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- Mechanics of rigid bodies 3. A straight bar of uniform cross section is tested in tension. The bar’s cross sectional are is 6.5 square centimeter and a length of 4m. when the tensile load reaches 85kN, the total elongation is 2.5mm What is the stress and the modulus of elasticity of the bar(d) Figure Q2 (d) shows a typical aluminum stress-strain curve. A mechanical engineer has to carry out a tensile test for a rod of aluminum that can withstand an applied force of 20kN. To ensure safety, the maximum allowable stress on the rod is limited to 400 MPa, which is below the yield strength of the aluminum. The rod must be at least 380 cm long and must deform elastically not more than 0.8 cm when the force is applied. Design the appropriate rod.2. An elastic rod of 25mm in diameter, 200mm long extends by 0.25mm under a tensile load of 40kN. Find the intensity of stress, the strain and the elastic modulus for the material of the rod.
- Table B2: Stress-strain data for uniaxial compression test on Sample Normal stress Uniaxial strain (%) Lateral strain (%) (MPa) 0.0 0.0000 0.0000 5.0 0.0319 -0.0150 10.0 0.0720 -0.0275 15.0 0.1025 -0.0425 20.0 0.1450 -0.0600 25.0 0.1755 -0.0725 30.0 0.2150 -0.0875 35.0 0.2455 -0.1025 41.0 0.2815 -0.1125 46.0 0.3125 -0.1209 52.0 0.3515 -0.1285 58.0 0.4000 -0.1325 (f) Based on the plotted curve, calculate the average/tangent Young's modulus and Poisson's ratio for this sample, at 50 % UCS?1. Find the strain that results from a tensile force of 1000 N applied to a 10 m long aluminium bar having cross-sectional area of 4x10 m2. The modulus of elasticity of aluminium is 69 GN/m². 2 A resistance wire strain gauge having a nominal resistance of 350 2 is subjected to a strain of 500 micro-strain. Find the change in the value of resistance neglecting the piezoresistive effect.A 8mm diameter rod, of unknown material, is subjected to 50kN tensile load. In the process, its length increased from 300mm to 303mm. If the stress is proportional to strain, determine the modulus of elasticity, in GPa. of the material?
- A circular solid piece of rock is tested in a compression testing rig to examine its stress/strain behavior. The sample is 6 inches in diameter and 12 inches in length, with the compression load cell imposing a constant load of 10000 lbf equally at both the top and bottom of the rock sample. Assuming a measured reduction in length of 0.02 inches, find the compressive stress and strain of the rock.In our previous topic regarding strain, repeat the problem on the strain using thefollowing parameters:F = 150000 +/- 150 lbfSide length = 1.2 +/- 0.025 inModulus of Elasticity = 25000 +/- 11.5 ksiDetermine the relative error. Is it above or below the accepted 5% error?A metal wire 75.0 cm long and 0.130 cm in diameter stretches 0.0350 cm when a load of 8.00 kg is hung on its end. Find the stress, the strain, and the Young's modulus for the material of the wire.
- 4. We want to draw a 7.5 mm diameter copper wire having a yield strength of 140 MN.m²² into a 6 mm diameter wire. Will the drawn wire break during the drawing process? Strength (MN.m-2) 600 500 400 300 200 100 0 0 Tensile strength 20 Yield strength % Elongation 60 40 Percent cold work 80 100 90 80 70 60 50 40 30 20 10 100 % Elongation1. A circular rod of diameter 20mm and 500mm long is subjected to atensile force 50kN. The modulus elasticity for steel may be taken as 200kN/??2. Find stress and strain due to applied load.Poisson's ratio is defined as (a) longitudinal strain/lateral strain (b) lateral strain/longitudinal strain (c) lateral strain x longitudinal strain 1 (d) (lateral strain) x (longitudinal strain) -