Truss bridge laboratory

Bridge Truss - Jun 29, 3 B 8 D -49.2 µStrain (-51.4 µStrain) 1 2 5 -51.2 µStrain (-51.4 µStrain) 53.4 µStrain (51.4 µStrain) 6 -13.2 µStrain (-12.8 µStrain) 4 A F -62.5 µStrain (-64.3 µStrain) 9 12.9 µStrain (12.8 µStrain) 64.5 µStrain (64.3 µStrain) 7 24.6 µStrain (25.7 µStrain) R1 -16.66 LBS C -64.6 µStrain (-64.3 µStrain) 11 55.3 µStrain (57.9 µStrain) P1 12.5 LBS 10 E 32.6 µStrain (32.1 µStrain) P2 25 LBS G R2 -20.83 LBS Tension Compression Loads Loads P1 P2 25 Pounds 50 Pounds member member No Load 1 2 Initial voltage (V) -0.0030198 -2.6593813 Initial strain (in/in) 0 0 Date 7/23/2020 Poisson's Ratio 0.32 Gage Factor 2.100 member member member member member 3 4 5 6 7 -0.005779 -0.0053892 -0.0049036 -0.0042041 -0.0054136 0 0 0 0 0 Strains Loads added: 1 2 3 4 5 6 7 Voltage (V) -0.0026399 -2.6597673 -0.0054133 -0.0055718 -0.0048053 -0.0042998 -0.0058239 Strain Gage Voltage 7.098E-05 -7.413E-05 6.833E-05 -3.411E-05 1.836E-05 -1.788E-05 -7.667E-05 Micro Strain (in/in) -51.212147 53.483378 -49.296332 24.612358 -13.247019 12.90355 55.321757 (X 10-6) (Strain Values in Parenthesis are Theoretical) truss element length: 13" truss material: Al Tube O.D. Tube Wall Area in2 Young's Modulus 0.375 0.035 10000000 member member member 8 9 10 -0.0030731 -0.00747385 -0.0006312 0 0 0 Strain Gage Excitation member 11 Voltage (V) -0.005943497 5.3515682 0 8 9 10 -0.0026091 -0.00795293 -0.0001515 8.67E-05 -8.9527E-05 8.965E-05 -62.549911 64.5966536 -64.676358 11 -0.006185753 -4.52729E-05 32.6651702 5.3515467 ME220 – Mechanics of Materials Laboratory TEST TITLE: Bridge Truss Experiment NAME: (refer to lab manual pp. 63-74) 1. Summary (1/12) (The summary should be succinct (limited to one page), but contain the following four pieces of information, namely, the purpose of the experiment; experimental methods; results; and conclusion.) 2. Calculations (8/12) 1. List the truss properties as follows. TRUSS PROPERTIES Truss Material Young’s Modulus psi Member Cross-Sectional Area sq. inches Gage Factor Test Loads: P1 = lb. P2 = _______________ lb. 2. Using the analysis techniques that you learned from Statics or Mechanics of Materials, determine forces and strains caused in the members, 1(AB), 3(BD), 5(CD), 7 (CE), 11(EG), by load P1 and P2 acting together. 3. Construct graphically the vector force polygon for joints C & E. The polygon must close because the joint is in equilibrium. 4. Present the experimental data and the calculation results in the following format. Member Member Strain Member Strain Percentage (calculated) (Experiment) error in/in in/in 2 5. Compare the above results with those determined experimentally. 3. Discussion (2/12) 1. How well do the analytical and experimental results compare? And What are the reasons for the differences in the analytical and experimental values? 2. Does it appear that bending loads are present in any member? Why may this occur? 4. Conclusion (1/12) 3 ME220 : Materials Laboratory Bridge truss Experiment Prof. Jow Ding Summer 2020 ME220 : Materials Laboratory Objective: Use experiment to determine the strain and stress on selected truss members and compare with the theoretical results. Theoretical Analysis: • Carry out force analysis to determine the internal forces (F) on specified truss members. 𝝅𝝅 • Determine stress: 𝝈𝝈 = 𝑭𝑭/𝑨𝑨 where𝑨𝑨 = ( )(𝑶𝑶𝑶𝑶𝟐𝟐 -𝑰𝑰𝑰𝑰𝟐𝟐 ). 𝟒𝟒 • Determine strain: 𝜺𝜺 = 𝝈𝝈/𝑬𝑬, where 𝑬𝑬 = 𝟏𝟏𝟏𝟏 × 𝟏𝟏𝟏𝟏𝟔𝟔 psi for aluminum. Experiment: The device to be used for measuring local strain is “strain gage” ME220 : Materials Laboratory What is strain gage and how does it work? • Strain gage is essentially a conductor wire whose resistance changes with elongation or strain. • Strain gage is glued to the structure at the point of interest and thus experiences the same strain as the structure. • By establishing a correlation between resistance change and strain experienced by the strain gage, i.e. calibration, strain of the structure can be determined by the measured resistance change of strain gage and calibration relation. ME220 : Materials Laboratory The resistance of an electrical conductor R (in ohms) varies according to the relation l : conductor length, cm. 𝑙𝑙 A : conductor cross-sectional area, 𝑐𝑐𝑐𝑐2 𝑅𝑅 = 𝜌𝜌 𝐴𝐴 𝜌𝜌 : resistivity of conductor material, ohm-cm. 𝑑𝑑𝑑𝑑 = 𝑑𝑑𝜌𝜌 𝑑𝑑𝑑𝑑 𝑅𝑅 = 𝐴𝐴 = 𝑑𝑑𝑑𝑑 𝑅𝑅 = 𝑑𝑑𝑑𝑑 𝑙𝑙 𝜌𝜌𝐴𝐴 𝑙𝑙 𝐴𝐴 = 𝜋𝜋 2 𝐷𝐷 4 𝑑𝑑𝑑𝑑 𝜌𝜌 + d𝑙𝑙 𝑑𝑑𝑑𝑑 𝜌𝜌 + + 𝑑𝑑𝑑𝑑 𝑙𝑙 𝜌𝜌 𝐴𝐴 1 𝐴𝐴 + ρ𝑙𝑙𝑙𝑙( )= 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑 𝑙𝑙 𝑑𝑑𝑑𝑑 𝐴𝐴 −( ) 𝑙𝑙 𝐴𝐴 + 𝑑𝑑𝑑𝑑 𝜌𝜌 𝐴𝐴 − 𝜌𝜌𝑙𝑙(𝑑𝑑𝑑𝑑/𝐴𝐴2 ) 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑 =2 𝐴𝐴 𝐷𝐷 𝑑𝑑𝑑𝑑 ) 𝐷𝐷 −( 𝑑𝑑𝑑𝑑 = 𝜀𝜀𝑎𝑎 ∶ axial strain along the strain gage direction 𝑙𝑙 𝑑𝑑𝑑𝑑 = 𝜀𝜀𝑡𝑡 ∶ transverse strain along the perpendicular direction 𝐷𝐷 ME220 : Materials Laboratory 𝜀𝜀