# Deflection Analysis of Beam-Column Joint

• JohnRalston
In summary, the conversation discusses an issue with the deflection of a beam column. The beams and column are both circular hollow sections with specific dimensions, and the joint between them is assumed to be translating moment. The aim of the problem is to determine the horizontal deflection and tip deflection under separate applied forces. The initial attempt at solving the problem was incorrect as it did not account for the possible movement of the joint. The conversation also addresses labeling points on a diagram and the importance of including equations and a valid solution attempt. Additionally, it suggests checking mechanics of materials or strength of materials textbooks for information on beam deflection, specifically using the concept of superposition. It also mentions the proper formatting for numeric values and unit symbols.
JohnRalston
I'm having a bit of an issue with the deflection of a beam column. I've attached an image to show the problem. Please note the following:

- Assume the beams and column are both circular hollow sections of diameter 76.1mm. Wall thickness 5mm.

- The joint of the beam and column can be assumed as translating moment i.e. it is not pinned.

- F1 and F2 are applied separately, not simultaneously. The aim of the problem is to establish the horizontal deflection under F2, and the tip deflection under F1.

My initial attempt at solving this assumed that the horizontal deflection is basically tip deflection of a cantilever beam i.e. no contribution from the beam. And that the tip deflection at F1 is essentially tip deflection of a cantilever fixed where the joint between the 2 is. This is clearly wrong, as I haven't accounted for the possible movement of the joint i.e. it is not entirely fixed in reality.

Any help would be greatly appreciated, I can't seem to find anything relevant in my textbooks.

John

#### Attachments

• frame.jpg
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JohnRalston: Could you label the points on your diagram (such as A, B, C, ...), so we know which point(s) you are referring to in your discussion in post 1? You can hit the Edit button, if you wish. Is this school work? Is it an exam question? I notice you deleted the homework template. No relevant equations are listed, and no solution attempt is shown. You must list relevant equations, and show a valid attempt; and then someone might check your math. Are you interested in buckling, or only tip deflection? And which tip(s), and which deflection(s)? Deflection of problems like this is covered in any Mechanics of Materials or Strength of Materials textbook. Are you sure you could not find it in these books, under beam deflection? Perhaps look for the word "superposition" in the index.

(1) By the way, always leave a space between a numeric value and its following unit symbol. E.g., 100 kN, not 100kN. See the international standard for writing units (ISO 31-0).

Last edited:

## 1. What is the difference between a beam and a column?

A beam is a structural element that is used to resist bending and carry horizontal loads, while a column is used to resist compressive forces in a structure. Beams are typically horizontal or inclined, while columns are vertical.

## 2. How is the deflection of a beam-column calculated?

The deflection of a beam-column is calculated using the Euler-Bernoulli beam theory, which takes into account the material properties, cross-sectional geometry, and loading conditions of the beam-column. This theory can be solved analytically or numerically using software.

## 3. What factors affect the deflection of a beam-column?

The deflection of a beam-column is affected by various factors such as the material properties of the beam-column, the cross-sectional shape and dimensions, the type and magnitude of loads applied, the support conditions, and the length of the beam-column. Any changes in these factors can significantly impact the deflection of the beam-column.

## 4. How does a beam-column fail under excessive deflection?

A beam-column can fail under excessive deflection through various modes such as excessive bending, buckling, or crushing. This failure can occur due to the material reaching its maximum stress capacity, the beam-column losing its stability, or the supports failing to resist the deflection. The mode of failure depends on the specific conditions of the beam-column.

## 5. How can the deflection of a beam-column be controlled?

The deflection of a beam-column can be controlled by using stronger materials, increasing the cross-sectional dimensions, providing additional supports, and limiting the applied loads. Design codes and standards also provide guidelines for ensuring safe and acceptable deflection levels for beam-columns in different structures.

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