Project #1 Bicycle Frame Design In this project, we are going to design a frame of bicycle using a hollow aluminum tube. The schematic dimensions of the bicycle are shown in the figure. Initially, the flowing cross-sectional dimensions are used for all frames: outer diameter = 25mm and thickness t =2mm. The material properties of aluminum are given in the table. Even if the bike is under the dynamic loads, only two static design criteria are considered here. -Vertical bending test: When an adult rides the bike, the nominal load can be estimated by the vertically downward load of 600N at the seat position and a load of 200N at the pedal crank location. When a dynamic environment is simulated using the static analysis, the static loads are often multiplied by a certain G-factor. In this design project, use G = 2. Use ball-joint boundary condition for the front dropout ( 1 ) and sliding boundary condition for rear dropouts (5 and6 ). -Horizontal Impact: The BNAs (Bureau of National Affairs) Requirements for Bicycles manual calls for a single compressive loading test. A load of 980N is applied to the front dropout horizontally with rear dropouts constrained from any translational motion. Use G = 2. x y 825400400325 502020Seat PedalUnit: mm 1 2 3 45 650020 Material PropertyValue Youngs Modulus (E)70 GPa Poissons Ration ()0.33 Density ()2,580 kg/m3 Ultimate Tensile Strength(U)210 MPa Elongation at Break10% The report is supposed to be readable and complete by itself, for example, including introduction, approach, assumptions, results, conclusion, discussion, and references. You dont have to submit your computer model file. However, you are supposed to keep the file during the semester. If necessary, the instructor will ask the computer file individually. In your report, you must include followings: 1. Clearly specify the unit system that you used in the model and report. 2. Carry out preliminary analysis of vertical bending test and estimate the maximum stress and maximum vertical displacement. 3. Using beam finite elements, carry out finite element analysis at the initial design for both cases and tabulate the maximum stress and displacement as follows: Test CaseMax. StressMax. x-displ.Max. y-displ. Vertical Test Horizontal Impact You have to clearly identify boundary conditions and applied loads. Provide the cross-sectional shape of the hollow beam, the finite element model with node numbers, the finite element model with element numbers, von Mises stress contour plots on the deformed geometry. Optionally, plot the bending moment diagram if your software allows them. Also, plot the stress distribution on the cross-section at the maximum stress point. 4. By considering the fatigue property of aluminum, it would be appropriate to limit the maximum stress less than 70 MPa. In addition, the maximum displacement in either direction should be less than 0.6 mm. In the design stage, the cross-section of each line in the figure can be modified (only diameter not thickness). The design goal is to find the best combination of the bicycle frame diameters to minimize the weight of the frame while satisfying the design criteria for vertical bending test. Using you engineering sense or any design tools, find the best combination of diameters. For manufacturing cost reason, only five different diameters are allowed. Provide the same information as in question 2 at the optimum design. Tabulate the weight, max. stress, and max. displacement at each design stage. Limit your maximum design iterations by five. 1.Unit:ton (103 kg), mm, sec 2.Preliminary Analysis (vertical bending test) If we assume the bike frame is a straight beam structure, then the configuration of the problem can be depicted as in the figure. .4 .5 .825 400N 1200N 678.8N 921.2N From the elementary beam theory, the bending moment can be obtained, as 678.8 , 0 0.4( ) 278.8 160, 0.4 0.5921.2 760, 0.5 0.825x xMx x xx x< < !"= +