Chapter_3_高等材料力学课件.pptVIP

* b) Step 1: Part (a) still applies. Step 2: Same as part (a) ? n=1 Step 3: (?A)w = -wL3/24EI Step 4: (?A)MA = MAL/3EI Step 5: -wL3/24EI + MAL/3EI = 0 ? MA = wL2/8 Step 6: RBL + wL2/8 = wL2/2 ? RB = 3wL/8 RA + 3wL/8 = wL ? RA = 5wL/8 3.8 Solution (Continued) * 3.8 Example 3.8-3 Example 3.8-3: The steel rods AD and CE: d = 10 mm, E = 200 GPa. The threads at the ends of the rods are single-threaded with a pitch of 1.5 mm. The nuts are first snugly fit with bar ABC horizontal, next the nut at A is tightened one full turn. Determine the resulting tension in each rod and the deflections of points A and C, if (a) bar ABC is considered to be rigid. (b) bar ABC is elastic with I = 62.5?103 mm4. * 3.8 Solution to Example 3.8-3 Step 1: ? F = 0 ? FA + FC = FB ? MB = 0 ? (200)FA – (150)FC = 0 ? FA = 0.75FC Step 2: There are two equations and three unknowns in this problem ? n = 3-2 =1 * 3.8 Solution to Ex. 3.8-3 (II) Step 3: point C moves (150/200)?1.5 = 1.125 mm Step 4: * 3.8 Solution to Ex. 3.8-3 (III) Step 5: Step 6: * (b) 3.8 Solution to Ex. 3.8-3 (IV) * Thus: 3.8 Solution to Ex. 3.8-3 (V) * 3.9 Stress and Strain Transformations Example 3.9-1 Determine the principal stresses for Example 2.1-2 and show the element containing these stresses properly oriented w. r. t. the initial xyz coordinate system using: (b) Eq.(3.9-6) and the single-valued solution of Eq.(3.9-7). (a) Eqs.(3.9-7) and (3.9-4). * Solution: (a) (b) 3.9 Solution to Example 3.9-1 * Topics of Today Chapter 3 Review of Fundamental Formulations of Stress, Strain and Deflection 3.1 Assumptions and limitation 3.2 Axial Loading 3.3 Torsion of Circular Shafts 3.4 Beams in Bending 3.5 Bending of Symmetric Beams in two Planes 3.6 Thin-walled Pressure 3.7 Superposition 3.8 Stati