Columns 10/23/07

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

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

Temple at Luxor

Temple of Hephaestus

Colannade

Washington Monument

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?

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

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

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.

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

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 6061 - T6 SR < 9.5 9.5 < SR < 66 SR > 66 Aluminum Alloy AA 2014 - T6 SR < 12 12 < SR < 55 SR > 55 Wood SR < 11 11 < SR < (18~30) (18~30) < SR < 50

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.

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.

Moment of Inertia

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

What about a rectangular column? Buckles in smaller dimension!

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

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

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

End Restraint and Effective Length

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

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

Bearing wall

Non-load bearing wall

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

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

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

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

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

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

Monadnock Building (1891)

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

Mesa Verde

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