Biaxial Direct Stress

Q. At a point in a strained material, if two mutually perpendicular tensile stresses of 2000 $kg/c{m}^2$ and 1000 $kg/c{m}^2$ are acting, then the intensity of tangential stress on a plane inclined at 15° to the axis of the minor stress will be

1. 125 $kg/c{m}^2$
2. 250 $kg/c{m}^2$
3. 500 $kg/c{m}^2$
4. 1000 $kg/c{m}^2$

Q. A square element is subjected to principal stresses in $N/m{m}^2$ as shown in figure below. The intensity of normal stress ${\sigma }_n$ on plane BD is

1. $200\sqrt{2}$
2. 100
3. 200
4. 0

Q. A plane rectangular element is subjected to two normal stresses ${}^{\prime }{\rho }_1^{\prime }an{d}^{\prime }{\rho }_2^{\prime }$ on two mutually perpendicular planes $({\rho }_1>{\rho }_2$) as shown in the figure.

Which one of the following statements is NOT true in this regard?

1. The plane BC and CD are pricipal planes.
2. Shear stress will act on plane inclined to planes AB and CB.
3. There will not be any normal stress on planes having maximum shear stress.
4. There will not be any shear stress on planes AB and BC.

Q. In a piece of stressed material, the principal stress are ${\sigma }_1=3.0kN/m^2$ tensile and ${\sigma }_2=7.0kN/m^2$ compressive as shown in the diagram below.

The line of action of the tensile stress makes an angle $\theta =30°$ to the normal to the plane AB. What is the normal stress ${\sigma }_n$?

1. $+0.5kN/m^2$
2. $-1.5kN/m^2$
3. $+2.0kN/m^2$
4. $-2.5kN/m^2$

Q. '$p_1$' and '$p_2$' are two equal tensile principal stresses. On the plane AB inclined at 45° to the plane of '$p_1$' as shown in the figure below

1. the shear stress is maximum
2. the normal stress is zero
3. the shear stress is zero
4. the normal stress is maximum

Q. A small element at the critical section of component is in a bi-axial state of stress with the two principal stresses being 360 MPa and 140 MPa. The maximum shear stress is

1. 220 MPa
2. 180 MPa
3. 314 MPa
4. 330 MPa

Q. A point in two-dimensional stress state subjected to biaxial stress is shown in figure below. What is the normal stress acting on the plane AB?

1. Zero
2. $\sigma$
3. $\sigma co{s}^2\theta$
4. $\sigma sin\theta .cos\theta$

Q. A square element of a structural part is subjected to biaxial stresses as shown in the figure. On a plane along BD, the intensity of the resultant stress due to these conditions will be

1. $25\sqrt{5}N/m{m}^2$
2. $50\sqrt{5}N/m{m}^2$
3. $75\sqrt{5}N/m{m}^2$
4. $100\sqrt{5}N/m{m}^2$

Q. The biaxial stress system in an element is shown in the figure. Which of the following will give the normal stress in $N/m{m}^2$ in plane BD making an angle of 45° with the plane BA?

1. 25
2. 20
3. 15
4. 10