546_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

546_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 06Ch06.qxd 9/24/08 540 5:54 AM Page 540 CHAPTER 6 Stresses in Beams (Advanced Topics) Problem 6.5-12 A C 200 17.1 channel section has an angle with equal legs attached as shown; the angle serves as a lintel beam. The combined steel section is subjected to a bending moment M having its vector directed along the z axis, as shown in the figure. The centroid C of the combined section is located at distances xc and yc from the centroid (C1) of the channel alone. Principal axes x1 and y1 are also shown in the figure and properties Ix1, Iy1 and up are given below. Find the orientation of the neutral axis and calculate the maximum tensile stress st and maximum compressive stress sc if the angle is an L 76 76 6.4 section and M 3.5 kN # m. Use the following properties for principal axes for the combined section: Ix1 18.49 106 mm4 Iy1 1.602 106 mm4, up 7.448° (CW), xc 10.70 mm, yc 24.07 mm. y1 y C C1 M z yc up xc L 76 76 lintel x1 C 200 6.4 Solution 6.5-12 M 3.5 kN # m ANGLE: ca CHANNEL: up zpA 7.448° 21.2 mm cc 14.5 mm bc La zpA 76 mm dc ypA 203 mm 57.4 mm ypA st BUILT-UP SECTION: ybar 24.07 mm Izp Ix1 Izp 18.49 Iyp xbar 10.70 mm st (yA) sin ( up) up) + (yA) cos ( (zA) cos ( up) up) 63.18 mm (zA) sin ( 69.83 mm Myp(zpA) Mzp(ypA) Iyp Izp ; 31.0 MPa Iy1 106 mm4 Iyp 1.602 106 mm4 MAXIMUM COMPRESSIVE STRESS (AT POINT B) zB BENDING MOMENTS xbar cc Myp Msin( up) Myp 454 N # m zpB (zB) cos ( Mzp Mcos( up) Mzp 3470 N # m zpB 20.05 mm ypB (zB) sin ( ypB dc + ybar 2 yB 124.0 mm NEUTRAL AXIS nn b a tan a Izp Iyp tan( up) b b 56.5° sc MAXIMUM TENSILE STRESS (AT POINT A) zA xbar cc bc ; yA dc + ybar 2 sc up) (yB) sin ( up) up) + (yB) cos ( up) Myp(zpB) Mzp(ypB) Iyp Izp 29.0 MPa ; 17.1 ...
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This note was uploaded on 12/22/2011 for the course MEEG 310 taught by Professor Staff during the Fall '11 term at University of Delaware.

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