Método das Forças - Tabelas

Appendix B\nDisplacements of prismatic members\nThe following table gives the displacements in beams of constant flexural rigidity EI and constant torsional rigidity GJ, subjected to the loading shown on each beam. The positive directions of the displacements are downward for translation, clockwise for rotation. The deformations due to shearing forces are neglected.\n\nq per unit length\n\nf1 = 5q l 4 / 384 EI (B.1)\nf2 = f3 = 19q l 4 / 2048 EI (B.2)\nf4 = -f5 = q l 3 / 24 EI (B.3)\nf6 = -qx / 24 EI( l 3 - 2l 2 x + x 3 ) (B.4)\n\nf1 = P(l - b)x / 6 EI (2l - b 2 - x 2 ) when x << b (B.5)\nf1 = Pb(l - x) / 6 EI (2l x - x 2 - b 2 ) when x >> b (B.6)\nf2 = Pb(l - b) / 6 EI (2l - b 2 ) (B.7)\nf3 = -Pb / 6 EI (l 2 - b 2 ) (B.8)\n\nWhen b = l/2, f2 = f3 = P l / (16 EI), and f1 = P l 3 / 48 EI at x = l / 2 (B.8) Appendix B 753\n\nf1 = MI / 3 EI (B.9)\nf2 = MI / 6 EI (B.10)\nf3 = 15M 2 / 384 EI (B.11)\nf4 = M 2 / 16 EI (B.12)\nf5 = 21M 2 / 384 EI (B.13)\n\nf1 = MI / 4 EI (B.14)\nf2 = -9M 2 / 256 EI (B.15)\nf3 = -32 MI / EI (B.16)\nf4 = -3M 2 / 256 EI (B.17)\n\nf1 = TI / GJ (B.18)\n(Effect of warping ignored)\nf1 = P l 3 / 3 EI (B.19)\nf2 = P l 2 / 2 EI (B.20)\nf4 = f1 + df2 (B.21)\nf3 = P l 3 / 3 EI (1 - 3b / 2 l 2 + b 3 / 2 β) (B.22) for 0 ≤ b ≤ l\n\nf1 = q l 4 / 192 EI (B.23)\nf2 = -q l 3 / 48 EI (B.24) 754 Appendix B\n\nf1 = 7P l 3 / 768 EI (B.25)\nf2 = P l 2 / 32 EI (B.26)\n\nq per unit length\n\nf1 = q l 4 / 8 EI (B.27)\nf2 = q l 3 / 6 EI (3ξ 3 - 3ξ 2 + ξ 3 ) (B.28)\nf3 = q l 4 / 24 EI (θ 2 - 4θ 3 + θ 4 ) (B.29)\n\nf1 = M l 2 / EI β(1 - 0.5β) (B.30)\nf2 = [M/EI / (EI) with ξ ≤ β\nM / EI / (EI) with β ≤ ξ ≤ 1 (B.31)\nf3 = M(β) 2 / (EI) with ξ ≤ β (B.32) with β ≤ ξ ≤ 1\n\nf1 = q l 2 / 24 EI β 2 ξ(2 - β 2 - 2ξ 2 ) (B.33)\nf2 = q l 4 / 384 EI β 3 (32 - 39β + 12β 2 ) (B.34)\nf3 = q l 3 / 24 EI β 2 (2 - β 2 ) (B.35)\nf4 = -q l 3 / 24 EI β 2 (4 - 4β + β 2 ) (B.36) Appendix B 755\n\nM\n\nf1 = -f2 = -M I / 2 E I (B.37)\n\nf3 = -M x(l - x) / 2 E I (B.38)\n\nf4 = -M I^2 / 8 E I (B.39)\n\nf1 = \u03c8 / 8 (B.39)\n\nf2 = \u03c8 x(l - x) / 2 (B.40)\n\nf3 = -f4 = \u03c8 l / 2 (B.41)\n\nBeam depth\n\n\u03c8 = curvature\n\nThermal expansion (strain)