By Mechanics of meteriels -CoN cept of strain Prove 4hat G 2(1+v) - modulus of frigidity E = modulus of elasticity
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- On the surface of a structural component in a space vehicle, the strains arc monitored by means of three strain gages arranged as shown in the figure. During a certain maneuver, the following strains were recorded: e, = 1100 X l0_6, 6h = 200 X lO_6, and e = 200 X 10-6. Determine the principal strains and principal stresses in the material. which is a magnesium alloy for which E = 6000 ksi and v = 0.35. Show the princ ipal strains and principal stresses on sketches of properly oriented elements.A solid spherical ball of magnesium alloy (E = 6.5 × l0-6 psi, v = 0.35) is lowered into the ocean to a depth of 8000 ft. The diameter of the ball is 9.0 in. (a) Determine the decrease ?d in diameter, the decrease, ?V in volume, and the strain energy U of the ball. (b) At what depth will the volume change be equal to 0.0324% of the original volume?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?
- Using the equations of strain in isotropic elasticity, find the stress tensor that cause the following strain state determined from an experiment (material has Young’s modulus of 190 GPa): ?? = 0.001 0.001 0 0.001 −0.002 0.0005 0 0.0005 0shear moduli is 70GPa.Use the principle of Strain energy due to direct stresses strength of materials 2A tensile bar is stressed to 250 N/mm2 which is beyond its elastic limit. At this stage the strain produced in the bar is observed to be 0.0014. if the modulus of elasticity of the material of the bar is 205000 N/mm2 then the elastic component of the strain is very close toa. 0.0004b. 0.0002c. 0.0001d. 0.00005 PLS EXPLAIN YOUR ANSWER THOROUGHLY
- EXPLAIN THIS IMAGE https://www.researchgate.net/profile/Carlos-Cuenca-Cabrera/publication/326753159/figure/fig4/AS:659386125008898@1534221311272/Engineering-Stress-Strain-curve-for-both-Brittle-and-Ductile-material-Source.pngspecimen of oil having an initial volume of 600 cm3 is subjected toa pressure increase of 3.6 x 106Pa and the volume is found todecrease by 0.45 cm3. What is the bulk modulus of the material?The diameter (d) of a solid rod (i.e., with a circular cross-section) is 16 mm and ismade from a homogeneous material. The length (L) of the rod is 1.75 m andYoung’s Modulus for the material (E) is 250 GPa. When the rod is placed undertension it experiences deformation and a stress (?) of 650 MPa. Calculate thefollowing:(i) Strain energy (U) to 2 decimal places in Joules.(ii) Strain energy per unit volume (U/V) in J/m3.(iii) The change in length ∆L to 2 decimal places in mm.(iv) The strain (?) due to deformation to 2 significant figures
- A wire 2 m long and 2 mm in diameter, when stretched by weight of 8 kg has its length increased by 0.24 mm. Find the stress, strain and Young’s modulus of the material of the wire. (Note: g = 9.8 m/s2). Answers: (2.5 x 107 N/m2, 1.2 x 10-4 m/m, 2.08 x 1011 N/m2)One spring is placed inside the other, not touching each other, and compressed between a pair of parallel plates until the distance between the plates is 40 mm. Make a neat detailed sketch of the spring and plate assembly. If G = 83 GPa for both springs, calculate the following: 1. The force applied to the spring assembly. 2. The shear stress induced in each spring. 3. The total strain energy stored in the spring assembly. 4. The stiffness of each spring. 5. The equivalent stiffness of a single spring that can be substituted in place of these springs.Modulus of Elasticity, E (Young’s Modulus): E = σ/e e: Strain, unit-less σ : Stress, in N/m2 E : Young's modulus (Modulus of Elasticity), in N/m2