674_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

674_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 08Ch08.qxd 9/18/08 668 11:04 AM Page 668 CHAPTER 8 Applications of Plane Stress Problem 8.4-6 A beam of wide-flange cross section (see figure) has the following dimensions: b b 120 mm, t 10 mm, h 300 mm, and h1 260 mm. The beam is simply supported with span length L 3.0 m. A concentrated load P 120 kN acts at the midpoint of the span. At a cross section located 1.0 m from the left-hand support, determine the principal stresses s1 and s2 and the maximum shear stress tmax at each of the following locations: (a) the top of the beam, (b) the top of the web, and (c) the neutral axis. t h1 h Probs. 8.4-6 and 8.4-7 Solution 8.4-6 Simply supported beam sy 0 txy 0 Uniaxial stress: s1 0 82.7 MPa s2 tmax 41.3 MPa ; K (b) TOP OF THE WEB (POINT B) P M 120 kN Pc 2 L 3.0 m 60 kN # m b 120 mm t h 300 mm h1 3 I bh 12 (b V c 60 kN sy 0 Q (b) a 10 mm 260 mm t)h 3 1 12 h h1 2 ba h + h1 b 4 336 * 103 mm3 (60 kN)(336 * 103 mm3) VQ It txy 108.89 * 106 mm4 (a) TOP OF THE BEAM (POINT A) 108.89 * 106 mm4 71.63 MPa 1.0 m P 2 (60 kN # m)(130 mm) My I sx (108.89 * 106 mm4)(10 mm) A 18.51 MPa sx + sy s1,2 ; 2 a sy sx 2 2 2 b + txy 35.82 ; 40.32 MPa s1 A 4.5 MPa, s2 tmax a 76.1 MPa sy sx 2 ; 2 2 b + txy 40.3 MPa (c) NEUTRAL AXIS (POINT C) sx Q sx Mc I (60 kN # m)(150 mm) 108.89 * 106 mm4 82.652 MPa 0 hh ba b a b 24 sy 0 (b 420.5 * 103 mm3 t) a h1 h1 ba b 2 4 ; ...
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