# VTU Previous Question Papers BE-ME 5th Semester

# Design of Machine Elements-1 June 2010

Important Note : 1. On completing your answers, compulsorily draw diagonal cross lines on me remaining oi<ui* pages.

2. Any revealing of identification, appeal to evaluator and ‘or equations written eg, 42+8 “ 50, will be treated as malpractice.

Fifth Semester B.E. Degree Examination, May/June 2010 Design of Machine Elements – I

Note: 1.Answer any FIVE full questions, selecting at least TWO questions from each part.

2. Use of design data hand book is permitted.

**PART-A**

1.(a)Sketch and explain, biaxial and tri-axial stresses, stress tensor and principal stress.

(b) The state of stress at a point in a structural member is shown in principal stress is known to be 84 N/mm^{2}. Determine i) the maximu point and orientation of its plane ii) the shearing stress txy .

Ql (b). The tensile shearing stress at the

(c) Briefly discuss the factors influencing the selection of suitable material for machine element.

2.(a)A round rod of diameter 30mm is to sustain an axial compressive load of 20 kN and twisting moment of 1 .5 kN. m. The rod is made of carbon steel C40 (0=328.6 MPa). Determine the factor of safety as per following theories of failure:

i) Maximum principal strain theory.

ii) Maximum elastic strain energy theory.

(b) A flat plate subjected to a tensile force of 5 kN is shown in Fig.Q2(b). The plate material is grey cost iron having a_{u} value of 200 MPa. Determine the thickness of the plate. Factor of safety is 2.5.

(c) Determine the maximum torsional impact that can withstand, without permanent deformation by a 100mm cylindrical shaft 5 m long and made of SAE 1045 annealed steel (ty = ISO MPa and G = 82 GPa). Factor of safety = 3.

3. (a) Derive the Soderberg’s equation ^{1}

(b) where A is surface finish factor, B is size factor and C is the load factor.

A hot rolled steel shaft is subjected to a torsional moment that varies (clockwise) to 110 Nm (counter clockwise) as the applied bending mom section varies from +440 Nm to -220 Nm. The shaft is of uniform cro; way is present at the critical section. Determine the required shaft di an ultimate strength of 550 MPa and yield strength of 410 MPa. Talc half the ultimate strength, factor of safety = 2, size factor of Q.85_and of 0.62.

4.(a)An M20x2 steel bolt, 100mm long is subjected to ai the bolt is 2 N.m. Take E = 206 GPa.

i) Determine the stress in the shank of the boltif there the nut and the bolt head.

ii) Determine the stress in the shank if the entire length of the bolt is threated

(b)Determine the size of the bolts for the loaded . if the allowable tensile stress in the bolt material is limited to 80 Mpa.

5. (a)A power transmission shaft 1800 mm long, is supported at two points A and B. Whereas A is at distance of 300 mm from the left extreme end of the shaft, B is at the right extreme end. A power of 50 kN is received at 500 rpm, through a gear drive located at the left extreme end of the shaft. The gear mounted on the shaft here, has a pitch diameter of 300 mm and weighs 700 N. The driver gear is located exactly behind. 30 kW of this power is given out through a belt drive located at a distance of 600 mm from the left support. The pulley mounted on the shaft has a diameter of 400 mm and weighs 1000N. The belt is directed towards the observer below the horizontal and inclined 45° to it. The ratio of belt tensions is 3. The remaining power is given out through a gear drive located at a distance of 400 mm from the right support. The driver gear has a pitch diameter of 200 mm and weighs 500 N. The driven gear is located exactly above. Selecting C40 steel (a_{y} = 328.6 MPa) and assuming factor of safety 3, determine the diameter of a solid shaftfor the purpose, ‘l ake k_{b} = 1.75 ; k_{t} = 1.5 & pressure angle <> = 20° for both the

**PART-B**

6.(a) Design a protected type cast iron flange coupling for a steel shaft transmitting 30 kW at 200 rpm. The allowable shear stress in the shaft and key material is 40 MPa. The maximum torque transmitted to be 20% greater than the full load torque. The allowable shear stress in the bolt is 60 MPa and allowable shear stress in the flange is 40 MPa.

(b)Design a sleeve type cotter joint, to connect two tie rods, subjected to an axial pull of 60 kN. The allowable stresses of C30 material used for the rods and cotters are <frt = 65 N/mm^{2}; a_{c} = 75 N/mm^{2}; x = 35 N/mm^{2} ; cast steel used for the sleeve has the allowable stresses CT| = 70N/mm^{2}; c_{c} = 110N/mm^{2}; x = 45 N/mm^{2}. ,

7. (a)The lengths of a flat tie bar, 15mm thick, are connected by a butt jobt with equal cover plates on either side. If 400 kN is acting on the tic bar, design the joint, such that the section of the bar is not reduccd by more than one rivet hole. Working stresses for the material of the bar are 85 MPa in tension, 60 MPa in shear and 110 MPa in crushing.

(b)A 16mm thick plate is welded to a vertical support by two fillet welds as shown in Fig.Q7(b). Determine the size of weld, if the permissible shear stress for the weld material is 75 MPa.

8. (a) Explain self locking and overhauling in power screws.

(b) A screw jack is to lift a load of 80 kN through a height of 400 mm. Ultimate strengths of screw material in tension and compression arc 200 N/mm^{2} and in shear it is 120 N/mm^{2}. The atcrial for the nut is phosphor bronze for which the ultimate strength is 100 N/mm^{2} in tension, 90 N/mm^{2} in compression and 80 N/mm^{2} in shear. The bearing pressure between the nut and the screw is not to exceed 18 N/mm^{2}. Design the screw and the nut and check for the stresses. Take FOS = 2. Assume 25% overload for the screw rod design.

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