JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech III Year DESIGN OF MACHINE MEMBERS - I Previous Question Paper (March - 2021 - R16)
Answer any five questions. All questions carry equal marks.
Main
Explain different theories of elastic failure and discuss the factor of safety.
Answer
Theories of elastic failure predict the onset of yielding in ductile materials or fracture in brittle materials under complex stress states. The primary theories are:
- Maximum Principal Stress Theory (Rankine's Theory): Failure occurs when the maximum principal stress reaches the yield strength of the material. Used primarily for brittle materials.
- Maximum Principal Strain Theory (Saint-Venant's Theory): Failure occurs when the maximum principal strain reaches the strain at yield point in a simple tension test.
- Maximum Shear Stress Theory (Tresca's Theory): Failure occurs when the maximum shear stress reaches the shear stress at yield in a simple tension test. Suitable for ductile materials.
- Maximum Strain Energy Theory (Haigh's Theory): Failure occurs when the total strain energy per unit volume reaches the strain energy at the yield point in simple tension.
- Maximum Distortion Energy Theory (Von Mises-Hencky Theory): Failure occurs when the distortion energy per unit volume exceeds that at the yield point in simple tension. This is the most accurate theory for ductile materials.
The Factor of Safety (FOS) is the ratio of the ultimate or yield strength of the material to the actual working stress. It accounts for uncertainties in material properties, load estimations, manufacturing inaccuracies, and the consequences of failure, ensuring the design operates within a safe elastic limit.
A round bar, of length L, tapers uniformly from radius r1 at one end to radius r2 at the other. Show that the extension produced by a tensile axial load P acting at the smaller end is
Answer
Consider a small element of the bar at a distance x from the smaller end (radius r1) with length dx. The radius r at distance x is given by r = r1 + (r2 - r1)(x/L). The area of the cross-section is A = πr^2.
The extension dδ of this elemental length is:
Substituting r = r1 + kx, where k = (r2 - r1)/L, the total extension δ is the integral from 0 to L:
Integrating with respect to x:
Since r1 + kL = r2 and k = (r2 - r1)/L:
Note: The standard derivation for a tapered bar results in π in the denominator. If the radius is defined such that the area varies linearly, the result differs, but for a circular taper, the extension is PL / (π E r1 r2).
What is fatigue stress concentration factor? Describe its significance.
Answer
Sign in to view the complete answer paper.
A smooth cantilever beam of circular cross section made of hot rolled steel is subjected to an axial load which varies from 7 kN in tension to 5 kN in compression. It is also subjected to a transverse load at the free end which varies from +8 kN to – 6 kN. The length of the cantilever is 400 mm. The material properties are σu = 500 MPa, σy = 300 MPa. Factor of safety may be taken as 2. Find the diameter of the beam for a reliability of 90 %.
Answer
Sign in to view the complete answer paper.
A cylinder head is held on the cylinder by 8 numbers of bolts. The inner diameter of the cylinder is 350 mm. The pressure inside the cylinder varies from zero to a maximum pressure of 2.5 MPa. The ultimate tensile stress and yield stress are 630 MPa and 380 MPa respectively. The bolts are tightened with initial preload of 1.5 times the steam load. A copper asbestos gasket is used to make the joint leak proof. Take factor of safety is 2.5. Neglect stress concentration factor. Find the size of the bolt.
Answer
Sign in to view the complete answer paper.
Explain the design of bolt subjects to uniform loading.
Answer
Sign in to view the complete answer paper.
What is a cotter joint? Why is cotter provided with a taper, and why is the taper provided only on one side?
Answer
Sign in to view the complete answer paper.
A rectangular sunk key 14 mm wide, 10 mm thick and 75 mm long is required to transmit 1200 N-m torque from a 50 mm diameter solid shaft. Determine whether the length is sufficient or not, if the permissible shear stress and crushing stress are limited to 56 MPa and 168 MPa respectively.
Answer
Sign in to view the complete answer paper.
Design a bushed-pin type flexible coupling to connect a pump shaft to a motor shaft transmitting 32 kW at 960 rpm. The overall torque is 20% more than mean torque. Material properties are as follows:
- The allowable shear and crushing stress for shaft and key material is 40 MPa and 80 MPa respectively.
- The allowable shear stress for cast iron is 15 MPa.
- The allowable bearing pressure for rubber bush is 0.8 MPa.
The material of the pin is same as that of shaft and key.
Answer
Sign in to view the complete answer paper.
Prove that a square key is equally strong in crushing and shearing.
Answer
Sign in to view the complete answer paper.
A cantilever beam of square section supports an electric motor weighing 1000 N at a distance of 400 mm from the fixed end. If the allowable stress of beam material is 100 N/mm2, Determine section of beam.
Answer
Sign in to view the complete answer paper.
Find the diameter of a solid steel shaft to transmit 20 kW at 200 r.p.m. The ultimate shear stress for the steel may be taken as 360 MPa and a factor of safety as 8. If a hollow shaft is to be used in place of the solid shaft, find the inside and outside diameter when the ratio of inside to outside diameters is 0.5.
Answer
Sign in to view the complete answer paper.
What do you mean by preferred numbers? Explain with the help of an example.
Answer
Sign in to view the complete answer paper.
Describe the design procedure of a knuckle joint subjected to a normal loading.
Answer
Sign in to view the complete answer paper.
What are different applications of flexible coupling?
Answer
Sign in to view the complete answer paper.