3. Static analysis of the truss girder by akimbo

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									Steel Structures I. Project



3.           Static analysis of the truss girder
Static analysis is performed using AxisVM computer program.

3.1.         Truss geometry and restraints

3.1.1.        Static scheme
The truss is simply supported. Lateral restraint is provided at the top chord by secondary beams,
located in the node points. All joints of the truss are pinned. Truss geometry is shown in the next
figure.

                                             λ              strut                         top chord




                                                                                                           h
                                                 diagonal                          bottom chord
                                                                          L

Modelling of the truss in a finite element program (AxisVM) requires definition of truss elements
connected in nodes.

3.1.2.        Node and bar numbering
The following is the numbering of nodes:

    8         9          10           11         12          13          14          15         16         17         18




    1          2                      3                       4                      5                      6          7

The following is the numbering of bars:

         7          8             9         10         11           12         13          14         15         16


17 24         18        25       26   19     27       28     20      29       30    21      31       32    22     33       23

         1                   2                    3                       4                      5               6



3.2.         Loads

3.2.1.        Load cases
Loads are acting in the nodes of the top chord.

    P1         P2            P2        P2         P2          P2          P2         P2          P2         P2         P1




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Steel Structures I. Project

The following loads act on the truss girder:
   permanent load:
   - secondary beams (chequered table + IPE270): 1.38 kN/m
        ⇒ intermediate nodes = 1.38x7.0=9.66 kN
        ⇒ end nodes = 9.66/2=4.83 kN
   - truss girder self weight (rough estimate): 20 daN/m2 = 0.2 kN/m2        Table 7.3, Mateescu
        ⇒ intermediate nodes = 0.2x7.0x2.0=2.8 kN                            et al., 1980
        ⇒ end nodes = 2.8/2=1.4 kN

    total:
        ⇒ intermediate nodes = 9.66 + 2.8 = 12.46 kN
        ⇒ end nodes = 12.46/2 = 6.23 kN
    ULS partial safety factor: 1.35
    SLS partial safety factor: 1.0

    live (imposed) load: 3.0 kN/m2
        ⇒ intermediate nodes = 3.0x7.0x2.0 = 42 kN
        ⇒ end nodes = 42/2 = 21 kN
    ULS partial safety factor: 1.5
    SLS partial safety factor: 1.0
 type                 value, kN        ULS load factor   SLS load factor
 permanent            12.46 / 6.23     1.35              1.0
 live                 42 / 21          1.5               1.0

3.2.2.    Load combinations
                                                                             Eq. 4.9 from
ULS load:      P2,ULS = 1.35x12.46+1.5x42 = 79.8 kN                          CR-0/2005
               P1,ULS = P2,ULS /2 = 39.9 kN
SLS load:      P2,SLS = 1.0x12.46+1.0x42 = 54.5 kN                           Eq. 4.14 from
               P1,SLS = P2,SLS /2 = 27.25 kN                                 CR-0/2005


3.3.     Data input
The truss girder will be modelled as a plane structure in the X-Z plane.

3.3.1.    Define geometry: nodes
Node coordinates can be defined either graphically or in a table format. Nodes shall be defined in
the order they were numbered. Display nodes on the screen using Settings>Display>Labels
[Nodes]. Snap settings can be changed from Settings>Options>Grid&Cursor.




3.3.2.    Define geometry: lines
Lines can be defined either graphically or in a table format. Lines shall be defined in the order they
were numbered. Display lines on the screen using Settings>Display>Labels [Nodes].

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Steel Structures I. Project




3.3.3.   Define material: steel




3.3.4.   Define cross-sections
Choose a trial cross-section. The truss is statically determined, therefore internal forces will not be
affected by cross-section properties. Deflections will however be affected by cross-section size.




3.3.5.   Define truss elements
Assign the same cross-section to all elements.




Node and truss element numbering is presented in the following figure.




3.3.6.   Define supports




Node 1: Rx=Rz=1010, all other directions are set to 0.
Node 2: Rz=1010, all other directions are set to 0.

3.3.7.   Degrees of freedom
Specify degrees of freedom for all nodes as "Truss in plane XZ".




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Steel Structures I. Project
3.3.8.   Define load cases
Define two load cases: ULS and SLS.




3.3.9.   Assign loads
Assign loads P1 and P2 to nodes, for each load case. Gravitational loads are entered as negative
values along the Fz direction.




3.3.10. Run static analysis




3.3.11. Display axial force diagram for the ULS loads




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Steel Structures I. Project


3.3.12. Display results in a table



Write down obtained results. Find the maximum (in absolute value) axial force for each type of
truss girder element: bottom chord, top chord, diagonals, and struts. Positive axial force denotes
tension.

Element         Cross-        Length [m]     Nx [kN]        Elements       max Nx [kN]
number          section                                     type
1               1             2.000          0
2               1             4.000          638.40
3               1             4.000          957.60         bottom
                                                                           957.6
4               1             4.000          957.60         chord
5               1             4.000          638.40
6               1             2.000          0
7               1             2.000          -359.10
8               1             2.000          -359.10
9               1             2.000          -837.90
10              1             2.000          -837.90
11              1             2.000          -997.50
                                                            top chord      -997.5
12              1             2.000          -997.50
13              1             2.000          -837.90
14              1             2.000          -837.90
15              1             2.000          -359.10
16              1             2.000          -359.10
17              1             2.000          -399.00        column
18              1             2.000          -79.80
19              1             2.000          -79.80
20              1             2.000          -79.80         struts         -79.8
21              1             2.000          -79.80
22              1             2.000          -79.80
23              1             2.000          -399.00        column
24              1             2.828          507.84
25              1             2.828          -394.99
26              1             2.828          282.14
27              1             2.828          -169.28
28              1             2.828          56.43                         +507.8
                                                            diagonals
29              1             2.828          56.43                         -395.0
30              1             2.828          -169.28
31              1             2.828          282.14
32              1             2.828          -394.99
33              1             2.828          507.84




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