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 5 thickness (constant) ( t is in millimeters) b 1 5 b 2 2 t 5 120 mm 2 2 t Stresses at the top and bottom are in the ratio 7:3. Determine the thickness t . L OCATE CENTROID c 2 5 3 10 h 5 15 mm c 1 5 7 10 h 5 35 mm s top s bottom 5 c 1 c 2 5 7 3 A REAS OF THE CROSS SECTION (mm 2 ) A 1 5 ht 5 50 tA 2 5 b 1 t 5 120 t 2 2 t 2 A 5 2 A 1 1 A 2 5 220 t 2 2 t 2 5 2 t (110 2 t ) F IRST MOMENT OF THE CROSS - SECTIONAL AREA ABOUT THE LOWER EDGE B-B 5 t (2500 1 60 t 2 t 2 )( t 5 mm; Q 5 mm 3 ) D ISTANCE c 2 FROM LINE B-B TO THE CENTROID C S OLVE FOR t 2(110 2 t )(15) 5 2500 1 60 t 2 t 2 t 2 2 90 t 1 800 5 0 t 5 10 mm 5 2500
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This note was uploaded on 09/20/2009 for the course COE 3001 taught by Professor Armanios during the Spring '08 term at Georgia Institute of Technology.

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