Machine Design Miscellaneous
 A thin spherical pressure vessel of 200 mm diameter and 1 mm thickness is subjected to an internal pressure varying from 4 to 8 MPa. Assume that the yield, ultimate, and endurance strength of material are 600,800 and 400 MPa respectively. The factor of safety as per Goodman's relation is

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Stress induced,
σ_{1} = σ_{2} = pr 2t σ_{1max} = 8 × 100 = 400MPa 2 × 1 σ_{1min} = 4 × 100 = 200MPa 2 × 1
σ_{2max} = 400 MPa
σ_{2min} = 200 MPa
σ_{1m} = 300 MPa
σ_{1a} = 100 MPa
σ_{2m} = 300 MPa
σ_{2a} = 100 MPa
Equivalent stress are as follows:
σ_{me} = √σ_{1m}² + σ_{2m}² − σ_{1m}σ_{2m}
= σ_{me} = √300² + 300² − 300 × 300
= 300 Mpa
Similarly, σ_{ae} = 100 MPa
From Goodman equation,σ_{ae} + σ_{me} = 1 S_{e} S_{ut} n ⇒ 100 + 300 = 1 400 800 n
= n = 1.6Correct Option: B
Stress induced,
σ_{1} = σ_{2} = pr 2t σ_{1max} = 8 × 100 = 400MPa 2 × 1 σ_{1min} = 4 × 100 = 200MPa 2 × 1
σ_{2max} = 400 MPa
σ_{2min} = 200 MPa
σ_{1m} = 300 MPa
σ_{1a} = 100 MPa
σ_{2m} = 300 MPa
σ_{2a} = 100 MPa
Equivalent stress are as follows:
σ_{me} = √σ_{1m}² + σ_{2m}² − σ_{1m}σ_{2m}
= σ_{me} = √300² + 300² − 300 × 300
= 300 Mpa
Similarly, σ_{ae} = 100 MPa
From Goodman equation,σ_{ae} + σ_{me} = 1 S_{e} S_{ut} n ⇒ 100 + 300 = 1 400 800 n
= n = 1.6
 A carpenter glues a pair of cylindrical wooden logs by bonding their end faces at an angle of θ = 30° as shown in the figure.
The glue used at the interface fails if
Criterion 1: the maximum normal stress exceeds 2.5 MPa
Criterion 2: the maximum shear stress exceeds 1.5 MPa
Assume that the interface fails before the logs fail. When a uniform tensile stress of 4 MPa is applied, the interface

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Normal stress on inclined plane
σ = σ_{x cos² θ = 4 × cos²30 = 3 MPa}Shear stress on inclined plane τ = σ_{x} sin2θ 2
= 2 × sin 60° = 1.73 MPa
Since both the stress exceeds the given limits, answer is option (c).Correct Option: C
Normal stress on inclined plane
σ = σ_{x cos² θ = 4 × cos²30 = 3 MPa}Shear stress on inclined plane τ = σ_{x} sin2θ 2
= 2 × sin 60° = 1.73 MPa
Since both the stress exceeds the given limits, answer is option (c).
 If σ_{1} and σ_{3} are the algebraically largest and smallest principal stresses respectively, the value of the maximum shear stress is

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Maximum shear stress = Radius of Mohr’s Circle (for plane stress condition)
Correct Option: B
Maximum shear stress = Radius of Mohr’s Circle (for plane stress condition)
 A pin jointed uniform rigid rod of weight W and length L is supported horizontally by an external force F as shown in the figure below. The force F is suddenly removed. At the instant of force removal, the magnitude of vertical reaction developed at the support is

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I = 1 W L^{2} ; W × L Iα ⇒ α = 3g 3 g 2 2L ∴ Linear acceleration at centre = α × L = 3g 2 4 ∴ Inertial force at centre = 3 W 4 ∴ Reaction at support = W – 3W = W 4 4 Correct Option: B
I = 1 W L^{2} ; W × L Iα ⇒ α = 3g 3 g 2 2L ∴ Linear acceleration at centre = α × L = 3g 2 4 ∴ Inertial force at centre = 3 W 4 ∴ Reaction at support = W – 3W = W 4 4
 A blockbrake shown below has a face width of 300 mm and a mean coefficient of friction of 0.25. For an activating force of 400 N, the braking torque in Nm is

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Taking moment about A,
R_{N} × 200 = 400 × 600
⇒ R_{N} = 1200 N∴ Braking torque T_{B} = μ.R_{N} × D = 45 Nm 2
Correct Option: C
Taking moment about A,
R_{N} × 200 = 400 × 600
⇒ R_{N} = 1200 N∴ Braking torque T_{B} = μ.R_{N} × D = 45 Nm 2