Question

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Consider a member wih a rectangular cross sechion subjected to a Campressive Icad p which is delivered tragh a rigid block on me upper end of me membe as illu stated belon Tne uper end of hhe member is free to rotare aut axis dvechons ! он is constored forn loleral, deflection in cre ce the divections by me rigid guicle plates ilIuShaked, he lonr end is ninged and this allons rotaans albout one axiS dlirection only. Assunre me member is made of Steel wh a modlulus of elasticity of 210 GPa and yield shergth Of 250 MPa. (a). Deter mine the value of p at which tne membe wlI that yield Meld in commpression Cassuming L s smail enaugh occurs be fore ouckling (b) Te initial vethcal seporation of the rigid blact and tre guide plaks is d 5mm. Assiuming 140mm, me lead P is incteased unhil me member yields and deforms plcrstically Tne lcad is removed when the rigid blockk on the upper end of me memloer contachs the rigid guide plates Treat the steel member as a perfectly elasto- plastic material and determire the anal vertical separation of the nigicl bloclc and me guide plates Cie, detcrm the value of dwhen the load has been fully remored. (c) 1f L 1500 mm , deter mine the lowest critical buccling lood, p (d) sketuh me bucklinrg shope af hhe member if the [cwest crticol buckling load identified in pr 4 (C) ís reacted Prease inclucle sctton on Rge 4 of 05, (a) 220 kN, 1.33mm; () 2ON (d) figune required Consider a member wim a rectanqular cross sechon subjected to a campressive icod P which is delvered tmagh a rigid block on me upper end of me membe as tilu Shated belos Tre upper end of he member iS free to rotate abut axis ivechons D is constcured from lateral defiection in ane clirechians loy tme vigic guicle plates lusaed. The lonr end is ninged and his allons rotartions alcut one axis dlirection onl Assume member is made of steel with G moolulus of elashicity of 210 GPa and yieid stergth of 250 Mpa (a). Determine the value oF at wnich ne member wll yield in compression Cassuming LS Smal encughやat yield (b). Te initial verthcal separation of the rigid blbct and the guide plates is d=1.5 mm. Assuming L-140mm, melcod P is inceased unhil he member yields and deforms plashcally Tne load is removed when the rigid blecle on the upper endl of tme memloes contacts the rigid guide plates. reat the steel member as a perfectly elasto- asthc material and determire the fihal vertical separation of the vigicl blecke and me guide plates Cie, deicrmine me value of d) when hhe lcad has lbeen fully remcred. (c) 1f L 1500 mm , dehe mine the lonest critical buccling load, p (d) slcetuh he buckling shope of hhe member if the lonvest citical buctling load identified in pat (c) is reacred 05. () 220EN, ()1.33mm,( 2OŁN j(d) figure rigid block guide plate d = 1.5 : 40 Le=0.7L し,-2L Lc-I L,-05L

Answer 1

Solution cay e pblem Ly The Reckangular Column The uper erd of ist lade about is vetical oeis but not n Lae daveution Similat성 1k louer end Laderal direhan Therefore The Column 's hinged Gr pinned about so erds matenia USed for Coumnsteel yield strengB of m deney : 950 Hpa MPa Yie lding load ppng load Con buckling )oad P = ㅠ)をエ じ wher moment of tneha of Column IeTBd 2 l 2 22x2. 12 AsSumed