JNTU
JNTU B.Tech III DESIGN OF MACHINE MEMBERS - I Previous Question Paper (October - 2020 - R13)
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Main
A solid circular shaft, 15 mm in diameter, is subjected to torsional shear stress, which varies from 0 to 35 N/mm2 and at the same time, is subjected to an axial stress that varies from -15 to +30 N/mm2. The frequency of variation of these stresses is equal to the shaft speed. The shaft is made of steel FeE400 (Sut=540 N/mm2 and Syt=400 N/mm2) and the corrected endurance limit of the shaft is 200 N/mm2. Determine the factor of safety.
Answer
To determine the factor of safety, we first calculate the mean and alternating components of the stresses.
For torsional shear stress (τ):
For axial stress (σ):
Next, we calculate the equivalent von Mises stresses using the distortion energy theory for both mean and alternating components:
Using the Soderberg criterion for factor of safety (FOS):
Substituting the given values (Se = 200 N/mm2, Syt = 400 N/mm2):
How does stress concentration occur in machine members and how is it measured? Discuss the methods to reduce stress concentration with sketches.
Answer
Stress concentration occurs in machine members due to irregularities in geometry such as holes, notches, keyways, shoulders, or threads. These discontinuities disrupt the uniform flow of stress lines, causing high localized stress levels significantly greater than the average stress. It is quantified by the stress concentration factor (Kt), defined as the ratio of the maximum stress at the discontinuity to the nominal stress in the member.
Methods to reduce stress concentration include:
- Providing fillets: Adding generous radii at sharp corners to allow a smoother transition of stress flow.
- Using elliptical holes: Replacing circular holes with elliptical shapes oriented to minimize stress gradients.
- Adding relief grooves: Machining additional notches or grooves near the primary stress raiser to redistribute the stress lines.
- Increasing transition sections: Using gradual tapers instead of abrupt changes in cross-section.
A simply supported shaft of 50 mm diameter and 0.5 m long is subjected to, at its mid-section, a load that varies cyclically from 2P to 4P. Determine the value of P. Yield strength=450 MPa, endurance limit=350 MPa, factor of safety=2, size correction factor=0.85 and surface correction factor=0.9.
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A flanged bearing for a horizontal shaft is fastened to a frame by means of 6 bolts, equally spaced on 200 mm pitch circle diameter. A 100 kN force acts at a distance of 50 mm from the frame. The diameter of the flange is 270 mm. Determine the size of the bolts, if the tensile stress for the bolt material is 80 MPa.
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Describe the procedure to design an eccentrically loaded welded joint.
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A double riveted, chain, lap joint is to be made for joining two plates of 10 mm thick. The allowable stresses are 60 MPa in tension, 80 MPa in crushing and 50 MPa in shear. Determine the rivet diameter, pitch of the rivets and row pitch. Also find the efficiency of the joint.
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Design a knuckle joint to connect two circular rods subjected to an axial tensile force of 35 kN. The rods are co-axial and a small amount of angular movement between their axes is permissible. Assume permissible stresses as: σt=65 N/mm2; all τ=30 N/mm2; σc=70 N/mm2.
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Design a socket and spigot type cotter joint to resist a load of 30 kN. Assume safe stresses as: σt=55 MPa; all τ=40 MPa; σc=70 MPa.
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A shaft is supported between two bearings placed 1.2 m apart. A 0.6 m diameter pulley is mounted at a distance of 0.30 m to the right of the left hand bearing. This drives a pulley directly below it with the help of a belt having a maximum tension of 2.5 kN. Another pulley 0.4 m in diameter is placed 0.2 m to the left of the right hand bearing and is driven with the help of an electric motor and belt which is placed horizontal to the right. The coefficient of friction for the belt drives is 0.24 and the angle of contact for both pulleys is 180°. Determine suitable diameter of a shaft. Take all τ=62 MPa, σt=102 MPa, Kb=1.5 and Kt=1.0.
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Write the design procedure of helical compression springs under fatigue loading.
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Design a helical torsion spring subjected to a torque of 5 N-m, using the particulars: Angle of twist=90°; Spring index=8; Modulus of elasticity= 2×105 MPa; Allowable stress= 450 MPa. Take G=81 GPa.
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