Assignment 4
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The document contains 8 problems involving determining stresses acting on elements in plane stress subjected to normal and shear stresses. The problems involve calculating stresses on elements oriented at various angles when given the original normal and shear stresses on the element. Additionally, there are problems calculating changes in length, thickness, volume, and strain energy of a brass plate subjected to normal stresses when given its dimensions and material properties.
Assignment 4
- 1. Mechanics of Solids (NME-302) Assignment Yatin Kumar Singh Page 1 7.2-1 An element in plane stress is subjected to stresses σx = 6500 psi, σy = 1700 psi, and τxy = 2750 psi, as shown in the figure. Determine the stresses acting on an element oriented at an angle θ = 60° from the x axis, where the angle θ is positive when counterclockwise. Show these stresses on a sketch of an element oriented at the angle θ. (see figure 7.2-1). 7.2-2 Solve the preceding problem for σx = 80 MPa, σy = 52 MPa, τxy = 48 MPa, and θ = 25° (see figure 7.2-2). 7.2-3 Solve Problem 7.2-1 for σx = 9,900 psi, σy = 3,400 psi, τxy = 3,600 psi, and θ = 50° (see figure 7.2-3). 7.2-4 The stresses acting on element A in the web of a train rail is found to be 42 MPa tension in the horizontal direction and 140 MPa compression in the vertical direction (see figure 7.2-4). Also, shear stresses of magnitude 60 MPa act in the directions shown. Determine the stresses acting on an element oriented at a counterclockwise angle of 48° from the horizontal. Show these stresses on a sketch of an element oriented at this angle. 7.2-5 Solve the preceding problem if the normal and shear stresses acting on element A are 7,500 psi, 20,500 psi, and 4,800 psi (in the directions shown in the figure) and the angle is 30° (counterclockwise). (see figure 7.2-6 An element in plane stress from the fuselage of an airplane is subjected to compressive stresses of magnitude 25.5 MPa in the horizontal direction and tensile stresses of magnitude 6.5 MPa in the vertical direction (see figure 7.2-6). Also, shear stresses of magnitude 12.0 MPa act in the directions shown. Determine the stresses acting on an element oriented at a clockwise angle of 40° from the horizontal. Show these stresses on a sketch of an element oriented at this angle. 7.2-7 The stresses acting on element B in the web of a wide-flange beam are found to be 11,000 psi compression in the horizontal direction and 3,000 psi compression in the vertical direction (see figure 7.2-7). Also, shear stresses of magnitude 4,200 psi act in the directions shown. Determine the stresses acting on an element oriented at a counterclockwise angle of 41° from the horizontal. Show these stresses on a sketch of an element oriented at this angle. 7.2-8 Solve the preceding problem if the normal and shear stresses acting on element B are 54 MPa, 12 MPa, and 20 MPa (in the directions shown in the figure 7.2-8) and the angle is 42.5° (clockwise). (Fig. 7.2-1) (Fig. 7.2-2) (Fig. 7.2-3) (Fig. 7.2-4) (Fig. 7.2-5)
- 2. Mechanics of Solids (NME-302) Assignment Yatin Kumar Singh Page 2 7.5-12 A circle of diameter d = 200 mm is etched on a brass plate (see figure). The plate has dimensions 400 × 400 × 20 mm. Forces are applied to the plate, producing uniformly distributed normal stresses σx = 42 MPa and σy = 14 MPa. Calculate the following quantities: (a) the change in length Δac of diameter ac; (b) the change in length Δbd of diameter bd; (c) the change Δt in the thickness of the plate; (d) the change ΔV in the volume of the plate, and (e) the strain energy U stored in the plate. (Assume E = 100 GPa and ν = 0.34.) (Fig. 7.2-6) (Fig. 7.2-7) (Fig. 7.2-8)