# Applied Mechanics and Design (Test 4)

## Gate Exam : Me Mechanical Engineering

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Q.1
A single riveted lap joint of two similar plates as shown in the figure below has the following geometrical and material details: Width of the plate w=200 mm, thickness of the plate t=5 mm, number of rivets n=3, diameter of the rivet dr = 10mm, diameter of the rivet hole dh = 11mm, allowable tensile stress of the plate σp = 200 MPa, allowable shear stress of the rivet σs = 100 MPa and allowable bearing stress of the σc = 150 MPa
If the plates are to be designed to avoid tearing failure, the maximum permissible load P in kN is
A. 83
B. 125
C. 167
D. 501
Explaination / Solution:
No Explaination.

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Q.2
A single–point cutting tool with 12o rake angle is used to machine a steel work– piece. The depth of cut, i.e. uncut thickness is 0.81mm. The chip thickness under orthogonal machining condition is 1.8mm. The shear angle is approximately
A. 22o
B. 26o
C. 56o
D. 76o
Explaination / Solution:

Relation between shear angle (φ), chip thickness ratio (r) and rake angle (α) is given by Workspace
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Q.3
A solid shaft of diameter, d and length L is fixed at both the ends. A torque, T0 is applied at a distance, L/4 from the left end as shown in the figure given below. The maximum shear stress in the shaft is
A. 16T0/πd3
B. 12T0/πd3
C. 8T0/πd3
D. 4T0/πd3
Explaination / Solution:
No Explaination.

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Q.4
The principal stresses at a point in a critical section of a machine component are σ= 60MPa, σ= 5MPa and σ= -40 MPa. For the material of the component, the tensile yield strength is σ= 200 MPa. According to the maximum shear stress theory, the factor of safety is
A. 1.67
B. 2.00
C. 3.60
D. 4.00
Explaination / Solution: Workspace
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Q.5
The cross sections of two hollow bars made of the same material are concentric circles as shown in the figure. It is given that r3> r1 and r4> r2, and that the areas of the cross-sections are the same. J1 and J2 are the torsional rigidities of the bars on the left and right, respectively. The ratio J2/J1 is A. >1
B. <0.5
C. =1
D. Between 0.5 and 1
Explaination / Solution:

Torsional rigidity for any Shaft is given by,
J = GIP
Or J α IP (Polar moment of Inertia) And for a hollow shaft, Workspace
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Q.6
A band brake having band-width of 80mm, drum diameter of 250mm, coefficient of friction of 0.25 and angle of wrap of 270 degrees is required to exert a friction torque of 1000N-m. The maximum tension (in kN) developed in the band is
A. 1.88
B. 3.56
C. 6.12
D. 11.56
Explaination / Solution:
No Explaination.

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Q.7
Which one of the following types of stress-strain relationship best describes the behavior of brittle materials, such as ceramics and thermosetting plastics, (σ = stress and ε = strain)?
A. B. C. D. Explaination / Solution:
No Explaination.

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Q.8
In a simply-supported beam loaded as shown below, the maximum bending moment in Nm is A. 25
B. 30
C. 35
D. 60
Explaination / Solution:
No Explaination.

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Q.9
A model of a hydraulic turbine is tested at a head of 1/4th of that under which the full scale turbine works. The diameter of the model is half of that of the full scale turbine. If N is the RPM of the full scale turbine, the RPM of the model will be
A. N/4
B. N/2
C. N
D. 2N
Explaination / Solution:
No Explaination.

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Q.10
A thin spherical pressure vessel of 200 mm diameter and 1 mm thickness is subjected to an internal pressure varying form 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
A. 2.0
B. 1.6
C. 1.4
D. 1.2