Question

Retur 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 = 9.5 in. Modulus of elasticity Allowable stress Wood 2 x 10 psi 2000 psi Steel 29 x 10 psi 22,000 psi 2 in. 2 in. 2 in. Lin kip-in. The largest permissible bending moment when the member is bent about a vertical axis is 218..43

Answer 1

We first compute the ratio ES 117 EN 29x10 2x10 = 14.5 Multiplying the vertical dimensions of the steel portions of the section by n=14.5, we obtain a transformed section made entirely of wood. 9.5 in 137.75 in. Transformed section containing wood only Neutral Axis (y-axis) passes through the Centroidal of the section. Moment of inertia about vertical neutral axis in transformed section is 9.5x6.53 6.5. + (137.75x0.25)(1.125)? x2 I= - = 325.029 in.

Maximum distance from vertical Neutral Axis is 1 1 2 +2 +2+-+- 1 4 4 C=- 4 - 6.5 = 3.25 in. 1 C We know * - Here Om = 2000 psi for wood 1 - 2000x325.029 x10-3 (or) 3.25 M = 200.02 kip.in. Largest permissible bending moment when the member is bent about vertical axis is M= 200.02 kip.in.