Download 2014S

Code No: R21011
R10
SET - 1
II B. Tech I Semester Supplementary Examinations, Dec - 2014
MECHANICS OF MATERIALS
(Civil Engineering)
Time: 3 hours
Max. Marks: 75
Answer any FIVE Questions
All Questions carry Equal Marks
1. a) Explain the different types of coplanar forces and also write their equations of equilibrium.
b) A circular cylinder of weight 2.5 kN and diameter 300 mm is supported by a right angled
groove as shown in Figure 1. Determine the reactions at the points of contact. Assume all
surfaces are to be smooth.
300
Figure 1
2. a) State and explain the Laws of Friction.
b) A ladder of length 8 m and weight 200 N is placed against a smooth vertical wall and a
rough horizontal floor. The ladder is at an inclination of 60 0 with respect to horizontal.
Determine the coefficient of friction of the floor to keep the ladder in equilibrium
configuration.
3. An open-belt drive connects two pulleys 1 m and 0.6 m diameters, on parallel shafts 4.5 m
apart. The maximum tension in the belt is 2 kN. The driver pulley of diameter 1 m runs at 225
rpm. The coefficient of friction is 0.32. Find the power transmitted and the torque on each of
the two shafts.
4. Determine the directions of principal axes and the principal moments of inertia of the crosssection shown in Figure 2.
10 mm
100 mm
10 mm
75 mm
Figure 2
1 of 2
|''|'||||''|''||'|'|
R10
Code No: R21011
SET - 1
5. a) Draw the stress-strain diagram for mild steel and explain salient points.
b) Determine the elongation of the stepped steel bar subjected to axial forces as shown in
Figure 3.
2
50 kN
A = 125 mm
300 mm
A = 250 mm2
75 kN
A = 500 mm2
450 mm
750 mm
150 kN
Figure 3
6. Draw the shear force and bending moment diagrams for a beam of span 6 m supported and
loaded as shown in Figure 4.
75 kN
50 kN
50 kN/ m
25 kN/ m
2m
2m
Figure 4
2m
7. A simply supported beam of span 4.5 m has an I-section with flanges 150 mm wide, overall
depth 250 mm, flanges12 mm thick and the thickness of web is 10 mm. Determine the intensity
of the uniformly distributed load which will produce a maximum stress of 125 N /mm2.
8. A steel beam cross-section shown in Figure 5, is subjected to a shear force of 150 kN. Draw the
shear stress distribution across the depth of the section. Also find the ratio of maximum shear
stress and the average shear stress.
200 mm
16 mm
250 mm
12 mm
16 mm
150 mm
Figure 5
2 of 2
|''|'||||''|''||'|'|
Code No: R21011
R10
SET - 2
II B. Tech I Semester Supplementary Examinations, Dec - 2014
MECHANICS OF MATERIALS
(Civil Engineering)
Time: 3 hours
Max. Marks: 75
Answer any FIVE Questions
All Questions carry Equal Marks
1. Two identical rollers, each of weight 2.25 kN, are supported by an inclined plane making an
angle 600 with respect to horizontal and a vertical wall as shown in Figure1. Find the reactions
at the points of contact. Assume all surfaces are to be smooth.
600
Figure 1
2. A ladder of length 6 m and weight 300 N is supported by a vertical wall and a horizontal floor.
The ladder is making an angle 60 0 with respect to horizontal. A man weighing 600 N climbs
the ladder. Determine the position of the man on the ladder, will cause slipping of the ladder.
The coefficient of friction between all contact surfaces is 0.25.
3. An open belt running over two pulleys 300 mm and 600 mm diameters connects two parallel
shafts 3.6 m apart and transmits 4.25 kW from smaller pulley that rotates at 325 rpm. The
coefficient of friction between the belt and the pulleys is 0.32 and the safe working tension is
10 N/mm width. Find the minimum width of the belt and the initial tension in the belt.
4. Determine the directions of principal axes and the principal moments of inertia of the cross75 mm
section shown in Figure 2.
12 mm
150 mm 12 mm
12 mm
100 mm
Figure 2
1 of 2
|''|'||||''|''||'|'|
R10
Code No: R21011
SET - 2
5.
A solid steel bar 600 mm long and 72 mm diameter, is placed inside an aluminium tube having
75 mm inside diameter and 100 mm outside diameter. The aluminum tube is 0.25 mm longer
than steel bar. An axial load of 750 kN is applied to the bar and tube through rigid cover plates.
Find the stresses developed in the steel bar and aluminium tube. ESt is 2× 105 N/mm2 and EAl is
0.7× 105 N/mm2.
6.
Draw the shear force and bending moment diagrams for the beam supported and loaded as
shown in Figure 3.
100 kN
50 kN
2m
50 kN/ m
4m
2m
Figure 3
7.
A steel beam of unsymmetrical I-section, top flange 150 mm × 16 mm, web 12 mm × 225 mm
and bottom flange 200 mm × 16 mm, is supported over a span of 5.2 m. If the permissible
stresses are 175 N/mm2 in compression and 100 N/mm2 in tension, determine the safe
uniformly distributed load carried by the beam.
8. A beam of I -section 300 mm deep and 200 mm wide, has equal flanges 20 mm thick and web
16 mm thick. It carries, at a section a shear force of 250 kN. Draw the distribution of shear
stress across the section and also indicate the values at important points. Find the ratio of
maximum to mean shear stress.
2 of 2
|''|'||||''|''||'|'|
R10
Code No: R21011
SET - 3
II B. Tech I Semester Supplementary Examinations, Dec - 2014
MECHANICS OF MATERIALS
(Civil Engineering)
Time: 3 hours
Max. Marks: 75
Answer any FIVE Questions
All Questions carry Equal Marks
1. Two circular cylinders, each of weight 1.5 kN and diameter 300 mm, are connected at their
centers by a flexible but inextensible string of length 500 mm and rest upon a horizontal plane,
supporting above them a third cylinder of weight 2.5 kN and diameter 300 mm as shown in
Figure 1. Find the reactions at the various points of contact and also the force in the string.
Assume all surfaces are to be smooth
Figure 1
2. A force of 250 N, acting parallel to the plane, is required just to move a block up an inclined
plane making an angle 180 with respect to horizontal. If the angle of inclination of the plane is
changed to 220 the effort required, acting parallel to the plane is 300 N. Find the weight of the
block and the coefficient of friction.
3. An open-belt drive connects two pulleys 1.5 m and 1.0 m diameters, on parallel shafts 4.5 m
apart. The maximum tension in the belt is 3 kN. The driver pulley of diameter 1.5 m runs at
250 rpm. The coefficient of friction is 0.3. Find the power transmitted and the torque on each of
the two shafts.
4. Determine the directions of principal axes and the principal moments of inertia of the crosssection shown in Figure 2.
12 mm
150 mm
12 mm
100 mm
Figure 2
1 of 2
|''|'||||''|''||'|'|
R10
Code No: R21011
SET - 3
5.
A mild steel bar 25 mm in diameter and 500 mm long is encased in a brass tube having external
diameter is 40 mm and internal diameter is 32 mm. The composite bar is heated through 500 C.
Calculate the stresses induced in each metal. The coefficient of expansion for steel and brass
are 11 × 10-6 and 16 × 10-6 per oC respectively. ESteel = 2× 105 N/mm2 and EBrass = 1× 105
N/mm2.
6.
Draw the shear force and bending moment diagrams for the beam supported and loaded as
shown in Figure 3.
50 kN
100 kN
25 kN/ m
1.5 m
25 kN
10 kN/ m
3m
1.5 m
Figure 3
7.
A simply supported beam of span 4.2 m has unsymmetrical I-section, top flange 125 mm × 12
mm, web 10 mm × 150 mm and bottom flange 150 mm × 12 mm. It carries a uniformly
distributed load of 60 kN /m over its entire span. Fine the maximum tensile and compressive
stresses due to bending.
8.
A simply supported beam of span 4.2 m carries a uniformly distributed load of 50 kN /m over
the entire span. The cross-section of the beam is a T-section having flange width 150 mm,
flange thickness 16 mm, web thickness 10 mm and overall depth 200 mm. Draw the
distribution of shear stress across the section and also find the ratio of maximum shear stress to
the mean stress.
2 of 2
|''|'||||''|''||'|'|
R10
Code No: R21011
SET - 4
II B. Tech I Semester Supplementary Examinations, Dec - 2014
MECHANICS OF MATERIALS
(Civil Engineering)
Time: 3 hours
Max. Marks: 75
Answer any FIVE Questions
All Questions carry Equal Marks
1. a) Derive the equations of equilibrium of various types of coplanar forces.
b) Find the resultant of the system of forces shown in Figure 1.
Y
25 kN
15 kN
10 kN
300
600
20 kN
X
450
50 kN
30 kN
Figure 1
2. A flexible but inextensible string connects two blocks of weights 500 N and 1000 N. The two
blocks are placed on an inclined plane and the string is parallel to the plane. The 500 N block is
below the 1000 N block. The coefficient of friction between the 500 N block and the inclined
plane is 0.2 and that for 1000 N block is 0.3. Find the angle of inclination of the plane and the
force in the string when the motion is about to take place down the plane.
3. An open belt running over two pulleys 500 mm and 750 mm diameters connects two parallel
shafts 4 m apart and transmits 5 kW from smaller pulley that rotates at 350 rpm. The
coefficient of friction between the belt and the pulleys is 0.3 and the safe working tension is 12
N/mm width. Find the minimum width of the belt and the initial tension in the belt.
1 of 2
|''|'||||''|''||'|'|
R10
Code No: R21011
SET - 4
4. Determine the directions of principal axes and the principal moments of inertia of the crosssection shown in Figure 2.
50 mm
10 mm
100 mm 10 mm
10 mm
75 mm
Figure 2
5.
a) Derive the relation between various elastic constants.
b) A vertical steel rod 1000 mm long is fixed at its top and a weight of 500 N is dropped from a
height of 250 mm on to a collar at the lower end. The upper 500 mm length of the rod is has
a diameter of 20 mm while the reaming portion has 16 mm diameter. Determine the
maximum instantaneous stress induced in the rod.
6.
A simply supported beam of span 6 m carries a uniformly distributed load of 25 kN/m run over
the length of left half of its span, together with concentrated loads of 25 kN, 50 kN and 75 kN
situated at 1m, 2m and 3m respectively from right support. Draw the shear force and bending
moment diagrams and find out the magnitude and position of the maximum bending moment.
7.
A beam of T-section, flange 150 mm × 16 mm, width of the web 12 mm and overall depth of
the section 200 mm is simply supported over a span 4.5 m and is so arranged that the flange is
uppermost. It carries a uniformly distributed load of 50 kN/m over its entire span. Fine the
maximum tensile and compressive stresses.
8.
A steel beam cross-section shown in Figure 3, is subjected to a shear force of 125 kN. Draw the
shear stress distribution across the depth of the section.
150 mm
12 mm
200 mm
10 mm
12 mm
125 mm
Figure 3
2 of 2
|''|'||||''|''||'|'|