Biaxial Direct Stress with Shear Stress

Q. In a two dimensional stress analysis, the state of stress at a point is shown in the figure
If $\sigma =120$ Mpa and $\tau =70$ MPa, then ${\sigma }_x$ and ${\sigma }_y$ are respectively

1. 26.7 MPa and 172 MPa
2. 54 MPa and 128 MPa
3. 67.5 MPa and 213.3 MPa
4. 16 MPa and 138 MPa

Q. Consider the following statements:
1. On planes having maximum and minimum principal stresses, there will be no tangential stress.
2. Shear stresses on mutually perpendicular planes are numerically equal.
3. Maximum shear stress is equal to half the sum of the maximum and minimum principal stresses.
Which of these statements is/are correct?

1. Only 1 is
2. 1 and 2
3. 2 and 3
4. 1 and 3

Q. Which of the following statements are correct for stresses acting on mutually perpendicular faces of a plane element?
1. The sum of the normal stresses in mutually perpendicular planes is equal to the sum of the principal stresses.
2. The shearing stresses in two mutually perpendicular planes are equal in magnitude and direction.
3. Maximum shear stress is half of the difference between principal stresses.

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

Q. The state of two dimensional stresses acting on a concrete lamina consists of a direct tensile stress, ${\sigma }_x=1.5N/m{m}^2$, and shear stress $\tau =1.20N/m{m}^2$, which cause cracking of concrete. Then the tensile strength of the concrete in $N/m{m}^2$ is

1. 1.50
2. 2.08
3. 2.17
4. 2.29

Q. The state of stress on a element in plane stress is shown as in the figure.


What is the value of $\sigma$ if the values of the principal stresses are 164 $N/m{m}^2$ and 36 $N/m{m}^2$, both tensile?

1. 100 $N/m{m}^2$
2. 75 $N/m{m}^2$
3. 62.5 $N/m{m}^2$
4. 50 $N/m{m}^2$

Q. Two triangular wedges are glued together as shown in the following figure. The stress acting normal to the interface, ${\sigma }_n$ is MPa.

1. 0

Q. A thin wooden plate PQRS is made by gluing two pieces of wood along PR as shown in the diagram below.

If ${\sigma }_x=-30MPa,{\sigma }_y=10MPaand{\tau }_{uy}=0,$ then what is the normal stress on the surface PR?

1. -10 MPa
2. -20 MPa
3. 10 MPa
4. 20 MPa