This document analyzes a framed truss structure with over 50 steel members using the finite element software SAP 2000. The author models a five-panel truss with hinge supports and various steel sections. Axial forces, displacements, and stresses are obtained from dead, live, and wind loads. Manual calculations validate some results from SAP 2000. A parametric study examines changing a support to roller and reducing the coefficient of thermal expansion, finding different member forces and displacements in each case. The author concludes FEM software is useful but has errors, and boundary conditions and other factors significantly impact structural behavior and load transfer.

1. Term Paper: CE542
Analysis of Truss Elements by SAP 2000
Introduction
In this term paper, I will analyze a framed truss structure which is having more than 50 steel members. This
structure will have five panels, one after other. I will get axial forces and deformations for this structure
from four points. I will validate them from my manual calculations. The objective of this term paper is the
measure of the accuracy of the results obtained from the Finite Element Software, SAP 2000. Then in this
term paper, I will also include the parametric study which will give us an idea of the variations, produced
from the changes in the model.
Figure 1 Framed Truss Member

2. Term Paper: CE542
Analysis of Truss Elements by SAP 2000
I have used SAP 2000 as a Finite Element Software for the term paper. For the modelling, I selected grid
lines as shown in the given figure. The height of the frame from ground to the base of the frame is 18 ft.
The units used is lbs., ft. The breadth of the frame is 5 ft. The length of the structure is 40 ft. I have four
replicates of my truss structure in the overall length of 40 ft. The hinge support is taken as boundary
conditions.
The steel section I used for the frame section is rectangle. The steel is A500 Grade B 46, HSS 8X8X(3/8).
And I used I-Section for my truss, the steel includes W8X10, W8X18. W8X28, W8X67. The steel used for
truss structure is same as for frame section. The truss section is a wide-flange section. I joined each steel as

3. median mode. For that assignment, I made an Auto Select list. I used 4000 psi as the characteristics strength
of concrete.
Figure 2 Frame with Steel Section
Figure 3 Modelling in SAP 2000

4. The loadings are:-
Dead Load- 30000 lbs. on the shown points given in the figure.
Figure 4 Dead Load

5. Live Load: 30 lbs. on the slab surface,
Wind Load: 15 lbs. on one side, -6 on other side.
Figure 5 Wind Load
Figure 6 Live Load

7. Axial Force Diagrams:

13. Joint Displacements:
At B1 position, due to Dead, Live and Wind load respectively,

14. At B4 Upper,
At B5 lower,

15. Numerical Validation
From Simulation, The reactions are VA=120289.58 lbs.
But from manually calculation,
MA = 0
So,
{L(B1) X (5/8) +…….+ 7 X L(B7) X (5/8)} – VG X 5 = 0
Then, VG = 105000 lbs.
We get large value of reactions from Simulations.
1. Try to find out force in FCB1:
FBD.
FBC + 10500 = FCB1 cos 45̇
H = FCB1 sin 45̇
FCB1 = sqr(2) H
From triangle vector theorem,
FCB1 = FBC + FBB1

16. FCB1 = FBC + H
sqr(2) H = FBC + H
Hence, H = FBC / (sqr(2) -1)
FCB1 sin 45̇ = FBC / (sqr(2) -1)
FBC = (sqr(2) -1) sin 45̇ FCB1
Now, insert it in above equation,
FCB1 sin 45̇ (sqr(2) -1) + 105000 = FCB1 cos 45̇
FCB1 = 179487.1795 lbs. /ft.
From simulation, FCB1 = 184231.79 lbs. /ft.
2. FBC = (sqr(2) -1) sin 45̇ FCB1
FBC = 52551.40899 lbs. ft.
From simulation, FBC = 105946.81 lbs. /ft.
3. H = FBC / (sqr(2) -1)
H = 126935.7705 lbs.
From simulation, H = 169961.77 lbs. /ft.
We cannot depend on the Finite Element software for the whole calculations. As we know that
SAP 2000 has so many bugs, so there will be some errors. But the answers that I got from
analysis is somewhat in the range of acceptable answers.

17. Parametric Study
I have done the parametric study in two cases.
Case 1: One of the hinged support is changed to roller support. Then the deformed case is-

25. For the upper horizontal truss member, the member axial forces are approximately same. For the lower
horizontal truss member, the member axial forces are larger in the roller case than from the hinged case.
Reactions are - Original Case ; H=532.64 and V=120289.58
Case 1 ; H=655.68 and V=120689.09
Case 2: I have changed-
Coefficient of Thermal Expansion, A = 6.5E-06 to 4.5E-06
Reactions are: H=631.28 and V=120300.09

30. The decrement in the Coefficient of thermal expansion leads to the decrement in the member axial forces
in the original model. In all the figures above, it is clearly depicted that the steel yields early because of less
value for thermal expansion, but it possess less forces at the appropriate temperature.
Conclusion
What I have found from my comparative study is that even a single change in entity can bring a magnificent
change in the values of the forces, displacements and stresses. Hinged support cause less forces than the
roller ones. Roller ones cause the large member axial forces. The thermal expansion is also a major entity.
It can help in the decrement of the member forces.
As I learnt how Finite Element Analysis Software work in the design and analysis of a structure. I have also
learnt how I can model a structure in FEM Software. This comparative study lets me to access with SAP
2000 and its some important tools like replicate, frames, single axis point, etc.
Structure reacts different with different loading and boundary conditions. It matters how the load is
transferred, and it actually depends on the degree of freedoms. The lesser degree of freedom is, the more
complications exist because of the roller support or the same conditions.