A  Brief  Introduction  to  Trusses  Julian  J.  Rimoli  

School  of  Aerospace  Engineering  Georgia  Institute  of  Technology  

 Trusses   are  one  of   the  most  widely   adopted   structural   designs,  many   times  being  utilized  as  the  structural  solution  of  choice  for  bridges,  roofs,  cranes,  aircrafts,  and  even   robots   and   spaceships!   Figure   1   shows   some  well-­‐known   examples   of   truss  structures.    

     (a)   (b)   (c)  

 Figure  1:  Examples  of  structures  composed  of  trusses.  (a)  Little  Belt  truss  bridge  in  Denmark,  (b)  

Eiffel  Tower  in  Paris,  and  (c)  NASA’s  Morpheus  moon  lander.    Trusses   are   defined   as   structures   composed   of   slender   bars   connected   to   each  other  through  pins  at  their  end  points.  In  practice,  joints  do  not  have  to  be  pinned:  we   can   assume   a   joint   behaves   as   if   it  was   pinned   as   long   as   all   the   bars   passing  through  a  joint  intersect  at  a  single  point.  For  example,  figure  2(a)  shows  a  real  truss  bridge.  Its  members  are  joined  together  through  metallic  plates  and  bolts.  Since  all  members  intersect  at  a  single  point  for  every  joint,  we  can  idealize  the  structure  of  the  bridge   for  purposes  of  analysis.  Figure  2(b)  shows  the   idealized  bridge,  where  the  light  blue  joints  represent  frictionless  pins.      

 

 

 (a)    

(b)  

Figure  2:  (a)  Real  truss  bridge,  and  (b)  idealized  structure.    Another  characteristic  of  trusses  is  that  they  can  be  connected  to  the  supports  only  through   its   joints.   Consequently,   2-­‐dimensional   trusses   can   only   use   two   types   of  supports:  pins  and  rollers.  Figure  3  shows  the  common  schematic  representations  

for  these  supports.  Since  bars  are  attached  to  its  supports  through  frictionless  pins,  a  single  bar  attached  only  to  one  support  is  always  free  to  rotate  about  it,  regardless  of  the  type  of  support.  Thus,  the  only  difference  between  pins  and  rollers  is  that  pins  prevent  all  possible  translations,  while  a  single  bar  attached  to  a  roller  is  allowed  to  translate  in  the  roller  direction.    

   (a)    

(b)  

Figure  3:  Schematics  for  typical  supports.  (a)  Pin:  attached  bars  could  possibly  rotate  about  the  pin,  but  translation  is  prevented.  (b)  Roller:  attached  bars  could  possibly  rotate  about  the  pin  and  

translate  in  a  specified  rolling  direction.      The   final   consideration   when   dealing   with   trusses   is   related   to   the   point   of  application   of   external   loads:   all   external   loads  must   be   applied   at   the   joints,   see  Figure  4.  If  an  external  load  is  applied,  for  example,  at  some  point  within  the  central  region   of   a   bar,   then   the   structure   will   stop   behaving   like   a   truss   and   common  analysis  methods  for  trusses  cannot  be  applied.  In  addition,  application  of   loads  to  places   other   than   joints   would   most   likely   result   in   premature   failure   of   the  structure  due  to  bending  of  the  bar  under  consideration.    

 Figure  4:  Loads  can  only  be  applied  on  joints  of  trusses,  either  by  directly  placing  them  on  the  joints  

(left)  or  by  using  an  extra  bar  to  attach  them  to  the  desired  joint  (right).    In  summary,  a  structure  should  satisfy  the  following  requirements  to  be  considered  as  a  truss:  

1) It   must   be   composed   of   slender   bars   joined   to   other   bars   only   through  frictionless  pins  at  their  ends.  

2) It  is  connected  to  external  supports  (if  any)  only  through  its  joints.  3) External  loads  are  applied  only  on  its  joints.  

 If  all  these  conditions  apply,  methods  of  analysis  become  really  simple,  as  we  will  see  in  the  document  entitled  “The  Method  of  Joints”.