Deflection of beam formula NOT considering loads

In summary, the conversation is discussing the deflection formula for beams and whether there is a way to find deflection directly without considering load. It is mentioned that without load, there is no deflection, but the person is asking if there is a specific formula for this scenario. It is also suggested that beam formulas can be derived using various methods. However, it is reiterated that beams do not deflect without a load. The person asking the question clarifies their confusion and asks for further explanation.
  • #1
bandramir.raj
2
0
The actual deflection formula:

v= wx(Lx2-x3-L3)
EI 12 24 24 24

requires me to consider load then shear, bending moment, slope and finally deflection.

Is there any way it can be found directly without considering the above?
 
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  • #2
I too would be interested to know this.

In my mind, if there is no load, then there is no deflection.

Unless its deflecting under its own weight that is?
 
  • #3
If there is no load then w = 0 therefore v = 0, meaning there is no deflection.
 
  • #4
Bolts said:
If there is no load then w = 0 therefore v = 0, meaning there is no deflection.

if there was no load, of course there won't be any deflection, what I'm trying to say is that is there any direct formula to find deflection WITHOUT considering load?
 
  • #5
Beam formulas can be derived through use of equation of the elastic curve, singularity functions, and the moment of area method. Read up on those methods.
 
  • #6
Beams do not deflect without having a load on them to cause that deflection.

What do you mean when you say you want to find deflection without considering load? As stated previously, with no load, there is no deflection, but that did not seem to satisfy you. What exactly do you want?
 

1. What is the formula for calculating beam deflection?

The formula for calculating beam deflection is: δ = (FL^3)/(3EI), where δ is the maximum deflection, F is the applied load, L is the length of the beam, E is the Young's modulus, and I is the moment of inertia.

2. How do I determine the value of the Young's modulus?

The Young's modulus (E) is a measure of the stiffness of a material and can be determined experimentally or by consulting a materials table. It is typically measured in pascals (Pa) or gigapascals (GPa).

3. Can this formula be used for all types of beams?

The beam deflection formula can be used for most types of beams, including simply supported, cantilever, and overhanging beams. However, it may not be accurate for beams with complex geometries or materials with non-linear stress-strain relationships.

4. What are the assumptions made when using this formula?

The beam deflection formula assumes that the beam is made of a homogeneous and isotropic material, the cross-sectional area is constant along the length of the beam, and the beam is subjected to a single concentrated load at the center.

5. Is there a limit to the length of the beam that can be calculated using this formula?

Yes, there is a limit to the length of the beam that can be accurately calculated using this formula. If the beam is too long, it may experience buckling or other instability, which is not accounted for in this formula. It is important to consult a structural engineer for beams with a length-to-height ratio greater than 20:1.

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