lab-assignment-z5260160

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University of New South Wales *

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2303

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Mechanical Engineering

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Jan 9, 2024

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pdf

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z5260160 Part 1.1: Calculate theoretical axial forces of the Warren and Roof trusses 1. Created the reference system for both trusses. For both trusses, I went from left to right. There are 0 DoF at the pin on the left and 1 horizontal DoF on the roller at the right. All the other joints have 2 DoF. Both trusses have 11 DoF. Warren: Roof:

z5260160 2. The stiffness matrices for each member can be determined on MATLAB using the following function with inputs: lambda x, lambda y, member length and the product of elastic modulus and cross-sectional area. Warren Truss: Stiffness matrices for e.g. member 1,2 of warren truss: Roof Truss:

z5260160 Stiffness matrices for e.g. member 1,2 of roof truss: 3. Using the stiffness matrices, the global matrices for both trusses can be found using MATLAB. Global matrix for warren:

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z5260160 Global matrix for roof: 4. The load vector for both trusses is the same due to the -300 N force acting on the 8 th degree of freedom. 5. The internal force matrices for both can be determined using the code:

z5260160 Internal force matrices for e.g. member 1,2 of warren truss: Internal force matrices for e.g. member 1,2 of roof truss:

z5260160 The theoretical axial forces can be calculated by hand using the following method: E.g. member 11 of warren truss. 𝑁 11 = − √ 200.00 2 + 115.4701 2 = −230.94 𝑁 = 230.94 𝑁(𝐶) Part 1.2: Determine the experimental axial forces of the Warren and Roof trusses. The experimental axial forces can be calculated from the given equation: 𝑁 = 𝐸𝐴𝜀 Where 𝐸 is the elastic modulus, 𝐴 is the cross-sectional area and 𝜀 is the measured strain multiplied by 10 6 .

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z5260160 Error is determined using the following equation: 𝐸𝑟𝑟?𝑟 = | 𝑇ℎ𝑒?𝑟𝑒𝑡𝑖𝑐𝑎? − 𝐸𝑥?𝑒𝑟𝑖?𝑒?𝑡𝑎? 𝐸𝑥?𝑒𝑟𝑖?𝑒?𝑡𝑎? | × 100 E.g. calculating the error for member 11 of the warren truss: 𝐸𝑟𝑟?𝑟 = | −230.94 − −264.38 −264.38 | × 100 = 12.65% Warren Truss Member Theoretical axial force (N) Experimental axial force (N) Error (%) 1 -115.47 -114.38 0.96 2 57.74 63.75 9.44 3 115.47 138.13 16.40 4 -115.47 -113.75 1.51 5 -115.47 -115.63 0.13 6 173.21 162.50 6.59 7 115.47 120.63 4.27 8 -230.94 -240.00 3.77 9 230.94 241.88 4.52 10 115.47 129.38 10.75 11 -230.94 -264.38 12.65

z5260160 Roof Truss Member Theoretical axial force (N) Experimental axial force (N) Error (%) 1 -200 -213.13 6.16 2 173.21 176.88 2.07 3 0 10.63 100 4 -200 -210 4.76 5 0 -3.13 100 6 173.21 173.13 0.05 7 346.41 361.25 4.11 8 -400 -421.5 3.03 9 0 16.25 100 10 346.41 339.38 2.07 11 -400 -417.5 4.19

z5260160 Part 1.3: Results discussion The experimental results were obtained in the lab by reading measurements from the strain gauges after applying the load. Then the experimental axial forces were calculated by multiplying the strain reading by the elastic modulus and cross-sectional area of the truss members. On the other hand, the theoretical results were calculated using the stiffness method. Most errors in the warren truss were within 10%. Most errors in the roof truss were within 5%. The results were quite accurate with the highest error of 16.40%, excluding 0 force members on the roof truss. Temperature may be one of the underlying factors towards the discrepancies as it can cause the truss members to expand when heated and contract when cooled which will affect the strain in the members. Friction in pin joints of the truss members may also have an affect on the strain readings when undergoing loading. The truss used in the demonstration may have small manufacturer defects like an uneven cross- sectional area which will affect the strain readings. The strain gauges may not be entirely accurate due to being faulty from wear and tear or unproperly calibrated. Furthermore, temperature may also affect the strain gauge. The loading mechanism may also be faulty due to wear and tear or unproper calibration which may cause a slightly heavier or lighter load which will have an affect on the strain readings.

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