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
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
