columns
DESCRIPTION
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. . - PowerPoint PPT PresentationTRANSCRIPT
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Columns
10/23/07
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Topics to discuss
• Columns– Failure of columns– Moment of Inertia– Buckling– Column Shapes
• Bearing Walls
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Columns
• A column is a vertical support intended to be loaded with compressive forces along its axis.
• Columns have been used extensively since antiquity.
![Page 4: Columns](https://reader035.vdocuments.net/reader035/viewer/2022081604/56815fe9550346895dceef56/html5/thumbnails/4.jpg)
Temple at Luxor
![Page 5: Columns](https://reader035.vdocuments.net/reader035/viewer/2022081604/56815fe9550346895dceef56/html5/thumbnails/5.jpg)
Temple of Hephaestus
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Colannade
![Page 7: Columns](https://reader035.vdocuments.net/reader035/viewer/2022081604/56815fe9550346895dceef56/html5/thumbnails/7.jpg)
Washington Monument
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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?
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Short Columns
• A material can be crushed if the compressive stress exceeds its ultimate strength.
• When is this a concern?– fairly short columns
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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
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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.
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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
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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
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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.
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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.
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Moment of Inertia
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Moment of Inertia
• Can you guess which way a round column will buckle?
• Can you guess which way a square column will buckle?
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What about a rectangular column?
• Buckles in smaller dimension!
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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
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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
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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
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End Restraint and Effective Length
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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
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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
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Bearing wall
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Non-load bearing wall
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Bearing walls
• Often larger at base (either uniformly or with a separate footing) to reduce the pressure on the ground and increase lateral stability
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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
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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
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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
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Castles
• Bearing walls were used to build castles• Buttresses were used to distribute the load
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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
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Monadnock Building (1891)
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Adobe architecture
• Adobe buildings of southwest – weak structures requiring thick walls for even one story
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Mesa Verde
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Pilaster
• If there are areas of high stress within the bearing wall, a pilaster (essentially an integrated column) can be added for greater support