Statically indeterminate built in beams

In summary, Richard is seeking help with calculating the bending moment and deflection of a beam that is built in on both ends, has 2 different distributed loads not equally spaced, and 2 point loads that are also not equally spaced. He has looked through his engineering notes and books but has only found examples for simply supported beams or fixed end beams with symmetrically spaced loads. He is wondering if superposition is the easiest method and if anyone has an example to share.
  • #1
Richardpaul
2
0
Hi,
I don't know if anyone can help. I would like to be able to calculate the bending moment and deflection of a beam that is:
Built in on both ends (no rotation)
It has 2 different distributed loads not equ ispaced along the beam
and has 2 point loads which are also not eqi spaced.
I can only find nice standard cases of 1 concentrated load OR a distributed load both equally spaced along the beam length.
I was thinking that superposition might be the easiest method

Thanks for any help

Richard
 
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  • #2
Richardpaul: Yes, use the case of a noncentered applied load, and use superposition, four times. Is this a school assignment?
 
  • #3
nvn
Thanks for the reply. I have looked through all my engineering notes from graduation and a few books. Most of them have simply supported beam examples and only very few fixed end examples. They all seem to follow the same type. eg. concentrated load at the centre or two loads that are nicely spaced symetrically. I wanted to know if the solution was very difficult and how to carry out the process. I am still looking for an example on the method how to do this. If you know would you mind letting me know

Thanks

Richard
 

What is a statically indeterminate built in beam?

A statically indeterminate built in beam is a type of structural element that is designed to support loads and resist bending moments. It is called "indeterminate" because its behavior cannot be fully determined using traditional equations of statics, and therefore requires more advanced analysis techniques.

How does a statically indeterminate built in beam differ from a statically determinate beam?

A statically determinate beam is a simpler type of structural element that can be fully analyzed using the equations of statics. This means that the reactions, internal forces, and deflections can be determined using a limited number of equations. In contrast, a statically indeterminate built in beam requires more complex analysis methods, such as the slope-deflection method or the moment distribution method.

What are the advantages of using statically indeterminate built in beams?

One advantage of using statically indeterminate built in beams is that they can resist larger loads and have higher load-carrying capacities compared to statically determinate beams. They also have the ability to distribute loads more evenly along the beam, resulting in a more efficient use of materials. Additionally, statically indeterminate beams can provide more stability and stiffness to a structure.

What are some common methods for analyzing statically indeterminate built in beams?

There are several methods that can be used to analyze statically indeterminate built in beams, including the slope-deflection method, the moment distribution method, and the virtual work method. These methods involve solving a system of equations to determine the reactions, internal forces, and deflections of the beam. The choice of method depends on the complexity of the beam and the preferences of the engineer.

What are some real-world applications of statically indeterminate built in beams?

Statically indeterminate built in beams are commonly used in building and bridge construction, as well as in the design of large mechanical and aerospace structures. They are also used in the design of support structures for heavy machinery and equipment. In addition, statically indeterminate beams are often used in advanced structural analysis and design courses to teach students about more complex structural systems.

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