Question 1 |

Which of the plot(s) shown is/are valid Mohr's circle representations of a plane
stress state in a material? (The center of each circle is indicated by O.)

M1 | |

M2 | |

M3 | |

M4 |

Question 1 Explanation:

Mohr's circle is a graphical representation
of plane stress and shear stress.

Mohr's circle is always symmetrical about the x-axis.

Mohr's circle is always symmetrical about the x-axis.

Question 2 |

A linear elastic structure under plane stress condition
is subjected to two sets of loading, I and II. The
resulting states of stress at a point corresponding
to these two loadings are as shown in the figure
below. If these two sets of loading are applied
simultaneously, then the net normal component of
stress \sigma _{xx} is ________.

\frac{3\sigma }{2} | |

\sigma \left (1+\frac{1}{\sqrt{2}} \right ) | |

\frac{\sigma }{2} | |

\sigma \left (1-\frac{1}{\sqrt{2}} \right ) |

Question 2 Explanation:

\sigma _x=0,\sigma _y=0,\tau _{xy}=0,\theta =-45^{\circ}

\begin{aligned} \sigma _{xx}&=\sigma +\sigma _\theta \\ \sigma _\theta&=\left [ \frac{\sigma _x +\sigma _y}{2} \right ] +\left [ \frac{\sigma _x -\sigma _y}{2} \right ] \cos 2\theta +\tau _{xy} \sin 2\theta \\ \sigma _\theta &= \frac{0+\sigma }{2} +\left [\frac{0-\sigma }{2} \right ] \cos 2(-45)+0\\ \sigma _\theta &= \frac{\sigma }{2}\\ \sigma _{xx} &=\sigma +\sigma _\theta =\sigma +\frac{\sigma }{2}=\frac{3\sigma }{2} \end{aligned}

Question 3 |

The stress state at a point in a material under plane stress condition is equi-biaxial tension
with a magnitude of 10 MPa. If one unit on the \sigma -\tau plane is 1 MPa, the Mohr's circle representation of the state-of-stress is given by

a circle with a radius equal to principal stress and its center at the origin of the
\sigma -\tau plane | |

a point on the \sigma axis at a distance of 10 units from the origin | |

a circle with a radius of 10 units on the \sigma -\tau plane | |

a point on the \tau axis at a distance of 10 units from the origin |

Question 3 Explanation:

The given state of stress is represented by a point on \sigma -\tau graph which is located on \sigma-axis at a distance of 10 units from origin.

Question 4 |

The state of stress at a point in a component isrepresented by a Mohr's circle of radius 100MPa centered at 200 MPa on the normal stress axis. On a plane passing through the same point, the normal stress is 260 MPa. The magnitude of the shear stress on the same plane at the same point is ______ MPa.

48 | |

63 | |

96 | |

80 |

Question 4 Explanation:

In triangle CEF

\begin{array}{l} \mathrm{CF}^{2}=\mathrm{CE}^{2}+\mathrm{EF}^{2} \\ 100^{2}=60^{2}=\mathrm{EF}^{2}\\ \mathrm{EF}^{2}=100^{2}-60^{2}=6400 \\ \mathrm{EF}=80 \mathrm{MPa} \end{array}

\mathrm{EF} \rightarrow Represents shear stress at the same point =\mathrm{EF}=\tau=80 \mathrm{MPa}

Question 5 |

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

9.45 | |

18.88 | |

37.78 | |

75.5 |

Question 5 Explanation:

\begin{aligned} \sigma_{x} &=100 \mathrm{kPa}, \tau_{x y}=50 \mathrm{kPa} \\ \text { Minimum principal stress } &=\frac{\sigma_{x}+\sigma_{y}}{2}-\sqrt{\left(\frac{\sigma_{x}-\sigma_{y}}{2}\right)^{2}+\tau_{x y}^{2}} \\ 10 &=\frac{100+\sigma_{y}}{2}-\sqrt{\left(\frac{100-\sigma_{y}}{2}\right)^{2}+50^{2}} \\ \therefore \quad \sqrt{\left(50-\frac{\sigma_{y}}{2}\right)^{2}+50^{2}} &=50+\frac{\sigma_{y}}{2}-10=40+\frac{\sigma_{y}}{2} \end{aligned}

By squaring

2500+\frac{\sigma_{y}^{2}}{4}-50 \sigma_{y}+2500=1600+\frac{\sigma_{y}^{2}}{4}+40 \sigma_{y}

\begin{aligned} \therefore \quad 90 \sigma_{y} &=3400 \\ \sigma_{y} &=37.78 \mathrm{MPa} \end{aligned}

By squaring

2500+\frac{\sigma_{y}^{2}}{4}-50 \sigma_{y}+2500=1600+\frac{\sigma_{y}^{2}}{4}+40 \sigma_{y}

\begin{aligned} \therefore \quad 90 \sigma_{y} &=3400 \\ \sigma_{y} &=37.78 \mathrm{MPa} \end{aligned}

There are 5 questions to complete.

Question 6 and 10, questions are wrong, in 6 th question Txy=40, not 20

And in 10 , data incomplete

Thank you for your suggestions. We have updated the correction suggested by You.

Question 12, Explanation given is right but Answer given is wrong. Answer would be option B (175 MPa, 175 MPa) …However Answer Provided is Opion D (0,0) which is wrong.

Thank You DURGA SINGH,

We have updated the answer.

Question number 9 answer is not accurate

No bro, it’s correct,

Yes.. the correct answer should be 90.. if I am wrong, please reply with explanation..

Maximum shear is radius of mohr circle.

So (-100-(-10))/2=-90

But we will just take absolute value of 90MPa

{Maximum–minimumStress}=(yield lodaing /2)

{-100-(-10)}/2=(yeild/2)

90ans

Q.10 answer is wrong .

Correct answer is 120 .

-100-(-10)=90