/n MAAE 2202 Mechanics of Solids I Laboratory Experiments 1 Laboratory experiments: 35% Note: Failure in either final examination or laboratory component will constitute failure of this course. Requirements of the Experiments Each student (including those who are retaking this course) must complete and pass FOUR experiments (A, B, C and D) during the semester. Each experiment is conducted in group during the lab time (3 hours), but all students must submit their own lab report to the appropriate submission section on Brightspace ONE week after the lab is done. Absenteeism from any laboratory without a valid reason automatically results in a “Fail” grade for the course. Penalty for late submission of lab report is 20% of laboratory grade for each day late. 2 CARLETON UNIVERSITY Department of Mechanical & Aerospace Engineering MAAE 2202 Mechanics of Solids I Experiment D Stresses in Beam Bending OBJECTIVES 1. (a) (b) To gain familiarity with strain measurement technique using electrical resistance strain gauges To verify simple beam theory for flexural stresses in a beam 2. (c) To obtain the Poisson's ratio for the beam material APPARATUS (a) A rigid support frame with fixtures for holding a cantilever beam (b) Computer running LabVIEW to record strain values. (c) Aluminium cantilever beams with symmetric cross-sections (d) Weights and hanger 3. PROCEDURE Before proceeding with the load tests, record the dimensions of both beam specimens to be tested, and note the positions and orientations of all the ten gauges mounted on the specimen. (a) (b) (c) Set the strain gauge readings to zero for every channel before any load is applied. Apply in incremental magnitudes an end load W on the beam. The maximum end load Wmax should not exceed about 25 kgf. Record the strain gauge readings. Remove the end load and check the readings in all the strain gauge channels again. They should remain at "zero". 26 4. (d) Repeat the test for another beam specimen. If required, recalibrate the strain gage readings to zero. REQUIREMENTS (a) (b) (c) (d) (e) Referring to Figure 1, calculate, using the simple beam bending formula, σ = = M·y/I, the maximum longitudinal tensile stress in terms of the bending moment at positions A, B, C, D and F. Plot the theoretical results of σ vs. M for both beam sections on a single plot. The arrangement of strain gauges 5, 6, 7 and 8 is shown in Figure 2. The transverse strain gauge 9 and longitudinal stain gauge 10 pair at position F is shown in Figure 3. The strain gauge readings on the strain indicator are shown in Figure 4 as an example. Tabulate the longitudinal stresses at all the positions of the strain gauges from the measured strains. Put on the corresponding plots in (a), positions for the stresses obtained from the experiment. Calculate the stresses across the depth of the section at position D using simple beam theory. Plot a graph of σ vs. y showing the theoretical line and the experimental data for both beam sections. Plot the transverse strain versus the longitudinal strain at position F. From this plot, obtain the Poisson's ratio for the beam material. (f) Compare and discuss the results obtained for the two specimens. Explain what properties of a beam affect flexural rigidity. How can flexural rigidity be increased? F 9,10 C2 D2| 5 6 7 ∞❘ 8 В B3 << A 4 Figure 1 Diagram of the strain gauge arrangement for experimentally measuring stresses in beam bending 27 5 6 Figure 2 Arrangement of strain gauge 5, 6, 7 and 8 on the beam Figure 3 Transverse and longitudinal stain gauge pair at position F 28