1. Columns
10/23/07

2. Topics to discuss Columns Bearing Walls Failure of columns
Moment of Inertia
Buckling
Column Shapes
Bearing Walls

3. Columns
A column is a vertical support intended to be loaded with compressive forces along its axis.
Columns have been used extensively since antiquity.

4. Temple at Luxor

5. Temple of Hephaestus

6. Colannade

7. Washington Monument

8. How do columns fail? The column is a fundamental building element
As shown in the previous pictures, the columns are carrying all of the weight.
What is an obvious question about a column when designing a structure?
How much weight can it take before it breaks?

9. Short Columns
A material can be crushed if the compressive stress exceeds its ultimate strength.
When is this a concern?
fairly short columns

10. Longer Columns How do longer columns fail?
It will collapse or fail before it gets crushed
Buckling causes the column to bend in the middle
Buckling is the most common and catastrophic form of failure

11. Slenderness Ratio
The slenderness ratio is the ratio of the effective length to the radius of the column
SR = Leff / r
The slenderness ratio is large if Leff is large compared to the radius.

12. Slenderness Ratio – con’t
Different limits come into play depending on the length of the column
Short columns are limited by the compressive strength of the material
Intermediate length columns are limited by their inelastic stability
Longer columns are limited by their elastic stability

13. Slenderness Ratio Slenderness Ratio ( SR = Leff / r) Structural Steel
Material
Short Column
(Strength
Limit)
Intermediate
Column
(Inelastic
Stability Limit)
Long Column
(Elastic Stability Limit)
Slenderness Ratio ( SR = Leff / r)
Structural Steel
SR < 40
40 < SR < 150
SR > 150
Aluminum Alloy AA  T6
SR < 9.5
9.5 < SR < 66
SR > 66
Aluminum Alloy AA  T6
SR < 12
12 < SR < 55
SR > 55
Wood
SR < 11
11 < SR < (18~30)
(18~30) < SR < 50

14. Column Buckling
What factors determine how much weight a column can take before it buckles?
The type of material (steel is better than wood)
The dimensions of the column:
Broader columns can take more weight
Longer columns can take less weight
Max load varies as the inverse square of
length, subject to the maximum for the
material.

16. Column Buckling – con’t
What other factors determine how much weight a column can take before it buckles?
DISTRIBUTION of the material of the column about its axis
This is the MOMENT OF INERTIA.

17. Moment of Inertia

18. Moment of Inertia Can you guess which way a round column will buckle?
Can you guess which way a square column will buckle?

19. What about a rectangular column?
Buckles in smaller dimension!

20. Moment of Inertia
The load on a column can be increased by taking advantage of the moment of inertia
I-beam or hollow arrangement is better than solid piece
Moment of i-beam is
Moment of hollow square is

21. End Constraints
The load on a column can be increased by constraining the ends
The way the column is attached at either end changes the weight limit
A column that goes into the ground can take more weight that one that is just resting on the floor

22. End Constraints
Constraining the column causes it to buckle less easily, effectively makes it a shorter column.
Constraining one end and pinning the other doubles the buckling load

23. End Restraint and Effective Length

24. Bearing Walls Columns are a common support structure in buildings
Many more structures seem to just have walls. 
A wall designed to hold the weight of a structure (as opposed to just a facing)
A bearing wall

25. Bearing wall
A bearing wall is a continuous column, i.e. extension of a column
The material is a single piece
A bearing wall has greater strength to handle lateral displacements or concentrated loads

26. Bearing wall

27. Non-load bearing wall

28. Bearing walls
Often larger at base (either uniformly or with a separate footing) to reduce the pressure on the ground and increase lateral stability

29. Construction Issues
Disadvantage of using an entire wall to support the weight is difficulty building
Walls near the bottom must be wider to support the greater weight
Putting in gaps for windows and doors are a problem
You can’t build the walls without the floors, so construction must be done in stages and proceeds more slowly

30. Load on bearing walls
Bearing walls must support the cumulative weight of floors above as well as itself
Load becomes greatest at bottom
Bearing walls of masonry tend to get very thick towards the bottom to support the weight of the load above

31. Application of middle third rule for bearing walls
Load must remain in the “middle third” or the opposite side will be in tension.
Concrete/masonry must be kept in compression or they will fail
Middle third

32. Castles Bearing walls were used to build castles
Buttresses were used to distribute the load

33. Monadnock building (1891)
The office space is between two bearing walls
Very heavy
has settled 20 inches into the ground over the past century
The weight of the upper floors limited the height of the building

34. Monadnock Building (1891)

35. Adobe architecture
Adobe buildings of southwest – weak structures requiring thick walls for even one story 

36. Mesa Verde

37. Pilaster
If there are areas of high stress within the bearing wall, a pilaster (essentially an integrated column) can be added for greater support