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. Ew = 12 GPa, Es = 200 GPa. 25 kN 3.00 m 200 mm 200 mm Steel 500 mm Wood 500 mm Cross-section of the cantilever

Answer 1

Given data 25kN K load P = 25kN + 2 max Bending stress 3.00m Nood Ewa 12 GPA steel 2 200 Gpa. Moment Maximum Bending 2 75 kNm. Mz 2583 wood to an Transform Section corresponding to equirater equivalent bar made of entirely of Steel n z 16.67 200 Es 2 2 Ew 12 2 2 Area of steel As a 200 mm = 40,000 mm? 200mm 200mm, Area of Somm. woo ood steel Awe - (500-2004) wood. 2 Z 210,ooo mm. 500mm t A Equivalent area of steel for Wood section. Ew A es als AX 12 EW Awx Aes 210, ooox N 200 Aes z 12600 mm 2

Area of equivalent Steel z Total steel area area - 12 600 A - 2002 12660 =B² - 200² 2 2 B. 12600+ 200 B 229.34 mm 4 bd3 229-34 2 12 + mm 230.53x106 3 229.34. 20-23053 mt mt 2.3053 X10 y z B / 2 z 229-34 114.67 mm 2 M max 2 x Yman (75 x 106) 114.67 230.53x106 lomaxs 37-30 MPa. max, shers in steel equivalent Cantilever. Max shan in equivalent wood of Cantilever. ow omars xn Ow 2 2.23 MPa .: Max stress the cantilever is 37-30 mpa. on