Indeterminate and Statically Determinate Cantilever Structures - Lab Report Example

Name: Instructor: Institution: Date: Contents 1.0Introduction 2 1.1Experiment Acknowledgement 2 1.2Experiment Background 3 1.3Aim 3 2.0Experimental Data 3 2.1Statically Determinate Truss 3 1.1.1Data recorded 3 1.1.2Data Analysis 6 2.2Statically Indeterminate Truss 8 1.1.3Data Recorded 8 1.1.4Data Analysis 10 3.0Discussion 12 1.0 Introduction The lab repot is documentation and analysis of the experiment related to cantilever truss structure with a pin jointed frame. The experiment analyzes and compares the experimental data to the theoretical data that has been obtained though calculation. The experiment is divided into two pats, first, it analyses the data of a statically indeterminate structure and then it analyzes a statically determinate structure with an additional redundant member. 1.1 Experiment Acknowledgement STR17 truss Experiment student guide was the main reference material and guide during the experimental process. It gives a detailed description of the experiment, list of the equipment needed and the procedure for conducting the experiment. 1.2 Experiment Background The experiment is in the form of a framework assembled into the test frame. The framework is made of steel rods joined into joint bosses or pieces. The redundant member can disassembled by undoing the nets that holds them together. The redundant can be either include or exclude in the framework depending on the stage of the experiment. The first stage is the frame of the statically indeterminate structure which does not include the redundant member and the second part is the frame of the statically determinate structure where the redundant member is included. The framework has two supports holding it , a pinned and a roller support. The pinned support allows pivoting while the roller allows linear translation. Electronic load cell are applied on the framework to represent the loading and during the experimental process the digital forces display measures the amount of force they produce. A digital indicator measures the deflection of the framework. 1.3 Aim The aim of the experiment was to give a demonstration and principles that are used to analyze and examine statically indeterminate and statically determinate cantilever structures. The experiment was divided into two; the first part examined the cantilever truss when it is statically determinate meaning that the redundant member is not engaged which will enabled the group analyze the frame using the pin joint theory. The second part tested and examined the frame when the redundant member is engaged meaning that the structure was statically indeterminate. 2.0 Experimental Data 2.1 Statically Determinate Truss 1.1.1 Data recorded The first part examined the cantilever truss when it is statically determinate meaning that the redundant member is not engaged which will enabled the group analyze the frame using the pin joint theory. The loading was applied with intervals of 50N from 0N to 250N. The strain readings are produced from each loading and recorded in table two. The true strain readings are obtained by subtracting the initial strain readings and they were then recorded on table two. Table 3 shows the force in the members, which is obtained by multiplying the true strain readings with the young’s modules of elasticity and the area of the steel rod. Load Displacement Experimental Strain 1 Experimental Strain 2 Experimental Strain 3 Experimental Strain 4 Experimental Strain 5 Experimental Strain 6 Experimental Strain 7 Experimental Strain 8 Rod Diameter Material N mm me me me me me me me me mm GPa 2 0.001 -0.4 0.1 -0.1 -0.1 0.1 --- 0.1 -0.2 6.00 210.0 47 0.020 6.0 -6.3 -2.8 0.0 0.2 --- 8.7 8.2 6.00 210.0 99 0.035 18.4 -18.4 -14.7 -15.0 0.5 --- 26.1 24.6 6.00 210.0 148 0.051 28.5 -28.8 -24.8 -36.0 0.8 --- 40.5 38.9 6.00 210.0 200 0.061 38.3 -38.0 -34.5 -54.9 1.0 --- 53.9 51.7 6.00 210.0 251 0.067 46.9 -46.1 -42.4 -71.6 0.7 --- 65.9 63.0 6.00 210.0 Load Displacement Experimental Strain 1 Experimental Strain 2 Experimental Strain 3 Experimental Strain 4 Experimental Strain 5 Experimental Strain 6 Experimental Strain 7 Experimental Strain 8 Rod Diameter Material N mm me me me me me me me me mm GPa 2 0.001 -2.5 0.0 -0.4 -0.5 0.3 --- 0.2 -0.9 6.00 210.0 47 0.020 35.7 -37.4 -16.8 0.3 0.9 --- 51.8 48.7 6.00 210.0 99 0.035 109.4 -109.0 -87.3 -89.1 2.7 --- 154.8 146.1 6.00 210.0 148 0.051 169.1 -171.1 -147.3 -213.5 4.6 --- 240.7 231.2 6.00 210.0 200 0.061 227.7 -225.7 -205.2 -325.6 4.9 --- 320.9 306.9 6.00 210.0 251 0.067 278.5 -273.5 -251.5 -424.9 4.1 --- 391.2 374.3 6.00 210.0 Load Displacement Experimental force 1 Experimental force 2 Experimental force 3 Experimental force 4 Experimental force 5 Experimental force 6 Experimental force 7 Experimental force 8 Rod Diameter Material N mm me me me me me me me me mm GPa 2 0.001 -14.8 0.0 -2.4 -2.97 1.762 --- 1.2 -5.34 6.00 210.0 47 0.020 212.4 -222.7 -592,8 1.78 5.3 --- 308.2 289.2 6.00 210.0 99 0.035 650.9 -1130.5 -518.6 -529.5 16.0 --- 919.51 867.8 6.00 210.0 148 0.051 1006.1 -1018 -874.96 -1265.2 27.3 --- 1423.2 1373.3 6.00 210.0 200 0.061 1352.5 -1340.6 -1218.8 -1934.1 29.1 --- 1906.1 1822.98 6.00 210.0 251 0.067 1654.2 -1621 -1493.91 -2523.9 24.1 --- 2323.7 2223.34 6.00 210.0 1.1.2 Data Analysis Before the data analysis was conducted the group drew two graphs comparing the true strains to the experimental strain of two members form the truss as shown in graph one and two. The members were member to and member four. From the graphs we can see that there is a difference between the recorded strains and the true strain. Graph three shows the deflection that the cantilevers truss when the loading is applied. Graph 1: of load vs. strain and true strain readings Graph 2: A graph of load vs. strain and true strain Graph 3:A graph of load vs. Deflection The table below shows a comparison of the theoretical forces and the experimental forces. Form the members we can see that the forces are either positive r negative with the positive forces meaning that the member is in tension while a negative showing that the member is compression. The experimental readings of member five is close to zero given the fact that all the joints in the member are in equilibrium and the forces equal to zero Member Experimental force Theoretical force State 1 1654.2 250 Tension 2 -1621 -250 Compression 3 -1493.91 -250 Compression 4 -2523.9 -500 Compression 5 24.1 0 Zero force 7 2323.7 354 Tension 8 2223.34 354 Tension 2.2 Statically Indeterminate Truss 1.1.3 Data Recorded The second part of the experiment tested and examined the cantilever frame when the redundant member is engaged meaning that the structure was statically. The loading was applied with intervals of 50N from 0N to 250N. The strain readings are produced from each loading and recorded in table two. The true strain readings are obtained by subtracting the intial strain readings and they were then recorded on table two. Table 6 shows the force in the members, which is obtained by multiplying the true strain readings with the young’s modules of elasticity and the area of the steel rod. Member Strains (µɛ) Load Displacement Experimental Strain 1 Experimental Strain 2 Experimental Strain 3 Experimental Strain 4 Experimental Strain 5 Experimental Strain 6 Experimental Strain 7 Experimental Strain 8 Rod Diameter Material N mm me me me me me me me me mm GPa 1 -0.001 0.2 -0.3 0.0 0.0 -0.1 0.3 -0.1 0.0 6.00 210.0 51 -0.003 17.7 -6.8 0.2 0.2 5.6 -7.1 16.8 9.0 6.00 210.0 100 0.019 29.2 -10.6 -5.3 0.2 9.1 -12.2 28.0 14.1 6.00 210.0 149 0.029 45.0 -16.0 -16.0 0.3 14.3 -19.6 42.9 21.4 6.00 210.0 200 0.036 62.1 -21.6 -27.9 0.6 20.3 -27.6 59.5 29.8 6.00 210.0 250 0.043 75.8 -26.1 -36.4 -10.4 24.3 -33.5 72.2 35.9 6.00 210.0 Load Displacement Experimental Strain 1 Experimental Strain 2 Experimental Strain 3 Experimental Strain 4 Experimental Strain 5 Experimental Strain 6 Experimental Strain 7 Experimental Strain 8 Rod Diameter Material N mm me me me me me me me me mm GPa 1 -0.001 1.2 -1.5 -0.1 -0.1 -1.2 2.1 -1.3 -0.6 6.00 210.0 51 -0.003 105.3 -39.8 1.4 1.1 33.3 -42.8 101.1 54.0 6.00 210.0 100 0.019 174.0 -63.4 -31.4 1.4 53.8 -72.2 165.3 84.5 6.00 210.0 149 0.029 267.1 -95.3 -95.3 2.0 84.8 -116.6 254.5 126.8 6.00 210.0 200 0.036 368.5 -128.0 -165.4 3.8 120.3 -163.8 353.4 176.7 6.00 210.0 250 0.043 448.8 -155.3 -215.8 -63.0 144.7 -199.6 428.3 213.2 6.00 210.0 Load Displacement Experimental force 1 Experimental force 2 Experimental force 3 Experimental force 4 Experimental force 5 Experimental force 6 Experimental force 7 Experimental force 8 Rod Diameter Material N mm me me me me me me me me mm GPa 1 -0.001 7.1 -8.61 -0.59 -0.594 -7.12 12.47 -7.722 -3.56 6.00 210.0 51 -0.003 625.5 -236.4 8.316 6.53 197.8 -254.23 580.3 320.7 6.00 210.0 100 0.019 873.2 -376.59 -186.51 8.31 319.57 -428.86 981.8 501.3 6.00 210.0 149 0.029 1586.5 -566.1 -566.1 11.33 503.7 -692.6 1511.1 753.2 6.00 210.0 200 0.036 2115.2 -760 -982.47 22.57 714.58 -972.9 2099.19 1049.59 6.00 210.0 250 0.043 2665.8 -155.3 -215.8 -374.2 144.7 -1185.6 428.3 213.2 6.00 210.0 1.1.4 Data Analysis Before the data analysis was conducted the group drew two graphs comparing the true strains to the experimental strain of two members form the truss as shown in graph one and two. The members were member to and member four. From the graphs we can see that there is a difference between the recorded strains and the true strain. Graph three shows the deflection that the cantilevers truss when the loading is applied. Graph 5: A graph of load vs. strain and true strain Graph 7: A graph of load vs. strain and true strain Graph 8: of load vs. Deflection Member Experimental force Theoretical force State 1 2665.8 375 Tension 2 -155.3 -125 Compression 3 -215.8 -250 Compression 4 -374.2 -375 Compression 5 144.7 125 Tension 6 -1185.6 -177 Compression 7 428.3 354 Tension 8 213.2 177 Tension 3.0 Discussion The table displays the comparison of the experimental forces obtained in the two parts of the experiment; the fist is the statically determinate while the second is the statically indeterminate .The graph below is a comparison of the displacements from the two parts of the experiment; the fist is the statically determinate while the second is the statically. Although a truss can function without the need of the redundant member the graph and table below shows the importance and the benefits of having it in the frame. The loading in the first part is less than the loading in the second part meaning the second part takes a longer time before deflection occurs. The graph cleanly shows that the second part of the experiment has a smaller deflection compared to the first part of the experiment. Member Experimental 1 (N) Experimental 2 (N) 1 1654.2 2665.8 2 -1621 -155.3 3 -1493.91 -215.8 4 -2523.9 -374.2 5 24.1 144.7 6 2323.7 -1185.6 7 2223.34 428.3 8 1654.2 213.2 Graph 3:A graph of load vs. Deflection Read More

Load Displacement Experimental Strain 1 Experimental Strain 2 Experimental Strain 3 Experimental Strain 4 Experimental Strain 5 Experimental Strain 6 Experimental Strain 7 Experimental Strain 8 Rod Diameter Material N mm me me me me me me me me mm GPa 2 0.001 -0.4 0.1 -0.1 -0.1 0.1 --- 0.1 -0.2 6.00 210.0 47 0.020 6.0 -6.3 -2.8 0.0 0.2 --- 8.7 8.2 6.00 210.0 99 0.035 18.4 -18.4 -14.7 -15.0 0.5 --- 26.1 24.6 6.00 210.0 148 0.051 28.5 -28.8 -24.8 -36.0 0.8 --- 40.5 38.9 6.00 210.0 200 0.061 38.3 -38.0 -34.5 -54.9 1.0 --- 53.9 51.7 6.00 210.0 251 0.067 46.9 -46.1 -42.4 -71.6 0.7 --- 65.9 63.0 6.00 210.0 Load Displacement Experimental Strain 1 Experimental Strain 2 Experimental Strain 3 Experimental Strain 4 Experimental Strain 5 Experimental Strain 6 Experimental Strain 7 Experimental Strain 8 Rod Diameter Material N mm me me me me me me me me mm GPa 2 0.001 -2.5 0.0 -0.4 -0.5 0.3 --- 0.2 -0.9 6.00 210.0 47 0.020 35.7 -37.4 -16.8 0.3 0.9 --- 51.8 48.7 6.00 210.0 99 0.035 109.4 -109.0 -87.3 -89.1 2.7 --- 154.8 146.1 6.00 210.0 148 0.051 169.1 -171.1 -147.3 -213.5 4.6 --- 240.7 231.2 6.00 210.0 200 0.061 227.7 -225.7 -205.2 -325.6 4.9 --- 320.9 306.9 6.00 210.0 251 0.067 278.5 -273.5 -251.5 -424.9 4.1 --- 391.2 374.3 6.00 210.0 Load Displacement Experimental force 1 Experimental force 2 Experimental force 3 Experimental force 4 Experimental force 5 Experimental force 6 Experimental force 7 Experimental force 8 Rod Diameter Material N mm me me me me me me me me mm GPa 2 0.001 -14.8 0.0 -2.4 -2.97 1.762 --- 1.2 -5.34 6.00 210.0 47 0.020 212.4 -222.

7 -592,8 1.78 5.3 --- 308.2 289.2 6.00 210.0 99 0.035 650.9 -1130.5 -518.6 -529.5 16.0 --- 919.51 867.8 6.00 210.0 148 0.051 1006.1 -1018 -874.96 -1265.2 27.3 --- 1423.2 1373.3 6.00 210.0 200 0.061 1352.5 -1340.6 -1218.8 -1934.1 29.1 --- 1906.1 1822.98 6.00 210.0 251 0.067 1654.2 -1621 -1493.91 -2523.9 24.1 --- 2323.7 2223.34 6.00 210.0 1.1.2 Data Analysis Before the data analysis was conducted the group drew two graphs comparing the true strains to the experimental strain of two members form the truss as shown in graph one and two.

The members were member to and member four. From the graphs we can see that there is a difference between the recorded strains and the true strain. Graph three shows the deflection that the cantilevers truss when the loading is applied. Graph 1: of load vs. strain and true strain readings Graph 2: A graph of load vs. strain and true strain Graph 3:A graph of load vs. Deflection The table below shows a comparison of the theoretical forces and the experimental forces. Form the members we can see that the forces are either positive r negative with the positive forces meaning that the member is in tension while a negative showing that the member is compression.

The experimental readings of member five is close to zero given the fact that all the joints in the member are in equilibrium and the forces equal to zero Member Experimental force Theoretical force State 1 1654.2 250 Tension 2 -1621 -250 Compression 3 -1493.91 -250 Compression 4 -2523.9 -500 Compression 5 24.1 0 Zero force 7 2323.7 354 Tension 8 2223.34 354 Tension 2.2 Statically Indeterminate Truss 1.1.3 Data Recorded The second part of the experiment tested and examined the cantilever frame when the redundant member is engaged meaning that the structure was statically.

The loading was applied with intervals of 50N from 0N to 250N. The strain readings are produced from each loading and recorded in table two. The true strain readings are obtained by subtracting the intial strain readings and they were then recorded on table two. Table 6 shows the force in the members, which is obtained by multiplying the true strain readings with the young’s modules of elasticity and the area of the steel rod. Member Strains (µɛ) Load Displacement Experimental Strain 1 Experimental Strain 2 Experimental Strain 3 Experimental Strain 4 Experimental Strain 5 Experimental Strain 6 Experimental Strain 7 Experimental Strain 8 Rod Diameter Material N mm me me me me me me me me mm GPa 1 -0.001 0.2 -0.3 0.0 0.0 -0.1 0.3 -0.1 0.0 6.00 210.0 51 -0.003 17.7 -6.8 0.2 0.2 5.6 -7.1 16.8 9.0 6.00 210.0 100 0.019 29.2 -10.6 -5.3 0.2 9.1 -12.2 28.0 14.1 6.00 210.0 149 0.029 45.0 -16.0 -16.0 0.3 14.3 -19.6 42.9 21.4 6.00 210.0 200 0.036 62.1 -21.6 -27.9 0.6 20.3 -27.6 59.5 29.8 6.00 210.0 250 0.043 75.8 -26.1 -36.4 -10.4 24.3 -33.5 72.2 35.9 6.00 210.

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