Transcript Columns - Siena College

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