Question

The assembly shown consists of two posts, AB and CD, each made from material 1 having a modulus of elasticity of E1 and a cross-sectional area A1, and a central post EF made from material 2 having a modulus of elasticity E2 and a cross-sectional area A2.

If posts AB and CD are to be replaced by those having a material 2, determine the required cross-sectional area of these new posts so that both assemblies deform the same amount when loaded.

The aencyhowh.con ot tARdCD oerom na1hngamoaar o cayol Enoa ooeon antacepast EEmade hore mon 2 hvnga modul f et boty Ey and acoss sene are A Part A d detemne he required os sectonal ae of ee ew pos se hth e a t wten oaded it posts All and CDa to te epaced by those having a materal 2 and As and any secessary consats of he vanables Express your answ as an expression in te AE ve BeaA Submi Provide Feedback

Answer 1

Sel Sels. * Ety=0 2F + f - P = 0 . Fr . Compatibility & Sin Side FL HL A,E, A E₂ F (A,E, f Α, ΕΣ) from 0 & above Sub we get , A, E, le (2A, E, FALE): F2 120,Auba) A, Ez - PL Sin = F L QA, E, tĄ Ez after change of material.

S: 8- I FL - F E * A E2 Fila from 0 & above ear. Fr 2A, TA2 PL do - - L A2E2 do - A Sin- of - E. (Alitte) condition P.L PL 2 A, E, TAE E₂ (2A, A-) E₂ (2A, +42) = 2A, E, +42E2 (2A) E = 2A, E,