Young Modulus Experiment

Experiment 1: Young Modulus Title:Bending of beam and coefficient of elasticity. Objective: To study the relationship between load, span, width, height and deflection of a beam, places on two bearers and affected by a concentrated load at the centre. :To ascertain the coefficient of elasticity for aluminium, brass and steel. Results: Measurement of test specimen (a) For beam material – Steel | Length, L (mm)| Thickness, h (mm)| Width, b (mm)| 1st reading| 650| 3. 15| 18. 97| 2nd reading| 650| 3. 11| 19. 03| 3rd reading| 650| 3. 12| 18. 97| Average reading| 650| 3. 13| 18. 99| (b) For beam material – Aluminium Length, L (mm)| Thickness, h (mm)| Width, b (mm)| 1st reading| 650| 3. 25| 19. 15| 2nd reading| 650| 3. 21| 19. 23| 3rd reading| 650| 3. 21| 19. 18| Average reading| 650| 3. 22| 19. 19| (c) For beam material –Brass | Length, L (mm)| Thickness, h (mm)| Width, b (mm)| 1st reading| 650| 3. 31| 19. 05| 2nd reading| 650| 3. 34| 19. 20| 3rd reading| 650| 3. 35| 19 . 09| Average reading| 650| 3. 33| 19. 11| Two simple supports end. (a) Deflection of test specimen [ Beam material-Steel ] Mass(gram)| Load (N)| Deflection #1 (mm)| Deflection #2 (mm)| Deflection #3 (mm)| Average Deflection (mm)| 100| 0. 981| 0. 5| 0. 45| 0. 48| 0. 43| 200| 1. 96| 0. 85| 0. 88| 0. 85| 0. 86| 300| 2. 94| 1. 30| 1. 32| 1. 38| 1. 33| 400| 3. 92| 1. 74| 1. 80| 1. 81| 1. 78| 500| 4. 91| 2. 20| 2. 24| 2. 25| 2. 23| (b) Deflection of test specimen [ Beam material-Aluminium ] Mass(gram)| Load (N)| Deflection #1 (mm)| Deflection #2 (mm)| Deflection #3 (mm)| Average Deflection (mm)| 100| 0. 981| 1. 18| 1. 15| 1. 16| 1. 16| 200| 1. 96| 2. 43| 2. 54| 2. 40| 2. 46| 300| 2. 94| 3. 72| 3. 67| 3. 72| 3. 70| 400| 3. 92| 4. 98| 5. 08| 5. 10| 5. 05| 500| 4. 91| 6. 07| 6. 20| 6. 15| 6. 14| (c) Deflection of test specimen [ Beam material-Brass ]Mass(gram)| Load (N)| Deflection #1 (mm)| Deflection #2 (mm)| Deflection #3 (mm)| Average Deflection (mm)| 100| 0. 981| 1. 02| 0. 97| 0. 90| 0. 96| 200| 1. 96| 1. 80| 1. 78| 1. 74| 1. 77| 300| 2. 94| 2. 67| 2. 78| 2. 66| 2. 70| 400| 3. 92| 3. 49| 3. 57| 3. 52| 3. 53| 500| 4. 91| 4. 37| 4. 41| 4. 37| 4. 41| One fixed end and one simple support end. (a) Deflection of test specimen [ Beam material-Steel ] Mass(gram)| Load (N)| Deflection #1 (mm)| Deflection #2 (mm)| Deflection #3 (mm)| Average Deflection (mm)| 100| 0. 981| 0. 26| 0. 23| 0. 27| 0. 25| 200| 1. 96| 0. 48| 0. 45| 0. 47| 0. 47| 300| 2. 94| 0. 69| 0. 70| 0. 70| 0. 0| 400| 3. 92| 0. 97| 0. 88| 0. 88| 0. 89| 500| 4. 91| 1. 15| 1. 12| 1. 12| 1. 13| (b) Deflection of test specimen [ Beam material-Aluminium ] Mass(gram)| Load (N)| Deflection #1 (mm)| Deflection #2 (mm)| Deflection #3 (mm)|Average Deflection (mm)| 100| 0. 981| 0. 60| 0. 67| 0. 69| 0. 65| 200| 1. 96| 1. 28| 1. 19| 1. 20| 1. 22| 300| 2. 94| 1. 80| 1. 80| 1. 82| 1. 81| 400| 3. 92| 2. 37| 2. 43| 2. 45| 2. 42| 500| 4. 91| 2. 97| 2. 98| 3. 01| 2. 99| (c) Deflection of test specimen [ Beam material-Brass ] Mass (gram)| Load (N)| Deflection #1 (mm)| Deflection #2 (mm)| Deflection #3 (mm)| Average Deflection (mm)| 100| 0. 81| 0. 47| 0. 42| 0. 48| 0. 46| 200| 1. 96| 0. 90| 0. 86| 0. 86| 0. 87| 300| 2. 94| 1. 30| 1. 28| 1. 30| 1. 29| 400| 3. 92| 1. 73| 1. 70| 1. 71| 1. 71| 500| 4. 91| 2. 14| 2. 14| 2. 13| 2. 14| Calculations: * Two simple supports end To calculate the moment of inertia : I = bh312 I = Moment of Inertia ( m4 ) b = Width of beam ( m ) h = Thickness of beam ( m ) To determine the beam Young modulus : E = F? (L348I) E = Young modulus ( Pa ) F = Force/load applied ( N ) ? = Deflection ( m ) L = Beam length ( m ) I = Moment of Inertia ( m4 ) F? = Slope of graph line deflection versus force ( N m-1 )Beam material – Steel I = bh312 = 18. 99 ? 10-33. 13 ? 10-33 12 = 4. 853? 10 -11m4 E = F? (L348I) = 4. 9-0. 980. 00223-0. 00043(600? 10-3)3484. 853? 10-11 = 3. 920. 00180. 2162. 329 ? 10-9 = 201. 94 GPa Beam material – Aluminium I = bh312 = 19. 19 ? 10-33. 22 ? 10-3312 = 5. 339? 10 -11m4 E = F? (L348I) = 4. 9-0. 980. 00614-0. 00116(600? 10-3)3485. 339? 10-11 = 3. 920. 004980. 2162. 563 ? 10-9 = 66. 35 GPa Beam material – Brass I = bh312 = 19. 11 ? 10-33. 33 ? 10-3312 = 5. 880? 10 -11m4 E = F? (L348I) = 1. 962-0. 9810. 00177-0. 00096(600? 10-3)3485. 880? 10-11 = 0. 9810. 000810. 2162. 822 ? 0-9 = 92. 69GPa * One fixed end and one simple support end I = bh312 I = Moment of Inertia ( m4 ) b = Width of beam ( m ) h = Thickness of beam ( m ) E = F? (3. 5L3384I) E = Young modulus ( Pa ) F = Force/load applied ( N ) ? = Deflection ( m ) L = Beam length ( m ) I = Moment of Inertia ( m4 ) F ? = Slope of graph line deflection versus force ( N m-1 ) Beam material – Steel I = bh312 = 18. 99? 10-33. 13? 10-3312 = 4. 853? 10 -11m4 E = F? (3. 5L3384I) = 4. 91-0. 9810. 00113-0. 000253. 5(600? 10-3)33844. 853? 10-11 = 3. 9290. 000880. 7561. 86 ? 10-8 = 181. 47 GPa Beam material – AluminiumI = bh312 = 19. 19? 10-33. 22? 10-3312 = 5. 339? 10 -11m4 E = F? (3. 5L3384I) = 4. 91-0. 9810. 00299-0. 000653. 5(600? 10-3)33845. 339? 10-11 = 3. 9290. 002340. 7562. 05 ? 10-8 = 61. 92 GPa Beam material – Brass I = bh312 = 19. 11? 10-33. 33? 10-3312 = 5. 880? 10 -11m4 E = F? (3. 5L3384I) = 4. 905-0. 9810. 00214-0. 000463. 5(600? 10-3)33845. 880? 10-11 = 3. 9240. 001680. 7562. 26 ? 10-8 = 78. 13GPa Theoretical value for young modulus of Steel = 200GPa Theoretical value for young modulus of Aluminium = 69GPa Theoretical value for young modulus of Brasses = 100-125GPa Discussion :Based on the results, the experimental young modulus for Steel is 201. 94 GPa by using two simple supports end. Besides that, the experimental young modulus for Aluminium is 66. 35 GPa and for Brass is 92. 69 GPa. On the other hand, when the test is carried out by using one fixed end and one simple support end, the experimental young modulus for Steel is 181. 47 GPa, Aluminium is 66. 35 GPa and Brass is 92. 69 GPa. Based on the results from the both method, the coefficient of elasticity for Aluminium is the highest among Steel and Brass as it has the lowest value of young modulus.By comparing with the theoretical young modulus for Steel, Aluminium and Brass, the experimental young modulus for specimen by using two simple supports end is more accurate than using one fixed end and one simple support end. This is because when the beam is tighten only at one side, it will causes the beam to deflect unequally at both side. Thus, the dial gauge readings recorded will be inaccurate. There are some factors that may affect the experimental results to be inaccurate when this experiment is carried out.One of the factors that lead to inaccurate results is because of the atmosphere around the laboratory. The strong air from the air-conditioner will cause the load to be unstable and shaking when the reading is taken. Thus, the readings in the dial gauge will be changing as the load is moving. Besides that, misalignment error will also affect the experi mental results to be inaccurate. The dial gauge is not placed to the center of the test specimen. This is important because the deflection of a beam placed on two bearers will be affected by a concentrated load at the centre.Moreover, parallax error may be occur when adjusting the height of the gauge so that the needle touched the test specimen. This error occurs because different people have different viewing of the measurement at an angle. Furthermore, the dial gauge must be set to 0. 00mm every time the load hanger is mount on the center of the test specimen. This steps need to be done before the readings is taken so that the results will not be interfere by the previous experimental results. The readings by the dial gauge must be taken when it is already fixed and stabilize.Therefore, softly tap on the dial gauge until the reading did not change to ensure that the load had already stabilize before the dial gauge reading is recorded. Conclusion : When the width and the height of the beam increases, the moment of inertia calculated will increase. Besides that, when the load and span increases, the deflection of a beam will also increases. This shows that the load and span is directly perpendicular to the deflection of a beam. Based on the results from both method, the coefficient of elasticity is increasing from steel, brass and aluminium.