Question

A 20- ftft-long column is made of aluminum alloy 2014-T6.

If it is pinned at its top and bottom, and a compressive load PP is applied at point AA, determine the maximum allowable magnitude of PP using the equations σallow=[54000(KL/r)2]σallow=[54000(KL/r)2] and P/A(σa)allow+Mc/Ar2(σb)allowP/A(σa)allow+Mc/Ar2(σb)allow, with (σb)allow(σb)allow = 22 ksiksi .

Express your answer to three significant figures and include appropriate units.

Problem 13.118 11 of 21 A 20-ft-long column is made of aluminum alloy 2014-T6. A 5.25 in. 0.5 in. X x 10 in. 0.5 in. 0.5 in. 10 in. Part A 54000 M/Ar and P/A (a) allow + with (KL/r)? (obellow If it is pinned at its top and bottom, and a compressive load P is applied at point A, determine the maximum allowable magnitude of P using the equations O allow (ob allow = 22 ksi Express your answer to three significant figures and include appropriate units. μΑ ? P = Value Units

Answer 1

Calculate the sectional area of the column. A = (bh), -(bh). A =(10)(10+0.5+0.5)-(10)(10-0.5) A =(10x11)-(10x9.5) A = 15 in. Calculate the moment of inertia about x axis. = bh 12 -bh w 1 9.5 12 12 1 = 317.5 in. Calculate the moment of inertia about y axis. 1; =(ns), Cano"). 1, +(11(103)-(621000.5)) I = 83.4375 in. Calculate the radius of gyration about x axis. I A 317.5 15 r = 4.60 1in. Calculate the radius of gyration about y axis. I A 183.43 15 r = 2.35 in.

Calculate the slenderness ratio of the of the aluminum alloy 2014-T6 about y-y axis. KL I KL 1(20)(12) 2.358 T y KL =101.76 r Calculate the condition for the slenderness ratio to check the column length for aluminum alloy 2014-16. KL > 55 1 101.76 > 55 Here the condition for slenderness ratio satisfies and the column is long column. Calculate the allowable stress for the long column for aluminum alloy 2014-16. 54000 allow KL 1 allow 54000 (101.76) allow = 5.215ksi Calculate the maximum allowable magnitude of P on the column about x-x axis using the interaction formulae. P/A McAr2 + -1 (a) allow() allow + =1 P/15 (Px5.25)(11/2)/15(4.601)? 5.215 22 0.01278P+4.13x10-?P=1 P = 59.11kip