE

Q12: A cylindrical specimen of a hypothetical metal alloy is stressed in compression. If its original and final diameters are 20.000 and 20.025mm, respectively, and its final length is 74.96mm, compute its original length if the deformation is totally elastic. The elastic and shear moduli for this alloy are 105GPa & 39.7GPa, respectively.

Solution:

Lateral strain є_x : LEC – 15 MECHANICAL PROPERTIES TUTORIAL Q1 A PIECE

In order to determine the longitudinal strain є_z , we need Poisson's ratio which may be computed as:

LEC – 15 MECHANICAL PROPERTIES TUTORIAL Q1 A PIECE

Now, є_z may be computed as :

LEC – 15 MECHANICAL PROPERTIES TUTORIAL Q1 A PIECE

Now, solving for I₀ :

LEC – 15 MECHANICAL PROPERTIES TUTORIAL Q1 A PIECE

Q13: Consider a cylindrical specimen of some hypothetical metal alloy that has a diameter of 8.0mm . A tensile force of 1000 N produces an elastic reduction in diameter of 2.8 x 10^-4mm .

Compute the modulus of elasticity for this alloy, given that Poisson’s ratio is 0.30.

Solution:

LEC – 15 MECHANICAL PROPERTIES TUTORIAL Q1 A PIECE

But:

LEC – 15 MECHANICAL PROPERTIES TUTORIAL Q1 A PIECE

And the transverse strain is:

LEC – 15 MECHANICAL PROPERTIES TUTORIAL Q1 A PIECE

Then:

LEC – 15 MECHANICAL PROPERTIES TUTORIAL Q1 A PIECE

Q14: A cylindrical rod 100mm long and having a diameter of 10.0mm is to be deformed using a tensile load of 27,500 N. It must not experience either plastic deformation or a diameter reduction of more than 7.5 x 10^-3mm. Of the materials listed as follows, which are possible candidates? Justify your choice(s).

LEC – 15 MECHANICAL PROPERTIES TUTORIAL Q1 A PIECE

Solution :

LEC – 15 MECHANICAL PROPERTIES TUTORIAL Q1 A PIECE

Relative to the second criterion, it is necessary to calculate the change in diameter ∆d for these two alloys:

LEC – 15 MECHANICAL PROPERTIES TUTORIAL Q1 A PIECE

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