Download AKTU (Dr. A.P.J. Abdul Kalam Technical University (AKTU), formerly Uttar Pradesh Technical University (UPTU) B-Tech 3rd Semester (Third Semester) 2016-2017 NME 302 Mechanics Of Solids Question Paper
(Following Paper ID and Roll No. to be ?lled in your
' Answer Books) .
I?upcr ll): 2289778 Roll No.
B. TEC-H.
Regular Theory Examination (Odd Sem-IH), 2016-17
MECHANICS OF SOLIDS ?
T ime : 3 Hours, .Max. Marks : 100
Note : Attempt questions as per instructions.
SECTION -A
1'. ?Attempt all parts of the following : , (10X2=20) .
a) What is Hook?s law? Explain.
b) What are thermal stress and thermal strain.
c) What are principal stresses and strains?
d) What is slenderness ratio and equivalent length of
a column?
e) What are ?itched beam and ?xed beam?
0 Differentiate between resilience and proof
resilience.
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NME - 302
g) What is spring? What are different types of springs?
h) What is the di??erence between column and strut?
'_ i) Explain:
i) Section Modulus
ii) Modular ratio
j) Differentiate between thin cylinder and thick
. cylinder.
SECTION - B
Note: Attempt any ?ve questions from this section.
(5X10=50)
Derive the expression for shearing stress at any section
on a beam, also show the distribution of sharing stress
over a rectangular section. '
AsimplysuppatedbemnofspanLiscanyingalmifonnly
disuibuted load of w per unit length over the entire span.
Find the maximum slope and de?ection of the beam.
A solid shaft of iMm diameter has the same cross
sectional area as the hallow sha? 'of the same material
with inside diameter of 150 mm. Find the ratio of
302/12001025120 (2) .
NME - 302
i) Powers transmitted by both the sha?s at the same
angular velocity.
ii) Angles oftwistinequal length ofthese shafts, when
stmssed to same intensity.
A?cylindn'cal shell 90 cm long 20 cm internal diameter
having thickness of metal as 8 mm is ?lled with fluid at
atmospheric pressure. If an additional 20 cm3 of ?uid is
pumped into the cylinder, ?nd
i) The pressure exerted by the ?uid on the cylinder
and _ .
ii) The hoop stress induced. Take E = 200 GPa and .
,p = 0.3 l
A shott length of tube, 4 cm internal diameter and 5cm
? external diameter, failed in compression at a load of 240
KN. Whena2mlength ofthesametubewastestedwith
the ?xedends, the loadatfaihn?ewas 158KN.Assmning
that the ultimate crushing stress in Rankine?s formula is
given by the ?rst test, ?nd the value of the constant a in
the same fonnula. What will be crippling load of this tube
if it is used as a strut 3m long with one end ?xed and .
other is hinged. '
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NME - 302
What are the various theories of failure? Explain with
diagram. '
A bar of uniform cross section area A and length L hangs
vertically, subjected to its own weight. Prove that the
strain energy stored within the bar is given by
_ AxpzxL3
6E
U
Where E is modulus of elasticity and p is weight per
unit volume.
A beam oflength 6 m is simply supported at its ends and
carries two point loads of 48 KN and 40 KN at a distance
of 1 m and 3m respectively from the left support. Find:
i) De?ection under each load
ii) Maximum de?ection
iii) The point at which maximum de?ection occurs.
Give E=200 GPa and 1:85 mm?
302/12/2016/25120 . (4)
10.
NME - 302
A rectangular block of material is subjected to a tensile
stress of 1 10 MPa on one plane and a tensile stress of 47
MPa at right 'angles to the former. Each of the above
stresses is accompanied by a shear stress of 63 Mpa and
that associated with the former tensile stress tends to
rotate the block anticlockwise. Find :
i)' The direction and magnitude of each of the principal
stress.
ii) Magnitude of greatest shear stress
SECTION - C
Note: Attempt any two questions from this section.
11.
(2x15=30)
Attempt all parts of the following: (3X5=15)
a) In a hallow circular shaft of Outer and inner
diameters of 20 cm and 10cm respectively, the
shear stress in not to exceed 40 MPa. Find the
maximum torque which can be safely transmitted.
' b) Determine the poisson?s ratio and bulk modulus of
a material, for which young?s modulus is 120 GPa-
and modulus of rigidity 4.8 Mpa.
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NME -0302 ' ~ NME - 302
c) At a point in a strained material the principal 13. A closely coiled helical spring is to carry a load of 500
stresses are 100 MPa (Tensile) and 60 Mpa ? N. Its mean coil diameter is to be 10 times that of the
(Compressive). Determine the normal stress, shear _ wire diameter. Calculate the mean diameter if the
stress and resultant stress on a plane inclined at maximum shear stress 'in the material ofthe spring is to
50?? to the axis of major principal stress. Also be 80 MPa. If the stiffness of the spring is 20 N per mm
?etermine the maximum shear stress at a point.? t ' de?ection and modulus of rigidity =? 86000 MPa. Find
, , > the number of coils in the closely helical springs.
12. Attempt all parts of the following :? (3X5=15)
a) Derive the expression for elongation of a unime
bar due to its self-Weight. ' ' ?
b) Derive the expression for elongation of a conical
bar due to its self-weight.
c) A steel rod 6f 3cm diameter is enclosed centrally
? in a hallow copper tube of external diameter 5 cm
and internal diameter 4 cm. The composite bar is
then subjected to an axial pull of 45000 N. If the
length 'ofeach bar is equal to 15 cm. -
Determine:
i) The stresses in the rbd arid the tube.
ii) Load carried by each load
E for steel =200 GPa and for Copper = 100 GPa.
' mmmmmsno (6) 302/12/2016/25120 (b
This post was last modified on 29 January 2020