the forces that act on every joint using engineering structure pin joint truss technique, calculate the static determinant pin-jointed frameworks

the forces that act on every joint using engineering structure pin joint truss technique, calculate the static determinant pin-jointed frameworks

In structural frameworks, structural trusses are enjoined or connected through various methods. This lab report was carried out to find out the forces that act on every joint using engineering structure pin joint truss technique, calculate the static determinant pin-jointed frameworks, deflection and how incremental loads are used on every member from 0.1 Kg to 0.7 Kg. Various strain values were recorded, as shown in Table 1. The results of experimental and theoretical values were also recorded, as shown in Table 2 and compared. In Table 3 are deflection results calculated from the experiment results. The Strain Energy Method was used to calculate the theoretical deflection. Based on the theoretical and experimental values, it was noted that the per cent error, > 60%. However, the objectives of this experiment were achieved as the calculation of pin-jointed truss internal forces was useful to help understand how the deflection of each member transfer forces.

Introduction and Background

In the structural framework, structures are enjoined using elements at joints through various methods, namely bolting or welding as in the case of steel; monolithic reinforcement or jointing as in the case of reinforced concrete structures and use of nails or glues as in the case with timber structures (Longo, P. et al.). There are two joint types, namely pin- and stiff-joint (Arita, Masaki, et al.).

Aim and Objective

The main aim of this experiment was to find out the forces acting on every joint by using the engineering structure pin joint truss technique. This report aimed to achieve two objectives, namely to calculate the internal forces in a pin-pointed truss subject to a set of external loading conditions and lastly, to understand how the deflection of a member can be used to obtain the force.

Methods

This experiment was carried out using Pin-Joint Truss method to observe what effect varying the load has on the truss members. The readings obtained from the strain gauges positioned on each truss member were recorded, as shown in Table 1. The equipment was set up, as shown in Figure 1. Subsequently, the variation in the actual configuration of joints and members were then noted; this was followed by applying a-100 N preload in the direction of loading as well as zero as the load cell. Next, a 500N load was carefully applied, and the frame checked if secure and stable. The load was carefully returned to zero, and the indicator zeroed without interfering with its sensitive. The loads were then applied in 100 N load increments up to a maximum of 500 N. The true member strains were then recorded as shown in Tables 1. The theoretical deflection in every unit load is determined using a framework of a simple pin-pointed method; this is used as a free-body diagram in which each joint at the equilibrium in each direction is satisfied using equations below.

Figure 1: A bending moment of a beam experiment in the frame of the structure.

Results

1. Theoretical Results

The Strain Energy and pin-jointed method were used to determine the theoretical results applied to the Statically Determinant Pin-Pointed truss members, as shown in Figure 2.

Figure 2: Pin-Jointed Truss Static Determinant

The downward applied load (W) is countered by two upward reaction forces (R1 and R2); symmetrically, R1=R2;

Therefore, by upward and downward resolution, R1 + R2 = W

Thus, R1 = R2 = W/2

Each point force is calculated to satisfy the equations of equilibrium; equations 1 and 2.

Since this is an equilateral triangle, it measures 140mm on every side; therefore, L1=140mm (0.14m), L2= 140mm (0.14m) and L3= 140mm (0.14m).

Thus,

Hence,

At point 1, the vertical and horizontal forces would be calculated as;

At point 2, the horizontal forces; P1 and P2 is equal to zero that is, P1=P2=0

At point 3;

At point 4:

Therefore,

The formula gives the work done for the entire system;

Therefore, work done

But work done is also given by the formula

Therefore,

Experimental Results

Table 1: True Member Strains (με)

Calculate the equivalent member forces for an applied load of 500 N and complete the “Experimental Forces” column in Table 2. You may find the following information useful:

,                          ,

Where

E=Young’s Modulus (GPa)

σ=Member Stress (Nm-2)

ε= Strain displayed (Nm-2).

F= Force

A= Cross-sectional area of the member.

The nominal diameter of the rods to the nearest 0.01mm is 6.15 mm

Area of the rod would be calculated as;

By making  the subject of the formula,

Therefore, this is as;

The force due to strain 1, at load 0N, would be calculated as;

Table 2: Comparison of Experimental and Theoretical Force for W = 500 N

Table 3: Load and deflection

Figure 3: A graph of deflection vs load

From the graph, the gradient value of

Discussion

There is a significant difference between the experimental and theoretical values for the loads acting on every member per deflection. Based on this report, the theoretical value was 3mm/Kg while the experimental value was 9.23mm/Kg. based on these values, the percentage error can be calculated as;

Although the per cent error is high, it is vital as far as building framework structures is concerned because it tells structural and mechanical engineers how much deflection is needed or should be eliminated to avoid adverse effects. The theoretical aspect of this lab report is based on the view that every member takes equal force. Besides, other obvious sources of error, such as materials properties and overall experimental reading inaccuracies; this significant error could also have been attributed by ignoring each member’s thickness. For example, the thickness of each member in this experiment was completely ignored. Other factors could be slippage or support movement within joints can also highly impact on the structure resulting in the significant difference. Also, differences in stresses and temperature contribute to the structure of a different response.

Conclusion

The pin-jointed truss structural performance was dependent on each member ability to resist bending with the joints maintaining the angles between fitted members. The experiment reported a high per cent error between experimental and theoretical results. However, despite the high per cent error, the objectives of this experiment were achieved as the calculation of pin-jointed truss internal forces subject to a set of external loading conditions was useful in helping to understand how the deflection of each member transfer forces on them.

References

Arita, Masaki, et al. “STRUCTURAL BEHAVIOUR OF JOINT BETWEEN STEEL BEAM AND CONCRETE ENCASED STEEL COMPOSITE COLUMN.” ce/papers 3.5-6 (2019): 294-304.

Longo, P., et al. “Analysis of Truss Structures with Uncertainties: From Experimental Data to Analytical Responses.” (2016).