STRENGTH OF MATERIALS
UNIT I
1.
A round steel bar 20 mm diameter and 300 mm long is placed concentrically within a brass tube which has an outside diameter of 30 mm and an inside diameter of 22.5 mm, the length of the tube exceeds that of the bar by 0.2 mm. Rigid plates are placed on the ends of the tube through which an axial compressive force applied to the compound bar. Determine the compressive stresses in the bar and the tube due to a force of 50 KN.Take Esteel = 210
Gpa, Ebrass= 100Gpa.
2.
The composite bar shown in fig. is attached to the end supports. The temperature of the structure is raised by 50° C. Find the stresses in the three portions of the bars if: i) The supports are unyielding. Ii) The supports yield by 0.5 mm. Take, Ecu = 1x10
0.7 x 10
5
Mpa, Esteel = 2x 10
5
5 Mpa, Eal=
Mpa, αcu=16 x 10 -6 /° C , αal=20 x 10 -6 /° C, αsteel=12 x
10
-6 /° C Areacu = 15 sq.cm, Area ai= 10sq.cm, Area steel = 20 sq.cm, Lcu=50cm,Lal =
50cm, Lst = 100cm.
.
Steel
Copper
Al
Al
3.
Draw stress strain curve for tension test on a M.S. specimen and mark the significant point on it.
4.
Derive the relation between Young’s modulus & Modulus of Rigidity.
5.
A hollow cylindrical drum of 600 mm internal has thickness of 40 mm. The length of the cylinder is 3m. It is closed with plates at ends and is subjected to an internal air pressure of
3 Mpa. Determine the increase in volume of the drum. Take E= 2x10
5
Mpa, μ=0.3
6.
A masonry chimney having the shape of a frustum of a cone is 25m high. The external dia.
At top and internal dia. At bottom is 2 m. The chimney is 0.5 m thick at the base. If the weight of the chimney is 1800 KN, find the uniform horizontal wind pressure that may act/unit projected area of the chimney in order tension at the base is just avoided.
7.
A cylindrical thin drum 80 cm in diameter and 3m long has a shell thickness 10 mm. If the drum is subjected to an internal pressure of 2.5 Mpa, determine i) change in diameter ii)
Change in length. Iii) change in volume
8.
A hollow cylindrical drum 500 mm in diameter has a thickness of 10 mm. If the drum is subjected to an internal air pressure of 4 Mpa, determine the increase in volume of drum.
UNIT II
9.
A beam of span 6 mts. Has one support at the left end and the other support at a distance of
2m from the right end. The beam carries a udl of 10 KN/m over the entire span. Draw the
SFD and BMD and prove that the middle point of the beam is the point of contra flexure.

10.
A beam ABC has a total length of 9m with A and B as supports, 7m apart. Overhanging portion BC= 2m. A is hinged. The beam carries moments and loads as follows i) 6 KN load at a point 3m from A. ii) udl 1KN/m over the portion BC ii) An anticlockwise moment 3.5
KN-m at the middle point of span AB. Draw BM and SF diagrams for the beam. Locate point of contra flexure.
11.
A beam ABCD is simply supported at A and C. AB= 3m, BC= 2m and CD = 1m. Span AB carries a udl of 20 KN/m while a point load of 50 KN acts at the free end D. Draw the shear force and bending moment diagram and locate the point of contra flexure. If any.
12.
A beam ABCDE has total length 9 m supported at A and D. AB= 2m, BC= 2m, and
CD=3m Overhang portion DE=2m subjected to loading as given below i)6KN load at B ii)udl 1 KN/m over the portion BC iii)10 KN load at D iv) udl of 2 KN/m for the portion
DE. Draw SFD and BMD and locate point of contra flexure.
UNIT III
13.
Derive the flexure formula stating various assumptions made therein.
14.
Explain the relation between Bending moment, shear force, loading, deflection and curvature of a beam.
15.
Show the relation between maximum shear stress and average shear stress for a rectangular beam subjected to shear force.
16.
A beam of 5m span and simply supported is loaded with udl 5 KN/m. Calculate the bending stress and also the % of moment of resistance shared by the web and the flanges.
The cross section of beam is I section. Size of flange= 200mm x 20mm, size of web =
20mm x 400mm.
17.
A timber beam 150 mm wide and 200 mm deep is to be reinforced by bolting on two steel flitches each 150 mm by 12.5 mm in section. Find the moment of resistance when i) the flitches are attached symmetrically at top and bottom end. ii) the flitches are attached symmetrically at the sides.
Allowable stress in timber is 6 Mpa. What is the stress in steel in each case.? Take Es= 20 Ew.
UNIT IV
18.
A hollow shaft of internal diameter 400 mm and external diameter 460 mm is required to transmit power at 180 rpm. Determine the power it can transmit if the shear stress is not to exceed 60 Mpa and the maximum torque exceed the mean torque by 28%.
19.
Define torsional rigidity and torsional stiffness.
20.
Derive the expression for stiffness in closely coiled helical spring.

21.
A closely coiled helical spring made of 10 mm diameter steel rod has 10 complete coils each of mean diameter 80mm. Calculate the deflection under the pull and the amount of energy stored in the spring during the extension if it is subjected to an axial pull of 200N.
Assume C= 0.84 x10
5
N/mm
2
.
22.
Derive the torsional formula for a circular shaft with usual notation and state the assumptions made therein.
23.
Explain the types of spring.
UNIT V
24.
A beam has supports L apart with equal overhangs L/4 over each support. It carries a load
W at each end and a load 2W at the centre. Find the slopes at free end and at the support.
Find also the deflection at the free ends in terms of EI.
25.
A uniform beam AB of span 6m is simply supported at its ends A and B. The beam carries a udl of 30 KN/m over the whole span and a concentrated load of 40 KN placed at a distance 2 m from left support A. A clockwise moment of KNm is also applied at end B.
Obtain the equation to the elastic line. Find deflection of beam at the poit where the concentrated load is placed.
26.
A beam ABCDEF is supported at A and E. EF is overhang. AB=3m , BC=3m, DE=4m,
EF=2m. The beam carries a point load of 40 KN at B, a clockwise moment of 10 KN-m at
C, a point load of 35 KN at D, a udl of 10 KN-m over DE and a udl of 15 KN/m over EF.
Using Macaulay’s method calculates the deflection at free end and under moment in terms of EI.
27.
Derive the relation between deflection, moment, shear and load.
UNIT VI
28.
Two planes AB & BC which are at right angles carry shear, stress of intensity 5 N/mm
2 while these planes also carry a tensile stress of 70 N/mm
2
and a compressive stress of 35
N/mm
2
resp. Determine the principal plane and principal stresses, Also determine the maximum D shear stress and the plane on which it acts.
29.
A rectangular block of concrete material is subjected to tensile stress of fx on one plane of tensile stress of fy on plane at right, together with shear stresses of (Tau xy) on the same planes. Derive the equations xy from the principle to find i)magnitude of principal stresses, ii) direction of principal stresses.
30.
A masonry dam is 8 m high, the maximum depth of water impounded being 7.5 m. The top width of dam is 1.5 m. The weight of masonry is 22000N/m
3
while the weight of water is

9810N/m
3
Find the minimum width of section at base for no tension. The coefficient of friction between masonry to masonry is 0.6. The water face of the dam is vertical.
31.
Define shear flow and shear centre. Find the shear stress distribution and position of shear centre for a channel placed with its outer arms (flanges) horizontal. The overall depth is 25 cm with flange outer dimensions as 10.5cm. The thickness of the section is 1 cm throughout. A shear force of 60 KN acts through the shear centre. Neglect the minor shear forces.
32.
Explain the concept of shear flow and shear centre in case of thin walled sections.
33.
Explain “ Core of a circular section.”
34.
Draw a neat sketch of Hollow circular cylinder with external diameter of 300 mm and thickness of 50 mm.
35.
What is the principal plane and principal stresses. What is the angle between principal plane and a plane carrying maximum shear?. What is the angle of obliquity?