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Unit I
Q. 1. An aluminum rod is rigidly attached between a
steel rod and a bronze rod as shown in figure.
Axial loads are applied at the positions indicated.
Find maximum value of P that will not exceed a
stress 140 MPa in steel, 90 MPa in aluminum of and
100MPa in bronze.
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Q. 2. A jet aircraft made from titanium and of length 30 m measured on ground at temperature 350C.
When the jet flies in the sky at a considerable altitude maximum temperature recorded of body is
5350C. Find overall change in length of aircraft for this temperature. Co-efficient of thermal
expansion for titanium is 10 x 10-6/C.
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Q. 3. Two triangular holes to be punched through 8 mm thick aluminium alloy plate in a single
punching operation. If the ultimate shear strength of aluminium alloy is 410 MPa and safe
compressive strength for punch is 260 MPa, determine the maximum size of triangular holes that can
be punched.
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Q. 4. State Hook’s Law and define
a)
Poisson’s ratio.
b)
Modulus of elasticity.
c)
Modulus of rigidity.
d)
Bulk modulus.
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Q. 5. For a bar shown in figure, find the reactions
produced by upper and lower support on the bar due to
application of load P at B, which is utilized to bridge the
gap of x. The AB part of the bar is having cross-sectional
area of 3A and L/2 length, whereas BC part is having
cross-sectional area A and length L/3. Assume modulus
of elasticity of bar is E. Also find stresses in the bar AB
and BC. Assume relevant units for each parameter.
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Q. 6. A rigid bar ABC, supported by
two links AD and BE is of uniform
cross-sectional area A and of lengths
3h and h respectively and are made of
same material. A force F is applied at
point B. Determine the stresses in each
link and maximum deflection of point
B.
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Q. 7. Derive the relation between modulus of elasticity, bulk modulus and modulus of rigidity of a
material within linear elastic range.
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Q. 8. A copper bar AB of length 600
mm of a “tripper circuit box” is placed
in position as shown in figure below at
room temperature with a gap of 0.3
mm between the end B and the rigid
wall. Calculate the axial compressive
stress in the bar, if the temperature
rises to 600 C. For copper bar, take E
= 120 GPa and α= 17 x 10-6 per 0C.
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Q. 9.A bronze bar is fastened between a steel bar and an aluminium bar as shown in figure. Axial
loads are applied to the positions shown. Find the largest value of P that will not exceed an overall
deformation of 4 mm or
the following stresses: sst =
140MPa, sb = 120MPa,
sal =80MPa, Est =200GPa,
Eb =83GPa, Eal =70GPa
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Q. 10.Define the following terms:
a.) Strain energy
b.) Thermal stresses and strains
c.) Volumetric strain
d.) Statically indeterminate structure.
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Q. 11. A solid steel shaft of 50 mm diameter fits concentrically in a hollow aluminium tube, as shown
in figure below. Compute the
minimum internal diameter of
aluminium tube so that no contact
pressure exists, when the steel
shaft carries an axial compressive
load of 300kN. Assume µ = 0.3
and Est = 2 x 105 N/mm2.
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Q. 12.Find the stresses in the wires of the
system, shown in figure below if the
cross-sectional area of wires is 65 mm2,
the load is 18 kN and the temperature of
the system rises by 10 K. Assume:
αc = 16 x10-6 per K, Ec = 110kN/mm2,
αs = 12 x 10-6 per K, Es =210kN/mm2
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Q. 13. Determine the tensile force on the steel bar circular cross section , 25 mm diameter , if the
strain is equal to 0.75 x 10-3. Consider Esteel= 200 GPa.
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Q. 14. Two bars, one of steel and the other of copper are subjected to same tensile stresses of σ =
60 N/mm2. If the ratio of their unit elongation is 8:15 determine their modular ratio. Also determine
their elongation if the bars have a length of 500 mm. For steel Es= 200 GPa.
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Q. 15. A compound bar made of aluminium and steel
subjected to a load of 200 kN is shown in figure. The crosssectional area of aluminium section is twice the steel section.
If the elongation of the two section is equal, determine the
length of each section. Take E= 210 GPa for steel and E= 70
GPa for aluminium.
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Q. 16. A cylindrical piece of steel 80 mm diameter and 120 mm long is subjected to an axial
compressive force 70 kN. Calculate the change in volume of the piece if Bulk modulus is 1.7 × 105
N/mm2 and Poisson’s ratio is 0.3
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Q. 17. A bar 30 X 30 X 250 mm long is subjected to pull of 90kN in the direction of its length. The
extension of the bar was found to be 0.125mm, while decrease in each lateral dimension is found to be
0.00375mm. Find the Young’s modulus, Poisson’s ratio. Modulus of rigidity and bulk modulus.
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Q. 18. A rectangular block 75mm long in x-direction , 50mm long In Y
direction and 100mm in Z direction is subjected to uniformly distributed
forces on x, y, and z faces whose resultant are Px=200kN , Py=240kN
compression and ,Pz=75kN The Poisson’s ratio v = 0.3 and E =
200GPa. Determine a single uniformly distributed force in X direction
that would produce the same deformation in y-direction as the original
loading.
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Q. 19. The rigid bar BDE is supported by two links AB and
CD. Link AB is made of aluminum (E = 70 GPa) and has a
cross-sectional area of 500 mm2. Link CD is made of steel
(E = 200 GPa) and has a cross-sectional area of 600 mm2.
For the 30-kN force shown, determine the deflection a) of
B, b) of D, and c) of E.
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Q. 20. A steel rod of 30 mm diameter is placed centrally inside hollow Bronze tube of external
diameter 40 mm. The steel rod is tightly fitted with bronze tube so that entire section acts as
composite section subjected to compressive force of 30 kN. Determine stresses in rod and tube when
temperature falls by 30°C. Assume : Esteel = 2 × 105 N/mm2 Ebronze = 8 × 104 N/mm2
αsteel = 12 × 10–6/°C αbronze = 18 × 10–6/°C.