528_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

528_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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522 CHAPTER 6 Stresses in Beams (Advanced Topics) Problem 6.4-4 A simply supported wide-flange beam of span length L carries a vertical concentrated load P acting through the centroid C at the midpoint of the span (see figure). The beam is attached to supports inclined at an angle a to the horizontal. Determine the orientation of the neutral axis and calculate the maximum stresses at the outside corners of the cross section (points A, B, D , and E ) due to the load P . Data for the beam are as follows: W 250 ± 44.8 section, L ² 3.5 m, P ² 18 kN, and a ² 26.57°. ( Note : See Table E-1b of Appendix E for the dimensions and properties of the beam.) Probs. 6.4-4 and 6.4-5 z y n n C A D P E B a b Solution 6.4-4 L ² 3.5 m P ² 18 kN a ² 26.57 deg Wide-flange beam: W 250 ± 44.8 I y ² 6.95 ± 10 6 mm 4 I z ² 70.8 ± 10 6 mm
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Unformatted text preview: 4 d 267 mm b 148 mm B ENDING MOMENTS N EUTRAL AXIS NN b a tan a I z I y tan( a ) b b 78.9 ; M z P cos( a ) L 4 M z 14087 N # m M y P sin( a ) L 4 M y 7045 N # m B ENDING STRESSES P OINT A: P OINT B: P OINT D: P OINT E: s E s A s E 102 MPa ; s D s B s D 48 MPa ; s B s x ( z B , y B ) s B 48 MPa ; z B b 2 y B d 2 s A 102 MPa ; z A b 2 y A d 2 s A s x ( z A , y A ) s x ( z , y ) M y z I y M z y I z N EUTRAL AXIS nn b a tan a I z I y tan( a ) b b 42.8 ; M AXIMUM TENSILE STRESS ( AT POINT A) s max 1036 psi ; s max M y a b 2 b I y M z a h 2 b I z 06Ch06.qxd 9/24/08 5:54 AM Page 522...
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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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