Measuring Forces in Truss Members - Lab Report Example

Measuring Forces in Truss Members Using Strain Gages In the laboratory project, allowable load that can beapplied on each of trusses by considering the appropriate safety and failure modes are determined. This is done theoretically to determine causes of failure in the pin connections and theoretically calculating the yield that causes yielding of stressed members. Also, the critically buckling load for the trusses is calculated theoretically. The laboratory project’s main objective was to become familiar with the operation and application of electrical resistance wire strain gages to measure stresses in simple structures and to experimentally determine the internal forces in simple structures, and to compare those results with values obtained analytically. Introduction Trusses used widely in most construction projects. These include in buildings such things as scaffoldings, bridges towers, roofs to name but a few. Trusses can be defined as structural elements that are long and assembled by connecting them at the end. The basic structure of a truss is shown in figure 1 below; Figure 1: Basic Structure of a Truss with Forces acting on the members. The use of trusses is mainly to provide stiffness to structures, For instance in bridges, trusses are used to protect suspension bridges against buckling by providing stiffness. The use of trusses in construction process is at times faced with problems of determining the failure modes of the specific structure and determination of appropriate factors of safety. This can be achieved theoretically by calculating the amount of load that is capable of causing failure in the pin connections, theoretically calculating the load to cause yielding on members that are severely stressed and theoretically calculating the critical buckling load. In this laboratory project, the allowable load that can be applied to each of the trusses is determined. Also, the forces in each of the members of the truss are determined. Basically, the ultimate goal of the lab project is measuring Forces in Truss Members Using Strain Gages Background As stated above, trusses are mainly used for stiffening structures. This implies that the truss is subjected to various forces that may be tension, compressional or both. A truss is made up of members joined together at the edges. Since the trusses are subjected to forces by the structures they support and the truss is made of members, then it implies that each member is subjected to 2 forces i.e. each member is a two force member. In the use of trusses, the weight is not considered since they are assumed to possess negligible weight as compared to the load imposed on them. Trusses exist in various types that include simple trusses, and complex trusses. Trusses are subjected to compression, tensional or both tensional and compression force due to the load imposed on them. Since trusses are predominantly made of steel, they respond to the forces by either stretching or reducing in size. The stretching and the reduction in size can be utilized to determine the amount of strain a member of the truss is exposed to. This can be measured using various tools specifically designed to perform such tasks. One of the commonly used tool in measuring the stain in the truss is the strain gauge. Basically, a strain gauge harnesses the stretching of a member and converts it to form that can be used to determine the amount of force the member is experiencing. A strain gauge is designed such that its electrical resistance is directly proportional to the amount of strain experienced by a member of a truss. There are various methods of analysing trusses after the determination of the forces acting on it using strain gauges. One of the methods in analysing trusses is the use of methods of joints. Basically in this method, free body diagrams of the joints are taken and then solved using equilibrium relationships. These process can be done easily by diving it into two parts, determination of the external reactions and determination of internal forces on each o the member of the truss. The force be either compressional or tensional. In determining the external forces, newton law are used where by F = Ma, But since there is no acceleration in the trusses, then all the forces in the truss must sum to zero. Both the forces in the vertical direction must sum to zero, as also, forces in the horizontal dimension must sum to zero. The strain in a member can also be calculated using Hooke’s law. To determine the axial load on the member, the determined strain us used using the relationship, pressure is given by the strain times the area. Methods and Procedures Material used in the experiment were triangular pinned trusses, dial callipers, digital strain equipment, Tinius-Olsen Testing Machine, Procedure The initial stage of the practical was the determination of the load that can cause failure in pin connections, determination of yielding load on members and calculating of the buckling load. All these were determined theoretically using equations highlighted below. Area : Total allowable axial load Critical bending force ( Minimum moment of Inertia, Pexp Absolute Error Percentage Error * 100% At the above determination, the cross sectional dimensions, and length of each pin were carefully measured and recorded. The strain gauge was then checked for broken leads, in cases the broken leads were identified, they were repaired. A truss was then setup in the Tinius – Olsen Testing machine and in the process, all the reactions and loads were made sure to be applied at truss joints making sure they do not interfere with the members. The strain gauge was then connected to the balance and the strain indicator, and all the gauges calibrated using the provided manual. Five loads were then applied on the stress. The application of the load was such that it was started with the smallest load that gives a reasonable strain reading. To find the maximum load to be applied on the truss, the failure load was divided with a factor of safety. The loads were increased in intervals one. Each load increments was done such that it was approximately equally spaced between the minimum and the maximum reading i.e. between the first and the fifth reading. The applied load together with corresponding strain reading for all the members was recorded and stored. Results and Calculations Table 1 30 – 60 – 90 truss Strain = x10^6 P[lb] AB Member AC member EC member F B AV F B AVE F B Av 250 -32 +31 -0.5 -48 -30 -39 20 37 28.5 500 -32 +33 0.5 -91 -31 -61 15 39 27 750 +5 -18 -6.5 -130 -67 -98.5 -15 4 -5.5 1000 +14 -12 1 -172 -92 -132 -12 7 -2.5 1250 +14 -11 1.5 -216 +114 -51 -11 7 -2 Table 2 60-60-60 truss Strain = x10^6 P[lb] AB Member AC member EC member F B AV F B AVE F B Av 250 18 -8 5 -39 -4 -21.5 -123 84 -19.5 500 33 -11 11 -61 -22 -41.5 -188 113 -37.5 750 41 -9 16 -83 -43 -63 -259 133 -63 1000 56 -9 23.5 -100 -72 -86 -289 132 -78.5 1250 72 -12 30 -118 -96 -107 -304 107 -98.5 Table 3 45– 45– 90 truss Strain = x10^6 P[lb] AB Member AC member EC member F B AV F B AVE F B Av 250 67 -18 24.5 -63 13 -25 -68 17 -25.5 500 103 -16 43.5 -120 25 -47.5 -115 17 -49 750 145 -11 67 -181 40 -70.5 -152 5 -73.5 1000 181 -5 88 -242 56 -93 -180 -15 -97.5 1250 215 -2 106.5 -300 67 -116.5 -204 -38 -121 Where: F is the experimental force Is the stress A is the cross-section area of the member (1”by ¼ ”) The equation below shows the absolute error equation that was used in comparison of results. Absolute error = [Experimental value – Theoretical value ] (Equation 3) The percentage error will be given by equation 4 shown below: Relative error = x 100 (Equation 4) Results and Calculations The table below shows the calculation for member AB (30-60-90 truss). Table 1: Member AB P(lb) Actual average(psi) Stress(lb/in2) Experimental force(lb) Absolute error(lb) Relative error (%) 250 500000 1.45E +13 3.625E +12 3.6255E +12 NA 500 2000000 5.8E +13 1.45E +13 1.45E +13 NA 750 3500000 1.015E +14 2.5375E +13 2.5375E +13 NA 1000 5000000 1.45E +14 3.625E +13 3.625E +13 NA 1250 6500000 1.885E +14 4.7125E +13 4.7125E +13 NA The table shows calculations from the experiment for each of the loads applied on member AB. From the absolute error, it is indicated that the experimental results widely varied from the analytical calculations. Both the experimental and analytical results show that member AB experienced tensional force, because of the positive values of both experimental and analytical results. The table below shows the calculation for member AC (30-60-90 truss). Table 2: Member AC P(lb) Actual average(psi) Stress(lb/in2) Experimental force(lb) Absolute error(lb) Relative error (%) 250 -32000000 -9.28E +14 -2.32E +14 2.32E +14 9.28E +13 500 -63500000 -1.842E +15 -4.60375E +14 4.60375E +14 9.2075E +13 750 -94500000 -2.741E +15 -6.85125E +14 6.85125E +14 9.135E +13 1000 -1.27E +08 -3.669E +15 -9.17125E +14 9.17125E +14 9.17125E +13 1250 -1.59E +08 -4.597 +15 -1.14913E +14 1.14913E +14 9.193E +13 The table shows calculations from the experiment for each of the loads applied on member AC. From the absolute error, it is indicated that the experimental results widely varied from the analytical calculations. The percentage error indicates that there is a significant difference between experimental results and analytical calculations. Both the experimental and analytical results show that member AC experienced compression force, because of the negative values of both experimental and analytical results. The table below shows the calculation for member BC (30-60-90 truss). Table 3: Member BC P(lb) Actual average(psi) Stress(lb/in2) Experimental force(lb) Absolute error(lb) Relative error (%) 250 -4000000 -1.16E +14 -2.9E +13 2.9E +13 N/A 500 -5500000 -1.595E +14 -3.9875E +13 3.9875E +13 N/A 750 -7000000 -2.03E +14 -5.075E +13 5.075E +13 N/A 1000 -8500000 -2.465E +14 -6.1625E +13 6.1625E +13 N/A 1250 -1050000 -3.045+14 -7.6125E +13 7.6125E +13 N/A The table shows calculations from the experiment for each of the loads applied on member BC. From the absolute error, it is indicated that the experimental results widely varied from the analytical calculations. Both the experimental and analytical results show that member BC experienced compression force, because of the negative values of both experimental and analytical results. The table below shows the calculation for member AB (60-60-60 truss). Table 4: Member AB P(lb) Actual average(psi) Stress(lb/in2) Experimental force(lb) Absolute error(lb) Relative error (%) 250 70500000 2.0445E +15 5.11125E +14 5.11125E +14 7.07439E +14 500 65500000 1.8995E +15 4.7487E +14 4.7487E +14 3.28633E +14 750 10500000 3.045E +14 7.6125E +13 7.6125E +13 3.51211E +13 1000 9500000 2.755E +14 6.8875E +13 6.8875E +13 2.38322E +13 1250 -3500000 -1.015E+14 -2.5375E +13 2.5375E +13 7.2422E +12 The table shows calculations from the experiment for each of the loads applied on member AB. From the absolute error, it is indicated that the experimental results widely varied from the analytical calculations. The percentage error indicates that there is a significant difference between experimental results and analytical calculations. Both the experimental and analytical results show that member AB experienced tensional force, because of the positive values of both experimental and analytical results. The table below shows the calculation for member AC (60-60-60 truss). Table 5: Member AC P(lb) Actual average(psi) Stress(lb/in2) Experimental force(lb) Absolute error(lb) Relative error (%) 250 -19500000 -5.655E +14 -1.41375E +14 1.41375E +14 9.80069E +13 500 -39000000 -1.131E +15 -2.8275E +14 2.8275E +14 9.80069E +13 750 -57500000 -1.668E +15 -4.16875E +14 4.16875E +14 9.63316E +13 1000 -73000000 -2.117E +15 -5.2925E +14 5.2925E +14 9.17244E +13 1250 -91000000 -2.639E+15 -6.5975E +14 6.5975E +14 9.14731E +13 The table shows calculations from the experiment for each of the loads applied on member AC. From the absolute error, it is indicated that the experimental results widely varied from the analytical calculations. The percentage error indicates that there is a significant difference between experimental results and analytical calculations. Both the experimental and analytical results show that member AC experienced compression force, because of the negative values of both experimental and analytical results. The table below shows the calculation for member BC (60-60-60 truss). Table 6: Member BC P(lb) Actual average(psi) Stress(lb/in2) Experimental force(lb) Absolute error(lb) Relative error (%) 250 -21000000 -6.09E +14 -1.5225E +14 1.5225E +14 1.05546E +14 500 -40000000 -1.16E +15 -2.9E +14 2.9E +14 1.0052E +14 750 -61000000 -1.769E +15 -4.4225E +14 4.4225E +14 1.02195E +14 1000 -82500000 -2.393E +15 -5.98125E +14 5.98125E +14 1.03661E +14 1250 -103500000 -3.002E+15 -7.50375E +14 7.50375E +14 1.04038E +14 The table shows calculations from the experiment for each of the loads applied on member BC. From the absolute error, it is indicated that the experimental results widely varied from the analytical calculations. The percentage error indicates that there is a significant difference between experimental results and analytical calculations. Both the experimental and analytical results show that member BC experienced compression force, because of the negative values of both experimental and analytical results. The table below shows the calculation for member AB (45-45-90 truss). Table 7: Member AB P(lb) Actual average(psi) Stress(lb/in2) Experimental force(lb) Absolute error(lb) Relative error (%) 250 19000000 5.51E +14 1.3775E +14 1.3775E +14 1.102E +14 500 36000000 1.044E +15 2.61E +14 2.61E +14 1.044E +14 750 54000000 1.566E +15 3.915E +14 3.915E +14 1.044E +14 1000 71500000 2.0735E +15 5.18375E +14 5.18375E +14 1.0367E +14 1250 89500000 2.5955E+15 6.48875E +14 6.48875E +14 1.0382E +14 The table shows calculations from the experiment for each of the loads applied on member AB. From the absolute error, it is indicated that the experimental results widely varied from the analytical calculations. The percentage error indicates that there is a significant difference between experimental results and analytical calculations. Both the experimental and analytical results show that member AB experienced tensional force, because of the positive values of both experimental and analytical results. Conclusion The main objective was to experimentally determine the internal forces experienced in a simple structure, and to do a comparison of the values obtained with analytical values. Three different trusses were tested by five different loads to achieve this objective. The same loads were applied on each member and the strain in each member was obtained, and compared with the analytic values. References Davis, Harmer Elmer, George Earl Troxell and George F. W. Hauck. The testing of engineering materials. McGraw-Hill Higher Education, 1982. Print. Read More