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This laboratory focusses on the bending of a simply-supported beam, as shown in the following schematic (Figure 1). W/2 Z a 6.4mm X W/2 23mm Figure 1 the loading scheme of a beam It can be shown that for this loading case, the bending moment for a ≤ x ≤ L-a is constant and equal to Wa/2. In this experiments, a = 350 mm and L = 835 mm. Loading the beam in this way, rather than loading the beam at just one point, has two main advantages: (i) it allows a strain gauge to be placed at the top of the beam and (ii) the constant bending moment area that it creates gives better strain gauge performance when stretched or compressed. 6.4mm W/2 8mm a 38.1mm W/2 indicates strain gauge 38.1mm Figure 2 the dimensions of the cross section of the beam and the position of the strain gauges 1. The calculation of the bending moment distribution for a ≤ x ≤ L. 2. The calculation of the second moment of area about the centroidal z axis (I) of the section of the beam. 5. Given that the Young's modulus of the material is approximately 70 GPa and the equations: 0 M 0 E = - and == E I y a. Calculate the maximum theoretical stress (at W = 500 N) in the beam (0max (theoretical)) using the theoretical ymax value. b. Calculate the maximum stress using the experimental ymax value (using the centroid obtained from the experimental data). c. Calculate the maximum theoretical stress by converting the strains into stresses at the maximum load. d. How do these three values compare (e.g. how close are they)?

This laboratory focusses on the bending of a simply-supported beam, as shown in the following schematic (Figure 1). W/2 Z a 6.4mm X W/2 23mm Figure 1 the loading scheme of a beam It can be shown that for this loading case, the bending moment for a ≤ x ≤ L-a is constant and equal to Wa/2. In this experiments, a = 350 mm and L = 835 mm. Loading the beam in this way, rather than loading the beam at just one point, has two main advantages: (i) it allows a strain gauge to be placed at the top of the beam and (ii) the constant bending moment area that it creates gives better strain gauge performance when stretched or compressed. 6.4mm W/2 8mm a 38.1mm W/2 indicates strain gauge 38.1mm Figure 2 the dimensions of the cross section of the beam and the position of the strain gauges 1. The calculation of the bending moment distribution for a ≤ x ≤ L. 2. The calculation of the second moment of area about the centroidal z axis (I) of the section of the beam. 5. Given that the Young's modulus of the material is approximately 70 GPa and the equations: 0 M 0 E = - and == E I y a. Calculate the maximum theoretical stress (at W = 500 N) in the beam (0max (theoretical)) using the theoretical ymax value. b. Calculate the maximum stress using the experimental ymax value (using the centroid obtained from the experimental data). c. Calculate the maximum theoretical stress by converting the strains into stresses at the maximum load. d. How do these three values compare (e.g. how close are they)?

Mechanics of Materials (MindTap Course List)
Mechanics of Materials (MindTap Course List)
9th Edition
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Barry J. Goodno, James M. Gere
Chapter10: Statically Indeterminate Beams
Section: Chapter Questions
Problem 10.3.13P: A counterclockwise moment M0acts at the midpoint of a fixed-end beam ACB of length L (see figure)....
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This laboratory focusses on the bending of a simply-supported beam, as shown in the following schematic (Figure 1). W/2 Z a 6.4mm X W/2 23mm Figure 1 the loading scheme of a beam It can be shown that for this loading case, the bending moment for a ≤ x ≤ L-a is constant and equal to Wa/2. In this experiments, a = 350 mm and L = 835 mm. Loading the beam in this way, rather than loading the beam at just one point, has two main advantages: (i) it allows a strain gauge to be placed at the top of the beam and (ii) the constant bending moment area that it creates gives better strain gauge performance when stretched or compressed. 6.4mm W/2 8mm a 38.1mm W/2 indicates strain gauge 38.1mm Figure 2 the dimensions of the cross section of the beam and the position of the strain gauges
Transcribed Image Text:This laboratory focusses on the bending of a simply-supported beam, as shown in the following schematic (Figure 1). W/2 Z a 6.4mm X W/2 23mm Figure 1 the loading scheme of a beam It can be shown that for this loading case, the bending moment for a ≤ x ≤ L-a is constant and equal to Wa/2. In this experiments, a = 350 mm and L = 835 mm. Loading the beam in this way, rather than loading the beam at just one point, has two main advantages: (i) it allows a strain gauge to be placed at the top of the beam and (ii) the constant bending moment area that it creates gives better strain gauge performance when stretched or compressed. 6.4mm W/2 8mm a 38.1mm W/2 indicates strain gauge 38.1mm Figure 2 the dimensions of the cross section of the beam and the position of the strain gauges
1. The calculation of the bending moment distribution for a ≤ x ≤ L. 2. The calculation of the second moment of area about the centroidal z axis (I) of the section of the beam. 5. Given that the Young's modulus of the material is approximately 70 GPa and the equations: 0 M 0 E = - and == E I y a. Calculate the maximum theoretical stress (at W = 500 N) in the beam (0max (theoretical)) using the theoretical ymax value. b. Calculate the maximum stress using the experimental ymax value (using the centroid obtained from the experimental data). c. Calculate the maximum theoretical stress by converting the strains into stresses at the maximum load. d. How do these three values compare (e.g. how close are they)?
Transcribed Image Text:1. The calculation of the bending moment distribution for a ≤ x ≤ L. 2. The calculation of the second moment of area about the centroidal z axis (I) of the section of the beam. 5. Given that the Young's modulus of the material is approximately 70 GPa and the equations: 0 M 0 E = - and == E I y a. Calculate the maximum theoretical stress (at W = 500 N) in the beam (0max (theoretical)) using the theoretical ymax value. b. Calculate the maximum stress using the experimental ymax value (using the centroid obtained from the experimental data). c. Calculate the maximum theoretical stress by converting the strains into stresses at the maximum load. d. How do these three values compare (e.g. how close are they)?
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