ENGI 1100 ASSIGNMENT 5 SPRING 2023 Problem 2 Strain gauges were mounted on a structure and...

Transcribed Image Text:

ENGI 1100 ASSIGNMENT 5 SPRING 2023 Problem 2 Strain gauges were mounted on a structure and recorded the strain () versus stress () as load was applied to the structure. Measurements at two different locations were recorded: Location 1 Strain 0 Stress [MPa] Location 2 Stress [MPa] 90 208 0.0001 132 229 0.0002 154 244 0.0003 180 224 0.0004 206 247 0.0005 221 282 0.0006 231 330 0.0007 273 312 0.0008 250 311 0.0009 305 364 We are interested in obtaining the linear relationship between the strain () and stress (). For Location 1, analysis showed the material stress () followed the relationship: =214000 + 108 This relationship shows there is a residual stress RS of 108 MPa already existing on the structure, when the applied strain & is zero. The material modulus of elasticity (E) is 214 000[MPa]. You are expected to develop a similar relationship for Location 2. You should consider strain as the independent variable X, and stress as the dependent variable Y. a) Calculate X;. (You may use Excel) b) Calculate Y. (You may use Excel) c) Calculate XX. (You may use Excel) d) Calculate YY. (You may use Excel) e) Calculate XY. (You may use Excel) f) Using the least squares approach, calculate the slope m and y-intercept b for the straight line which best fits the data for Location 2. You may NOT use Excel. g) Calculate the coefficient of correlation (r) for the line found in step f. You may NOT use Excel to calculate r, but only to verify your result. h) Plot both Location 1 and Location 2 data found in the table along with the trend line evaluated in step f. You may present the plot using Excel output. i) For Location 2, what is the modulus of elasticity E and the residual stress RS on the structure? ENGI 1100 ASSIGNMENT 5 SPRING 2023 Problem 2 Strain gauges were mounted on a structure and recorded the strain () versus stress () as load was applied to the structure. Measurements at two different locations were recorded: Location 1 Strain 0 Stress [MPa] Location 2 Stress [MPa] 90 208 0.0001 132 229 0.0002 154 244 0.0003 180 224 0.0004 206 247 0.0005 221 282 0.0006 231 330 0.0007 273 312 0.0008 250 311 0.0009 305 364 We are interested in obtaining the linear relationship between the strain () and stress (). For Location 1, analysis showed the material stress () followed the relationship: =214000 + 108 This relationship shows there is a residual stress RS of 108 MPa already existing on the structure, when the applied strain & is zero. The material modulus of elasticity (E) is 214 000[MPa]. You are expected to develop a similar relationship for Location 2. You should consider strain as the independent variable X, and stress as the dependent variable Y. a) Calculate X;. (You may use Excel) b) Calculate Y. (You may use Excel) c) Calculate XX. (You may use Excel) d) Calculate YY. (You may use Excel) e) Calculate XY. (You may use Excel) f) Using the least squares approach, calculate the slope m and y-intercept b for the straight line which best fits the data for Location 2. You may NOT use Excel. g) Calculate the coefficient of correlation (r) for the line found in step f. You may NOT use Excel to calculate r, but only to verify your result. h) Plot both Location 1 and Location 2 data found in the table along with the trend line evaluated in step f. You may present the plot using Excel output. i) For Location 2, what is the modulus of elasticity E and the residual stress RS on the structure?