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QUESTION: 1

A solid circular shaft is subjected to bending moment M and twisting moment T. What is the equivalent twisting moment T_{e} which will produce the same maximum shear stress as the above combination?

Solution:

Maximum shear stress,

QUESTION: 2

Strain rosettes are used to

Solution:

QUESTION: 3

The principal stresses at a point in an elastic material are 60 N/mm^{2} tensile, 20 N/mm^{2} tensile and 50 N/mm^{2} compressive. If the material properties are: μ^{ }= 0.35 and E = 10^{5} N/mm^{2} then the volumetric strain of the material is

Solution:

Volumetric strain,

QUESTION: 4

The state of stress at a point in a body under plane state of stress condition is given by MPa . The maximum shear stress (in MPa) is

Solution:

QUESTION: 5

If at a point in a body σ_{x }= 70 MPa, σ_{y }= 60 MPa and τ_{xy} = - 5 MPa, then the radius of Mohr’s circle is equal to

Solution:

Radius of Mohr’s circle

QUESTION: 6

The state of stress at a point in a loaded member is shown in figure below. The magnitude of maximum shear stress is

Solution:

Maximum shear stress

= 50 MPa

QUESTION: 7

The cross-section of a bar is subjected to a uniaxial tensile stress 'p' The tangential stress on a plane inclined at θ to the cross-section of the bar would be

Solution:

Normal stress = pcos^{2}θ

Tangential stress = psinθ cosθ

QUESTION: 8

The figure shows the state of stress at a certain point in a stressed body. The magnitudes of normal stresses in the x and y directions are 100 MPa and 20 MPa respectively. The radius of Mohr’s stress circle representing this state of stress is

Solution:

Radius of Mohr’s circle

= 60 MPa

QUESTION: 9

Match List-I (State of stress) with List-II (Kind of loading) and select the correct answer using the codes given below the lists:

List-I

List-II

1. Combined bending and torsion of circular shaft

2. Torsion of circular shaft

3. Thin cylinder subjected to internal pressure

4. The bar subjected to tensile force

Codes:

A B C D

(a) 2 1 3 4

(b) 3 4 2 1

(c) 2 4 3 1

(d) 3 1 2 4

Solution:

Torsion of circular shaft (pure shear)

Bar subjected to tensile force (shear will not be present)

Combined bending and torsion

Thin cylinder subjected to internal pressure

QUESTION: 10

Consider the Mohr’s circle shown below. What is the state of stress represented by this circle?

Solution:

The state of stress is represented by σ_{x} = σ_{y} = 0, τ_{xy} ≠ 0

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