Aryabhatta Knowledge University
Sem. iv 2013
Time 3hr Full marks: 70
Mechanics of solid-1
Attempt any five questions in which question no 1 is
compulsory
1.
Answer any seven from the following in short:
(a)
Explain internal and external forces.
(b)
Discuss generalized Hooke’s law.
(c)
Define the terms ‘longitudinal strain’, ‘lateral
strain’ and ‘poison’s ratio’.
(d)
What do you mean by strain energy? Illustrate clearly with suitable example.
(e)
How do you find the maximum bending moment in a
beam?
(f)
How can you determine the maximum instantaneous
deflection of a beam subjected to impact loading?
(g)
Define the term ‘pure torsion’.
(h)
Distinguish between major and minor principal
stresses.
(i)
State the criteria for a thin cylinder. What types
of stresses are induced in a thin cylindrical shell subjected to an internal
pressure?
(j)
Define helical spring .name the two important
types of helical springs.
2.
A steel bolt of 12 mm diameter passes through a
brass tube of 16 mm diameter, 25 cm long and 20 mm external diameter. The bolt
is tightened by nut at 15 degree Celsius so as to exert a compressive force
1500 kg on the tube .calculate the stress in each (a) 15 degree Celsius (b)
when the temperature of the tube and bolt is raised to 50 degree Celsius.
Take
Eѕ =2х106kg/cm2
αs=
12х10-6/°c
Eb = 1х106kg/cm2
αb= 19х10-6/°c
3.
Derive the torsion formula
T∕J=Ƭ∕r=Gθ/L
With assumption where all terms indicate
usual meanings.
4.
A close –coiled helical spring, consisting of 8
coils , each having mean diameter 80 mm
and wire diameter 10 mm . The spring is fixed at one end and twisting
moment of 10 Nm applied axially at other end in such a way that the spring
tends to open . Determine (a) the maximum bending stress produced in the wire
of the spring ,(b)the angle of twist ,(c) the resistance and (d) the number of
turns after the application of torque. Take, E=2х10^5N/mm^2.
5.
Show that in a strained material under two
dimensional stress system , the sum of normal
components of stresses acting on any two mutually perpendicular planes
is constant . the principal stresses at a point in a strained material are √(σ₁2+σ₂2)/2
6.
Cast iron T section having overall depth 150 mm,
flange and web 30 mm is used as bracket. The length of the bracket is 300mm. If
the tensile stress is restricted to 20 n/mm2 , what will then be
placed at the top of bracket ? What will then be the compressive stress
developed?
7.
Draw the shear force ,bending moment and axial
force diagrams for the beam supported and loaded as shown in the figure below:
8.
A cantilever AB of 6 m length is subjected to a
u.d.l. of intensity w t/m spread over the entire length. Assuming rectangular
cross section with depth equal to twice breadth , determine the minimum
dimensions of the beam so that the vertical deflection at the free end of does not exceed 1.5 cm and
the maximum bending stress does not exceed 1000 kg/cm2 .Take E=2 x 106 kg/cm2
9.
Two round bars of varying diameter A and B are
shown in Fig . Below made of same material. An axial blow on bar A produces a
maximum stress of 100 N/mm2.Find the maximum stress produced by the
same blow on the bar B. If the bar B is also stressed to 100 N/mm2,
find the ratio of strain energies stored in the bars A and B.
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