Cochin University of Science and Techology (CUST) 2002 B.Tech Civil Engineering Strength of Materials - Question Paper
B.TECH. DEGREE ID SEMESTER (SUPPLEMENTARY) EXAMINATION IN CIVIL ENGINEERING JUNE 2002
CE 303 STRENGTH OF MATERIALS
(1998 Admissions)
Time: 3 Hours Maximum Marks: 100
Define the following terms:
(a)
(b)
(i) S Stress
(ii) y Strain
(iii) Hook's law
(iv) Limit of proportionality (8) A compound bar of steel 50cm long is loaded with lOkN
as shown in figure below. Find its change in length and
volume. Take E = 0.21Af/V/ mm2. (12)
il = 20cm tj = 30cm d\ = 2 cm d2 = 1cm
Derive expression for stresses on inclined plane of a block subjected to normal stresses and shear stresses along > two planes at right angles. (8)
H
(a)
(b)
An element has a tensile stress of 500N/mm2 and compressive stress of 300N/mm2 acting at mutually perpendicular planes and two equal shear stresses of 150N/mm2 on these planes. Find the principal stresses and maximum shear stress with direction. (12)
Define shear force and bending moment. Establish relationship between bending moment and shear force. (6) Calculate the BM and SF at section A, B, C, D and E and plot BMD and SFD for a team loaded as in figure below: (14)
4
ffl. (a) (b)
OR
State the assumptions made in simple bending theory. (4) Derive expression for moment of resistance of a beam. (6) A timber beam rectangular in cross section is loaded . with UD1 of W Kg/m. If the shear stress and bending stress of 8.5 Kg/cm2 and 85Kg/cm2 reach maximum of thesp values simultaneously find the span to depth ratio. (10)
IV. (a) (b) (c)
Derive expression for deflection for a rectangular beam due to bending shear. (8)
V. (a) (b)
VI.
A simply supported beam of length L caarries a load W at a distance of 'a from one end and 'b' from other end.
Find magnitude and position of maximum deflection. (12) OR
A horizontal beam simply supported at ends having a length of 5.0m is loaded with 8kN/m at one end and 20 kN/m at the other end as varying load. The section is 50cm deep. Maximum bending stress is 950Kg/cm2.
Contd...................3.
VII. (a) Derive conditions for the boundary of the core for the
case of an eccentrically loaded rectangular strut. (6)
(b) Derive Rankine's formula for columns. (6)
(c) Find Euler's crippling load for a hollow cylindrical column of external dia of 4cm and internal dia of 3cm fixed at both ends. The length of the column is 2.4m.
Take = 2.1 x 105 iV / mm2. (8)
OR
VIII. Calculate the safe load the column can carry if its length is S.2m having one end fixed and other end hinged with a factor of safety of 3. The column is of I section.
(Area = 22cm2; Ixx - 840cm4; Iyy = 95cm4).
Take Rankine's constants a =
fc = 3200Kg/cm2. (20)
IX. (a) Derive Torque equation. (8) (b) The internal dia of a hollow shaft is two third of its
external dia. Compare the resistance to twisting and stiffness of a shaft with that of a solid shaft of same material and same weight. (12)
OR
X. A thin cylinder 15cm internal dia and 15.5cm external dia has its ends closed by rigid plates and then filled with water. When an external pull of 2000 Kg is applied to the ends, the water pressure is observed to fall by
0.56 Kg/cm2. Determine the Poissons Ratio.
Take E - 2 x 106 Kg / cm2. Bulk modulus of
water K = 25600 Kg/cm2. (20)
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