UNIT – I
1. Derive relation for strain energy due to shear.
2. State Maxwell’s reciprocal theorem.
3. What do you mean by unsymmetrical bending?
4. Define the term Poisson’s ratio and Bulk modulus.
5. Explain the effect of change of temperature in a
composite bar.
6. State Castigliano’s first theorem.
7. What is meant by Strain energy?
UNIT – II
1. Derive a relation fro prop reaction for a simply
supported beam with uniformly
distributed load
and propped t the centre.
2 A Steel fixed beam AB of span 6 m is 60 mm wide and 100 mm
deep. The support B
sinks down by 6
mm. Fine the fixing moments at A and B. Take E = 200 GPa.
3. Sketch the bending moment diagram of a cantilever beam
subjected o udl over the
entire span.
4. The section modulus w.r.t.x-axis of a rectangle of width
‘b’ and depth ‘d’ is --------
and in case of
circle, the section modulus is--------.
5. What is meant by point of contraflexure?
6. A cantilever beam 4 m long carries a load of 20 kN at its
free end. Calculate the shear
force and Bending
moment at the fixed end.
7. Write the equation giving maximum deflection in case of a
simply supported beam
subjected to udl
over the entire span.
UNIT – III
1. Discuss the effect of crippling load (Pc) obtained by
Eulers formula on Rankine’s
formula for short
columns.
2. Differentiate a thin cylinder and a thick cylinder with
respect to hoop stress.
3. Express the strength of a solid shaft.
4. Give the expression for finding deflection of closely
coiled helical spring.
5. Give the equivalent length of a column for any two end
conditions.
6. A boiler of 800 mm diameter is made up of 10 mm thick
plates. If the boiler is
subjected to an
internal pressure of 2.5 MPa, determine circumferential and
longitudinal
stress.
7. Write down Rankine-Gordon formula for eccentrically
loaded columns.
8. Define : Middle Third Rule.
UNIT – IV
1.What do you mean by triaxial state of stress.
2. Define principal planes and principal stresses.
3. What is meant by principal plane?
4. Find the principal stresses if the normal stresses sx
and sy
and shear stess t act at a
point?
UNIT – V
1. State any four assumptions made in the analysis of
stresses in curved bars.
2. What do you mean by unsymmetrical bending.
3. When will you use the simple flexure formula for curved
beams?
4. State the assumptions in Winkler – Bach Analysis
5. What are the reasons for unsymmetrical bending?
6. What are the assumptions made in Winkler – Bach theory?
SIXTEEN – MARK QUESTIONS
UNIT – I
1. A simply supported
beam of span “l” carries an uniformly distributed load of W per
unit length over
the entire span. Using Castigliano’s theorem determine (16)
(i)
The mid-span deflection of the beam
(ii)
The slope at the left support.
2. A simply supported
beam of span 8 m carries two concentrated loads of 20 kN and 30
kN at 3 m and 6 m
from left support. Calculate the deflection at the centre by strain
energy
principle.
(16)
3. The external
diameter of a hollow shaft is twice the internal diameter. It is subjected
to pure
torque and it attains a maximum shear stress ‘τ’. Show that the strain
energy
stored per unit volume of the shaft is
5 τ2 / 16C. Such a shaft is required to transmit
5400 kw at
110 r.p.m. with uniform torque, the maximum stress not exceeding 84
MN / m2.
Determine,
(i)
The shaft
diameter (8)
(ii)
The strain
energy stored per m3. Take C = 90 GN / m2. (8)
4. Using Castigliano’s theorem, determine the deflection of
the free end of the cantilever
beam shown in
fig. A is fixed and B is free end. Take
EI = 4.9 MNm2.
(16)
UNIT – II
1. A fixed beam of span 8 m carries an udl of 2 kN/m over a
length of 4 m from the left
support and a
concentrated load of 10 kN at a distance of 6m from the left support.
Find the fixed end
moments and draw the B.M. and S.F. diagrams. (16)
2. A propped cantilever of span of 6 m having the prop at
the end is subjected two
concentrated loads
of 15 kN and 30kN at one third points respectively from left fixed
end support. Draw
SFD and BMD with salient points.
(16)
3. A fixed beam of 8
m span carries a uniformly distributed load of 40 kN/m run over
4 m length
starting from left end and a concentrated load of 80 kN at a distance of
6 m from the
left end. Find
(i)
Moments at the
supports. (12)
(ii)
Deflection at the centre of the beam.
(4)
Take EI =
15000 kNm2.
4. A cantilever AB
of span 6 m is fixed at the end ‘A’ and propped at the end B. It
carries a
point load of 50 kN at the mid span. Level of the prop is the same as that
of
the fixed
end.
(i)
Determine reaction at the prop.
(12)
(ii)
Draw the S.F. and B.M. diagrams.
(4)
UNIT – III
1. (i) Derive the
Lame’s equations for thick cylinder.
(12)
(ii) A thick
cylinder has diameter 1.2 m and thickness 100 mm is subjected to an
internal
fluid pressure 15 N/mm2. Sketch the hoop stress distribution. (4)
2. (i) Derive the formula to find the crippling load
in a column of length ‘l’ hinged at
both
ends.
(12)
(ii) Differentiate between thin and thick
cylinders.
(4)
3. Derive Euler’s
crippling load for the following cases :
(i)
Both ends
hinged.
(8)
(ii)
One end is fixed and other end free. (8)
4. A column with one
end hinged and other end fixed has a length of 5 m and a hollow
circular
cross-section of outer dia 100 mm and wall thickness 10 mm. If E = 1.60 x
105
N/mm2 and crushing stress σc = 350 N/ mm2,
find the load that the column may
carry with a
factor of safety of 2.5 according to Euler theory and Rankine – Gordon
theory.
(16)
UNIT – IV
1. The state of
stress at a certain point in a strained material is shown in Fig. Calculate
(i) principal
stresses (ii) inclination of the
principal planes (iii) Maximum shear
stress
and its
plane. (16)
2. Explain the
following:
(16)
(i)
Maximum
principal stress theory
(ii)
Maximum principal strain theory
(iii)
Maximum strain energy theory and
(iv)
Distortion energy theory.
3. Derive the
expressions for Energy of distortion and Energy of dilatation? (16)
4. Determine the
principal moments of inertia for an angle section 80 mm x 80 mm x
10 mm.
(16)
UNIT – V
1. Determine the
horizontal and vertical deflection of the end B of the thin curved beam
shown in fig.
Take E = 200 GN/m2, width and thickness of the beam 10 mm and 5
mm respectively.
P = 2 N.
(16)
2. (i) Briefly explain how the Winkler – Bach theory
shall be used to determine the
stresses
in a curved beam.
(8)
(ii) Write
short notes on: (8)
1.
Fatigue and
fracture
2.
Stress concentration.
3. A curved bar is
formed of a tube of 120 mm outside diameter and 7.5 mm thickness.
The centre line
of this beam is a circular arc of radius 225 mm. A bending moment of
3 kNm tending to
increase curvature of the bar is applied. Calculate the maximum
tensile and
compressive stresses set up in the bar. (16)
4. Two mutually
perpendicular planes of an element of a material are subjected to
direct stresses
of 10.5 MN/m2 (tensile); and 3.5 MN/m2 (compressive) and
shear
stress of 7 MN/m2.
Find,
(i)
The magnitude and direction of principal stresses.
(12)
(ii)
The magnitude of the normal and shear stresses on a
plane on which the shear stress is maximum.
(4)
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