Question

Problem 1: A round bar with a diameter of 29 mm, and 4880 mm in length was under tensile test to determine the mechanical properties of the material. The following table shows the load versus strain data collected from the testing machine and a strain gauge applied on the bar in the loading direction. The measured percentage elongations were 19.4 % and 14.2 % on gauge lengths of 100 mm and 200 mm respectively. Assume: the elongations include the necking: the strain outside the necking region was uniform. The griping lengths at both ends of the bar were neglected. Determine: 1. The 0.2% proof stress of the material (Unit: MPa) 2. The Young's modulus of the material (Unit: GPa) 3. The length of the bar when a tensile load of 510 kN is applied (Unit: mm) 4. The length of the bar at failure when the two broken pieces are fit together. (Unit: mm) Load (kN) Strain 0.0 0.00000 257.5 0.00200 377.3 0.00293 456.2 0.00354 515.1 0.00400 562.1 0.00439 601.3 0.00478 634.8 0.00527 664.2 0.00605 690.2 0.00736 713.7 0.00958 734.1 0.01299 754.5 0.01883 767.9 0.02475 778.0 0.03072 786.0 0.03671 792.7 0.04270 798.4 0.04869 803.4 0.05468 807.8 0.06066

Answer 1

solution;

at 1st plot sress strain curve from the given data

load (KN) stress (MP:strain(10^-3) 0 0 0 2 257.5 377.3 390 571.5 2.93 691 3.54 456.2 515.1 562.1 4 4.39 601.3 4.78 634.8 780.2 851.4 910.8 961.55 1006.1 1045.5 1081.1 5.27 664.2 6.05 7.36 690.2 713.7 734.1 754.5 767.9 1111.96 1142.86 1163.16 1178.46 1190.6 1200.72 9.58 12.99 18.83 24.75 30.72 778 786 36.71 792.7 42.7 798.4 1209.36 48.69 1216.93 54.68 803.4 807.8 1223.6 60.66

1400 1200 1163.16 1178.460 1190.6 © 1200.720 1209.360-1216.930 1223.6 1142.86 1000 01111.96 1081.1 1045.5 1006.1 961.55 910.8 O 851.4 800 780.2 STRESS (MPA) © 691 600 © 571.5 400 390 200 0 0 0 0 10 20 50 60 70 30 40 STRAIN (10^-3)

= E=195*103 mpa = /195 upa (i) Stres corres bonding to 0.2%. proofs Strees is Stress (usores pording 9 1006.1 impa to 0.2 % plastic stouin 2.e. 0.2% proof stress - firem above curve - (us young's is modules E gield strees gield strain = slope of linear portion of stress strain diagram ㄴ E = 390 N/mm2 2x10- -3 :5) (11) when when tensile load is 510 KN Street =772:51 mpa 510 = T -x660.18 2. e. from graph it Obeys brokes law up to 851.ampu hence length q bar = EXLAL= 6XL+L E 772.51 x 48807 4880 1958103 4899.33 mm]

thewegtis ТІ QA8+ + Q8 8+* a[ К 19-оя : +7xfЭ с at failure Length of bar at 6