Partial distributed load over fully fixed beam

In summary: If so, you would know that a reaction force is a force which opposes the motion of an object. In this case, the reaction force is the force which keeps the beam in equilibrium. The moment of inertia of the beam is also a reaction force, since it resists the change in momentum of the beam. In this problem, you are trying to find the deflection of the beam at any point, which means you are integrating the bending moment curve twice w.r.t. the x-axis. The equation for the deflection at any point is= mx-h(x), where m is the deflection and h is the slope of the bending moment curve at that point. The slope of the bending
  • #1
aqpahnke
3
0
I am trying to figure out the deflection in a fully restrained beam. A diagram of the beam can be found here on this website.
http://civilengineer.webinfolist.com/fb/fbcalcu.php

I have been able to find the reactionary forces as well as the moments at each end of the beam for any distributed load at any position on the beam.
I would like to relate this to the deflection of the beam at any point and am completely stuck.
If any of you have the know-how please help out.

Aric
 
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  • #2
If you have determined the reaction forces and moments which keep the loaded beam in equilibrium, then you can calculate the deflection curve of the beam by integrating the bending moment curve twice w.r.t. length and applying the boundary conditions to determine the unknown constants of integration, just like any other beam problem.
 
  • #3
Okay.. let's say that on that particular beam that the reactionary force for one direction is R1= (q*d/L^3)[(2b+L)a^2-((a-b)/4)d^2)]
I get stuck on the particulars. I don't really know where to integrate in this equation
 
  • #4
Okay.. let's say that on that particular beam that the reactionary force for one direction is R1= (q*d/L^3)[(2b+L)a^2-((a-b)/4)d^2)]
I get stuck on the particulars. I don't really know where to integrate in this equation
 
  • #5
'Reactionary' means something else than what you assume. The proper terminology in English is 'reaction force'.

http://en.wikipedia.org/wiki/Reactionary

You misunderstand the procedure to follow in analyzing beams to determine deflections. Once you have determined the end reactions and moments, you construct the bending moment diagram for the beam, using the end reactions and moments. This bending moment diagram, or the functions which generate it, is integrated twice w.r.t. the length coordinate, say x. After each integration, an unknown constant of integration is obtained, which constants can be calculated by applying the boundary conditions for the beam. In this case, both the slope and deflection of the beam will be equal to zero at each end.

Have you studied any strength or materials courses?
 

1. What is a partial distributed load?

A partial distributed load refers to a force or weight that is distributed across a portion of a beam, rather than being concentrated at a single point. This type of load is typically applied over a specific length or area of the beam.

2. How is a partial distributed load different from a point load?

A point load is a force or weight that is applied at a single point on a beam, while a partial distributed load is spread out over a length or area. This means that the effects of a partial distributed load are distributed along the beam, while a point load has a concentrated effect at the point where it is applied.

3. What is a fully fixed beam?

A fully fixed beam is a beam that is supported at both ends and cannot rotate or move in any direction. This type of beam is also known as a fixed-end beam or a built-in beam. It is commonly used in structural engineering to support heavy loads or resist bending.

4. How does a partial distributed load affect a fully fixed beam?

A partial distributed load applied to a fully fixed beam will cause the beam to bend and experience internal stresses. The magnitude of the bending and stress will depend on the distribution and magnitude of the load, as well as the properties of the beam such as its size and material.

5. How can a partial distributed load over a fully fixed beam be calculated?

The calculation of a partial distributed load over a fully fixed beam involves determining the magnitude and distribution of the load, as well as the properties of the beam. This can be done using mathematical equations and principles of structural mechanics, or with the help of computer software programs specifically designed for beam analysis. It is important to note that the calculation of a partial distributed load is complex and should be done by a qualified engineer or scientist.

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