05-02ChapGere.0010

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Problem 5.6-15 A beam having a cross section in the form of an unsymmetric wide-flange shape (see figure) is subjected to a negative bending moment acting about the z axis. Determine the width b of the top flange in order that the stresses at the top and bottom of the beam will be in the ratio 4:3, respectively. Solution 5.6-15 Unsymmetric wide-flange beam SECTION 5.6 Design of Beams 313 M AXIMUM BENDING MOMENT 5 15,159 1 16,170 b 2 (N ? m) M max 5 s allow S 15,159 1 16,170 b 2 5 (15 3 10 6 N / m 2 ) ¢ 8 b 3 27 S 5 bh 2 6 5 8 b 3 27 M max 5 ( q 1 q 0 ) L 1 2 2 5 1 2 (6875 N / m 1 7333 b 2 )(2.1 m) 2 Rearrange the equation: (120 3 10 6 ) b 3 2 436,590 b 2 2 409,300 5 0 S OLVE NUMERICALLY FOR DIMENSION b b 5 0.1517 m R EQUIRED DIMENSIONS b 5 152 mm h 5 202 mm h 5 4 b 3 5 0.2023 m 1.5 in. 1.25 in. 1.5 in. z b y C 16 in. 12 in. Stresses at top and bottom are in the ratio 4:3. Find b (inches) h 5 height of beam 5 15 in. L OCATE CENTROID c 2 5 3 7 h 5 45 7 5 6.42857 in.
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