At a point on the surface of a plane stressed region, measured strains reduced to the following: E=+900µ, ɛ,=-100µ, and yxy=+400µ. The material on which strains were measured has the following properties: E=210 GPa and v=0.3. Determine the stresses, ox, Oy, and txy at the point. Note: µ means micro radian or 1x10-6 rad. Use biaxial stresses formulas and use Txy=GYxy:
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- The strains on the surface of an experimental device made of pure aluminum ( E=70 GPa, v=0.33 ) and tested in a space shuttle were measured by means of strain gages. The gages wereoriented as shown in the figure, and the measured strains were6a1100 10 ε−= × , and6b1496 10 ε−= × ,6c39.44 10 ε−= − × . What is the stressxσ in the x-direction ?3. Consider iron and its elastic constants (Find them from the net or some book). An iron specimen consists of grains with texturing distribution of [110] (20%), [112] (20%), [111] (30%) and [103] (30%) (all percentages by volume) along the loading direction is serving under a static force of 10,000 N. The metal rod has a 20 mm diameter perpendicular to the loading direction. a) Find the strain response of the specimen.A student wants to measure the strain at a particular point K on a loaded specimen, so she affixes a 45° strain rosette at point K and obtains the following results: €A = 390 μrad EB = 275 μrad Ec = 325 prad After packing up and going home to analyse her results, she realises that the strain rosette was misaligned by 0 degrees CW (where a negative corresponds to CCW) from the x-y axes-ie. Gauge C is not parallel with the x-axis and is instead parallel with a different x' axis that is rotated by 0 degrees-where: 0 = 16 deg Instead of replacing the rosette and retaking measurements, the student realises she can use what she learned in ENGG2400 to find the strains she's interested in. b 45° 45° a) Draw a diagram of the situation, showing both the x-y axes and the strain rosette. b) Calculate Exx, Eyy and Yxy. c) Calculate the maximum in-plane shear strain and the associated average normal strain. I X
- In a laboratory test of a beam loaded by end couples, the fiber at layer AB as shown are found to increase 20 x 10 mm while those at CD decrease 60 x 10 mm in the 250-mm-gage length. Using E= 150 GPa, determine the flexural stress at the bottom fiber. Answer must be in MPa, Given: a = 60 mm, b = 120 mm, and c = 80 mm. gage length a mm b mm Library entation c mm Survey DENTS TIONA 5-mm-thick rectangular alloy bar is subjected to ajtensile load P by pins at A and B, as shown in the figure. The width of the bar is w = 33 mm. Strain gages bonded to the specimen measure the following strains in the longitudinal (x) and transverse (y) directions: €, =710 με and ε,--255 με (a) Determine Poisson's ratio for this specimen. (b) If the measured strains were produced by an axial load of P = 24 kN, what is the modulus of elasticity for this specimen? Answers: (a) v= (b) E= GPaIn a laboratory test of a beam loaded by end couples, the fiber at layer AB as shown are found to increase 40 x 10* mm while those at CD decrease 90 x 10 3 mm in the 240-mm-gage length. Using E = 120 GPa, determine the flexural stress at the bottom fiber. Answer must be in MPa. Given: a 50 mm, b = 130 mm, and c 80 mnm. gage length a mm b mm c mm Next>
- Q.1 The yield stresses (oy) have been measured using steel and aluminum specimens of various grain sizes, as follows: Material D (µm) σΥ (MPa) Steel 60.5 160 136 128 Aluminum 11.1 235 100 223 (a) Determine the coefficients o and kỵ in the Hall- Petch for these two materials. (b) Determine the yield stress in each material for a grain size of d=26 um.Q.3. (30%) A circular aluminum tube subjected to T pure torsion by torques T has an outer radius r2 equal to 2 times the inner radius r1. (a) If the maximum shear strain in the tube is measured as 500x10-6 rad, what is the shear strain y1 at the inner surface? (b) If the maximum allowable rate of twist (0) is 0.15°/m and the maximum shear strain is to be kept at 500x10-6 rad by adjusting the torque T, what is the minimum required outer radius (r2 )min?A test is conducted on a beam loaded by end couples. The fibres at layer CD are found to lengthen by 0.03 mm and fibres at layer AB shorten by 0.09 mm is 20 mm gauge length as shown in the figure. Taking E-2×10 N/mm², the flexural stress at top fibres would be CD A B 50 mm 100 mm (a) 900 N/mm² tensile (b) 1000 N/mm² tensile (c) 1200 N/mm² tensile (d) 1200 N/mm² compressive →→ 75 mm
- In a laboratory test of a beam loaded by end couples, the fiber at layer AB as shown are found to increase 30 x 10-3 mm while those at CD decrease 60 x 103 mm in the 220- mm-gage length. Using E = 130 GPa, determine the flexural stress at the bottom fiber. Answer must be in MPa. Given: a = 50 mm, b = 130 mm, and c = 70 mm. %3D gage length a mm A b mm c mm B.In a laboratory test of a beam loaded by end couples, the fiber at layer AB as shown are found to increase 30 x 10 3 mm while those at CD decrease 80 x 10 3 mm in the 270- mm-gage length. Using E = 150 GPa, determine the flexural stress at the top fiber. Answer must be in MPa. Given: a = 60 mm, b = 140 mm, and c = 70 mm. %3! gage length a mm A B. b mml c mmIn a laboratory test of a beam loaded by end couples, the fiber at layer AB as shown are found to increase 50 x 10 mm while those at CD decrease 60 x 10 mm in the 220-mm-gage length. Using E = 190 GPa, determine the flexural stress at the bottom fiber. Answer must be in MPa. Given: a = 60 mm, b 120 mm, and c = 80 mm. %3D gage length a mm A B b mm D. c mm