540_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

540_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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534 CHAPTER 6 Stresses in Beams (Advanced Topics) Solution 6.5-6 M ± 5kN m u ± 19.2° Z-S ECTION I zp ± I 1 I zp ± 32.6 ² 10 6 mm 4 I yp ± I 2 I yp ± 2.4 ² 10 6 mm 4 h ± 200 mm b ± 90 mm t ± 15 mm B ENDING MOMENTS M yp ± M sin( u ) M yp ± 1644 N m M zp ± M cos( u ) M zp ± 4722 N m N EUTRAL AXIS nn M AXIMUM TENSILE STRESS ( AT POINT A) yp A ± a t 2 b sin( u ) + a ³ h 2 b cos( u ) zp A ± a t 2 b cos( u ) ³ a ³ h 2 b sin( u ) zp A ± 39.97 mm b ± a tan a I zp I yp tan( u ) b b ± 78.1° ; # # # M AXIMUM C OMPRESSIVE STRESS ( AT POINT B) s c ±³ 40.7 MPa ; s c ± M yp ( zp B ) I yp ³ M zp ( yp B ) I zp yp B ± 91.97 mm yp B ± a ³ t 2 b sin( u ) + a h 2 b cos( u ) zp B ±³ 39.97 mm zp B ± a ³ t 2 b cos( u ) ³ a h 2 b sin( u ) s t ± 40.7 MPa ; s t ± M yp ( zp A ) I yp ³ M zp ( yp A ) I zp yp A ±³ 91.97 mm Problem 6.5-7 The cross section of a steel beam is constructed of a W 18 ² 71 wide-flange section with a 6in ² 1/2 in. cover plate welded to the top flange and a C 10 ² 30 channel section welded to the bottom flange. This
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Unformatted text preview: beam is subjected to a bending moment M having its vector at an angle u to the z axis (see figure). Determine the orientation of the neutral axis and calcu-late the maximum tensile stress s t and maximum compressive stress s c in the beam. Assume that u 30 and M 75 k-in. ( Note : The cross sectional properties of this beam were com-puted in Examples 12-2 and 12-5.) C 10 30 W 18 71 y 1 C 3 z u y C C 2 C 1 M Plate 6 in. in. 1 2 y 3 c 06Ch06.qxd 9/24/08 5:54 AM Page 534...
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