Analysis

Analysis i: Stresses of the First Design

In this analysis, the primary information gathered was seeing if there was too much stress in the beams for the original design. Since the most it can handle was 1.1MPa According to the calculation, the most stress in the beams was 1.7 MPa and the least was 856.2Kpa as shown in figure 6. This is too much for the bridge to handle and was not a good design.

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Analysis ii: Stresses in the New Design

Analysis ii was seeing the stresses in the beams if the new design was too much. As shown in figure 7, the stresses in the beams reach to 490.5KPa and stress of at least 265.25KPa within the beams. With these being the stresses in the trusses, the new design is a good enough design.

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Analysis iii: Finding the length of the 45-degree truss.

In analysis iii, the main information was to find the length of the truss at 45 degrees. Since the angle of the trusses is going to be either 90 degrees and 45 degrees, the length of the trusses matters. As shown in figure 8, the length of the 45 degrees truss turns needs to be 159.1mm long the fit the design.

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Analysis iV: Finding the bending stress in the road.

In analysis 4, the main objective was to see how much stress the road was going to endure with the 20kg. As shown in appendixa4, a free body diagram was needed to see where the forces are. With this information, a shear-moment diagram can be made from this. According to the diagram, the maximum moment the road will experience is 22.07Nm. With this finding and using the bending stress formula, the stress that the road would experience is 132.4Mpa.

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Analysis V: Finding the length of the horizontal truss.

In analysis V, there is a horizontal truss that connects the two main structures of the bridge and helps with requirement 2. The same technique used in appendix analysis 3 is going to be used here. since the height of this section is 66mm and has a length of 112.5mm. The angle that was needed was a 19.6degree angle. After finding this and using sohcahtoa, the length of the truss needed to be 119.2mm long.

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Analysis Vi: Deflection of the bridge.

In analysis 6, the main goal was to see how much the bridge would deflect under that much load at point b. Which correlates to requirements 6 and 1 for this project. By making the bridge 60mm wide and 10mm thick the inertia that the bridge experience was 5x10^-8mm^4. With this and using the equation y = (-P(L^3)) / (48*E*I). the deflection of the bridge turns out to be 2.01mm. This is in the requirements that are stated in requirements 6 and 1.

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Analysis Vii: Buckling on the Truss

In analysis 7, the main goal was to see what force would cause the trusses to buckle. By assuming the trusses are pinned at both ends, it can be solved. Salving for the slenderness ratio, it was 35.51 and for centrally loaded columns is 270.5. With this, it is too short and the Johnson formula is needed. after realizing this and plugging in the values, the critical value to cause it to buckle is 99.2N.

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Analysis Viii: Angle needed for the Bridge

In analysis 8, the main goal is to see what angle the bridge needs to take so it can pass the 140mm raise requirement. Considering the middle section needs to be the required higher, using sohcahtoa could find this value. using this formula, the angle needed for the bridge is 38.5 degrees.

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Analysis iX: Length of the String

In analysis 9, the purpose was to find the length of the string for the lifting mechanism. The string is connected 112.5mm from the end of the bridge. Furthermore, the string is connected to a tower that is 240mm tall and 50 mm into the tower. Using this and the Pythagorean theorem, the hypotonus of the string is 405.6mm. This needs to be doubled and add 240mm of the string due to the location of the crank and two strings are being used. . So, a maximum of 1051.3mm of string could also be used.

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Analysis X: Force to Lift the Bridge

In analysis 10, the purpose of it was to find the minimum amount of force that is needed for the string to lift up the bridge. The weight of 85g was believed to be evenly distributed in the analysis. With this, the weight force on the bridge would be .8339N. Using this and a moment to find the force in the y direction, the force needed to lift the bridge can be found. After plugging these values in a moment equation the minimum amount of force needed to lift the bridge is .5622N.

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Analysis Xi: Force to hold the Bridge

In analysis 11, the purpose was to see how much force is needed to hold the bridge upright. To find this value, the use of drawings, calculating the additional length in both the x and y directions, and using sohcahtoa. After calculating the additional length of 178.7mm horizontally and 144.8 mm vertically, the force used to hold the bridge can be found. With the current design, it takes a total of 1.05N just to hold the bridge.

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Analysis Xii: Estimate Mass of the Bridge

In analysis 12, the purpose was to see how much the weight of the bridge was. Since a requirement for this project is that the bridge must weigh less than 85g and using the average density of 175kg/m^3 it can be found. There are 5 different parts that make up this bridge. Of the 5 parts, the part with the less volume was 0.000004m^3 and the biggest volume was 0.00027m^3.After finding the volume of each piece and multiplying it by the density, it needs to be added up. By doing this the total weight of the bridge turns out to be.08235Kg or 82.35g.