Truss Analysis using Finite Element method

1. FINITE ELEMENT ANALYSIS
OF TRUSS
BY-
Ms. JAPE ANUJA S.
ASSISTANT PROFESSOR,
CIVIL ENGINEERING DEPARTMENT,
SRES, SANJIVANI COLLEGE OF ENGINEERING,
KOPARGAON-423603.
MAID ID: anujajape@gmail.com
japeanujacivil@sanjivani.org.in

2. FINITE ELEMENT ANALYSIS OF TRUSS
• Truss may be determinate or indeterminate truss
• Joint displacements are Unknown variables.
• Formulation of stiffness matrix of truss:
• The nodal displacement vector for the bar element is
• The stiffness matrix of a bar element is
1 2
AE, L
 
'
' 1
'
2
e
u
x
u
 
  
 
'
' 1
'
2
1 1
1 1
uAE
K
L u
 
       
' '
1 2u u

3. Transformation matrix for the truss:
• x' y'= Local coordinate systems
• x, y = global coordinate system
u1' , u2' = Displacements in local
coordinate system
• u1, u2, u3, u4= Displacements in
global coordinate system
• Ɵ=Angle measured in
anticlockwise sense w.r.t. positive
x-axis
Since axial directions of all members of truss are not same, hence in global coordinate
system (x-y) there are two displacement components at every node. Hence the nodal
displacement vector for typical truss element is
 
1
1
2
2
e
u
v
x
u
v
 
 
 
  
 
  

4. At Node1 At Node 2
Therefore, in matrix form above relation are
Where =vector of local unknowns
=vector of global unknowns
=Transformation matrix
where
'
1 1 1cos sinu u v   '
2 2 2cos sinu u v  
    
1
'
11
'
22
2
'
cos sin 0 0
0 0 cos sin
ee
u
vu
uu
v
x L x
 
 
 
      
    
    
  

 '
e
x
 e
x
 L
 
0 0
0 0
l m
L
l m
 
  
 
2 1
2 1
cos
sin
x x
l
L
y y
m
L



 

 

5. Stiffness matrix of truss element in global coordinate system:
     
 
 
'
0
0 1 1 0 0
0 1 1 0 0
0
0
0
0
0
T
K L K L
l
m l mAE
K
l l mL
m
l
m l m l mAE
K
l l m l mL
m
   
 
               
 
 
 
           
 
 
 
2 2
2 2
2 2
2 2
l lm l lm
lm m lm mAE
K
L l lm l lm
lm m lm m
  
 
  
  
 
  

14. THANK YOU