3/24/2015

List of Figures and Tables Figure 1: Steel Shelf and Element Cross Section ........................... .................................... 2 Figure 2: Simplified structure ............................................................................................. 3 Figure 3: Preference ............................................................................................................ 4 Figure 4: Element type ................................................... ..................................................... 4 Figure 5: Cross-sectional area (0.125 in2) ............................................... ........................... 5 Figure 6: Material Props ..................................................................................................... 5 Figure 7: Keypoints............................................................................................................. 6 Figure 8: Lines .................................................................................................................... 6 Figure 9: Number of elements ............................................................................................ 7 Figure 10: Mesh .................................................................................................................. 7 Figure 11: Boundary Conditions and Forces ...................................................................... 8 Figure 12: Deformed (+ un-deformed) plot ........................................................................ 9 Figure 13: Stress ............................................................................................................... 10 Figure 14: Support reactions .................................................. ........................................... 11 Figure 15: Deformed (+ un-deformed) plot using a composite tube ................................ 12 Figure 16: Stress using a composite tube ................................................. ......................... 13 Figure 17: Support reactions using a composite tu be ................................................. ...... 14

Table 1: Given data ............................................................................................................. 3

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Introduction In this report the maximum stress and deflection of the support structure shown below is analyzed using ANSYS APDL.

Figure 1: Steel Shelf and Element Cross Section

To simplify the problem a 2-D model of the pin-jointed structure that supports each joint of the shelf is considered. This is possible because o f the symmetry of the shelf, therfore, saving time required by ANSYS to compute the results. Furthermore, twisting of the structure is neglected by using truss element for simplicity of the problem.

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Figure 2: Simplified structure

The force of 1200 lbf acting on the middle of the shelf is divided by the four corners to give 300 lbf at each. Table 1: Given data

Steel

Cross Sectional Area

Young’s Modulus

Possoin’s

(in^2)

(Psi)

ratio

0.125

30E6

0.27

0.35

1.2E7

0.3

Composite tube

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Procedure

Click Preference and then select Structural

Figure 3: Preference

Define the Element type from Preprocessor and select link

Figure 4: Element type

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Click on Real Constants and add the cross-sectional area

Figure 5: Cross-sectional area (0.125 in2)

From Material Props click on Material Models and add the properties (Young’s modulus and the Poisson’s ratio)

Figure 6: Material Props

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From Modelling select Create and click Keypoints and then In Active CS

Add the coordinate and click on Apply

Figure 7: Keypoints

From Modelling select Create and click Lines, Lines and then In Active Coord

Figure 8: Lines

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From Meshing , Mesh Attributes , Size Cntrls, Lines select All Lines and type 1 in number of elements

Figure 9: Number of elements

From Meshing , Mesh, Lines select All Lines and click OK

Figure 10: Mesh

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From Solution , Apply, Structural , Displacement , click on On Nodes and select UX and UY to add the Boundary Conditions on nodes 1 and 3 From Solution , Apply, Structural , Force, add the force on nodes 1 and 2

Figure 11: Boundary Conditions and Forces

For the 5th part the material is assigned by going to Meshing , Mesh Attributes , Picked Lines and select the lines and set the material.

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Results

Figure 12: Deformed (+ un-deformed) plot

1. From the above figure it can be seen that the maximum deformation is at node 2. The value of the deformation is 0.00867 in. This is a valid result since all the other nodes are constrained, it makes sense that the node 2 will deform.

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Figure 13: Stress

2. From the above figure it can be seen that the maximum stress is on element 2 and the value is 4000 psi. This is because of the diagonal setting of the truss and since it has no fixed ends. While the minimum stress is on element 1 and the v alue is 3200 psi.

3. The yield strength of commonly used steel is 280 – 1600 MPa, but by converting the max stress of 4000 psi it turns out to be 27.58 MPa. This shows that it is much smaller than the yield strength; therefore, the steel shelf is safe.

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Figure 14: Support reactions

4. h

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Figure 15: Deformed (+ un-deformed) plot using a composite tube

5. From the above figure it can be seen that the maximum deformation is at node 2 again. The value of the deformation is 0.008091 in. This is a valid result since all the other nodes are constrained, it make sense that the node 2 will deform.

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Figure 16: Stress using a composite tube

From the above figure it can be seen that the maximum stress is on element 2 and the value is 1428.57 psi. This is because of the diagonal setting of the truss and since it has no fixed ends. This value is much smaller than that of steel trusses. Therefore, by adding a composite tube for element 2 we successfully reduced the stress acting in the steel shelf. While the minimum stress is still on element 1 and the value is -3200 psi. An important thing here that can be seen is that the min stress is larger than the max stress but it is compressive due to the negative sign. The yield strength of commonly used steel is 280 – 1600 MPa, but by converting the max stress of 1428.57 psi it turns out to be 9.85 MPa. This shows that it is much smaller than the yield strength, even smaller than the only steel truss; therefore, the steel shelf is much safer when the composite tube is used.

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Figure 17: Support reactions using a composite tube

The support reactions remain the same since the forces acting on the elements are the same.

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Conclusion In this project we learned to analyze the displacement and stresses on a 2-D truss structure. In the 1st part the truss is made using all steel elements. The maximum stress is found to be 4000 psi and the max displacement is 0.00867 in. In the 2nd part the element 2 material is changed to composite tube and the other elements were kept as steel. This resulted in a significantly lower max stress, 1428.57 psi. Th e max displacement did not change much, it decreased very slightly. When compared to the yield strength both the truss models were found to be safe since the values of the max stresses are much lower than the yield strength. The use of ANSYS APDL has made it much easier to solve FEM problems such as this project and others. It is also very helpful to be able to apply the analytical procedure in this program due to its method of input, which is very similar to that of how we solve by hand.

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