CIVE 310 Lecture 4, Fall 2011

Axial 5tiFfness of JRars | Definibion = - Jt ts the farce required t attain a unit eleformatan. Tt 13 elepenclent on. geometry and material o§ structural element and independent on loads. 4 0.€.; Nook’ law => FP2k.O , Sal => K=P. | From hooks Law:. P=2k.d. Ws 1 =—» Ke i: “P= P => k= Pe Sp \ Put a= FL — K= P A (Z) a k= ZA lOhen. bart subjected % aunit aval load (PI). ., Examples. j : CFrevieusly Solved). pe_1600""% _ 4 2000 pty 10001 | Remove all applied loads. Given: A,=t000 mm ; Ay = 2000mm. Le a Apply a. wnit axial lad.at tp... E£= 20G6R.= 200 KN . . mm* i. A= s PL - 1 (7/500) + 1 (2000) + 4(1000) _ 9, 0 16.25 mm. t=! EA 200 * 2000 200 * 1000 200%2000 NT KN . raN 0,01625 mm, ——_—_—_——X—_ nna Vreviously solved exarnypled..... = . LTapered Rodd... tL we. have computed . A, for. F=60 pasting at. end 7B. of hte bar. 12304 ate Ap =. 3955mm,». ke man at 6OKN ~ Ap 0. 3955 mm. i > ka. 191.91 KN 4 ene mn = 60 : = m | e8 his tapered. bar. 68. Agwivalent ont He Giaterms of axial stiffness). ta a linear. Clash... Spring. _.,. of Spring constant. K. equals te..154.H Kong Tate thickness E=25% kw? Koetst 4 Yc; _ 4 _of the member. and. ating Lhe. vanrajaonling > equilon tins. - + FThe. eg ult: A btietlthe equaltens.. must he. complemented. by. relations... 4 tnve lying... cleformations. obtained. Ay. Considering Lhe geomety ry of Le.. mau 4 prbkm.. Because. statics. 1s not sufficient to cletermine. either. the... external reactions._or- the..talernal at foes ye Such... Locklernina te P ble lens. ct EK co wpe Rap Ree Po pg el oe a One. equation. anil tuo. unknowns 4 Se Stakics not sufficteat...- a a The. indeterminate. system. tS. cp. C= 4 . ate superposition..of twa. statically | alelerminate... SYBLOMLS. 4 IB. SHOW. 2 CRixation at C ) \ ss Frimary System => Get ho= » Felease. one redundant mn allow bq clue te applied loads. ave w+Vve +Ve +VE _NLE.D. O-~ Diagram. .€ - Diag vom Reeth _CNormal Force Diagram) —.. i => Og = aay — Prom Me. Displacement Diagram)... t ee fed. Hl L LR simply =>. A,: Bn lk Un = [Ex dk = [&d dx .= Jew o 1. ap A= x Puli .- C2 Segments => t'=2.). i BAL Fils Fela é ‘| A,= Heh « i ee EA, , ZA 1 ans K F2P kK G20 se So re ... Cdownwards) . aa * se SetondanySy ster => Cet A= o. For Lhe Same primary system. clelermine, A, due. t Re. | A,= Feb --.. (upwards). ----~ C One. segment). |) Compatibility equation ; consistent cleforita lin atl . - > A, =0 oo 4, +4, =o > #- RK a as Res £ a Ctve inchtakes tn the assumed sense). K Ta = PR. = £ OR. Fy = Kay + Ra, = PeC Rod= EF. % oO. Diagvam. .€-Diagvam. . Displ. Diag. Relative to A - a STEPS ee . + dd). "Afterdeleumining: RU, Plot INE ea -Q).Plok..0 Diagram; Ty-= & pent (3). Plot _¢~ Diagram, 6, = Oe = fh A). Plot. -Displacement. Diagram. ‘Relative... poimnt._A.... A, raf Ex dx = My te _ Alrea.0f Stren. hapram. betacen oo £ A ANM. Koo oe Use. P,l- PL ee B > HEA Mes. tPh . Ft 20 Gone. support i D.