497_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

497_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 05Ch05.qxd 9/25/08 2:29 PM Page 491 SECTION 5.12 Beams with Axial Loads Problem 5.12-18 A short length of a 200 * 17.1 channel is subjected to an axial compressive force P that has its line of action through the midpoint of the web of the channel [(see figure(a)]. Two L 76 76 6.4 angles y y C 200 × 17.1 P P (a) Determine the equation of the neutral axis under this z z C loading condition. (b) If the allowable stresses in tension and compression (a) are 76 MPa and 52 MPa respectively, find the maximum permissible load Pmax. (c) Repeat (a) and (b) if two L 76 76 6.4 angles are added to the channel as shown in the figure part (b). See Table E-3(b) in Appendix E for channel properties and Table E-4(b) for angle properties. C C 200 × 17.1 (b) Solution 5.12-18 sc P 1 Ac tw = 5.59mm Pmax bf = 57.4 e c Ic 1 ; 67.3 kN (c) COMBINED COLUMN WITH 2-ANGLES C 200 * 17.1 L 76 * 76 * 6.4 Ac 2170 mm2 Ic 0.545 * 106 mm4 (z-axis) AL 929 mm2 c2 bf cL 21.2 mm dc c1 c2 203 mm c1 14.5 mm 42.9 mm 76 MPa s c A c1 tw 2 e 11.705 mm (a) LOCATION OF THE NEUTRAL AXIS (CHANNEL ALONE) y0 Ic Ac # e y0 ; 21.5 mm P sc Pe P + c A I2 165.025 kN P Pe c A I1 bf + 76 mm 4.028 * 103 mm2 A h P st 1 e + c2 Ac Ic 133.4 mm CENTROID OF COMPOSITE SECTION c12 + 2 AL 1bf + cL2 Ac 1bf c A c I 59.367 mm Ic + Ac 1bf c22 c1 + 2 IL + 2 AL 1bf + cL I (b) FIND PMAX st Ac + 2 AL h 52 MPa ECCENTRICITY OF THE LOAD e 0.512 * 106 mm4 COMPOSITE SECTION ALLOWABLE STRESSES st IL 2.845 * 106 mm4 e bf c22 bf tw 2 c e 4.762 mm 57.4 mm LOCATION OF THE NEUTRAL AXIS y0 I Ae y0 148.3 mm ; 491 ...
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