Columns 10/23/07. Topics to discuss Columns –Failure of columns –Moment of Inertia –Buckling –Column Shapes Bearing Walls.

Columns

10/23/07

Topics to discuss

• Columns– 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

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