Method to calculate beam deflection

In summary, the conversation discusses determining deflections of a fully restrained beam, with the question of how to do so and the mention of already solving for propped reactions and end moments. It is suggested to consider beam constraints and formulate equations for unknown reactions, and to use integration to calculate slope and deflection. The use of the area-moment method and cantilever beams is also mentioned.
  • #1
ErikaPanda
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How do you get deflections of a fully restrained beam? :)
I already solved for the propped reactions and end moments.. I'm not sure how to do that part. :/
ありがとうございます。 :)
 
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  • #2
Usually beam constraints are considered as points where they are fixed: one end only, both ends, middle, etc.

If all the points are fixed, of course it won't deflect.
 
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  • #3
Dr. Courtney said:
Usually beam constraints are considered as points where they are fixed: one end only, both ends, middle, etc.

If all the points are fixed, of course it won't deflect.

Thank you so much for the reply :)
We have two loads on the beam and our professor wants us to get the defections at those points.. but he hasn't taught us anything so...
 
  • #4
ErikaPanda said:
Thank you so much for the reply :)
We have two loads on the beam and our professor wants us to get the defections at those points.. but he hasn't taught us anything so...
The beam is not statically determinate with both ends fixed. Before you can find the deflections between the fixed ends, you must solve for the reaction forces and moments which put the beam in equilibrium.

Since there are two unknown reaction forces and two unknown reaction moments total, you have only two equations of static equilibrium which you can write for this beam. You need to develop two additional equations to allow you to calculate these unknown reactions. These additional equations can be formulated knowing what the slope and deflection of the beam must be at each end.

You can use the integration method to calculate the slope and the deflection of the beam in terms of the unknown reactions, and then apply the boundary conditions for the slope and deflection at the ends to solve for these unknowns.

PS: Please don't use all caps in your thread title. That is considered shouting at PF and is against the Rules.
 
  • #5
SteamKing said:
The beam is not statically determinate with both ends fixed. Before you can find the deflections between the fixed ends, you must solve for the reaction forces and moments which put the beam in equilibrium.

Since there are two unknown reaction forces and two unknown reaction moments total, you have only two equations of static equilibrium which you can write for this beam. You need to develop two additional equations to allow you to calculate these unknown reactions. These additional equations can be formulated knowing what the slope and deflection of the beam must be at each end.

You can use the integration method to calculate the slope and the deflection of the beam in terms of the unknown reactions, and then apply the boundary conditions for the slope and deflection at the ends to solve for these unknowns.

PS: Please don't use all caps in your thread title. That is considered shouting at PF and is against the Rules.

Thank you, Sir.
Hmm, I think I've already obtained those equations.. but if I solve for the deflections by area-moment method, would the procedure be the same as that in cantilever beams? If it isn't much of a bother, it can't be read but would you mind looking at how the problem looks like, Sir?

About the title, I'm really sorry.. I had no idea. Thank you. :)
 

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  • #6
ErikaPanda said:
Thank you, Sir.
Hmm, I think I've already obtained those equations.. but if I solve for the deflections by area-moment method, would the procedure be the same as that in cantilever beams? If it isn't much of a bother, it can't be read but would you mind looking at how the problem looks like, Sir?

About the title, I'm really sorry.. I had no idea. Thank you. :)
I'm sorry, but your attached image is too small and blurry for me to read.

After I re-read your OP, I realized that you had solved for the unknown reactions for this beam. Once you do that, it is a simple matter to construct the bending moment diagram for the beam and then find the slope and deflection by integration. I'm more familiar with the integration method than the area-moment method.

Since the slope and deflection for this beam are both zero at each end, you can assume that you are dealing with a cantilever beam initially, as long as you make sure the conditions at the opposite end of the beam match the initial conditions for the slope and deflection. In this integration method, this is usually accomplished by selecting the proper constants of integration for the slope and deflection integrals.
 
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  • #7
SteamKing said:
I'm sorry, but your attached image is too small and blurry for me to read.

After I re-read your OP, I realized that you had solved for the unknown reactions for this beam. Once you do that, it is a simple matter to construct the bending moment diagram for the beam and then find the slope and deflection by integration. I'm more familiar with the integration method than the area-moment method.

Since the slope and deflection for this beam are both zero at each end, you can assume that you are dealing with a cantilever beam initially, as long as you make sure the conditions at the opposite end of the beam match the initial conditions for the slope and deflection. In this integration method, this is usually accomplished by selecting the proper constants of integration for the slope and deflection integrals.

Well then, I guess I have to try it both ways.. lol
Thank you so much for all the help, Sir! Thank youuu.
 

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

Beam deflection is the amount of bending or deformation that occurs in a beam when a load is applied to it. It is important because it affects the strength and stability of a structure and can help engineers determine the appropriate size and materials for a beam.

2. How is beam deflection calculated?

The most commonly used method to calculate beam deflection is the Euler-Bernoulli equation, which takes into account the beam's length, material properties, and applied load. Alternatively, finite element analysis can also be used to calculate beam deflection in more complex scenarios.

3. What factors can affect beam deflection?

The amount of beam deflection can be influenced by various factors such as the beam's length, material properties, cross-sectional shape, and type of load applied. Other factors like temperature changes and structural imperfections can also affect beam deflection.

4. What units are used to measure beam deflection?

Beam deflection is typically measured in units of length, such as inches or millimeters. The amount of deflection can also be expressed as a percentage of the beam's original length.

5. How accurate are beam deflection calculations?

The accuracy of beam deflection calculations depends on various factors, such as the complexity of the beam's geometry and the accuracy of the input data used. Generally, the results of beam deflection calculations can be reliable if the assumptions and simplifications made in the calculation are appropriate for the specific scenario.

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