Problem 5.6-16A beam having a cross section in the form of a channel(see figure) is subjected to a bending moment acting about the zaxis. Calculate the thickness tof the channel in order that the bendingstresses at the top and bottom of the beam will be in the ratio 7:3,respectively. Solution 5.6-16Channel beam314CHAPTER 5Stresses in Beams (Basic Topics)zyC50 mmttt120 mmtthickness (constant)(tis in millimeters)b1b 2t 120 mm 2tStresses at the top and bottom are in the ratio 7:3.Determine the thickness t.LOCATE CENTROIDc2310h15 mmc1710h35 mmstopsbottomc1c273AREAS OF THE CROSS SECTION(mm2)A1ht50tA2b1t 120t2t2A2A1A2220t2t22t(110t)FIRST MOMENT OF THE CROSS-SECTIONAL AREA ABOUTTHE LOWER EDGEB-Bt(2500 60tt2)(tmm; Qmm3)DISTANCEc2FROM LINEB-BTO THE CENTROIDCSOLVE FORt2(110 t)(15) 2500 60tt2t290t800
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