Beam Deflection equation question

Click For Summary
SUMMARY

The discussion centers on the application of the beam deflection equation δ=(PL^3)/(48EI) for a beam with drilled holes. It is established that this formula is not valid when the beam is fixed at both ends with bolts, as the support conditions change the deflection characteristics. Instead, the correct formula for a beam with both ends fixed and a single load at mid-span is δ=(PL^3)/(192EI). The moment of inertia (I) for the beam can still be calculated using standard formulas, regardless of the holes.

PREREQUISITES
  • Understanding of beam deflection principles
  • Knowledge of structural support conditions
  • Familiarity with the moment of inertia calculations
  • Basic mechanics of materials
NEXT STEPS
  • Study the derivation of the beam deflection formulas for various support conditions
  • Learn how to calculate the moment of inertia for different beam shapes
  • Explore the effects of bolted connections on beam behavior
  • Investigate finite element analysis (FEA) tools for complex beam structures
USEFUL FOR

Structural engineers, mechanical engineers, and students studying mechanics of materials will benefit from this discussion, particularly those involved in beam design and analysis.

amir azlan
Messages
6
Reaction score
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
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.
 
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How to calculate the max deflection of beam, as the given formula of δ=(PL^3 )/(48EI) is no longer valid?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: 668
  • 2.png
    2.png
    13 KB · Views: 664
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.
 
yes,these holes are drilled to hold the beam onto the frame using bolts.
 

Attachments

  • 3.PNG
    3.PNG
    22.3 KB · Views: 718
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.
 
For the moment of inertia,I of the beam,is it still calculated using the formula
73f5793b73f3746e3a16f97c7dc70760.png

?
 
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.
 
SteamKing said:
Yes.

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

Similar threads

Bending Moments and max deflection
  • · Replies 1 ·
Replies
1
Views
2K
Deriving Strain in Cantilever Beam with Known Deflection
  • · Replies 4 ·
Replies
4
Views
6K
Beam deflection and curvature radius formula doubts
  • · Replies 13 ·
Replies
13
Views
6K
Simply supported beam with a spring support in the middle - deflection
  • · Replies 6 ·
Replies
6
Views
4K
A500 steel tubing beam deflection
  • · Replies 2 ·
Replies
2
Views
3K
Simplification of load on beam for Max M and D
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Base Motion and Vertical Beam - Basic Reaction Forces?
  • · Replies 9 ·
Replies
9
Views
2K
Calculating Moment and Deflection for Handrail Beam with Attached Bolt
  • · Replies 2 ·
Replies
2
Views
3K
Derivation of First Storey Shear Rigidity for a Rigid Frame
  • · Replies 2 ·
Replies
2
Views
2K
Deflection of a cantilever beam with applied tension at the free end
  • · Replies 9 ·
Replies
9
Views
4K