A truss is a structure consisting of beams that are triangularly connected and applied in costructing buildings and bridges (Taranath, 2016). A framework comprising of cross-members that are connected using pin joints and supported at both ends using rollers or hinged joints is considered to be statically determinate (Hibbeler, 2015). Therefore, statically intermediate trusses are structures with more than two support positions.
Different Types of Trusses
Figure 1: Types of truss, (Kassimali, 2014).
The Warren Girder
The experiment deals with the Warren girder system, which is used for simple bridges and cantilevered crane booms. The idealised structural model of the framework under study is shown in Figure 2 below.
Figure 2: Warren girder with a central load, (Kassimali, 2014).
Newton’s Law applies to the whole structure. A complete truss analysis involves establishing the internal forces (tension and compression) acting on each beam and the reaction forces at the truss anchor point (Kassimali, 2014). Because it is difficult to satisfy all the physical conditions, the study of forces in each member is based on three assumptions:
The bars are straight, and they only carry axial load.
There are no moments in the calculations because the members are connected to joints by frictionless pins. Thus, a more complex analysis is required when the joints are subjected to significant loading.
The loads are applied only at joints.
The method of joints is used to determine the theoretical values of member forces (Reis and Oliveira, 2011). Equation 1 below shows Young’s modulus, which is a correlation between stress and strain.
Where is the Young’s modulus in , is the stress in the member in , and is the strain.
The stress is the ratio of forces and cross-sectional area of the members as shown by Equation 2 below:
Where F is the force in member (N) and A is the cross-sectional area of the member ().
This experiment aims to investigate the forces in Warren Truss. The objective is to learn the application of structure engineering knowledge and develop technical competency. The exercise helps in understanding the visuals of relative deflections of a joint in a truss, demonstrates the basic theory of static equilibrium, and provides an understanding of joint deflection and how structures support loads. Furthermore, this lab exercise builds and understanding of statistical determinacy. In this experiment, a different set of loads were applied to a load cell of the Warren girder structure and their respective values recorded. From the results, the recorded values proved to be sufficiently close to the theoretical values. The subsequent sections of this report explore the theory of Truss, calculations, and a discussion of experimental results.
Procedure
1. Obtain the Warren truss and place one end on a roller support and the other on a pin support.
2. Ensure that the centre of the joint is in the middle of the two ends and loosen the screw jack to ensure that the framework is not under loading conditions.
3. Zero the readings of the load cell on each member.
4. Apply a load of 100N in a downward direction and record the magnitude of the load and gauge readings.
5. Check stability and safety of the frame by carefully applying 500N.
6. Reduce the load until the digital force display reads zero and carefully zero the deflection gauge
7. Apply loads in the increments 100N, 200N, 300N, 400N, 500N and record all the strain and gauge readings.
Results
Table 1: Experimental recordings of member strains.
Loading condition (N)
1 (AD)
2 (AE)
3 (AF)
4 (BD)
5 (CF)
6 (DE)
7 (EF)
Def (mm)
0
87
16
-6
35
42
158
46
0
100
76
6
-16
40
47
148
56
-0.005
200
65
-6
-27
46
52
160
67
-0.032
300
54
-17
-38
51
58
171
78
-0.057
400
43
-28
-49
57
63
181
88
-0.081
500
33
-38
-60
62
68
191
99
-0.1
Figure 3: A graph of strain against loading conditions for experimental figures.
Table 2: True member strain
Loading condition (N)
1 (AD)
2 (AE)
3 (AF)
4 (BD)
5 (CF)
6 (DE)
7 (EF)
Def (mm)
0
0
0
0
0
0
0
0
0
100
-11
-10
-10
5
5
-10
10
-0.005
200
-22
-22
-21
11
10
2
21
-0.032
300
-33
-33
-32
16
16
13
32
-0.057
400
-44
-44
-43
12
21
23
42
-0.081
500
-54
-54
-54
27
26
33
53
-0.1
Figure 4: A graph of strain against loading conditions for theoretical values
Table 3: Experimental and theoretical forces
Member
Experimental Forces (N)
Theoretical Forces (N)
1
-320.63
-318.625
2
-320.63
-318.625
3
-320.63
-318.625
4
160.31
159.31
5
154.38
153.432
6
195.94
194.71
7
314.69
312.72
Table 4: Percentage error in experimental and theoretical values.
Member
Experimental Forces (N)
Theoretical Forces (N)
Percentage Error (%)
1
-320.63
-318.625
-0.629266379
2
-320.63
-318.625
-0.629266379
3
-320.63
-318.625
-0.629266379
4
160.31
159.31
-0.627706986
5
154.38
153.432
-0.617863288
6
195.94
194.71
-0.631708695
7
314.69
312.72
-0.629956511
Table 1 and 2 above represent the experimental results and true values of strain for each member of the truss. The laboratory results were recorded from the load cells connected to each member, while the methods of joints was used to calculate the theoretical values. Table 3 shows the experimental and theoretical member forces at 500N and Table 4 shows their deviations. Figure 3 and 4 show a relationship between strains and loading conditions for members AD and BD.
Calculation for Experimental Area
In this case, the Rod diameter is 5.98 mm and Esteel= 210G. Subjecting these values to the Young’s modulus relationship
Calculation for Experimental Force
Member 1;
Member 2;
Member 3;
Member 4;
Member 5;
Member 6;
Member 7;
Discussion
The positive values show that a member is under tensional forces, while the negative values show compressional forces in both experimental and theoretical. Moreover, Figure 3 and 4 show varying trends between the lab results and calculated values. The former have both positive values for AD and BD, while the latter have positive AD values and negative BD values. This relationship is important because it shows that a beam could be in compression or tension for one load location and similarly, it can be a zero-force member for another. The overall experimental values show a small variation with the theoretical values. The various factors that could have led to a difference in results include:
1. Errors due to parallax.
2. The apparatus was not accurate.
3. Environmental factors such as heavy wind could affect the readings.
Conclusion
Through this structure, we were able to investigate the forces in a Warren girder under loading conditions of 100N, 200N, 300N, 400N, and 500N. Moreover, the experiment provided a better understanding of tensional and compressional forces for different members in a truss, static equilibrium, and how the framework supports different loads. The results show that there is a small difference between experimental and theoretical values, which could be as a result of errors.
References
Hibbeler, R.C. and Kiang, T., 2015. Structural analysis. Upper Saddle River, NJ: earson Prentice Hall.
Kassimali, A., 2014. Structural analysis. Boston: Cengage Learning.
Reis, A. and Oliveira Pedro, J.J., 2011. Composite truss bridges: new trends, design and research. Steel Construction, 4(3), pp.176-182.
Taranath, B.S., 2016. Structural analysis and design of tall buildings: steel and composite construction. Boca Raton, FL: CRC press.
