University:
Massachusetts Institute of Technology
Course:
15.097 | Prediction: Machine Learning and Statistics
Academic year:

2020
Views:

357

Pages:

9
Author:

ilikemyicons0y5

2.5. Redo Prob. 2.4 for the following system of strains: What relationships connecting the constants (aÕs, bÕs, and cÕs) make the foregoing expressions possible? 2.38. A 45¡ rosette is used to measure strain at a critical point on the surface of a loaded beam. The readings are ·a = Ð100 ¿, ·b = 50 ¿, ·c = 100 ¿ for »a = 0¡, »b = 45¡, and »c = 90¡ (Fig. 2.20b). Calculate the principal strains and stresses and their directions. Use E = 200 GPa and ¿ = 0.3. Find strain state in the strain element oriented along XY plane and the principal strains. 2.50. The stress Þeld in an elastic body is given by where c is a constant. Derive expressions for the displacement components u(x, y) and v(x, y) in the body. Show that the PoissonÕs ratio for an elastic, incompressible material is 0.5. 2.53. A uniform bar of rectangular cross section 2h × b and speciÞc weight ³ hangs in the vertical plane (Fig. P2.53). Its weight results in displacements Demonstrate whether this solution satisÞes the 15 equations of elasticity and the boundary conditions.

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