534_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 534_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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528 CHAPTER 6 Stresses in Beams (Advanced Topics) Solution 6.4-12 L ± 4.5 m P ± 500 N a ± 30° B UILT UP BEAM : Double C 200 ² 17.1 I cy ± 0.545 ² 10 6 mm 4 I cz ± 13.5 ² 10 6 mm 4 c ± 14.5 mm b c ± 57.4 mm A c ± 2170 mm 2 I y ± 2[ I cy ³ A c ( b c ´ c ) 2 ] I y ± 9.08 ² 10 6 mm 4 I z ± 2 I cz I z ± 27.0 ² 10 6 mm 4 d ± 203 mm b ± 2 b c b ± 114.8 mm B ENDING MOMENTS M y ±´ P cos( a ) LM y 1949 N m M z P sin( a ) z 1125 N m # # N EUTRAL AXIS nn M AXIMUM TEMSILE STRESS P OINT A: s A ± s x ( z A , y A ) s A ± 16.6 MPa ; z A b 2 y A ± d 2 s x ( z , y ) ± M y z I y ´ M z y I z b ± 79.0° ; b ± a tan a I z I y tan (90 ° ´ a ) b Problem 6.4-13 A built-up steel beam of I-section with channels attached to the flanges (see figure part a) is simply supported at the ends. Two equal and oppositely directed bending moments M 0 act at the ends of the beam, so that the beam is in pure bending. The moments act in plane mm , which is oriented at an angle a to the xy plane. (a) Determine the orientation of the neutral axis and calculate the maximum tensile stress s max due to the moments M 0 . (b) Repeat part a if the channels are now with their flanges pointing away from the beam flange, as shown in figure part b. Data for the beam are as follows:
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