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444_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 444_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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438 CHAPTER 5 Stresses in Beams (Basic Topics) OR simplfying Evaluate using numerical data (e) F IND MAX . BENDING STRESS INCLUDING UNIFORM LOAD b ( x ) ± b A a 1 + x 3 L b h ( x ) ± h A a 1 + x 3 L b P ± 12 kN M 0 ± 10 kN # m b B ± 80 mm h B ± 120 mm L ± 1.25 m b A ± 60 mm h A ± 90 mm s max s B ± 1.045 ; s B ± s ( L ) s B ± 221 MPa ; s A ± s (0) s A ± 210 MPa ; s max ± s ( x max ) s max ± 231 MPa agrees with plot above ; x max ± 0.625 m so x max ± 3( PL ² M 0 ) 2 P c ² 864 L 3 ² 3 PL + 2 Px + 3 M 0 p b A h A 2 (3 L + x ) 4 d ± 0 ² 2592 Px + M 0 p b A h A 2 L 3 (3 L + x ) 4 ± 0 864 P p b A h A 2 L 3 (3 L + x ) 3 d dx c 864 Px + M 0 p b A h A 2 L 3 (3 L + x ) 3 d ± 0 d dx s ( x ) ± 0 then solve for x max s ( x ) ± 864 a Px + M 0 p b A h A 2 b a L 3 (3 L + x ) 3 b s ( x ) ± Px + M 0 p b A h A 2 a 1 + x 3 L b 3 32 M ( x ) ± Px + M 0 s ( x ) ± M ( x ) S ( x ) s ( x ) ± M ( x ) S ( x ) M ( x ) ± P x + M 0 ² 10 3 P L x 2 2 S ( x ) ± p b A h A 2 a 1 + x 3 L b 3 32 S ( x ) ± p b ( x ) h ( x ) 2 32 I ( x ) ± p b ( x ) h ( x ) 3 64 S ( x ) ± I ( x ) h ( x ) 2 0 0.5 1 0 5 10 15 M(x)
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