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05-02ChapGere.0011 - 314 A-PDF Stresses in Beams(Basic...

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Problem 5.6-16 A beam having a cross section in the form of a channel (see figure) is subjected to a bending moment acting about the z axis. Calculate the thickness t of the channel in order that the bending stresses at the top and bottom of the beam will be in the ratio 7:3, respectively. Solution 5.6-16 Channel beam 314 CHAPTER 5 Stresses in Beams (Basic Topics) z y C 50 mm t t t 120 mm t thickness (constant) ( t is in millimeters) b 1 b 2 t 120 mm 2 t Stresses at the top and bottom are in the ratio 7:3. Determine the thickness t . L OCATE CENTROID c 2 3 10 h 15 mm c 1 7 10 h 35 mm s top s bottom c 1 c 2 7 3 A REAS OF THE CROSS SECTION (mm 2 ) A 1 ht 50 t A 2 b 1 t 120 t 2 t 2 A 2 A 1 A 2 220 t 2 t 2 2 t (110 t ) F IRST MOMENT OF THE CROSS - SECTIONAL AREA ABOUT THE LOWER EDGE B-B t (2500 60 t t 2 ) ( t mm; Q mm 3 ) D ISTANCE c 2 FROM LINE B-B TO THE CENTROID C S OLVE FOR t 2(110 t )(15) 2500 60 t t 2 t 2 90 t 800
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