Question

The cantilever, shown, has a steel core bonded to a wood casing. If a concentrated load 25 kN is applied at its end, determine the maximum bending stress in the cantilever. E.-12 GPa, E,- 200 GPA. 25 kN 3.00 m 200 mm 200 mm 500 mm Steel 500 m Cross section of the cantilever

Answer 1

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The maximum bending moment, M = 25*3 = 75 kNm (at Fixed end) modular ratio of the materials = 200 cola smo so 1 2 (N/mm2) 30 2.57 2002 24.222 200 2000 svo stut 137037 -84.24 wood -1.45 1 30 * * soo 30 108.6 = 30 mm = 13.03 mm 141.4 (Stres-distribution) The composite material com be converted into Equivalent strongest material, ie steel. wordth of the wood can be converted into bomo modular ralio wood up to steel & Equinalent width of Equivalent wrdim J wood at centie = Soo-denya .: Total width ge lead at top = 30mos Total Widt i Steel at sted extreme = 30mm Total width of stel at cente = 13.03+2005= 296 mois inertia about NA is given by I = miq meslöngle Boxsov + m29 4, 133x141.4 Svangles 13340411 A 133 30 133 1 .: moment 30 3 30 x 500 +4 12 12 Equivalent stul areag/s I = 437.837X10 mm 4 = 42.82 N/mm2 الماء كما 75x10 x 250 we have, Bending stress, o= my = 8 top = bottom 437.8378106 We have wood :, mau stress its wood = 5o = 49.82 = 2.57M/rom? (9) Stress at steel corner aman. Stress instw. og = 75x108 x 141.4 = 24.22 Nom 2 437.837X106 * stress in wood at same level, Twood = 24.23 = 1.45 N/mm² Sla The stress distribution in shows in the fig.