JNTU
JNTU B.Tech II DESIGN OF MACHINE MEMBERS - I Previous Question Paper (April/May - 2023 - R16)
Note: i) Question paper consists of Part A, Part B. ii) Part A is compulsory, which carries 25 marks. In Part A, Answer all questions. iii) In Part B, Answer any one question from each unit. Each question carries 10 marks and may have a, b as sub questions.
PART - A
What is the range of factor of safety for ductile and brittle materials?
Answer
For ductile materials, the factor of safety typically ranges from 1.5 to 2.0 based on the yield strength. For brittle materials, the factor of safety is generally higher, ranging from 3.0 to 5.0 or more, because these materials lack ductility and are more sensitive to stress concentrations and impact loads.
List the various theories of failures along with its mathematical form.
Answer
The theories of failure are used to predict the elastic failure of ductile or brittle materials under complex stress states. The primary theories and their mathematical expressions are:
- Maximum Principal Stress Theory (Rankine's Theory): Failure occurs when the maximum principal stress reaches the yield strength of the material. For a 2D state of stress:σ₁ = σ_y / FOS
- Maximum Shear Stress Theory (Guest's Theory): Failure occurs when the maximum shear stress reaches the shear stress at yield. For ductile materials:τ_max = (σ₁ - σ₂) / 2 = σ_y / (2 × FOS)
- Maximum Principal Strain Theory (Saint-Venant's Theory): Failure occurs when the maximum principal strain reaches the strain at yield point:ε₁ = (1 / E) * [σ₁ - ν(σ₂ + σ₃)] = σ_y / (E × FOS)
- Maximum Strain Energy Theory (Haigh's Theory): Failure occurs when the total strain energy per unit volume reaches the strain energy at yield point:σ₁² + σ₂² + σ₃² - 2ν(σ₁σ₂ + σ₂σ₃ + σ₃σ₁) = (σ_y / FOS)²
- Maximum Distortion Energy Theory (Von Mises-Hencky Theory): Failure occurs when the distortion energy per unit volume exceeds the distortion energy at yield point:(σ₁ - σ₂)² + (σ₂ - σ₃)² + (σ₃ - σ₁)² = 2(σ_y / FOS)²
What is meant by endurance strength of a material?
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Draw and explain Soderberg and Goodman diagrams.
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What is purpose of evaluating section modulus in bending and polar moment of inertia in torsion of a welded region?
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Sketch the following terms in connection with Riveted joint. (i) Pitch, (ii) Transverse Pitch, (iii) Diagonal Pitch and (iv) Marginal Pitch.
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What is the effect of keyways on the strength of the shaft?
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Explain the different types and applications of a cotter joint.
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Give comparison between rigid couplings and flexible couplings.
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Differentiate between active and inactive turns in helical spring.
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PART - B
Compare rectangular box section, hollow circular section, elliptical section subjected to bending moment in terms of economy of material.
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A rod made of aluminum alloy has length 500 mm and diameter 10 mm. What are its tensile stiffness and flexibility? Assume Young’s modulus as 70 GPa.
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A shaft is subjected to a twisting moment of 5 kN.m and a bending moment of 2 kN.m. If the material has yield strength of 300 MPa and safety factor of 2, find the diameter of the shaft using (a) the maximum normal stress theory, (b) the maximum shear stress theory and (c) the Distortion energy theory.
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A round shaft made of a brittle material and subjected to a bending moment of 15 N-m is shown in figure 1. The stress concentration factor at the fillet is 1.5 and the ultimate tensile strength of the shaft material is 200 MPa. Determine the diameter d, the magnitude of stress at the fillet and the factor of safety.
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Explain Miner’s cumulative fatigue damage rule. What are the drawbacks in this approach of cumulative fatigue damage?
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The work cycle of a mechanical component subjected to completely reverse bending stresses consists of the following three elements: (a) ± 300 MPa for 85% of time, (b) ± 400 MPa for 12% of time and (c) ± 500 MPa for 3% of time. The material for the component is 50C4 and the corrected endurance limit of the component is 280 MPa. Determine the life of the component.
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A bracket in the form of a plate is fitted to a column by means of four rivets A, B, C and D in the same vertical line, as shown in Figure 2. E is the mid-point of BC. Determine the diameter of the rivets which are made of steel having a yield stress in shear of 240 MPa. What would be the thickness of the plate taking an allowable bending stress of 120 MPa for the plate, assuming its total width at section ABCD as 240 mm?
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Derive an expression for the resisting force induced in a bolt when a bracket with circular base is bolted to a wall by means of “N” equally spaced bolts. What is the absolute maximum value of the force acting on any of the bolts?
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Show that the plane of maximum shear force occurs at 67.5 degree for a transverse load on a fillet weld of equal legs. Neglect bending.
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A solid shaft of 45 mm diameter transmits 15 kW at 750 rpm by means of Kennedy key of size 4 × 4 mm cross section. The permissible shearing and crushing strength of the key material are 70 MPa and 120 MPa respectively. Determine the length of the keys.
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Draw the schematic diagram of a knuckle joint. Indicate the various elements in the joint. Also explain the design procedure for knuckle pin.
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A line shaft is driven by means of a motor placed vertically below it. The pulley on the line shaft is 1.5 m in diameter and has a belt tension of 6 kN and 2 kN on the tight side and the slack side respectively. Both these tensions are assumed to be vertical. If the pulley is overhung from the shaft and the distance of the centre line of the pulley from the centre line of the bearing is 400 mm, find the diameter of the shaft. Assume allowable stress to be 40 MPa.
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Design a muff coupling which is used to connect two steel shafts transmitting 25 kW power at 500 rpm. The shafts and keys are made of plain carbon steel 30C8 with yield strength of 400 MPa. The sleeve is made of grey cast iron FG200 with ultimate strength of 200 MPa. The factor of safety for the shaft and key is 4. For the sleeve, the factor of safety is 6 based on ultimate strength. Draw the coupling based on the design.
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A coil spring is used for the front suspension of an automobile. The spring has a stiffness of 100 N/mm with squared and ground ends. The permissible shear stress for spring material is 500 MPa. The load on the spring causes a total deflection of 8 mm. Find the spring wire diameter and free length of the spring using a spring index of 6.
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A mass of 5 kg falls from a height of 500 mm on a helical compression spring of spring index 6 and material with safe shear stress of 500 MPa. Find wire diameter and stiffness of the spring. The number of active turns is 8.
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