# 2 span beam with 2 points loads. Statically indeterminate?

• Mech King
In summary, the conversation discusses a beam problem that appears to be statically indeterminate due to bolted and rigid connections at supports A, B, and C. The initial assumption of ignoring span AB is questioned and alternative methods of analysis are suggested, including the "Theorem of three moments." The type of connections at A, B, and C and their effect on rotation of the beam are also discussed. The conversation ends with appreciation for the input and a mention of using the information for a similar problem.
Mech King
Hey guys,

I'm just pondering a beam problem fir a structure that I'm analysing. It appears statically indeterminate to me? The beam is bolted to a support at locations A,B & C. There are two point loads between span B-C.

There are no symmetrical distances or support locations etc.

Initially, I just ignored span A-B, as I assumed that the load would not transfer to the far left hand end at A, because it is rigidly fixed at B & C? Is this incorrect?

Now I am thinking that I do need to consider the left hand span AB.

I thought that I could assume "A" does not support the beam, then calculate the deflection of the beam at the left hand side in the unsupported region and then calculate what the restoring force would need to be to prevent such deflection, therefore calculating reaction A, and then take moments to calculate reactions B and C?

Or is there a better approach? I'm really getting a bit stuck here and would appreciate any guidance!

Many thanks

Mech King,

I'm sure I read something in a book about a similar system. It was a long time ago, but if my memory serves me right, it mentioned something about a "3 moment system". I'm sorry I can't help you more.

It comes down to whether the connections at A, B, and C will allow the beam to rotate with respect to the longitudinal axis of the beam. You say they are bolted connections, but do you have any further details? If rotation can occur, you have a classic continuous beam. If the bolted connections do not allow rotation, then each span can be analyzed individually, assuming full fixed connections at A, B, and C.

Tax on Fear and steam king, thanks a lot for your input! Both methods make sense to me and I agree.

The supports at at A B and C consist of a block welded to each side of the support/beam and bolted to a column, which I will consider to be rigid.

I guess the beam won't rotate at its supports because it is built in at each support. I was unsure if I could just look at the section BC in isolation, but thanks Steam King for the direction! Also, thanks for the references Tax on Fear; I can use this for a similar problem I have :D.
Very much appreciated guys!

Thanks

You mentioned that A, B, and C are bolted to a support and are rigidly fixed, but the picture shows pinned connections. If they really are rigidly fixed, you have a statically indeterminate problem because statics won't give you all the equations you need to solve for all the unknowns. You really only have the Y-direction equation and the moment equations at A, B, and C to work with, and your unknowns are the 3 vertical reactions and the 3 moments at each of the rigid supports.

Even just looking at BC, it's statically indeterminate if they're rigid connections. You'll have to use mechanics of materials equations to solve for the reaction moments.

## 1. What is a 2 span beam with 2 point loads?

A 2 span beam with 2 point loads refers to a structural element that is supported at two points and has two concentrated loads placed on it.

## 2. What does it mean for a 2 span beam to be statically indeterminate?

A 2 span beam is statically indeterminate when the reactions at the supports and internal forces within the beam cannot be determined solely by the equations of static equilibrium.

## 3. What factors make a 2 span beam with 2 point loads statically indeterminate?

A 2 span beam with 2 point loads is statically indeterminate when there are more unknown reactions and internal forces than there are equations of equilibrium. This can occur when the beam has multiple supports or when the loads are not evenly distributed.

## 4. How do you solve for reactions and internal forces in a statically indeterminate 2 span beam with 2 point loads?

To solve for reactions and internal forces in a statically indeterminate 2 span beam with 2 point loads, additional equations must be generated using the principles of compatibility and equilibrium. These equations can then be solved using methods such as the method of consistent deformations or the slope-deflection method.

## 5. What are the practical applications of analyzing a 2 span beam with 2 point loads?

Understanding the behavior of a 2 span beam with 2 point loads is important in the design and construction of various structures, such as bridges, buildings, and other load-bearing structures. It can also be useful in troubleshooting and identifying potential failure points in existing structures.

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