USN

'fhird

Semester B.B. Degree

ExaMtffi

, Derc"Z0 1 5/Jan.2

0 tr 6

Mechanics of Materials Time: 3 hrs.

Marks:100

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Note: Answer any FtrVE.full questioms, selecting atleast TWO qwestioms.{ro*a eaeh part" ()

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PART - A

a. Define i) Proof stress ii) Proportionality limit iii) ['rin;iole r"o:*?ff;lfJ "t io) Hooke's law. b. Derive an expression for the total etongation of tlee tapered trar '','arfiiig'diarneter from dl to dz, when subjected to axiai loadlP.

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c" A brass bar having of uniform

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Fig.Ql(c)

2a.

Define

: i) Foisson's ratio i0

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Modular ratio. {S2 &{arks) (08lVtanks) b. Establish relationship between Young's modulus and rigidity modulus. L. For the stepped bar shown in fig.Q2(c), what is the maximum tempe:rature rise rn hich r.vill not produce stress in the bar. Also find the stress induced when the tenlperature rise is 400C. Take Es : 200GFa, Ee : lQOGPa I os : 12 x l0-6fc, o,a. : 18 x 10-6/0C. (lgMarks)

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Fig.Q2(c)

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(02 Marks) Define : i) Plane stress ii) Principal strain. b. Derive the expressions for normal stress, shear stress and resutrtant stress on a oblique plane inclined at an angle '0' with vertical axis in a biaxial direct stress system. (08 Nlarks) c. At a certain point in a strained material the values of normal stresses across two planes at right angles to each other are 80MPa and 32 MPa, both are tensiie and there is a shear stress af 32MPa clockwise on the plane carrying 80MPa stress. Determine principatr stresses, rnaximum shear stress and their planes. {18 }{au"ks)

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(08 Marks)

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cross *

sectional area of 300mm2 is sub.jected to a load as shown below. Find the total elongation of bar and the magnitude oli lc,ad 'P' if Young's rnodulus is 84 GPa. (0E Marks)

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63

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a. F

c.

Deterrnine the strain energy in a cantilever beam of uniform cross - srectian and length 'L' (CI4 Marlcs) subjected to a uniforrnly distributed load of 'W' kNim over the entire span. For a thin cylindrical shell, the L/d ratio is 3 and its initial volurre is 20m3. The ultimate stress for the cyiinder material is 200MPa. Determine the waltr thickness, if it has to convey (88 Manks) water under a head of 200m. Takei F.O.S as 2. Calculate the maximurn external to internal radius ratio for a thick r:ylinder with internal (08 &[arks) fluid pressure of 15MPa and maximum hoop stress is 60MPa. 1

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a.

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Deduce the relationship between relating loacl (W), shear force (F) and bending moment

(M).

(06 Marks)

b. A bearn ABCD is simply supported at B and C, 4.5m apart and overhanging

c.

g.

b.

Enurnerate the assumptions made in theory of pure bending. Write the bending equation (G6 Marks) with usual notations. A beam of an I - section consists of 180mm x 15mm flanges and a web of 280rnm x L5mm thickneiis" It is subjected to a bending moment of 120kN * m. Sketch the bending stress distribution along the depth of the section. (06 Marks) Provre that in case of a rectangular section of a bean-r the maximum shear stress is 1.5 times average s.herar stress. ({}8 lVlarks)

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parts ,48 and CD are 1.5rn and 2m long respectively. The beam carries a unif,orrarly distributed load of 10khtr/mL between A & C. There is a clock wise couple of 50kN-rn at D. Then draw S.F and (14 Marks) B.N[ rlia.granm and mark salient points.

L)erive an expression EI

M, with usual notations.

(10 Marks)

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throughout.

(10 Ntarks)

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A hollo'w circular steel shaft has to transmit 60KW at 210 rpm such that the rnaximum shear stress dr;es not exoeed 50MN/m2. If the ratio of internal to external diarneter is equatr to 3Z an,J the valu.e of rigidity modulus is 84GPa, find the dimensions of the shaft and angle of twist in a length of 3m. (10 Marks) Derirre an e,xrression for the critical load in a conumn subjected to cornpressive load, when botir entli "aie fi.xed" (10 Marks)

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=

Determine the deflection under the loads in the beam shown in fig.Q7(b). Take Plexural

rigidity

a.

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