Columns

Columns

1. Transfer loads down

   • Buckle at a certain slenderness
     • Either shorten or bend out (buckle) in compression

2. Column Failure

   • Short Columns
     • Crushing
   • Intermediate Columns
     • Buckling with Crushing
       • Buckle rather than crush depends on Euler equation
         • This equation tells us that the buckling load is reduced in proportion to the square of its length
           • i.e. if you double the length of the column, you reduce the load carrying capacity by 4
         • Stress compared to slenderness
           • Slope is allowable stress
   • Long Columns
     • Buckling
     • End conditions
       • When a column buckles is related to effective length (KL)
         • L = length
         • K = depends on end conditions
           • A fixed end condition will support 4x the load of pinned ends
           • A pinned end column will support 4x the load of one fixed one free (flagpole)
           • Generally, the conditions are fixed on one end, pinned on the other
       • Rotation fixed, translation fixed
       • Rotation free, translation free
       • Rotation free, translation fixed
       • Rotation free, translation free
       • Pinned end
         • does not constrain the rotation (no end moment)
       • Fixed ends
         • Integrated in the system

3. Bracing

   • Reduces effective length
   • Force required in brace is 10% of the P (force)

4. Shape Considerations

   • Rectangular and W shape columns will buckle about their weak axis (x)
     • They are more efficient than square planes if braced along x-axis
   • Angled columns
     • Methods for resolving forces (angled beams)
       • Graphical
       • Pythagorean
       • Trigonometry
       • Similar Triangles
     • A vector can also be broken down into components
       • Some of the forces can be induced by geometry