Plate four points bending equation for a plate

In summary: Roark. In summary, you may be able to solve the problem analytically using principles from a theory of plates and shells, but it would require a more modern book.
  • #1
pierebean
10
0
Hello,

I am no mechanical engineer and my knowledge in bending is limited to Euler-Bernouilli beam theory.

I wish to analytically calculate the normal stress of a plate bent by four points bending. I have already calculated this stress for a beam.

However I cannot apply the beam theory to a plate.

Does someone know a tutorial or an article giving specifically the four-points bending of a plate and its solution?

Thank you
 
Engineering news on Phys.org
  • #2
pierebean said:
Hello,

I am no mechanical engineer and my knowledge in bending is limited to Euler-Bernouilli beam theory.

I wish to analytically calculate the normal stress of a plate bent by four points bending. I have already calculated this stress for a beam.

However I cannot apply the beam theory to a plate.

Does someone know a tutorial or an article giving specifically the four-points bending of a plate and its solution?

Thank you
:eek: That's a tough one that i don't think even Roarke's Stress and Strain covers. This old timer took graduate courses in Theory of Plates and Theory of Elasticity eons ago. All I remember is a bunch of unsolvable partial differential equations.
Stay away from square or rectangular plates supported on 4 corners. Consider a statically determinate circular plate instead, supported at 3 equidistant simple supports, then get a copy of Roark's book. Beyond that, i cannot help, sorry.
 
  • #3
Well Roark's is definately the go to book but like PhantomJay I don't remember seeing that in there but you never know.

My solution would be use FEA. I know you won't get an analytical solution but you may be able to validate it via a simple experiment.
 
  • #4
"Theory of Plates and Shells", Timoshenko & Krieger

Article 49, p 218 in my copy

"Rectangular Plates Having Four Edges Supported Elastically or Resting on Corner Points with All Edges Free"
 
  • #5
Nice reference thanks.
 
  • #6
Nice reference thanks.

Roark is oft quoted at PF, (as here) however a much more modern book ( and at least twice as thick) is

Formulas for Stress Strain and Structural Matrices

Pilkey

go well
 

1. What is the plate four points bending equation for a plate?

The plate four points bending equation is a mathematical equation used to calculate the deflection and stress of a rectangular plate subjected to four-point bending. It takes into account the dimensions of the plate, material properties, and applied load to determine the bending stress and deflection at any point on the plate.

2. How is the plate four points bending equation derived?

The plate four points bending equation is derived by applying the principles of mechanics and elasticity to a rectangular plate under four-point bending. It involves solving the differential equations for bending stress and deflection, taking into account the boundary conditions and assumptions such as the plate being thin and homogeneous.

3. What are the assumptions made in the plate four points bending equation?

The main assumptions made in the plate four points bending equation are that the plate is thin, homogeneous, and has a rectangular shape. It also assumes that the material is elastic and obeys Hooke's law, and that the loads are applied at the center of each edge of the plate. These assumptions allow for a simplified calculation of bending stress and deflection.

4. What factors can affect the accuracy of the plate four points bending equation?

The accuracy of the plate four points bending equation can be affected by several factors, such as the accuracy of the material properties used, the boundary conditions, and the assumptions made. In reality, plates may not be perfectly rectangular or homogeneous, and loads may not be applied exactly at the center of each edge, which can lead to deviations from the calculated results.

5. What are the practical applications of the plate four points bending equation?

The plate four points bending equation has many practical applications in engineering, such as in the design and analysis of structural components like beams, bridges, and aircraft wings. It can also be used to determine the maximum load a plate can withstand before failure, and to optimize the design of plates for specific applications.

Similar threads

Solving for Bending Stress and Deflection in a Cantilever Plate
    • Mechanical Engineering
Replies
8
Views
4K
Plate - bending moment equation
    • Mechanical Engineering
Replies
2
Views
2K
Calculating the bending stress of a simply supported beam
    • Mechanical Engineering
Replies
5
Views
4K
Efficient hit detection on a shot plate with piezo disc
    • Mechanical Engineering
Replies
6
Views
977
I Calculating Combined Loading Stress: Neutral Axis and Bending Moment at Point A
    • Classical Physics
Replies
3
Views
587
Bending Moment & Bending Stress
    • Mechanical Engineering
Replies
1
Views
2K
Engineering Combined loading, where is the neutral axis?
    • Engineering and Comp Sci Homework Help
Replies
11
Views
1K
Analyzing the Mechanics of a Wobble Plate in a Cranked Axle Mechanism
    • Mechanical Engineering
Replies
10
Views
2K
Applying Bending Stress to a Model of Ship Section
    • Mechanical Engineering
Replies
11
Views
2K
Beam bending of an angled flat plate
    • Mechanical Engineering
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top