Code No: R21011
R10
SET - 1
II B. Tech I Semester Supplementary Examinations Dec - 2013
MECHANICS OF MATERIALS
(Civil Engineering)
Time: 3 hours
Max. Marks: 75
Answer any FIVE Questions
All Questions carry Equal Marks
1. a) State and explain the Lami’s theorem.
b) Two smooth circular cylinders each of weight w =1000N and radius 15cm, are connected at
their centers by a string AB of length = 40cm and rest upon a horizontal plane, supporting
above them a third cylinder of weight = 2000N and radius 15cm as shown in Figure 1. Find
the force (S) in the string AB and the pressure produced on the floor at the points of contact
D and E.
2. a) Explain the difference between co-efficient of friction and angle of friction.
b) A uniform ladder of length 12m and weighing 30 N is placed against a smooth vertical wall
with its lower end 6m from the wall. The coefficient of friction between the ladder and
floor is 0.45. Show that the ladder will remain in equilibrium in this position. What is the
frictional force acting on the ladder at the point of contact between the ladder and floor?
3. a) Derive the expression for optimum speed of flat belt for the transmission of maximum
power considering the effect of centrifugal tension.
b) A shaft which rotates at a constant speed of 160 r.p.m. is connected by belling to a parallel
shaft 75cm a part which has to run at 60, 80, and 100 r.p.m. the smallest pulley on the driver
shaft is 4cm in radius. Determine the remaining radii of the stepped pulleys for;
i) a cross belt , and ii) an open belt.
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Code No: R21011
R10
SET - 1
4. a) State and prove the theorem parallel axis.
b) Find the centre of gravity of the L- section shown in Figure 2.
5. a) Define a composite bar. How will you find the stresses and the load carried by each member
of a composite bar?
b) A rod, which tapers uniformly from 5cm diameter to 3cm diameter in a length of 50cm is
subjected to an axial load of 6500N. If E=2x 105N/mm2, find the extension of the rod.
6. a) Draw the S.F and B.M diagrams for a cantilever of length L carrying a point load W at the
free end.
b) A simply supported beam of length 12m carries point loads of loads 40KN and 60KN at a
distance of 3m and 7m from the left end. Draw the S.F and B.M diagrams for the beam.
7. a) Prove that the bending stress in any fibre is proportional to the distance of that fibre from
neutral layer in a beam.
b) From a given stress, compare the moments of resistance of a beam of square section placed.
i) With two sides horizontal and
ii) With a diagonal horizontal
8. a) Prove the maximum shear stress in a circular section of a beam is 4/3 times the average shear
stress.
b) A beam is of T-section, flange 12cm by 1cm, web 10cm by 1cm. What percentage of the
shearing force at any section is carried by the web?
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Code No: R21011
R10
SET - 2
II B. Tech I Semester Supplementary Examinations Dec - 2013
MECHANICS OF MATERIALS
(Civil Engineering)
Time: 3 hours
Max. Marks: 75
Answer any FIVE Questions
All Questions carry Equal Marks
1.
a) Explain and define the term:”Free body diagram”. Draw the free body diagram of a ball of
weight W, placed on a smooth horizontal surface.
b) A L - shaped body ABC is hinged at A with a force F acting at its end C as shown in
Figure 1. Determine the angle Ѳ which this force should make with the horizontal to keep
the edge AB of the body vertical.
2. a) What do you mean by ‘angle of repose ‘? Prove that angle of repose is equal to the angle of
friction.
b) A uniform ladder of length 13m and weighing 30N is placed against a smooth vertical wall
with its lower end 10m from the wall. In this position the ladder is just to slip. Determine:
i) the coefficient of friction between the ladder and the floor and
ii) frictional force acting on the ladder at the point of contact between ladder and floor.
3. a) Distinguish between slip and creep in a belt drive. Derive an expression for the ratio
of tensions in the tight and slack sides in terms of µ and Ѳ, when the belt is just on
the point of slipping.
b) A shaft rotating at 200 r.p.m. drives another shaft at 300r.p.m. , and transmits 8.H.P. through
a belt .The belt is 10cm wide and 1cm thick. The distance between the shaft is 4m. The
smaller pulley is 15 cm in diameter. Calculate the stress in i) open belt ii) crossed belt.
Take µ =0.3.Neglect the centrifugal tension.
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Code No: R21011
R10
SET - 2
4. a) Derive an expression for the momentum of inertia of a triangular section about an axis
passing through the centre of gravity of the section and parallel to the base.
b) Find the centre of gravity of the I- section shown in Figure 2.
5.
a) What do you mean by a bar of uniform strength?
b) Find the modulus of elasticity of a rod, which tapers uniformly from 40 to 25mm diameter
in a length of 400mm. The rod is subjected to a load of 8KN and the extension of the rod is
0.04mm.
6.
a) Draw the S.F and B.M diagrams for a cantilever of length L carrying a gradually Varying
load from zero at the free end to w per unit length at the fixed end.
b) A simply supported beam is carrying a uniformly distributed load of 3KN/m over the length
of 3.5m from the right end. The length of the beam is 6m. Draw the S.F and B.M diagrams
for the beam and also calculate the maximum B.M on the section.
7.
a) What do you mean by simple bending or pure bending? What are the assumptions made in
the theory of simple bending?
b) A timber beam of rectangular section is to support a load of 25KN over a span of 4m. If the
depth of the section is to be twice the breadth, and the stress in the timber is not to exceed
60N/mm2, find the dimensions of the cross section. How would you modify the cross
section of the beam if it was a concentrated load equal magnitude placed at the centre with
the same ratio of breadth to depth?
8.
a) The shear stress is not maximum at the N.A in case of the triangular section. Prove the
statement.
b) A beam of I-section is having over all depth as 500mm and overall width 190mm. the
thickness of flanges is 25mm where as the thickness of the web is 15mm. the moment of
inertia about the N.A is given by 6.45x108N/mm4. If the section carries a shear force of
50KN, calculate the maximum shear stress. Also sketch the shear stress distribution across
the section.
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Code No: R21011
R10
SET - 3
II B. Tech I Semester Supplementary Examinations Dec - 2013
MECHANICS OF MATERIALS
(Civil Engineering)
Time: 3 hours
Max. Marks: 75
Answer any FIVE Questions
All Questions carry Equal Marks
1.
a) How will you prove that a body will not be in equilibrium when the body is subjected to
two forces which are equal and opposite but are parallel?
b) A roller of radius 40cm, weighing 3000N is to be pulled over a rectangular block of
height 20cm as shown in Figure 1, by a horizontal force applied at the end of a string wound
round the circumference of the roller. Find the magnitude of the horizontal force which will just
turn the roller over the corner of the rectangular block. Also determine the magnitude and
direction of reaction at A and B. All surfaces may be taken as smooth.
2. a) Prove that the angle of friction is equal to the angle of the inclined plane, when a solid body
of weight W placed on the inclined plane, is about to solid down.
b) A cord connects two bodies of weights 500N and 1000N. The two bodies are placed on an
inclined plane and cord is parallel to the inclined plane. The coefficient of friction for the
weight of 500N is 0.20 and that of 1000N is 0.4. Determine the inclination of the plane to
the horizontal and tension in the cord when the motion is about to take place, down the
inclined plane. The body weight 500 N is below the body weighing 1000N.
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Code No: R21011
R10
SET - 3
3.
a) Distinguish between the initial tension and centrifugal tension in a belt .
b) Two parallel shafts 10m apart are to be connected by a belt running over pulleys of
diameters 480cm and 80cm respectively. Determine the length of belt required;
i) If the belt is open and
ii) belt is crossed.
4.
a) Prove that the moment of area of any plane figure about a line passing through its centroid
is zero.
b) For the T -section shown in Figure.2, determine the moment of inertia of the section about
the horizontal and vertical axis, passing through the centre of gravity of the section.
5.
a) Find an expression for the total elongation of a bar due to its own weight, when the bar is
fixed at its upper end and hanging freely at the lower end.
b) A rectangular bar is made of steel is 3m long and 10mm thick. The rod is subjected to an
axial tensile load of 60KN. The width of the rod varies from 70mm at one end to 28mm
at the other. Find the extension of the rod if E=2x105N/mm2.
6.
a) Draw the S.F and B.M diagrams for a simply supported carrying a uniformly varying load
from zero at each end to W per unit length at the centre
b) A simply supported beam of length 10m carries point loads of loads 4KN and 6KN at a
distance of 2m and 4m from the left end. Draw the S.F and B.M diagrams for the beam.
7. a) What do you understand by neutral axis and moment of resistance?
b) A cast iron pipe has 300mm bore and 10mm metal thickness, and is supported at two points
10m apart. Find the maximum stress in the metal when it is running full. Take unit eight of
cast iron as 70KN/m3 and that of water as 9.81kN/m3.
8.
a) Show that the rectangular section of the maximum shear stress is 1.5 times the average
stress.
b) A 12cm by 5cm I-section is subjected to a sharing stress of 15kN. Calculate the shear
stress at the neutral axis and at the top of the web. What percentage of shearing force is
carried by the web? Given I=220x104 mm4, area= 9.4x102mm2, web thickness= 3.5mm
and flange thickness =5.5mm
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Code No: R21011
R10
SET - 4
II B. Tech I Semester Supplementary Examinations Dec - 2013
MECHANICS OF MATERIALS
(Civil Engineering)
Time: 3 hours
Max. Marks: 75
Answer any FIVE Questions
All Questions carry Equal Marks
1. a) What do you mean action and reaction in the force systems? Give examples.
b) Draw the free body diagram of a ball of weight W supported by a string AB and resting on a
smooth horizontal surface at C when a horizontal force is applied to the ball as shown in
Figure.1
2. a) State the law of static and dynamic friction.
b) Block A weighing 20N is a rectangular prism resting on a rough inclined plane as shown
in Figure 2. The block is tied up by a horizontal string which has a tension of 6N as shown
in Figure 2. Find: i) the frictional force on the block,
ii) the normal reaction of the
inclined plane, and iii) the coefficient of friction between the surface of contact.
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Code No: R21011
3.
R10
SET - 4
a) Obtain the conditions for the maximum power transmitted by a belt from one pulley to
another.
b) The maximum allowable tension in a flat belt is 1600N. The angle of lap is 170˚. And the
coefficient of friction between the belt and material pulley is 0.27. Neglecting effect of
centrifugal tension, calculate the net driving tension and power transmitted if the belt speed
is 2.5 m/s.
4. a) State and prove the parallel axes theorem on moment of inertia for a plane area.
b) For the I-section shown in Figure.3, find the momentum of inertia about the centroidal
axis X-X perpendicular to the web.
5. a) Describe the procedure of calculating the thermal stresses in a composite bar?
b) The extension in a rectangular steel bar of length 800mm and thickness of 20mm is found to
be 0.21mm. The bar tappers uniformly in width from 80 mm to 40 mm. If E of the bar is
2x105N/mm2 determine the axial tensile load of the bar.
6. a) Draw the S.F and B.M diagrams for a cantilever of length L carrying a uniformly distributed
load W per meter length over its entire length.
b) A simply supported beam of length 8m carries point loads of loads 4KN, 10KN and 7KN
at a distance of 1.5m, 2.5m and 4m respectively from the left end. Draw the S.F and B.M
diagrams for the beam.
7. a) What is the meaning of the strength of the section?
b) A 100mmX200mm rolled steel joist of I-section has flange 10mm thick and web 10mm
thick. Find the safe uniformly distributed load that this section can carry over a span of 6m
if the permissible bending stress is limited to 165N/mm2.
8. a) How will you draw the shear stress distribution diagram for a composite section?
b) The shear force acting on a section of a beam is 120kN.The section of the beam is T-shaped
of dimensions 200mmx250mmx50mm. The flange thickness and web thickness are 50mm.
Moment of inertia about the horizontal neutral axis is 1.134x108 mm4. Find the shear stress
at the neutral axis and at the junction of the web and the flange.
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