Shear stress problem: What decides the sign of Tau_V?

In summary, the conversation is discussing the confusion surrounding the shear stresses in various solutions for a problem. The main question is why Tau_V is sometimes negative and sometimes positive, with specific examples given for points P and Q. The conversation also mentions the importance of using Latex and creating clear diagrams to better understand the problem.
  • #1
salamikorv
36
2
Homework Statement
What decides Tau_V sign?
Relevant Equations
Tau_T-Tau_V
Im so confused on these solutions here for the shear stresses. Why is Tau_V sometimes negative and sometimes positive? Can someone please explain this and maybe illustrate?
Here for example.
2022.png

Heres the solution for problem b):
2022sol.png

Here Tau_V (talking about F_xQ/(Ir) ) is negative, so how im thinking why it is negative is because the moment is making so that the shear force on point P is directed to the negative x-direction, but on the drawing its directed to the positive x-direction??

And for point Q, Tau_V is positive? Why is it not negative? I thought since the bending onto the cross section is going clockwise, making the shear force at Q go at positive z-direction, it should be positive? But its wrong and how should i think about this?
2022solQ.png
 

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  • #2
Could you be more clear about your force , moment breakdown. Try to draw something 3d like I did for this problem
1683774796313.png


1683774761292.png


Yours is an even messier problem, and it's too hard to decipher your handwritten notes.

Also, please learn to use Latex to provide your equations. It doesn't take much to learn, and it helps people trying to help you. Simply put "Help us to help you". I know...organizing your thought takes effort. Furthermore, when you make a good diagram for a problem, sometimes you will clear issues up on your own. This was made with PowerPoint, but a good hand drawing will work too.
 
  • #3
Are you still interested in the solution of this problem, @salamikorv ?
 

Related to Shear stress problem: What decides the sign of Tau_V?

What is shear stress (Tau_V) and how is it defined?

Shear stress, denoted as Tau_V (τ_v), is a measure of the force per unit area exerted parallel to the plane of interest in a material. It is defined as the component of stress coplanar with a material cross-section. The formula for shear stress is τ = F / A, where F is the force applied and A is the area over which the force is distributed.

What determines the sign of shear stress (Tau_V)?

The sign of shear stress (τ_v) is determined by the direction of the applied force relative to the plane of interest. Conventionally, if the force causes a clockwise rotation about the point of interest, the shear stress is considered positive. Conversely, if the force causes a counterclockwise rotation, the shear stress is considered negative. However, the sign convention can vary based on the specific context or field of study.

How does the orientation of the material affect the sign of shear stress?

The orientation of the material significantly affects the sign of shear stress. When analyzing shear stress, the orientation of the coordinate system and the plane on which the stress is acting are crucial. The direction of the applied force relative to these orientations will determine whether the shear stress is positive or negative based on the chosen sign convention.

Can the sign of shear stress change within the same material under different loading conditions?

Yes, the sign of shear stress can change within the same material under different loading conditions. For instance, if the direction of the applied force changes or if the material is subjected to different types of loading (e.g., torsion, bending), the direction of the induced shear stress can change, leading to a different sign based on the established sign convention.

Is the sign of shear stress important in practical applications?

Yes, the sign of shear stress is important in practical applications, especially in structural engineering and materials science. The sign helps in understanding the nature of the stress distribution within a material, which is crucial for predicting failure, designing safe structures, and ensuring the integrity and longevity of materials under various loading conditions.

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