Mohr's Circle for Stress

Q.

What is mechanical force?

Q. What is the radius of Mohr's circle in case of bi-axial state of stress?

1. Half the sum of the two principal stresses
2. Half the difference of the two principal stresses
3. Difference of the two principal stresses
4. Sum of the two principal stresses.

Q. Mohr's stress circle helps in determining which of the following?
1. Normal stresses on one plane.
2. Normal and tangential stresses on two planes.
3. Principal stresses in all three directions.
4. Inclination of principal planes.
Select the correct answer using the codes given below:

1. 1 and 2 only
2. 2 and 3 only
3. 3 and 4 only
4. 2 and 4 only

Q. Which one of the following Mohr's Circles represents the state of pure shear?

1. 
2. 
3. 
4. 

Q. The radius of Mohr's circle of stress of a strained element is 20 $N/m{m}^2$ and minor principal tensile stress is 10 $N/m{m}^2$. The major principal stress is

1. 30 $N/m{m}^2$
2. 50 $N/m{m}^2$
3. 60 $N/m{m}^2$
4. 100 $N/m{m}^2$

Q. Consider the following statements?
1. The maximum shear stress is one half of the normal stress in the case of uniaxial stress field.
2. In biaxial stress field, acted upon by normal stresses unaccompanied by shear stresses, the maximum shear stress is any one of the normal stresses.
3. The Mohr's stress circle will be tangential to the vertical axis in the case of uniaxial stress field.
Which of the above statements are correct?

1. 1, 2 and 3
2. 1 and 2 only
3. 2 and 3 only
4. 1 and 3 only

Q. The radius of Mohr's circle is zero when the state of stress is such that

1. Shear stress is zero
2. There is pure shear
3. There is no shear stress but identical direct stresses in two mutually perpendicular directions.
4. There is no shear stress but equal direct stresses, opposite in nature, in two mutually perpendicular directions.

Q. The state of plane-stress at a point is given by ${\sigma }_x=200MPa$, ${\sigma }_y=100MPa$ and ${\tau }_{xy}=100MPa$. The maximum shear stress (in MPa) is

1. 111.8
2. 150.1
3. 180.3
4. 223.6

Q. If the principal stresses at a point in a stressed body are 150 $kN/m^2$ tensile and 50 $kN/m^2$ compressive, then maximum shear stress at this point will be

1. 100 $kN/m^2$
2. 150 $kN/m^2$
3. 200 $kN/m^2$
4. 250 $kN/m^2$

Q. The state of stress at a point is given by ${\sigma }_x=-6MPa,{\sigma }_y=4MPa$, and ${\tau }_{xy}=-8MPa$. The maximum tensile stress (in MPa) at the point is

1. 8.43

Q. Consider the following statements:
If the planes at right angles carry only shear stress of magnitude q in a certain instance, then the
1. diameter of Mohr's circle would be equal to 2q.
2. centre of Mohr's circle would lie at the origin
3. Principal stresses are unlike and are of magnitude q each
4. angle between the principal plane and the plane of maximum shear would be 45°
Which of the above statements are correct?

1. 1, 2 and 3 only
2. 1, 2 and 4 only
3. 3 and 4 only
4. 1, 2, 3 and 4

Q. For the state of stress shown in the below figure, normal stress acting on the plane of maximum shear stress is

1. 25 MPa compression
2. 75 MPa compression
3. 25 MPa tension
4. 75 MPa tension

Q. On the element shown in the given figure, the stresses are:
${\sigma }_x=110MPa$

${\sigma }_y=30MPa$

${\tau }_{xy}={\tau }_{yx}=30MPa$

${\sigma }_1,{\sigma }_2$

The radius of Mohr's circle and the principal stresses ${\tau }_1,{\tau }_2$ are (in MPa)

1. Radius = R	${\sigma }_1$	${\sigma }_2$
   50	120	20

2. Radius = R	${\sigma }_1$	${\sigma }_2$
   55	30	110

3. Radius = R	${\sigma }_1$	${\sigma }_2$
   60	140	20

4. Radius = R	${\sigma }_1$	${\sigma }_2$
   70	140	20

Q. If the principal stresses in a plane stress problem are ${\sigma }_1=100$ MPa, ${\sigma }_2=40$ MPa, the magnitude of the maximum shear stress (in MPa) will be

1. 60
2. 50
3. 30
4. 20

Q. For the plane stress shown in figure, the maximum shear stress and the plane on which it acts are :

1. -50 MPa on a plane ${45}^o$ clockwise w.r.t. to x-axis
2. -50 MPa on a plane ${45}^o$ anti - clockwise w.r.t to x-axis
3. 50 MPa at all orientation
4. Zero at all orientation.

Q. Consider the following statements:
Mohr's Circle is used to determine the stress on an oblique section of a body subjected to
1. direct tensile stress on one plane accompanied by a shear stress.
2. direct tensile stresses in two mutually perpendicular directions accompanied by a simple shear stress.
3. direct tensile stress in two mutually perpendicular directions.
4. A simple shear stress
Select the correct answe using the codes given below:

1. 1 and 4
2. 2 and 3
3. 1, 2, 3 and 4
4. 1, 2 and 3

Q. Mohr's circle for the state of stress defined by $\left[\begin{array}{cc}30& 0\\ 0& 30\end{array}\right]$ MPa is a circle with

1. centre at (0, 0) and radius 30 MPa
2. centre at (0, 0) and radius 60 MPa
3. centre at (30, 0) and radius 30 MPa
4. centre at (30, 0) and zero radius

Q. The state of stress represented by Mohr's circle shown in the figure is

1. Uniaxial tension
2. Biaxial tension of equal magnitude
3. hydrostatic stress
4. Pure shear

Q. Which of the following stresses is measured on inclined surface in Mohr's Circle Method?

1. Principal stress
2. Normal stress
3. Tangential stress
4. Maximum stress

Q. In a plane stress condition, the components of stress at a point are ${\sigma }_x=20$ MPa, ${\sigma }_y=80$ MPa and ${\tau }_{xy}=40$ MPa. The maximum shear stress (in MPa) at the point is

1. 20
2. 25
3. 50
4. 100

Q. For a plane stress problem, the state of stress at a point P is represented by the stress element as shown in the figure.
By how much angle $\left(\theta \right)$ in degrees the stress element should be rotated in order to get the planes of maximum shear stress ?

1. 26.6
2. 48.3
3. 31.7
4. 13.3

Q. Consider the following statements:
If there is a state of pure shear $\tau$ at a point then
1. The Mohr's circle is tangential to the y-axis
2. The centre of the Mohrls circle coincides with the origin
3. Unlike principal stresses are each numerically equal to $\tau$
4. Principal stresses are like.
Which of these statements is/are correct/

1. 1 only
2. 1 and 2
3. 2 and 3
4. 3and 4

Q. The state of stress at a point under plane stress condition is
${\sigma }_{xx}=40MPa,{\sigma }_{yy}=100MPa$ and ${\tau }_{xy}=40MPa$ The radius of Mohr's circle representing the given state of stress in MPa is

1. 40
2. 50
3. 60
4. 100

Q. What is the diameter of Mohr's circle of stress for the state of stress shown below?

1. 20
2. 10$\sqrt{2}$
3. 10
4. Zero

Q. In a two-dimensional stress analysis, the state of stress at a point P is
$\left[\sigma \right]=\left[\begin{array}{cc}{\sigma }_{xx}& {\tau }_{xy}\\ {\tau }_{xy}& {\sigma }_{yy}\end{array}\right]$
The necessary and sufficient condition for existence of the state of pure shear at the point P, is

1. ${\sigma }_{xx}+{\sigma }_{yy}=0$
2. ${\tau }_{xy}=0$
3. ${\sigma }_{xx}{\sigma }_{yy}-{\tau }_{xy}^2=0$
4. $({\sigma }_{xx}-{\sigma }_{yy}{)}^2+4{\tau }_{xy}^2=0$

Q. The Mohr's circle give below corresponds to which one of the following stress conditions.

1. 
2. 
3. 
4. 

Q. The state of stress at a point P in a two dimensional loading is such that the Mohr's circle is a point located at $175MPa$ on the positive normal stress axis.

The maximum and minimum principal stresses respectively from the Mohr's circle are

1. +175 Mpa, -175 MPa
2. +175 Mpa, +175 MPa
3. 0, -175 MPa
4. 0, 0

Q. The state of 2D-stress at a point is given by the following matrix of stresses :
$\left[\begin{array}{cc}{\sigma }_{xx}& {\sigma }_{xy}\\ {\sigma }_{xy}& {\sigma }_{yy}\end{array}\right]=\left[\begin{array}{cc}100& 30\\ 30& 20\end{array}\right]$ MPa

What is the magnitude of maximum shear stress in MPa?

1. 50
2. 75
3. 100
4. 110

Q. The state of stress at a point, for a body in plane stress, is shown in the figure below. If the minimum principal stress is 10 kPa, then the normal stress ${\sigma }_y$ (in kPa) is

1. 9.45
2. 18.88
3. 37.78
4. 75.50

Q. What would be the shape of the failure surface of a standard cast iron specimen subjected to torque?

1. Cup and cone shape at the centre
2. Plane surface perpendicular to the axis of the specimen
3. Pyramid type wedge-shaped surface perpendicular to the axis of the specimen.
4. Helicoidal surface at 45° to the axis of the specimen.