Beam Deflection equation question

In summary, the given equation for calculating maximum deflection, δ=(PL^3 )/(48EI), may not be valid for a beam with 6 holes drilled into it. The validity depends on the location and purpose of these holes, as well as the support and attachment of the beam to other structures. If the holes are used for bolting the beam to a larger frame, the beam ends are not free to rotate, and the deflection formula is not valid. In this case, the formula for a beam with both ends fixed and a single concentrated load at mid-span, δ=(PL^3 )/(192EI), should be used. The moment of inertia, I, is still calculated using
  • #1
amir azlan
6
0
regarding this equation,


δ=(PL^3 )/(48EI)

For the calculation of maximum deflection, if my structure is not longer a full form beam (meaning the structure has 6 holes drilled to it), can this formula still be used?is this formula still valid for this structure?
 
Engineering news on Phys.org
  • #2
amir azlan said:
regarding this equation, δ=(PL^3 )/(48EI)

For the calculation of maximum deflection, if my structure is not longer a full form beam (meaning the structure has 6 holes drilled to it), can this formula still be used?is this formula still valid for this structure?
It depends on where the holes are located in this particular beam.
 
  • #3
SteamKing said:
It depends on where the holes are located in this particular beam.
Attached is the the drawing of the beam. 3 holes drilled to each end of the beam.
How to calculate the max deflection of beam, as the given formula of δ=(PL^3 )/(48EI) is no longer valid?
 

Attachments

  • 1.png
    1.png
    36.6 KB · Views: 608
  • 2.png
    2.png
    13 KB · Views: 594
  • #4
amir azlan said:
Attached is the the drawing of the beam. 3 holes drilled to each end of the beam.
How to calculate the max deflection of beam, as the given formula of δ=(PL^3 )/(48EI) is no longer valid?
The central deflection of a loaded beam also depends on how the ends are supported. The formula given is for calculating the central deflection of a beam with a single load P located in the middle of the span.

It's not clear from the description of the beam presented so far for what purpose the holes are drilled in the end. If these holds are placed there to allow bolts or rivets to attach this beam to another member for support at the ends, then the assumption that this beam is simply supported is probably not valid, in which case the formula for calculating deflection is also not valid.

Please provide more details about how the beam is supported or attached to a larger structure.
 
  • #5
yes,these holes are drilled to hold the beam onto the frame using bolts.
 

Attachments

  • 3.PNG
    3.PNG
    22.3 KB · Views: 650
  • #6
amir azlan said:
yes,these holes are drilled to hold the beam onto the frame using bolts.
In, this case, the beam ends are not free to rotate once bolted to the supporting structural supports, so the deflection formula mentioned in the OP is not valid for calculating the deflection in this case.

The formula for calculating the central deflection of a beam with both ends fixed with a single concentrated load P applied mid-span is ##δ=\frac{PL^3}{192EI} ##. Here, L should be taken as the length of the span between the innermost bolts.
 
  • #7
For the moment of inertia,I of the beam,is it still calculated using the formula
73f5793b73f3746e3a16f97c7dc70760.png

?
 
  • #8
amir azlan said:
For the moment of inertia,I of the beam,is it still calculated using the formula
73f5793b73f3746e3a16f97c7dc70760.png

?
Yes.

From your diagrams, it appears that h < b.
 
  • #9
SteamKing said:
Yes.

From your diagrams, it appears that h < b.
Yes, the dimension of the beam:
30mm width, 5mm thick
 

Related to Beam Deflection equation question

1. What is the Beam Deflection equation?

The Beam Deflection equation, also known as the Euler-Bernoulli equation, is a fundamental equation used to calculate the deflection of a beam under a load. It takes into account the material properties, geometry, and loading conditions of the beam to determine the amount of deflection at a specific point along its length.

2. How is the Beam Deflection equation derived?

The Beam Deflection equation is derived from the principles of mechanics, specifically the theory of elasticity. It is based on the assumption that the beam is elastic, meaning it can bend and stretch without experiencing permanent deformation. By applying these principles to the beam, the equation can be derived using calculus and other mathematical techniques.

3. What are the variables in the Beam Deflection equation?

The variables in the Beam Deflection equation include the material properties of the beam, such as its Young's modulus and moment of inertia, as well as the length, load, and support conditions of the beam. These variables are used to calculate the deflection at a specific point along the beam's length.

4. How accurate is the Beam Deflection equation?

The accuracy of the Beam Deflection equation depends on a variety of factors, including the assumptions made in its derivation, the accuracy of the input variables, and the complexity of the loading conditions. In general, it provides a good estimate of beam deflection for most engineering applications, but may not be accurate in certain scenarios.

5. Can the Beam Deflection equation be used for all types of beams?

The Beam Deflection equation is applicable to a wide range of beam shapes and loading conditions. However, it may not be accurate for more complex beam configurations or those with non-uniform loading. In these cases, alternative methods such as finite element analysis may be necessary to accurately calculate the beam deflection.

Similar threads

  • Mechanical Engineering
Replies
13
Views
3K
Replies
6
Views
1K
  • General Engineering
Replies
1
Views
2K
Replies
4
Views
5K
  • Mechanical Engineering
Replies
2
Views
2K
Replies
9
Views
1K
Replies
9
Views
2K
  • General Engineering
Replies
1
Views
1K
  • Mechanical Engineering
Replies
8
Views
2K
Replies
33
Views
3K
Back
Top