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, Es = 200 GPa. 25 kN 3.00 m 200 mm 6 200 mm Steel 500 mm Wood 500 mm Cross-section of the cantilever

Answer 1

25 Kn 3m max Bending moment M = (25 x 103 x3) 75x103 N-m. 200 mm 500 mm sted wood 4 500 mm Esteel Ewood = 12 Gpa . 200 Gpa, 1 Total Bending moment = M wood + Msted. 75x103 = Mwt Mst & Compatibility equation is rading Curvature is same is same for both beany, of st bin - R I st CGT N POCO X2 Est. Ist Ew. Yw

(I mon) wood 250 mm (man) 200 sin(us) - 200 mm. sled ost wood 200 x 200 12 X 250 32 st 9.428 W - a head 1st wood 비그 E R Mw Ist Est In. Ew Ist 2x 200V2 x 200 2 I pause - 663 12 4 Ist = 1.33 x 108 mm 3 I woord 500 500 12 (1-33 x 100) I wood 5.07 8109 many Mst Mw 1.33 x 108 x 200 5.07×109 x 12 Mst 0.4367 MW POCO X2

from equation & Mat Mat 75x100 ist 0.4367 M word from eg MW+ (0.4367 Mw) 75 x 106 6 52.18 x 10 N-mm & Mst 22.80 x 10 N-mm. G Moment resisted steel = 22.82 x 10 N-mo Moment resisted word - 52.18 x 106 N-mn. by now, Twood Mux Swood ΣΗ 619 I wood 52.18 X10 X 200 250 5.07 8109 wood 2.573 Mpal from eq 9.428 x W steel 9.428 X 2.573 Isted 24.24 MPa CO X2

(on check by another formula Msteel & Isteel steel I sted 6 22.82 X10 x 200 1.33 X 108 Isted. 24.24 Mpa .. maximam Bending Bending shers in cantilever is Produced in sled & Isted mod = 24.24 Mpa
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