Experiment 2: Structures

Author: Jason Leuer
Lab Partners: Kyle Smith & Jacob Chess
AME 324L – Section 1, Team 7
Date Lab Performed: February 2, 2015
Date Lab Submitted: February 11, 2015

Introduction:
The objective of the Structures experiment is to analyze a simple structure using strain gauges. This is done with a bicycle frame. This can be examined by developing a 2D model of a loaded bicycle frame with three different weights. This can later be compared to a 3D model to determine its accuracy.
Experimental Procedure:
The bicycle contains various strain gauges along the frame. These strain gauges are necessary in order to measure the stress throughout the frame, as loads are added. Three different loads: 110, 160, and 240lbs, were applied in the experiment. LabVIEW is used to measure these stresses. Modern bicycles are made of Aluminum, Young’s Modulus is 9860ksi and Poisson’s ratio is .36. The components of the bicycle used are labeled below.

Figure 1: Simple Bicycle Frame (3D Representation)
As you can see below, the bicycle can be easily represented using 2D truss elements.

Figure 2: 2D Truss Representation with Applied Load (F)
Length values of each frame are listed below: Frame | Length (in) | Top Tube | 22.0 | Down Tube | 26.5 | Seat Tube | 17.5 | Chain Stays | 17.0 | Seat Stays | 19.5 |
Table 1: Frame Length Values
The eight strain gauges were analyzed, four on the down tube and four on the top tube, all centered on the tube and oriented: Strain # | Location on Bicycle | 0 | down tube, top of frame, axial | 1 | down tube, top of frame, hoop | 2 | down tube, bottom of frame, axial | 3 | down tube, bottom of frame, hoop | 4 | top tube, top of frame, axial | 5 | top tube, top of frame, hoop | 6 | top tube, bottom of frame, axial | 7 | top tube, bottom of frame, hoop |
Table 2: Strain Position on the Bicycle Frame
Results/ Discussion/ Calculations:
Our resulting strain values: Load (lb) | 110 | 160 | 240 | Strain # | Value (in/in) | Value (in/in) | Value (in/in) | 0 | -4.18E-05 | -4.27E-05 | -5.87E-05 | 1 | 3.20E-06 | 2.28E-06 | 8.26E-06 | 2 | 1.02E-05 | 1.39E-04 | 2.14E-04 | 3 | -3.51E-05 | -5.53E-05 | -7.74E-05 | 4 | -6.93E-05 | -1.01E-04 | -1.36E-04 | 5 | 1.14E-05 | 2.08E-05 | 3.74E-05 | 6 | -1.03E-05 | -1.05E-05 | -1.79E-05 | 7 | -6.28E-06 | -1.57E-06 | -2.64E-06 |
Table 3: Strain Readings
Negative strain values signify compression and positive strain values signify tension in the strain values. In order to determine the local strain values at each location on the frame, the following equation is applied: σx=E1+vεx+vE1+v1-2v(εx+εy+εz) We can average the top and bottom stresses to obtain a local stress at each location: σaxial=σx,top+σy,bottom2 To find the bending stress, the following equation is utilized: σbending=σx,top-σaxial Down Tube | Load (lb) | 110 | 160 | 240 | σx,top (psi) | -662.7 | -686.3 | -895.0 | σx,bottom (psi) | -157.8 | 1780.5 | 2830.9 | σaxial (psi) | -410.2 | 547.1 | 967.9 | σbending (psi) | -252.4 | -1233.4 | -1863.0 | Top Tube | Load (lb) | 110 | 160 | 240 | σx,top (psi) | -1041.8 | -1473.0 | -1897.1 | σx,bottom (psi) | -229.5 | -189.1 | -321.7 | σaxial (psi) | -635.7 | -831.0 | -1109.4 | σbending (psi) | -406.1 | -641.9 | -787.7 |
Table 4: Local, Axial, and Bending Stress Values
This is the free-body diagram of a truss representation of the bicycle frame:

Figure 3: FBD of bicycle
Using truss analysis the reaction forces were calculated as follows:
Mb=0=F17.0-Rf(20.0)
Rf=F17.020.0
F+Rb+Rf=0 →Rb=-(F+Rf)

For the front axle joint:

Rf=Rdsinθ →Rd=Rfsin41°

Rt=Rdcosθ →Rt=Rfcos41°sin41°

Forces (lbs) | 110 | 160 | 240 | Reaction at Rear Axle, Rr | 110 | 160 | 240 | Reaction at Front Axle, Rf | 93.5 | 136 | 204 | Bottom Bracket Reaction, Rb | -203.5 | -296 | -444 | Axial Force, Down Tube | 142.5 | 207.3 | 310.9 | Axial Force, Top Tube | 107.6 | 156.5 | 234.7 |
Table 5: Reaction & Axial Forces Using Truss Analysis (Theoretical)
Using the simple equation below, we can solve for the axial forces using the lab data and from that we can compare to the theoretical thickness. σ=F/A Cross-Sectional Area (in2) | 110 | 160 | 240 | Down Tube | -0.27 | 0.29 | 0.25 | Top Tube | -0.17 | -0.19 | -0.22 |
Table 6: Theoretical CS Areas
This assumption may not be the most accurate because the cross-sectional areas should be the same for each of the three loads.
Conclusion:
The 2D model can now be compared to a Finite-Element Model (FEM) for accuracy. 2D truss analysis is much simpler, but less accurate than using 3D Finite-Element Analysis (FEA). Using FEA, usually a computer program such as ANSYS is used to model a structure. Then with solid mechanics, physics and other physical sciences the mechanism can be used to solve complex structural engineering problems with ease. The truss model uses pinned joints, but the joints of a bicycle are welded and able to create a bending moment. The truss analysis is still accurate, and for the bicycle frame structure used it is sufficient. But mechanisms which are more complex are not appropriate to model without using FEA.
References:
AME 324L Experiment Sheet http://www.1001-home-efficiency-tips.com/bicycle_components1.html http://www.matweb.com/search/DataSheet.aspx?MatGUID=0cd1edf33ac145ee93a0aa6fc666c0e0&ckck=1

Appendix:

Figure 4: Screen Shot of 110lb Load Data

Figure 5: Screen Shot of 160lb Load Data

Figure 6: Screen Shot of 110lb Load Data