Question

The column AB shown in the Figure below is made of A-36 steel, which is fixed at A and pinned at B. The column has a circular hollow section as shown in section a-a, which has an outer radius ro= 25mm and inner radius ri=20mm. (a) Determine the slenderness ratio of the column [5%] (b) Is the column safe? [12%) (c) What is the failure mode of the column [3%) I= (-), Gyle=250 MPa, E= 200 GPA T စ CP 10 KN 2 m 25 kN/m Detail at E 2 m 4 m 2.5 m Section a-a

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Mechanics of material

Answer 1

o solution Given data, outer radius ru= 25mm ; inner radius ri - 20 mm; > Yield = 250mpa ; E=200Gpa co Slender mens ratio of the Columns x= left lokn L radius of Gyration, 25KN lm RO B 2 pin at RB EMB=0; Roxy = 10x2 +(2544x2) Ro= 55 kn Efy=0; RB+ Ro= 110 KN ( 1042544=160) Riz=55kn.

@) Slender.ney ratio 1 = porno left RB end condition is pin - fixed 1 RB=55kn T 2.5ml t for end (*) for pin-fixed end, deffen deffa l 2 leffa 2.5m 25oo 51767.7 12 Radius of Gyration HI :: v= (254–204) Y; * (25-20%) Azł * (rouri") 16.008mm i. Slenderness ratio , x= left 1767.7 16.008 x= = 110.43 *

(6) Safe check buckling failure Comprenion failure of AB Now, 3 compression force on BA 55x10 I (25²20) JRB tha o=77.81 mpas applied Go Loyield (250 mpa), so it is safe in compression, NOW, check for buckling; der for buckling Txax105 (110-43) oor 161.86 mpa Per = 161-86 * * (25-20") 1140ul kw > 55 kw (applica] 80, column is safe,

u (c) fail ure modes :- (i) com presion 1) Buckling since ; or (buckling) yield (comp) so, if it fails, it will fail under Buckling mode first.