strength of materials (2003)

8/13/2019 Strength of Materials (2003)

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rotal No.of Questions-121 [rotal No. of *'[?d;j"j;S.E. (Civil) (First Semester) EXAMINATION, 2010

STRENGTH OF MATERIALS(2003couRsE)Time: Thr i 'e I lours Maximum Marks: 100

N.B. :- (l) Solve Q. No. 1 or Q. No. 2, Q. No. B or e. No. 4 andQ. No. 5 or Q. No. 6. from Sect ion .

(ii) SolveQ. No. 7 or Q. No. 8, Q. No. 9 or Q. No. 10 andQ. No. 11 or Q. L2 from Section II.

(lil) Answers o two Sections houldbe written in separateanswerbooks.(lu) pi*t"" to the right indicate full marks.(u) Assume suitable data, if necessary,and mention clearly.

r. @)SECTION I

A steel block of size (100 x 75 x 50) mm is subjected o thehydrostatic pressureof 180 MPa. Determine the change n thevolume, f E = 210 GPa and u = 0.30. t8lThree vertical wires of same length support a platform of30 kN. The outer wires are of copper and the middle wireis of steel. The area of each wire is 100 mm2. The wires areso adjustedthat eachwire carry equal load. Now an additional20 kN load is imposed on the platform. Find the stress in

t8lP.T.O.

(b)

each wire. Take Eg = 200 GPa, EC = 100 GPa.


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'2. (o) Derive the expression for elongation of a circular taperingrod (dI to d2 over a length Lt subjected to an axial

(b) A compositebar shown in Fig. 2. s rigidly fixed at ends Findthe stresses nduced in each material if there is an increasein iemperatdre by 60"c rake cr'g= 11 x 10-6/ileg c anilaA = 2,4 x l-0-6/tleg C, Es .: 210 GPa, Ea = 70 GPa t8l

load P. t8l

diagram for thet8l3. (a) Draw thebeam and

Irio 9.

shear force arid bending momentloadmg snown rn r 19. d.

[3762]-13I

F o 32

q=30 mm, ls= 1OOmm

Q =4o mm, l" = 12o mrn

18kN


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(b) A rolled steel joist of I section has the following dimensions.Flange.= (250 x 25) mm, web = 15 mm thick with overaildepth of the I section as 650 mm. If the section. s used fora simply supportedbeam of span 6 m subjected o udl of 50kN/m over its entire span, calculate he maximum bendingstress. 8]

moment diagram for the loadingt8l

4. (o)

(6)

125kN/ m

Fig.The horizontal beam of section shown in Fig. 5 is 4 m longand is simpiy supportedat its end. If the tensile and compressivestressesmust not exceed 25 MPa and 45 MPa respectively,

OrDraw the shear and bendingsnown rn -tlrg. 4

find the maximum udl that it can carry.

Fig. 53

4

t81120 T"In

t37621-r3 P.T.O.


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5. (o) The beam with-the cross-section hown in Fig. 6 is subjected -to vertical hear orce f 100kN. Draw he shearslress islribution

r 200 1q=l lUFig. 6

(b) Find the diameter of the shaft required to transmit 60 kW@ 150 r.p.m. if the maximum torque is likely to exceedby 25Vo or a maximum permissible shear stress of 60 MPa'Also find the angle of twist for the length of 2'5 rn., T a k e G = 8 x 1 0 4M P a .

' O rDerive the expfession for maximum shear stress forcircular section of radius R subjected o shear force S.snow lnaf, Tmax = +/o rmean.

(b What shoultl be the length of a 5 mm diameterwire so that i t can be' twisted through onerevolution without exceeding a shearlng slress ot

r ^ 4 a r n ,' l aKe u = z . t x t v ' \ t ( t 7 .. , 1

dlagram. te1

T50Ilr*

te1.

6. (a) a solidHence

L10laluminiumcomplete40 MPa.

t8l137621-13


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7. (e)SECTION II

The principal tensile stressesat a point across wo perpendicular,planes are 100 N/mm2 and 50 N/mm2. Find the normal andtangential stressesand resultant stress and its obliquity on aplane at 30' with the major principal plane. t8lFor a solid shaft of diameter d subjected to torsion T andbending moment M, derive the expression or maximum shearstress. t8l

, O r8. (a) An element in a stressed material has tensile stress of

400 N/mm2 and a compressive tress of 300 N/mm2 acting ontwo mutually perpendicular planes and equal shear stressesof 90 N/mm2 on these planes. Find principal stresses andposition of the principal planes.Also find the maxirnum shearingstresses. t8l

(b) A fly wheel weighing 5 kN is mounted on a shaft of 70 mmdiameterand midway betweenbearings600 mm apart. The shafttransmits60 kN @ 400 r.p.m. Calculate he principalstressesand the maximum shear stress at the ends of the vertical andhorizontal diameter in a plane close to the fly wheel. t8l

(b)

t37621-13 P.T.O,


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9. (o) Determine core of the section for :fa) rectangularsectionrb) circular sect ion. t8l

(6) A cast iron hollow column with its external diameter 260 mmand thickness 25 mm is rigidly fixed at ends. It canies anaxial oadof 1600kN. Calculate he factor of safetyusing Rankine'sformula. Take a = 1/6400 and o" = 550 MPa. t81

Or

the

10. (o) A column supports a load ofthe stressesat the corners

600 kN as shown-in Fig.7. Findof the column at its base. [8]

IIIr P, , _ ,_ . _ ,_ _ ._ ,a ,_ , _ . _

ilrlrII

(b) A T section has flangex 20 mm. It is usedCalcuiate the cripplingT a k e E = 2 0 0 G P a .

150 mm x 20as a columnload if the

mm and web 100 mmwith both ends fixed.column is 3.4 m long.

[3762]-13 6t81


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11. (o)

(b)

A beam of uniform. section arrd length 1 is simply supportedat its end and carries a s)'mrnetrical triangular loading. Theintensity of the load varies from zero at ends to zu at thecenter. Find the deflectionat center and slope at each end. 10]A cantilev'erbeam of length 3 m carries a point load of 60kNat a distance 2 m from the fixed end. Using conjugatebeammethod, calculate the slope and deflectionat the free end.Take EI = constant.

O r 'ta) A srmpry suppoTteoDeam oI tengln i] m ls' clockwise couple 20 kN at a distance of 3

support. Using Macauiay's method, find thedgflection at thb point of application

t81

t2, acted upon by am frorn the le{tslope at ends and

of the couple.Take EI = constant. tl0l

(6) A cantileverbeam of length I is subjected o a clockwisecoupleM at the free end. Calculate slope and deflection at the Ilee

. I8lnd.

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strength of materials (2003)

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