Roll No. ......................

Total No. of Questions: 09]

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[Total No. of Pages: 03

B.Tech. (Sem. "" 3rd). .

STRENGTH OF MATERIALS - I (2002 Batch)SUBJECT CODE: ME - 201

Paper ID : [A0801]

[Note: Please fill subject code and paper ID on OMR]

Time: 03 Hours,

Instruction to Candidates:

Ql)

Maximum Marks: 60

1)

2)

3)

Section -A is Compulsory.

Attempt any Four question§ from Section - B.

Attempt any Two questions from Section - C.

Section - A

(10 X 2 = 20)

a) Find the ratio of second moment of area about the centroidal axis to the

second moment of area about the base of a triangle with base = 200 mmand altitude = 600 min.

What will be the ratio of total elongation of a bar! of unifonn cr.oss-section produced under its own weight to the elongation produced by anexternal load equal to the weight of the.bar.

b)

c) A beam of square section with side' a' is used with its diagonal horizontal.Find the section modulus of the beam.

d) If the deflection at the free end of a cantilever of a reCtangular cross-section due to certain IQadingis 0.8 cm, find the deflection of the free

.end if the depth of the cross-section' is doubled k~eping the width assame. .

e) Find the ratio of the torsional moments of resistanc;eof a solid circularshaftof diameter' D' and a hollow circular shaft havingexternal diameter.'D' and internal diameter' d' . .

-of)"

A solid circular shaft is subjected to a bending moment 11.and torque T.What is,the ratio of maximum bending stress to maximum shear stress inthe shaft?

M-178 ./1859/ P.T.o.

g)

h)

Briefly explain the assumptions for pure bending theory~

Write the relationships between a uniformly distributed load 'q', shearforce 'V' and~bending monient 'M'. . ~

i) The Euler load for a column.is 1000 kN and the crushing load' is 1500 kN.Find the 'Rankine' load:

J) Explain polar Moment of Inertia and where is it used?

Section - B

(4 x 5 =20)

Q2) A solid shaft 6.5 m long is securely fixed at both ends. A torque of 91 Nm isapplied to the shaft at a secbon 2.5 'm from one end. Find the.fixing torquessetup at the ends of t~e shaft. If the shaft, is 35 mm in diameter, find themax.imumshear stresses in the two portions. Also find the' angle of twist forthe section where torque is applied. Take G = 84 GPa.

Q3)' A solid round bar 3 m long and 5 em in diameter is used as a column with bothends hinged. Determine the percentage change in the Euler's crippling load of thecolumn if the end conditions are changed to both ends fixed. Take E = 200 GPa.

Q4) The steel bars AC and BC, each of cross-sectional area 120 mm2, are joined atC with a pin. Determine the displacement of point C caused by the 15 kN load.Also' find axial stress in the two bars. Use E = 200 GPa for steel See Fig. I

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c. ,

t S' "1'4(Fig.! )

Q5) A cylindrical pressure vessel is fabricated from steel plating that has a thickness

. of 20 mm. The inner diameter of the vessel is '450 mm, and its length is,2 I..11.,petermine the maximum internal pressure that can be appliedif the longitudinalstress is limited to 140 MPa and the~circumferential stress is limited to 60 MPa.

Q6) Direct stresses of 160'MPa tensile and 120 MPa compressive exist on twoperpendi<;ularplanesat a certain point in a body. They are also accompaniedby.shear stress~s on the planes. The greatest principal stress at the point dueto these is 200 MPa. (i) What must be the magnitude of the shearing stresses.onthe two planes. Show the result on properly-oriented element~.

A-f-178 2

Section -C(2' xlO =20)

'- Q7) The compound bar, composed of three segments shown in Fig.2, is initiallystress free. Compute the stress in each material if the temperature drops by. . .3.0°C.Assume the walls do not yield and use the following data. .

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I AlUJA,..,tJM. ~TeElI . .,--I -I (Fig.2)

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Q'8) Plot the loadin.g diagram and subsequently the Bending moment diagram fromthe shear force diagram as shown in Fig. 3.

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J--!~---"':-'" .."'" :., ~-,:!, ~90) 3'W\

'00

...

x(m)

. (Fig.3)

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.Q9) The simply supported beam ABC (Fig.4) carries the uniformly distributedload between its supports and the concentratedload P at end C. Find the vahieof P, using the moment area method, for which

. (a) There is no deflection at C.

(b) . The deflection curve arB is horizontal. f P"

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r 5~~ J.

A. .' e c~~ . (Fig.4). .

.'" t" 2m t

0 (E 1. CO"S~Q",t)

~

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3

A(mm2).

Segment a(rC) E(GPa) .

Bronze 2400 19,0x 10--6 83

Aluminium 1200 23.0 x iO--6- 70

Steel 600 1L7 x 10--6 200