Question

A bar having the cross section shown has been formed by securely bonding brass and aluminum stock. Using the data given in the table, determine the largest permissible bending moment when the composite bar is bent about a vertical axis. Take x= 46 mm. Modulus of elasticity Allowable stress Aluminum 70 GPa 100 MPa Brass 105 GPa 160 MPa 10 mm 10 mm Aluminum 10 mm Brass 10 mm |_40 mm / 1 The largest permissible bending moment when the composite bar is bent about a vertical axis is D K N.m.

Answer 1

Ans=) Given 26=46 of the modulus of elasticity The ratio n = El into aluminum n = 105 - 1:5 70 convert the brass member bo = nxbb = 1:5810 = 15mm Transformed cross-section

15 mm 10mm 46mm 10mm - - Yorim - moment of Inertia of transformed section about centroidal axis. I = bo ho3. bihi3 I = 12 12 = 40 x63 - 108463 72 = 8772061667 mm for Alluminum (Ma) move = omansa I = -12 100 x 10 x 877 206667x10 33 X 10 3 = 2.6582x103 Nim = 21658 KN.m

For Brass (Mb) mow & Omax, 6 I Inc = .160x106X877206.667x102 15x 33 x10-3 = 208354x103 Nim Mo = 2.8354 KNim Therefore largest permissible 'bending moment when the bar is bent about a vertical axis is 2.658 / KNIM