Columns 10/23/07. Topics to discuss Columns –Failure of columns –Moment of Inertia –Buckling...
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Transcript of Columns 10/23/07. Topics to discuss Columns –Failure of columns –Moment of Inertia –Buckling...
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