Static analysis of a simple 2-D truss structure

2

1

L2=3 m

yP=280 kN

1

3

x

L1=1m

30o

60o

2

In the truss structure, for a link element (with nodes at two ends of the element) in the global

coordinate system we have

where is the nodal force vector, is the element stiffness matrix in the global C.S. and is the

nodal displacement vector and they can be shown as (Eq. 3.4.23 of [1])

{

}

(

)(

)

{

}

where is Youngs modulus of the element, is the cross-sectional area of the element,

and are the direction cosines, and is the angle between the global C.S. ( ) and the

local C.S. ( ) attached to the link element.

In this problem, assuming and , the parametric results can be obtained as the

following;

Stiffness Matrix of Element number 1:

(

)

Stiffness Matrix of Element number 2:

(

)

Assembled Stiffness Matrix of the system:

(

)

Displacements of node number 2 in x and y directions:

( )

Axial stress in each element can be obtained by using the following equation (Eq. 3.5.6 of [1])

(

) [ ]

{

}

Axial stress in element number 1:

Axial stress in element number 2:

Nodal reaction forces in x and y directions (Nodes 1&3):

&

&

Numerical parameters:

& & &

Hand calculations results:

& &

ANSYS Results:

NODE FX FY FZ 1 0.12124E+06 70000. 0.0000 3 -0.12124E+06 0.21000E+06 0.0000

ELEM STRAIN 1 -0.70000E-04 2 0.12124E-03