Mechanics Of Materials - BU 2021 Question Paper

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EW-58

B.E. III^rd Semester (New Scheme) Mech. Engg.

Examination, 2021-22

Mechanics of Materials

Paper - M - 302

Time : 3 Hours]

[Maximum Marks : 60

Note :-Attemp all questions from Each Unit. All questions carry equal marks. Assume suitable data wherever needed.

Unit-I

(a) Explain the following :-

(i) Ductility
(ii) Brittleness

(b) A rectangular bar made of steel is 2.8 m long and 15 mm thick. The rod is subjected to an axial tensile laod of 40 KN. The width of the rod varies from 75 mm at one end to 30 mm at the other. Find the extension of the rod if E = 200 GPA.

(c) Direct stresses of 120 N/mm² tensile and 90 N/mm² compressive exist on two perpendicular planes at a certain point in a body. They are also accompanied by shear stress on the planes. The greatest principal stress at the due to these in 150 N/mm².

(a) What must be the magnitude of the shearing stresses on the two planes ?

(b) What will be the maximum shearing stress at the point ?

Unit-II

(a) Prove that relation, M/I=σ/y=E/R. For Simple Bend ing.

(b) A steel plate of width 120 mm and of thickness 20 mm is bent into a circular arc of radius 10 m. Determine the maximum stress inuced and the bending moment which will produce the maximum stress. Take E = 200 GPA.

(c) A rectangular beam 300 mm deep is simply supported over a span of 4 meter's. Determine the uniformly distrib uted load per meter which the beam may carry, if the bending stress should not exceed 120 N/mm². Take I = 8 x 10⁶ mm⁴.

(c) A beam of length 6 m is simply supported at its ends and carries two point loads of 48 KN nad 40 KN at a dis tance of 1 m and 3 m respectively from the left support.
Find :-

(i) Deflection under each load
(ii) Maximum Deflection

Unit-III

(a) Explain Macaulay's method.

(b) Draw the shear force and bending moment diagram for a simply supported beam of a length 9 m and carrying a uniformly distributed laod of 10 KN/m for a distance of 6 m from the left end. Also calculated the maximum B.M. on the section.

Unit-IV

(a) Explain column and strut.

(b) A hollow shaft is to transmit 300 KW power at 80 rpm. If the shear stress is not to exceed 60 N/mm² and the inter nal diameter is 0.6 of the external diameter, find the ex ternal and internal diameters assuming that the maximum torque is 1.4 times the mean.

(c) A solid round bar 4 m long and 5 cm in diameter was found to extend 4.6 mm under a tensile load of 50 KN. This bar is used as a strut with both ends hinged. Deter mine the buckling load for the bar and also the safe load taking factor of safety as 4.

Unit-V

(a) Derive an expression for circumferential stress and longi tudinal stress for a thin shell subjected to an internal pres sure.

(b) Derive an expression for the change in volume of a thin cylindrical shell to an internal fluid pressure.

(c) A boiler is subjected to an internal steam pressure of 2 N/mm². The thickness of boiler plate is 2 cm and permis sible tensile stress is 120N/mm². Find out the maximum diameter, when efficiency of longitudinal joint is 90% and that of circumkferential joint is 40%