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 15,159 16,170 b 2 (N m) M max allow S 15,159 16,170 b 2 (15 10 6 N m 2 ) ¢ 8 b 3 27 S bh 2 6 8 b 3 27 M max ( q q 0 ) L 1 2 2 1 2 (6875 N m 7333 b 2 )(2.1 m) 2 Rearrange the equation: (120 10 6 ) b 3 436,590 b 2 409,300 0 S OLVE NUMERICALLY FOR DIMENSION b b 0.1517 m R EQUIRED DIMENSIONS b 152 mm h 202 mm h 4 b 3 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 height of beam 15 in. L OCATE CENTROID
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