Principal Stress and Principal Strain Civil Engineering (CE) Notes | EduRev

Topic wise GATE Past Year Papers for Civil Engineering

Civil Engineering (CE) : Principal Stress and Principal Strain Civil Engineering (CE) Notes | EduRev

The document Principal Stress and Principal Strain Civil Engineering (CE) Notes | EduRev is a part of the Civil Engineering (CE) Course Topic wise GATE Past Year Papers for Civil Engineering.
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Q.1 For a plane stress problem, the state of stress at a point P is represented by the stress element as shown in figure.
Principal Stress and Principal Strain Civil Engineering (CE) Notes | EduRev
By how much angle (θ) in degrees the stress element should be rotated in order to get the planes of maximum shear stress?    [2019 : 2 Marks, Set-II]
Principal Stress and Principal Strain Civil Engineering (CE) Notes | EduRev
(a) 31.7
(b) 13.3
(c) 26.6
(d) 48.3
Ans.
(A)
Solution:
Principal Stress and Principal Strain Civil Engineering (CE) Notes | EduRev
Principal Stress and Principal Strain Civil Engineering (CE) Notes | EduRev
Angle of plane of max shear
Principal Stress and Principal Strain Civil Engineering (CE) Notes | EduRev
Principal Stress and Principal Strain Civil Engineering (CE) Notes | EduRev
Principal Stress and Principal Strain Civil Engineering (CE) Notes | EduRev

Q.2 An element is subjected to biaxial normal tensile strains of 0.0030 and 0.0020. The normal strain in the plane of maximum shear strain is    [2019 : 1 Mark, Set-I]
(a) Zero
(b) 0.0050
(c) 0.0010
(d) 0.0025
Ans.
(D)
Solution:
Principal Stress and Principal Strain Civil Engineering (CE) Notes | EduRev
Normal strain in the plane of maximum shear strain
Principal Stress and Principal Strain Civil Engineering (CE) Notes | EduRev

Q.3 For the stress state (in MPa) shown in the figure, the major principal stress is 10 MPa.
Principal Stress and Principal Strain Civil Engineering (CE) Notes | EduRev
The shear stress τ is    [2016 : 2 Marks, Set-II]
(a) 10.0 MPa
(b) 5.0 MPa
(c) 2.5 MPa
(d) 0.0 MPa
Ans.
(B)
Solution:

Principal Stress and Principal Strain Civil Engineering (CE) Notes | EduRev
Principal Stress and Principal Strain Civil Engineering (CE) Notes | EduRev
Now,
Principal Stress and Principal Strain Civil Engineering (CE) Notes | EduRev
Principal Stress and Principal Strain Civil Engineering (CE) Notes | EduRev
Principal Stress and Principal Strain Civil Engineering (CE) Notes | EduRev
Principal Stress and Principal Strain Civil Engineering (CE) Notes | EduRev

Q.4 For the plane stress situation shown in the figure, the maximum shear stress and the plane on which it acts are    [2015 : 1 Mark, Set-II]
Principal Stress and Principal Strain Civil Engineering (CE) Notes | EduRev
(a) -50 MPa, on a plane 450 clockwise w.r.t. x-axis
(b) -50 MPa, on a plane 450 anti-clockwise w.r.t. x-axis
(c) 50 MPa, at all orientations
(d) Zero, at all orientations
Ans.
(D)
Solution:
Under hydrostatic loading condition, stresses at a point in all directions are equal and hence no shear stress.
Alternatively,
Principal Stress and Principal Strain Civil Engineering (CE) Notes | EduRev
Thus, Mohr’s circle reduces to a point. Hence shear stress at all orientations is zero.

Q.5 Two triangular wedges are glued together as shown in the following figure. The stress acting normal to the interface, σ is __________MPa.    [2015 : 1 Mark, Set-I]
Principal Stress and Principal Strain Civil Engineering (CE) Notes | EduRev
Solution:

As plane ABand BCare principle planes, therefore Mohr’s circle for the given condition is,
Principal Stress and Principal Strain Civil Engineering (CE) Notes | EduRev
Here, normal stress is zero at 450 to the principle plane.
Method-ll
Principal Stress and Principal Strain Civil Engineering (CE) Notes | EduRev
⇒ at 450, it is a plane of maximum shear stress
Principal Stress and Principal Strain Civil Engineering (CE) Notes | EduRev

Q.6 The state of 2D stress at a point is given by a matrix
Principal Stress and Principal Strain Civil Engineering (CE) Notes | EduRev
The maximum shear stress in MPa is    [2013 : 2 Marks]
(a) 50
(b) 75
(c) 100
(d) 110
Ans.
(A)
Solution:
Principal Stress and Principal Strain Civil Engineering (CE) Notes | EduRev
Principal Stress and Principal Strain Civil Engineering (CE) Notes | EduRev
But SS is not the option so taken (τmax)plain otherwise prefer (τmax)absolute.

Q.7 If a small concrete cube is submerged deep in still water in such a way that the pressure exerted on all faces of the cube is p, then the maximum shear stress developed inside the cube is   [2012 : 1 Mark]
(a) 0
(b) p/2
(c) p
(d) 2p
Ans. 
(A)
Solution:
Principal Stress and Principal Strain Civil Engineering (CE) Notes | EduRev
Maximum shear stress,
Principal Stress and Principal Strain Civil Engineering (CE) Notes | EduRev
Note: It is the case of hdyrostatic force, Mohr circle of which is a point hence τmax = 0.

Q.8 The major and minor principal stresses at a point are 3 MPa and - 3 MPa respectively. The maximum shear stress at the point is    [2010 : 1 Mark]
(a) zero
(b) 3 MPa
(c) 6 MPa
(d) 9 MP
Ans.
(B)
Solution:
Principal Stress and Principal Strain Civil Engineering (CE) Notes | EduRev


Principal Stress and Principal Strain Civil Engineering (CE) Notes | EduRev

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