542_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

542_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 06Ch06.qxd 9/24/08 536 5:54 AM Page 536 CHAPTER 6 Stresses in Beams (Advanced Topics) Solution 6.5-8 M 4.5 kN # m u MAXIMUM TENSILE STRESS (AT POINT A) 22.5° b 120 mm t h 180 mm b1 ybar tb1 a t 2 zA BUILT-UP SECTION: 30 mm Izp (yA) cos (uP) 93.14 * 106 mm4 zpA 52.03 mm 133.51 mm Myp(zpA) Mzp(ypA) Iyp Izp 27.3 deg Ix1 (zA) sin (uP) st 52.5 mm Izp (yA) sin (uP) ypA 2t)t] uP (zA) cos (uP) ypA t+h b 2 ybar ybar zpA 360 mm tb1 + [2tb + (h h 2 yA st Iyp MAXIMUM COMPRESSIVE STRESS (AT POINT B) Iy1 Iyp 152.7 * 106 mm4 BENDING MOMENTS zB b1 2 yB Msin(uP u) Myp 377 N # m Mzp Mcos(uP u) Mzp (yB) sin (uP) zpB 128.99 mm ypB (zB) sin (uP) (yB) cos (uP) ypB 142.5 mm sc Myp(zpB) Mzp(ypB) Iyp Izp NEUTRAL AXIS nn b 2.93° Izp Iyp tan(uP ybar (zB) cos (uP) 4484 N # m atan a h +t 2 zpB Myp b ; 6.56 MPa u) b sc 6.54 MPa ; ; Problem 6.5-9 A beam of semicircular cross section of radius r is subjected to a bending moment M having its vector at an angle u to the z axis (see figure). Derive formulas for the maximum tensile s, and the maximum compressive stress sc in the beam for u 0, 45°, and 90°. (Note: Express the results in the from M/r3, where is a numerical value.) y M z u O C r ...
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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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