Truss Structures - Term Paper Example

Title Page Abstract A truss is one of the main engineering structures that provide practical and economic solutions for engineering constructions. A truss can either be statically determinate or statically indeterminate. The problem with statically determinate structures is that if one member of the truss fails the truss collapse and can be dangerous for public use. The main reason for introducing redundant members in truss structures is for public safety. Truss is commonly used to support load, but the maximum bending moment increases with increase in span; hence they are not economical in the long run. In this case arches can be employed, as arches develop economical and effective solution for construction especially when building bridges. Two-hinged and fixed arch are curved beams supported at their ends and with convexity upward. They produce horizontal reaction that can minimize the bending moment. A horizontal reaction is a redundant reaction and can be found from minimum strain energy theorem. This report will explore three experiments that involves redundant truss, two-pinned arch and fixed arch structures. Table of Contents Title Page i Abstract ii Table of Contents iii 1.0 Introduction 1 2.0 Experiments 2 2.1 Redundant Truss 2 2.1.1 Statically Determined Truss 2 2.1.2 Statically In-determined Truss 2 2.2 Two Pinned Arch 2 2.2.1 Objective 2 2.2.2 Apparatus and procedure 2 2.2.3 Data and observations 3 2.2.4 Graphs and discussion 4 2.3 Fixed Arch 7 3.0 Conclusion 7 4.0 Works Cited 8 5.0 Group Work Contribution 9 1.0 Introduction 2.0 Experiments 2.1 Redundant Truss 2.1.1 Statically Determined Truss 2.1.2 Statically In-determined Truss 2.2 Two Pinned Arch 2.2.1 Objective To study two hinged arch for the horizontal reaction for a particular loading and to compare the results from those obtained from theory. 2.2.2 Apparatus and procedure The experiment was set as in the figure below. Figure 1: Two-pinned arc experiment It consists of an aluminium alloy parabolic arc and two supports. The left hand side is fixed to its support, but the right hand side rotates and slides up to an electronic load cell (force meter) which measures the horizontal reaction produced by the arc. After ensuring that the force meter was reading zero, a mass of 500 g was placed on the far left-hand side of the arc hanger. The resulting reading on the force meter was recorded. The mass was then moved along the top of the arc one position at a time, as the force meter reading was recorded at each position in a table. 2.2.3 Data and observations Table 2: Results for experiment 1 (500g load) Load Distance from left Fraction of span Experimental horizontal reaction Theoretical horizontal reaction Theoretical vertical reaction g mm N N N 500 50 0.1 1.5 1.5 0.5 500 100 0.2 2.8 2.8 1 500 150 0.3 3.9 3.9 1.5 500 200 0.4 4.5 4.6 2 500 250 0.5 4.7 4.8 2.5 500 300 0.6 4.4 4.6 2.9 500 350 0.7 3.8 3.9 3.4 500 400 0.8 2.8 2.8 3.9 500 450 0.9 1.5 1.5 4.4 For a distance of 50mm, horizontal reaction = 1.5N and the applied force = 500g, the influence values are calculated as follows. The span fraction is also calculated as follows. The table obtained is shown below. Table 2: Influence values 2.2.4 Graphs and discussion The graph obtained from the data above is shown below. Figure 1: Horizontal values verses distance from HB The horizontal reaction increases with increase in the distance from left to a distance of 250mm for both experimental and theoretical horizontal reaction. After reaching the distance of 250mm, the experimental horizontal reaction began to decrease with increase in distance from left. The experimental horizontal reaction reached zero at a distance of 500mm from left. The load would be placed at a distance of 250mm from left in order to achieve the maximum horizontal reaction. The maximum reaction is 4.7N and 4.8N for experimental and theoretical results respectively. An error of 2.08% was made. The position of maximum horizontal reaction can be explained from the following equation. Where HB is the horizontal reaction at B (N), W is the load (N), L is the span of the arch (m), r is the rise of the arch (m) and x is the distance from the left (m). When x ≤L/2 which is the distance of 250mm form the left, x is increasing with HB, and beyond 250mm, x increase with HB. x reaches the highest value x = 250mm (L/2). As it can be seen on the graph the formulae provided accurately predict the behavior of the arch with minimum error. The curve has a parabolic shape. The graph for influence values verses span fraction is shown below. Figure 2: Influence values verses span fraction Based on the results we obtained in this experiment, there is a slight difference between the theoretical and the experimental results. The experimental horizontal reactions are slightly less than the theoretical horizontal reactions. This is because there may be the influence due to change in the center of gravity. When there is slight deviation of the center of gravity to the left, the error occurs resulting in smaller horizontal reaction. The error can also be introduced due to friction on the roller which has not been taken into account in theory. Sensitivity of the instrument is another source of concern. Error may be introduced due to sensitivity of the instrument. The theoretical values are not affected by this phenomenon. This leads to the difference in the horizontal reaction (Sandaker, Eggen & Cruvellier, 2013). When a load is applied on the two-pinned arc, it tends to spread out. Since there is no at the ends, the horizontal reaction is produced at the support. A horizontal reaction is a redundant reaction and can be found from minimum strain energy (Raz, 2001). Essentially, the arc carries the shear, the bending and the axial forces. The legs are hinged at their base. Two pinned arc is statically indeterminate to the first degree. Vertical reaction of the leg on the right hand side can be found by taking the moment about the hinge of the leg on the left hand side. The load at a given point along the arc produces a bending moment (Marti, 2012). The load is distributed between the two arc ends as shown in the diagram below. Figure: Load is distribute between the two arc ends The resulting bending moment is shown in the diagram below. Figure: Bending moment diagram 2.3 Fixed Arch 3.0 Conclusion This experiment has shown a relationship between experimental values of the forces in the truss members and the values obtained from theory. Fixed arches and two-pinned arches are statically indeterminate structures. The horizontal reaction increases with increase in the distance from left, and the maximum thrust occurs when the load is halve way between the two ends of the arch. The advantage of using indeterminate structures is that they are safe and have better conservation of the integrity of structures. These types of structures have high overall structural stiffness, hence the displacement due to the loading is small and the structures stay closer to their original shape, which makes them safer to use. 4.0 Works Cited Marti, P., (2012). Theory of structures: fundamentals, framed, structures, plates and shells. Berlin: Ernst, Wilhelm & Sohn. Raz, S. A. (2001). Analytical methods in structural engineering. New Delhi: New Age International (P) Ltd., Publishers. Sandaker B. N., Eggen A. P., & Cruvellier M. R., (2013). The Structural Basis of Architecture, Routledge 5.0 Group Work Contribution Group 59: Contribution Chart Name Student ID Sections Covered Contribution Manpreet Singh Section 2.1, Outline & Editing 33.33% Section 2.2, 3.0 and Abstract 33.33% Dhruv Patel Section 2.3, and Section 1.0 33.33% Read More