Question

Consider a member with a rectangular cross section subjected to a compressive load P which is delivered through a rigid block on the upper end of the member as illustrated below. The upper end of the member is free to rotate about both axis directions, but is constrained from lateral deflection in one of the directions by the rigid guide plates illustrated. The lower end is hinged and this allows rotations about one axis direction only. Assume the member is made of steel with a modulus of elasticity of 210 GPa and yield strength of 250 MPa.

(a) Determine the value of P at which the member will yield in compression (assuming L is small enough that yield occurs before buckling).

(b) The initial vertical separation of the rigid block and the guide plates is d = 1.5 mm. Assuming L = 140 mm, the load P is increased until the member yields and deforms plastically. The load is removed when the rigid block on the upper end of the member contacts the rigid guide plates. Treat the steel member as a perfectly elasto-plastic material and determine the final vertical separation of the rigid block and the guide plates (i.e., determine the value of d) when the load has been fully removed.

(c) If L = 1500 mm, determine the lowest critical buckling load, P.

(d) Sketch the buckled shape of the member if the lowest critical buckling load identified in part (c) is reached.

rigid block guide plate d 1.5 40 Le =0.7L L, Lt =0.5L

Answer 1

La) For yieldi h Compne.ssin mation Elastic D uide plate P: 220 KN yield lood b: 22 mm L mm rom m Parta me mber start yield 80 らefore yielding deformation wiU be elatt . 나 étestil de-formation 1A.ey, As we know; ey. P L Pormula A E where, P→ rosssecton E→ young moduli . th of membes P: 220KN ,L AE mm : 016 mm (22x40) x(210xI As we know乡-from property of Elastoトkutic rnateriap , a堯 yield ad tt. continuously demm which plastic deformation le caut vedán 丫巳moving Load. So Co lumn com after that it stop deforming because takesupert from guide plate it

when Load wremovedt wilf regain e lasti deformation (ev) : Fina l Total defor metion Elastic Deformation De ormation For L: ISDDmm long colemn) eue's critical hoadPEImn 2. inm Moment of inanto min → TopView Le → effective le-nath Because membe movem ext ih not alloved at 'A' divection . Moment of intentia abou another latere dimenston be h check here. 22x40-こ117 333.3mn しminimum-4xx-354933 fiv buckle about x-x

min Pcr e:2 2. CY r32 Neton PLY- 31, 695 KN dDeflec Heal shabe

min Pcr e:2 2. CY r32 Neton PLY- 31, 695 KN dDeflec Heal shabe
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