# Details about Lab 3

The dead load (load of the structure) and the live load (us sitting in the lab) in the Bainer Hall (or any civil engineering building structure) is transmitted from the roof slab to the beams, then from the beams to the columns and finally to the foundation system via the columns. Columns are vertical members which carry the load axially through compression. Under earthquake and wind load, they can be designed to carry a component of the lateral forces. Greeks, Romans and many other old civilizations viewed columns as a symbol of strength and used columns as decorative members in front of their palaces.

Look at our UC Davis MU photos and see if you can spot the big cylindrical columns supporting the MU at https://www.ucdavis.edu/news/photos-inside-new-memorial-union/

Depending on the Length to Width ratio (slenderness ratio), the columns (and this lab) is divided into two sections:

## 1. Long columns

These columns usually fail under buckling. Read about it here.

For this lab, we looked at the primarily three different end condition.

1. Fixed, with no translation : Where no rotation and no translation is allowed. The end is screwed in and has a rubber stopper to stop it from moving.
2. Fixed, with translation : Where no rotation but translation is allowed. The end is screwed in and has a slot inwhich the whole end could move.
3. Pinned, with no translation : Where rotation but no translation is allowed. THe end has a ‘V’ notch and hasbeen screwed or a rubber stopper is used to stop it from moving.

Based on these three end conditions, we tested four different combinations of end conditions. First, we calculated the theoretical buckling force and then we applied the load experimentally to check it.

### What do I want in the report?

1. Sample calculation for your respective column:
1. Group a - Column a
2. Group b - Column b
3. Group c - Column c
2. In results:
1. Make a table of experimental and theoretical buckling forces for all columns
2. Make a table of end conditions as given at the end of the procedure in your lab manual
3. In attachments:
1. Attach a before and after photo of buckling, make sure every column is in one frame. Do not attach bubkling photo of each column separately.

## 2. Short columns

Short columns usually fail due to excessive stresses in the material. To define the failure stresses for a material/body there are many classical failure theories. You can read about failure theories here

### What do I want in the report?

We will use the table presented at the end of lab 3 in the lab manual.

1. Sample Calculation:
1. Pick a load (P (N), say 267 N), and calculate:
1. Principal normal stresses $\sigma_1$ and $\sigma_2$
2. Tresca’s failure stress $\sigma_T$
3. Von Mises failure stress $\sigma_M$
2. In results:
1. Copy the table and add columns for:
1. Principal normal stresses $\sigma_1$ and $\sigma_2$
2. Tresca’s failure stress $\sigma_T$
3. Von Mises failure stress $\sigma_M$
3. In attachements:
1. Graph for Principal normal stresses $\sigma_1$ and $\sigma_2$ vs load (P)
2. Graph for Tresca’s failure stress $\sigma_T$ and Von Mises failure stress $\sigma_M$ vs load (P)
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