Compression  Members  

COMPRESSION  MEMBERS  

Compression  members  are  structural  elements  that  are  subjected  only  to  axial  compressive  forces.    The  most  common  type  of  compression  member  occurring  in  buildings  and  bridges  is  the  column.    Compression  members  are  also  used  in  trusses  and  as  components  of  bracing  systems.  

COLUMN  THEORY   •  CRITICAL  BUCKLING  LOAD  •  Leonhard  Euler    •  Failure  may  occur  by  

compressive  yielding  rather  than  buckling.  

•   Prior  to  failure,  the  compressive  stress  will  be  uniform  over  the  cross  secMon  at  any  point  along  the  length,  whether  the  failure  is  by  yielding  or  by  buckling.  

•  Euler  Load  (Euler  buckling  load)  

A:  cross-­‐secMonal  area    r:  radius  of  gyraMon  with  respect  to  the  axis  of  buckling  L/r:  the  slenderness  raMo  and  is  the  measure  of  a  member’s  slenderness,  with  large  values  corresponding  to  slender  members.    At  this  compressive  stress,  buckling  will  occur  about  the  axis  corresponding  to  r.  

For  less  slender  members:  

•  Friedrich  Engesser  (1889)  •  Small   slenderness   raMo   for  

members,  the  stress  at  which  buckling   occurs   is   greater  than  the  proporMonal   limit  of  the   material,   the   relaMon  between   stress   and   strain   is  not  linear.  

Effec<ve  Length  Euler  and  tangent  modulus  equaMons  assumpMons:    1.  The  column  is  perfectly  straight,  with  no  

iniMal  crookedness.  2.  The  load  is  axial,  with  no  eccentricity.  3.  The  column  is  pinned  at  both  ends.  

KL:  effecMve  length  K:  effecMve  length  factor  

CODE  REQUIREMENT  The  nominal  compressive  strength  is:  

LRFD:  

ASD:  

NSCP  Note:  For  members  designed  on  the  basis  of  compression,  the  slenderness  raMo  KL/r  preferably  should  not  exceed  200.  

LOCAL  STABILITY  

LOCAL  BUCKLING    Two   types   of   elements   must   be   considered:   UnsMffened  elements,  which  are  unsupported  along  one  edge  parallel  to  the  direcMon   of   load,   and   sMffened   elements  which   are   supported  along  both  edges.    For   compression  members,   shapes   are   classified   as   slender   or  nonslender.   If  a  shape  is  slender,   its  strength  limit  state  is   local  buckling,   and   the   corresponding   reduced   strength   must   be  computed.