Solve Shear Stress Eqn Using Singularities/Heaviside Function

In summary, the conversation is about finding the shear stress equation using singularities or Heaviside function. The equation requires taking into account the joint forces between the upper and lower force, and the load density function is represented by q(x)=q_{0}-2q_{0}(x-l)^0. The conversation also mentions finding V(x) and M(x) and drawing the shear and moment diagrams.
  • #1
teng125
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0
http://www.savefiles.net/d/ieiwoixnjfw.html [Broken]

Can anybody pls write for me the shear stress eqn using singularities or heaviside function in which i have attach the in the file above

pls help

thanx
 
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  • #2
This is the homework help, not the do your homework forum. :grumpy:
 
  • #3
Looks like standard procedure to me?, on what exactly are you stuck?
 
  • #4
the equation for the middle part where the joint forces between the upper and lower force.Should i write 2q<x-l>^0 or any others??
 
  • #5
Taking downward direction as a positive direction, the load density function should be

[tex]q(x)=q_{0}-q_{0}(x-l)^0-q_{0}(x-l)^0=q_{0}-2q_{0}(x-l)^0[/tex]

Note that the [tex]q_{0}[/tex] is contributed by the upper distributed force, the first [tex]q_{0}(x-l)^0[/tex] is to diminish the effect of [tex]q_{0}[/tex] at position along the beam [tex]x=l[/tex] while the second [tex]q_{0}(x-l)^0[/tex] is the lower distributed force that acting in an upward direction, which means the negative direction here by convention.


Then, proceed to find [tex]V(x)[/tex] and [tex]M(x)[/tex]. Finally, draw the shear and moment diagrams.
 
Last edited:
  • #6
ok...thanx
 

What is shear stress and how is it calculated?

Shear stress is the force per unit area that acts in a direction parallel to a surface. It is calculated by dividing the force applied parallel to the surface by the area over which it acts.

What is the significance of singularities and Heaviside function in solving shear stress equations?

Singularities and Heaviside function are used to represent point or line loads in a structure. They are important in solving shear stress equations because they allow us to simplify the calculations and determine the stress at specific points or along specific lines.

How do you use singularities and Heaviside function in solving shear stress equations?

To use singularities and Heaviside function, we first identify the location and magnitude of the point or line load. We then substitute the appropriate singularity or Heaviside function into the shear stress equation and integrate over the region of interest to determine the stress at a specific point or along a specific line.

What are the limitations of using singularities and Heaviside function in solving shear stress equations?

One limitation is that they can only be used for simple, idealized loads. They cannot account for distributed loads or complex loading patterns. Additionally, singularities can lead to infinite stresses, which may not accurately reflect the behavior of a real structure.

Are there any other methods for solving shear stress equations besides using singularities and Heaviside function?

Yes, there are other methods such as the Mohr's circle method, the shear and moment diagrams method, and the direct integration method. These methods may be more appropriate for certain types of loads or structures, and it is important to consider the assumptions and limitations of each method before choosing one for a specific problem.

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