Part -B
1. A rectangular block of material is subjected to a tensile stress of 110 N/mm2 on one
plane and a tensile stress of 47 N/mm2 on the plane at right angle to the former.
Each of the above stress is accompanied by a shear stress of 63 N/mm2 Find (i)
The direction and magnitude of each of the principal stress (ii) Magnitude of
greatest shear stress.
2. At a point in a strained material, the principal stresses are100 N/mm2 (T) and 40
N/mm2 (C). Determine the resultant stress in magnitude and direction in a plane
inclined at 600 to the axis of major principal stress. What is the maximum intensity
of shear stress in the material at the point?
3. A cantilever truss is show in fig. Find the forces in the members of the truss by the
method of joint.
5 KN 10 KN
Error!
1.5m 3m
600
3m
4. A truss of span 9m is loaded as shown in fig. Find the reaction and forces in the
members marked 1, 2, and 3 by using method of section.
1
2 4m
3
3m 3m 3m
5. A thin cylindrical shell 3 m long has 1m internal diameter and 15 mm metal
thickness. Calculate the circumferential and longitudinal stresses induced and also
the change in the dimensions of the shell, if it is subjected to an internal pressure of
1.5 N/mm2 Take E = 2x105 N/mm2 and poison’s ratio =0.3. Also calculate change in
volume.
6. A closed cylindrical vessel made of steel plates 4 mm thick with plane ends, carries
fluid under pressure of 3 N/mm2 The diameter of the cylinder is 25cm and length is
75 cm. Calculate the longitudinal and hoop stresses in the cylinder wall and
determine the change in diameter, length and Volume of the cylinder. Take E =
2.1x105 N/mm2 and 1/m = 0.286.
7. Derive double integration method for cantilever beam concentrated load at free end.
8. A 2m long cantilever made of steel tube of section 150 mm external diameter and
10mm thick is loaded as show in fig If E=200 GN/m2 calculate (1) The value of W
so that the maximum bending stress is 150 MN/m2 (2) The maximum deflection for
the loading.
2W W
Error!
a = 0.5m
l = 2m
9. Determine the diameter of a solid shaft which will transmit 300 KN at 250 rpm. The
maximum shear stress should not exceed 30 N/mm2 and twist should not be more
than 10 in a shaft length 2m. Take modulus of rigidity = 1x 105N/mm2.
10. The stiffness of the closed coil helical spring at mean diameter 20 cm is made of 3
cm diameter rod and has 16 turns. A weight of 3 KN is dropped on this spring. Find
the height by which the weight should be dropped before striking the spring so that
the spring may be compressed by 18 cm. Take C= 8x104 N/mm2.
11. A compound tube consist of steel tube 140mm internal diameter and 160mm
external diameter and an outer brass tube 160mm internal diameter and 180mm
external diameter. The two tubes are of same length. The compound tube carries an
axial load of 900 KN. Find the stresses and the load carried by each tube and the
amount it shortens. Length of each tube is 140mm. Take E for steel as 2 x 105
N/mm2.
12. A rectangle block of material is subjected to a tensile stress of 110 N/mm2 on one
plane and a tensile stress of 47 N/mm2 on the plane at right angles to the former.
Each of the above stress is accompanied by shear stress of 63 N/mm2. Find (i) the
direction and magnitude of each of the principal stress (ii) magnitude of greatest
shear stress.
13. . At a point in a strained material, the principal stresses are 100 N/mm2 (T) and 40
N/mm2 (C) Determine the direction and magnitude in a plane inclined at 600 to the
axis of major principal stress. What is the maximum intensity of shear stress in the
material at the point
14. It is required to design a closed coiled helical spring which shall deflect 1mm under
an axial load of 100 N at a shear stress of 90 Mpa. The spring is to be made of
round wire having shear modulus of 0.8 x 105 Mpa. The mean diameter of the coil
is 10 times that of the coil wire. Find the diameter and length of the wire.
15. A steel shaft ABCD having a total length of 2400 mm is contributed by three
different sections as follows. The portion AB is hollow having outside and inside
diameters 80 mm and 50 mm respectively, BC is solid and 80 mm diameter. CD is
also solid and 70 mm diameter. If the angle of twist is same for each section,
determine the length of each portion and the total angle of twist. Maximum
permissible shear stress is 50 Mpa and shear modulus 0.82 x 105 MPa
16. Three planks of each 50 x200 mm timber are built up to a symmetrical I section for
a beam. The maximum shear force over the beam is 4KN. Propose an alternate
rectangular section of the same material so that the maximum shear stress
developed is same in both sections. Assume then width of the section to be 2/3 of
the depth.
17. Obtained the deflection under the greater load for the beam shown in fig using the
conjugate beam method.
60 KN 120 KN
2m 3m 1m
18. A beam of uniform section 10 m long carries a udl of KN/m for the entire length
and a concentrated load of 10 KN at right end. The beam is freely supported at the
left end. Find the position of the second support so that the maximum bending
moment in the beam is as minimum as possible. Also compute the maximum
bending moment,
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