Question

Three wooden beams and two steel plates are securely bolted together to form the composite member shown. Using the data given in the table, determine the largest permissible bending moment when the member is bent about a vertical axis. Take x= 6 in. Modulus of elasticity Allowable stress Wood 2 x 10 psi 2000 psi Steel 29 10psi 22,000 psi 2 in. 2 in. | 2 in. The largest permissible bending moment when the member is bent about a vertical axis is 99.16 kip-in.

Answer 1

Given, Ested 29x100 psi, Ewood = 2x100 psi . Modular ratio(m) Esteel 2 29x106. in. I Ewood 2x106 Converting whole sectim into steel sections, As moment is about vertical axis, width of section remains Constant. Depth of each wood section, y = 0.4138 - 14.5

T, 3 x 0.4) 38x23 . + २x6x/13 - + 2x6x/x २ 6m (I+1) 10.4158 २२ +2x0.4138 X २४ (8 र : 13.०३ ५

Stress at entreme fibres = . m xy su / 2+2+2+1+1 पप/ "13:91 3,25 m x ; 13:02 berl 2 22000...m . x 3.25 13.ga 88125 M - P im: 88.185 kip.in Converting whole section into wood section

each steel section a 6x 14.5 87 in Ily F 71 984 !) + ax 89 m 4 x (1++)? 87 in Gin + 3 x 2 x 64 12 x2x6 *(1+4+39 2 188.78125 in 4 entreme fibres stress at m x 4 m 3.25 188.78/25 allow).wood = 2000 psi 2 m x 3.25 188.78125 116173.08 m z 2309615 p.in 116.173 m= 730086 kip.in : Manimum permissible Bending moment abond vertical de nis ? 88.125 kipan