Beam bending problem, calculate deflection of a beam

In summary, the problem is to determine the maximum deflection when a person is standing on the beam in the attachment. The attempt at a solution is to put the person at the shear centre and obtain the deflection without twist.
  • #1
Robin91
7
0

Homework Statement



The problem is to determine the maximum deflection when a person is standing on the beam in the attachment.

E= 206.8 GPa, v=0.3

Homework Equations


fd061a8f3cdea89c026c7e28952b45b3.png
(although I am not completely sure if this one is relevant)

The Attempt at a Solution


I've thought a bit about the problem, but I don't know exactly where to start. The beam is asymmetical, which implies that it will most likely bend into the negative z direction and twist a bit.

If you could steer me into the right direction it will be most appreciated!

Thanks,
Robin
 

Attachments

  • beam.pdf
    51.8 KB · Views: 350
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  • #2
I've thought a bit more about it, but I'd like to know if I'm thinking in the right direction.. I think the person should stand on the spot of the picture, exactly in the middle (seen longtitudinal perspective) of the beam for maximum deflection. Then the beam will rotate and bend. Am I supposed to translate the force to one colinear with the shear center and then have a force and a moment? And what is next then?

Thanks in advance,
Robin
 

Attachments

  • beam.png
    beam.png
    291 bytes · Views: 440
  • #3
Suppose you put the person at the shear centre and obtain that deflection (without twist). If you then move the person to another position in the cross-section, how will that change the result you already have? I can't see the relevance of the stress equation, btw.
 
  • #4
I guess the beam then bends with

[tex]\delta_{max}=\frac{Pl^3}{48EI}[/tex]

Is that correct? But how can I calculate the [tex]I[/tex], what is the neutral axis? Is that just the horizontal line through the centroid (because I use the deflection with a force in the shear center)..? And how do I use the Poisson ratio in this problem?

Thanks in advance,
Robin
 
  • #5
There are two centroidal axes, x-x and y-y, origin at the centroid, not corresponding to the shear centre, When the load is passing through the shear centre, the neutral axis is the x-x axis and the I is Ixx obtained using the parallel axis theorem. If take account of the load not being at the shear centre, then you need to add a twisting moment, the angular twist requiring a formula similar to delta max you quote but involving the torgue T, and J instead of I. If you don't know what I am talking about, you need to do some background reading on torsion of open sections, and then it should become clearer. I can't see how Poisson's ratio is involved.
 
  • #6
Ok, thanks, that should get me started. I only wondered about the poisson's ratio because it is given in the exercise... ([tex]\nu=0.3[/tex])
 
  • #7
general idea to understand:did you have any idea how shear and moment diagram look like?if so it will be a great help!SAYING:ONE PICTURE'S WORTH A THOUSAND WORD,LEADING TO THE WAY I think,thank you, I 'll get back----
 
  • #8
Hi Diflection,

Indeed that's a good thing to remember. However, in the few months that passed by since I posted it, I already passed the course :).

Thanks for your help,
Robin
 

1. What is beam bending and why is it important?

Beam bending refers to the deformation of a beam when a load or force is applied to it. It is important because it helps engineers and designers understand how different materials and structures will behave under different amounts of stress, and allows them to design safe and efficient structures.

2. How do you calculate the deflection of a beam?

The deflection of a beam can be calculated using the Euler-Bernoulli beam theory, which takes into account the material properties, dimensions, and loading conditions of the beam. This theory involves solving a differential equation and can also be simplified using various beam deflection equations, such as for a simply supported or fixed beam. Alternatively, computer software can also be used to calculate beam deflection.

3. What factors can affect the deflection of a beam?

The deflection of a beam can be affected by various factors, including the material properties of the beam, its dimensions, the type and magnitude of the load applied, and the type of support at each end of the beam. Other factors such as temperature, moisture, and the presence of any external forces can also impact the deflection of a beam.

4. How is beam bending related to stress and strain?

Beam bending and stress are closely related, as the bending of a beam creates internal stresses within the beam. The amount of stress depends on the material properties, dimensions, and loading conditions of the beam. Strain, on the other hand, is a measure of how much a material deforms in response to stress. In beam bending, strain is directly related to the deflection of the beam.

5. What are some practical applications of beam bending calculations?

Beam bending calculations are used in various engineering and construction applications, such as designing and analyzing bridges, buildings, and other structures. They are also used in the design of mechanical components such as cranes, beams, and columns. Additionally, beam bending calculations are important in the fields of aerospace, automotive, and marine engineering.

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