Plane of Maximum Shear Stress

Q. The principal stresses at a point in a strained material are
${}^{\prime }{p}_1^{\prime }and{}^{\prime }{p}_2^{\prime }$. The resultant stress ${}^{\prime }{p}_r^{\prime }$ on the plane carrying the maximum shear stress would be

1. $\frac{{(p_1^2+p_2^2)}^{1/2}}{2}$

2. ${\left[\frac{p_1^2+p_2^2}{2}\right]}^{1/2}$

3. ${\left[2(p_1^2+p_2^2)\right]}^{1/2}$

4. $2{[p_1^2+p_2^2]}^{1/2}$

Q. If a prismatic member having area of cross-section A is subjected to a tensile load P, then the maximum shear stress and its inclination with the direction of load will be

1. $\frac{P}{A}and45°$
2. $\frac{2P}{A}and45°$
3. $\frac{P}{2A}and45°$
4. $\frac{P}{A}and60°$

Q. An axially loaded bar is subjected to a normal stress of 173 MPa. The shear stress in the bar is

1. 75 MPa
2. 86.5 MPa
3. 100 MPa
4. 122.3 MPa

Q. If a body carries two unlike principal stresses, what is the maximum shear stress?

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

Q. If principal stresses in a two dimensional case are - 10 MPa and 20 MPa respectively, then maximum shear stress at the point is

1. 10 MPa
2. 15 MPa
3. 20 MPa
4. 30 MPa

Q. For the state of stress (in MPa) shown in the figure below the maximum shear stress (in MPa) is

1. 5

Q. For a state of plane stress ${\sigma }_1={\sigma }_x=40MPaand{\sigma }_2={\sigma }_{y}MPa$. What are the values of the maximum in-plane shearing stress and absolute maximum shearing stress?

1. $(\pm 10,20)MPa$
2. $(\pm 10,10)MPa$
3. $(\pm 20,10)MPa$
4. $(\pm 20,20)MPa$

Q. The principal stresses at a point in a bar are $160N/m{m}^2$ (tensile) and $80N/m{m}^2$ (compr.). the accompanying maximum shear stress intensity is

1. 100 $N/m{m}^2$
2. 110 $N/m{m}^2$
3. 120 $N/m{m}^2$
4. 140 $N/m{m}^2$

Q. In a rectangular element subjected to like principal tensile stresses '${\rho }_1^{\prime }and{}^{\prime }{\rho }_2$' in two mutually perpendicular directions X and Y, the maximum shear would occur along the

1. plane normal to X-axis
2. plane normal to Y-axis
3. plane at 45° to Y-direction
4. plane at 45° and 135° to the Y-direction

Q. A rectangular bar of cross-sectional area A is subjected to an axial tensile load P. The maximum shear stress will occur on a plane at X° to any normal cross-section where X° is

1. 90°
2. 270°
3. 180°
4. 45°

Q. An element is subjected to stress as given below


For this state of stress, what is the maximum shear stress?

1. 2.5 MPa
2. 5 MPa
3. 10 MPa
4. 15 MPa

Q. 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

1. 0
2. $\frac{p}{2}$
3. p
4. 2p

Q. The state of stress at a point in 2-D stress system is characterized by direct stresses of 40 MPa compressive and 80 MPa tensile, on mutually perpendicular planes. Shear stress is absent on these planes. The maximum shear stress at this point (along duly identified plane) is

1. 20 MPa
2. 40 MPa
3. 60 MPa
4. 80 MPa