How to find max shear stress at a given point?

[Ganesh Ujwal]

The state of plane-stress at a point is given by σx = -200 MPa, σy = 100 MPa, σxy = 100 MPa
The Maximum shear stress (in MPa) is:
A) 111.8
B) 150.1
C) 180.3
D) 223.6
Explain Procedure also with Answer.

Attempt: i already used Max Shear Stress τ = QV/ib, then also answer is not matching to given 4 options.

 

[Orodruin]

Could you be a bit more specific with your attempt. What did you do and why? What numbers did you insert into the equations? What was your end result?

 

[Chestermiller]

Suppose you have a plane perpendicular to the x-y plane, and this plane makes an angle of theta with the x- axis. Do you know how to determine the normal and shear stresses acting on that plane?

Chet

 

[SteamKing]

The state of plane-stress at a point is given by σx = -200 MPa, σy = 100 MPa, σxy = 100 MPa
The Maximum shear stress (in MPa) is:
A) 111.8
B) 150.1
C) 180.3
D) 223.6
Explain Procedure also with Answer.

Attempt: i already used Max Shear Stress τ = QV/ib, then also answer is not matching to given 4 options.

It's not clear how you could use τ = QV/ib given only stress information. The problem seems suited for Mohr's circle.

 

[paranormal]

I would like to clarify that the formula you have used, τ = QV/ib, is for finding the maximum shear stress in a rectangular cross-section. However, in this scenario, we are dealing with a state of plane-stress at a point, which requires a different approach.

To find the maximum shear stress at a given point, we can use the Mohr's circle method. This method involves plotting the stress components σx and σy on the x and y axes of a graph, respectively. Then, we draw a circle with its center at the origin and a radius of (σx - σy)/2. The point where this circle intersects the x-axis represents the maximum shear stress.

In this case, we have σx = -200 MPa, σy = 100 MPa, and σxy = 100 MPa. Plotting these values on a graph, we get a circle with a radius of (100 - (-200))/2 = 150 MPa. The point of intersection on the x-axis corresponds to a maximum shear stress of 150 MPa.

Therefore, the correct answer is B) 150.1 MPa. It is important to note that the values given in the question are not exact, and hence, the answer may not match the given options exactly. However, the procedure and the concept used to find the maximum shear stress at a given point remains the same.