Cochin University of Science and Techology (CUST) 2006 B.Tech Civil Engineering Strength of Materials - Question Paper
BTS(C) - III - 06 - 058 (I)
B. Tech Degree III Semester Examination, December 2006
CE/SE 303 STRENGTH OF MATERIALS
(1999 Admission Onwards)
Time : 3 Hours Maximum Marks : 100
I. (a) Establish the relationship between Youngs modulus and Bulk modulus. (8)
(b) A weight of 20 tonnes is supported by three pillars, each 500mm2 in section.
The central pillar is of steel and the other ones are of copper. The pillars are so
adjusted that at a temperature of 15C each carries equal loads. Find the stress in
each pillar at 115C.
Take : Es - 2.0 xlO5 N / mm2 ;EC - 0.8xl05JV7 mm2
a, = 12 x 1 O'6 /c; ac = 18.5 x 10 /c C)'
OR
II. (a) A point in a strained element consists of normal stresses of 200N/mm2 (Tensile)
and 100N/mm2 (Tensile) on two mutually perpendicular planes, together with a shear stress of 50N/mm2. With the help of Mohrs circle, determine the principal planes and principal stresses and the stresses on an oblique plane inclined at 30 with the plane of 200 N/mm2 tensile stress. Also find the maximum shear stress. (12)
(b) A steel rod circular in section tapers from 2cm diameter to 1 cm diameter in a length of 60cm. Find how much its length will increase under a tensile force of 20KN.
Given E = 2x\05 N /mm2. (8)
III. (a) Draw the SFD and BMD for the beam shown in the figure and mark the salient
points. Find the point of contraflexure and maximum bending moment. (12)
\s- | yr\ (HI lin ->(
(b) Derive the relation between shear force, bending moment and intensity of load at a
section of a beam. (8)
OR
IV. (a) What is meant by pure bending? What are the assumptions made in simple
theory of bending? (8)
(b) A circular pipe of external diameter 70mm and thickness 8 mm is used as a simply supported beam over an effective span of 2.5m . Find the maximum concentrated load that can be applied at the centre of the span if permissible stress in tube is
150N/mm2. (12)
V. (a) Using Mohrs Theorem, derive an expression to find out the maximum slope and
deflection of a simply supported beam of length Land uniform El with a central
point load of W. ' (8)
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BGfcAJ |
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VI. (a) Find out the maximum slope and deflection of a cantilever of length L and uniform
(b) A simply supported R.C rectangular beam of span 4m and cross-section
150mm x 300mm is loaded as shown below. Find the maximum slope and deflection of the beam. Take E = 2xl04jV7 mm2. (12)
El carrying a Udl of intensity w per unit run for a length of a from the fixed end. (8) (b) A cantilever of length 2m carries a uniformly distributed load of 2500N/m on its full length and a point load of 1000N at the free end. If the section is rectangular 120mm wide and 240mm deep, find the deflection and slope at the free end.
VII. (a) Find the maximum torque that can- be safely applied to a shaft of 100mm diameter.
The permissible shear stress and the allowable twist are respectively 200N/mm2
and 3 per 10 diameter length of the shaft. Take C = lxl05N7 mm2. (10)
(b) In a close-coiled spring, the diameter of each coil is to be 10 times that of wire of
the spring, and the maximum shear stress is not to exceed 60N/mm2. Maximum permissible deflection under a load of 400N is 10cm. Taking the rigidity modulus as
9 x 104 N / mm2, determine the number of coils, the diameter of the coil and
energy stored in the coil. (10)
VIII. (a) What are the assumptions made in Eulers Theory? What is the limitation of this
theory? (8)
(b) A hollow cylindrical cast iron column of 150mm external diameter and 15mm thickness,
3m long and is hinged at one end and fixed at the other. Find
(a) the ratio of the Eulers and Rankines load
(b) for what length, the critical load by Eulers and Rankines formula will be equal?
Take E = %x\04N/mm2, fc = 550NI mm2 and a = 1/1600. (12)
IX. (a) A hollow cylinder has an external diameter of 250mm and the thickness of the wall
is 50mm . The cylinder is subjected to an internal fluid pressure of 35MPa and external pressure of 3.5MPa . Calculate the minimum and maximum circumferential stresses and plot the variation of the same across the wall thickness. (16)
(b) What are the assumptions made in the Lames theory for thick cylinders. (4)
OR
X. (a) Explain the significance of maximum principal stress theory in elastic failure. (4) (b) A bolt is subjected to an axial pull of 12KN together with a transverse shear force
of 6KN. Determine the diameter of the bolt by using.
(i) Maximum principal stress theory
(ii) Maximum strain theory
(iii) Maximum shear stress theory.
Elastic limit in tension = 300N/mm2 Factor of Safety = 3
Poissons ratio = 0.3 (16)
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