Deflection of Beams - Rearrange formula

In summary, the conversation discusses calculating the deflection and force on a support for a simply supported beam using the formula y = - (F x L^3)/(48 x E x I). The individual calculated a deflection of 9.72mm, but needed to adjust for a support 6mm from the original position. They attempted to rearrange the formula to find the force on the support but had doubts about their solution. It was later clarified that the beam was not supported by three supports.
  • #1
MikeNZ
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Deflection of Beams - Rearrange formula [URGENT]

Homework Statement



Deflection for a simply supported beam... I calculated the deflection of it to be 9.72mm downwards, but there is a support 6mm from the original position and need to calculate the force on the support...

The original formula for deflection is:

y = - (F x L^3)/(48 x E x I)

where 'x' is just the multiplication symbol.


Homework Equations



y = - (F x L^3)/(48 x E x I)

The Attempt at a Solution



To find the force on the support, I went 9.72-6 = 3.72mm

I substituted 3.72 into the equation above as 'y', now, how do i rearrange the formula to find F?

My attempt:

F = (48 x E x I)/(Y x L^3)

I get 2.212 MPa, this surely can't be right as the original load on top is 80KN. Did I rearrange correctly?


 
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  • #2


Is this a beam on 3 supports?
 
  • #3


Simply supported, no, not 3 supports, doesn't matter I've figured it out now. Thanks.
 

1. What is the formula for deflection of beams?

The formula for deflection of beams is: (5WL^4)/(384EI), where W is the load on the beam, L is the length of the beam, E is the modulus of elasticity, and I is the moment of inertia.

2. How can I rearrange the formula for deflection of beams to solve for different variables?

To rearrange the formula, you can use algebraic manipulation to isolate the desired variable. For example, if you want to solve for the load (W), you can multiply both sides by 384EI and divide by L^4 to get W = (384EI*d)/L^4, where d is the deflection of the beam.

3. What is the significance of the modulus of elasticity (E) in the formula for deflection of beams?

The modulus of elasticity is a measure of the stiffness of a material. It represents the amount of stress required to cause a given amount of strain in a material. In the formula for deflection of beams, a higher modulus of elasticity will result in a smaller deflection, indicating a stiffer material.

4. Can the formula for deflection of beams be used for different types of beams?

Yes, the formula can be used for different types of beams, as long as the beam is under the assumptions of linear elastic behavior and small deflections. However, the values for the variables (load, length, modulus of elasticity, moment of inertia) may differ depending on the type of beam.

5. Is the formula for deflection of beams accurate for all types of loading?

The formula is accurate for certain types of loading, such as point loads, distributed loads, and uniformly varying loads. However, it may not be accurate for more complex loading conditions, such as non-uniformly varying loads or concentrated moments. In these cases, more advanced methods of analysis may be necessary.

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