ENGE 1001 - Deflection of Beams Objective: To verify the relationship between load and deflection for a simply supported beam with a single concentrated central load. (Note: You may find other

objectives after doing the experiment) Apparatus: Knife edge supports, dial gauge, weights and weight carrier. Method: • 1 Mild steel bar 1 Brass bar 25.4mm x 4.76mm 25.4mm x 6.35mm Set up each beam in turn centrally on knife edge supports near the ends of the beam. Locate the dial gauge centrally between supports and set to zero. • Apply loads in 200 gram increments to 1600 grams, noting deflections. • Repeat while removing loads. NOTE: The beam should be vibrated gently before each reading is taken to ensure that it is properly settled on the knife edges. You may take a picture of the setup for your report. Results: Complete the following table:/nResults: Complete the following table: Load/(grams) 0 200 400 600 800 1000 1200 1400 1600 Add Load 0 0.68 1.35 2.00 2.65 3.25 3.85 4.45 5.12 Mild Steel Beam Remove Load 0 0.75 1.40 1.95 2.60 3.27 3.90 4.50 Dial Gauge Readings (mm) 5.12 Average 0 0.715 1.375 1.975 2.625 3.26 3.875 4.475 5.12 Add Load 0 0.54 1.10 1.60 2.12 2.62 3.20 3.70 4.20 Brass Beam Remove Load 0 0.62 1.15 1.65 2.10 2.60 3.15 3.70 4.20 Average 0 0.58 1.125 1.625 2.11 2.61 3.175 3.70 4.20/nCalculations: The equation for the deflection at the centre of the beam, for a simply supported beam with a single concentrated central load, is as follows: Given: Where y L I I = E for Mild Steel Beam: E for Brass Beam: b (breadth of the beam) d (depth of the beam) Deflection (m) W - Load (N) Length (m) E - Young's Modulus (N/m²) Second moment of Area [about the Neutral Axis] (m²) bd³ 12 Units Complete the following table by showing the relevant calculations: m y = m WL³ 48EI m4 207GPa 110GPa Cross section of the beam Mild Steel 25.4mm b 4.76mm Is =2.284x10^-20 m^4 Brass 25.4mm 6.35mm IB =5.419x10^-10 m^4/nGraph: Plot y / Deflection (mm) (Y-axis) vs. W/ Load (N) (X-axis) for both beams in a single graph. Discussion: • Is the deflection vs. load graph a straight line? Support your answer by (i) observing the graph and (ii) with the help of the deflection equation. • State three main errors that may have occurred in your assumptions and in the measurements. • Discuss why the brass beam is deflected less compared to the mild steel beam for the same load in this experiment; support this with evidence. Conclusion: • Summarise key points/findings of the experiment • Very briefly explains where this knowledge could be applied Additional note: • No more than 5 pages of report in total should be returned as additional pages will not be marked. This does not include the cover page. • Fonts should not be smaller than size 11. • The key for a good report is 5Cs - Clear, Concise, Complete, technically Correct and Critical analysis Show your calculations to prove that you know how to do them • Make the report looks nice and well-formatted - reuse the tables from the lab sheet but feel free to make adjustments Use diagrams or photos where appropriate (with figure number and description) • Conclusions are what you can conclude from your work (usually a summary of findings, a statement of opinion or decisions reached) - do not mix up with objectives, discussions, etc.