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a a AUNFLUENCE LINE : a Q) Defiviation . ae The. chrcturca, aime subyected to two type of Loads - 4 one is: static: Load. ood ' omnetirarc Lond . Is smoving Load, jhe ‘a Stroucturce. 1's sulsjecated to maving pads - the internal Stresses sone Jpn din the position of the Load Systm” Th is beathere AsfFreuelt © exerpt mA Simple cases sto placa the maoving loads « : x oY the: structerea, ito, prcadivea. MAK RAN Streassam (Re ee ot an Saation - Tho. - uses moda. of tfluanea, Una. - = ed: momen ; shoare forceos,, ghesser er deflection : ~ at a potnt is Varying pacitinns of a _ Lena 6M th Spo, i “Bo Trfluones. line. Sie. given point ave section a a Structure fs a ture a hase, arcdinate.. Pe presen) dy Seal the . Vartition fia finction, such as ; gpoar. feces barn moment, doflschion. Tha Taflumea, \tna. “ace val usefl © ay a &p deleroninech Or of thy volar of | afimohon ak tke given Sechon Under. Complex System oF Leading. . . “d binges which show the vareiation of ‘otsition- “ nara “The. oduincta, of a cure of BM | SF gives te 9 Nalus. of the BM/SF at tla sec where the —— attdinate has lean draun “Whdla vn tle Case an tnfluenca. Wre the ordinate. ot ond Pomt gives the Value ofthe BM/ SF. Tevfliuenes Une fore deterc ra nant Stuctune j Tnfluence Line fore Reaction 4. l (a) Simp Supparted bear —— p&p Unt Load Let aunit Load ack of a distance ! “ cae “eB “ye Fito A [ i) L 7 Ta Ki’ 1 Zt ~ | Ra Ra 4 amon}! atcoul Rn i Rexl = Ax (1c) : | \ Re = KH |. | Ue | + + i Whim xX=-0 Re=0 | } Kee Re =f TLD fore Re YF & Manoel abort (@) | ZVe =0 4 + + | Rat Re sd Rat Xo 4 Ry = 4% TLD fie R, A Wheree x=6 Ra = eb Ra=0 b ) To fluemee line foro On point in the Supported om, of Oar, dverchange at ona sido Unit Load To drcows trfluune fore SE gh a a Point E at distenesr °c’ eon wW) rnfluenee Une fore Ra is | clicaum ‘fost. | Unit \ood is to the laighto Eu (SPpin ope = TRA ". Tflumncs line for(aF) at E Wh the lead is totua Yor'ghtt of Seaton will be Sama 4% Mofluons line for Ra Lantt baad | (SPot wight of E = Wc) | La aa a (Sat path O= - & Y a | unit Lead 1's tothe Left of & (SBay let of & = Rav td = i_Cc_ Ak -~& L When Lhe Load fa at A, (SF), aa (Ra 9) =0 F ic, W Tafluance Line for teeactions fore a loeamn varth overchong m om side “shod , _ othe Let q voit Load ot a dishne >) We \ *f * . freom A, : . ~e Tekieg ° a momant ak poi Suppoct A _ i i i K Re= Sa CT] T+ al Thy | When %=40 Ra = 9 (+a) Kel Ra =4 . = =(4t & TLD fore Rg x=) Re= (tt) | a J Ra = (\-Re) 7 —_ =i) | F a YI A LE ' _ _ (+) ‘3 CY . When = 7 Ra = ; 44 | | X= bt Rasa i ee eS i SF/ RM C) TInfhunce Line foro a point (S®) § kann with averthare wn beth side it Load ; . Ay " To crews Enfiuene Lene fore SF wats ° r \ diskma. ¢. fcom 54 at a potal E at cis Rie ¢ + —-& 9 Ire A. enfluesne line fre Ra ts drcawn) = 6b, L TR Wagan Onntl Load ia to valght of Sectian {Loe (SE)or E =+Ka =(ES) | | infiurrea, Lene, fore SF ate vohsn | | | Lod ‘stothe Volant of Saotion will ez. | | Saves. 8 trfluenee. lina foo Ra. “a L . . QSYUGE re then Orit Leod toto Left off Setien } (@s) Y, Zs i | GSPat ES (Ka-4) =bE4 = (=) ILD fon Ka = | | When Load is at pon aA | (SF at RaTw4 = 0 by [EZ At Lone % OL, YA | When Lead is ot point ® F eo Ure i | ~ : L--f © (SFr g = Ran) i i | - ith, “4 “2 {)-Fofuence Line fon point CSF) a bean { . of Commi every ng dinates q ‘ betwen, oS 8 — Unik load ts lotaeen, ma ju. LE .Wron +4 the 8 ° MASE at E wi wn} bene luna. ling aredinate Udi tt we /es) 4 4 am £ 2e Lofluence line foro Bending Moment Influence line fore combilevers Brown : unit Load i 4 ¢ ie hen the Unit Load 1a between, At Sey A &e ,the BM at ¢ will be ‘ L ' Zoro - 1 Tinflumen ting. ordinate ors Si (Go) at € will be zero, When the Load belwean A and c. Me ¢ When the Unid Load betwen Bac al a distene. x feom B (BM)at @ = ~4¥ (OK) Whin ~=0 (BM Jat Bz7e x=e OM)ye = 0 nflune: Line fore BM in Simply Supporcted Boom + UnitLoad A ror 8 Simp Supported beomn AB | 4 wo __} ef Spon L: Let a amit Lead gz bia) Vo= & Move. from the end RW ty theend Jt ‘B) of tha beam, Let IE is the aren Sackler Sotho AE= C W296 : c : ERS (> @) “) Lek Aha anit Lead at o distomer Le. $8 % frm re le and A, | "Rectan at A Vin ($9 | Riaction at B Yo = a ts ae Tnfluence Line foe BM in one Side Unit Load ed A 5 & 8 F ' Cc {i= ¢) a Va. Vo Srenilare Vreneglt ate jel Cc) | “Ea L ac Y= 75 ) zZ | ey ac + c rey Seppactes tem AB of Sporn *? end overe hon aka gh arise al a ow fot a WO Lel SE) 1a the given Sechion onthe. beowy — <0 Let the Unt Load at a distance Freon the Left ° Racin ab A ® Va= (2%) Roochin at B My = L When Vil Lead behoen A SE Bending moment dus to oni Load Ma = Melt c) = 2S = oar a AE=c , EB= Q= ¢} ad A 2 qe loy fs Os* Coy, natal ace theme ll a Bering moment at (A) ohare “= 0 el | Ma = Gef).x = UES) oO L = O =A w= G Bending mowent ok ) Waa Doe = CEO = U9. See ~ “ el . ae | : Whey Uni \ead elueon _o, | @ volume ox i : (sje & A dua to nit Lood \'s avn a? we Benelivgy =o Va. ht pega st. rere Mz = Vax . avr | ° =U). ¢ Ms S (ee ees co £ON Bending moment at £ Chime wee - a Me=GP-c é 48s | Thy ~ PUD e gee wee . — N £ yo L er - f Bending Moment at B whens “=> @ eek | Me = WA) 9. Usb e = 022%) L a —- unit Load loetwomy 6 oF ; Bondi “4 eperene Ate. bo onl + \. oad Vea aly ey boy | Ma = Va & (EB)*< aie = | = Ur) Mee Oe | ~ Bo \ L 1 | | pending mennsat ao B Whe tel | Bm Mpa=a ak ynemurt Ob fF Whe a= La Gene” _ (Lee A Mp = UES a Lohan can ae ao Ag - & wa — LO alan be Banding monent at B whet Leh g. (eM) = = O Whur Y= (No Banh moma at OD (8m) = Vy io <) = *UeY = eG? Example: Nua ; i 200KN @OKN 2 A D nN 8B ot i 4—+ 12. ——1 on i Find out the — i » Max posihve, & negative Shaarc forces. | | . Max Bending ynorment hie i | Moxt mum positive SF at D | The heavier Lead 's Placed at D Cre R00 | and BakKN Load a IS Placed QB of D | l il Mox: SF at D = (200%3. 4 3, x 80) yi 1, =+200KN | \ 8 Max mew Yugetive oF al D BOKN Load ig Placed Loft of D | Mox SF af D (hy 200 4. xed) | | = - GOKN CASE 1. BOKN Load qs Placed Jon OF fy (Bm) = 200X3 4+ Sxaq _ T20KR) — CASE 2 | BOKN Lead Placad Right of p @) (BM) = 200x3 +t Bug = BORN. uM : lax Bending Moma 800 kN fo 2G-13) 3s a ee cif ox QV) se at Moa V2) Bencling amnemosTt (BM) nox = > [aeece re] . a ‘ a - Miox -t ve. SF ot &ehme = BoxXCGRQs)4 2Q0X0625 on F WOX 0:41 +100 X 0 B75 “G + 100X025 + 100xO''S = +4+242-5KN. * U®osimuny Banding mame u The Wheel Lead Shown lain ng aall over. ‘alo at a given Section & loconn 40 mettas, 20 158 ap oF Span A.D, 7 f CPE 800g a = 88 he hp Load Craose : nd Avg. Lead on Avg: L tee Section O 4 AO ore rs Pemarek ia a | GO: BO ‘Bok “20. Agtasd AD Aoa Lenk an | “ - \ BOOKN) : : 250 x * FSBO. eaenna > BO KN 200 Bog 4 ~“S . Avs Le aD 8 D Pane tonal AD 3 Afiern \BORN Load Crossed the section D, Ehon AD beoemeome, Lessee thom fyg: Loal ow BD. Hone, Modem BM af D. hon We will place the \BOKN Lead exch at D. 200 150 300 50 se des dad Tr }- 4 t | ) e224 92 ; 20 L 1 Sh roy H | too Mextinen Backing moment at D = QWOALGL + BO XNA + BoOKD ' + HOA OL | = 1420KN rm / i / i } A Live Load of BOKN per mets. gyn Lo A eves ON a Si ted) inde of S AON. Find tha Moy @ meg ee | 4 pow, xX BM ata Sadtlon, dyn from Left end _ A D B Let the vevixa “move. towande . ; E +. 4 We. TK ia 4 4 the. ight. Ley We need af thy ae 3 Loe ke ata distance 2 wale. * ow f From a Seehion D A 1 ..% * a = 8 a i Zao ~ Lead en AO a Rone ay et g ae BOB-Z) soz. + 1 : . S noon yyy ya : 120 409 15) 2h ag \ ag Mox Patras Nemedive. shearc, Vo = (280%) = 190.X0-24 4400 0 64 | + 120 XQ-48) | = 629-6 KN). | Wa 250. —"_ = = ]BiQ-B e “og = PR WatW24 = 134 | ro ' a y Wot ate we anor 2 tretale vocqut ead). Mextmuan Negative. (SF) = 689-60KN Maxi ram Shear ot agin section ofa Beam The Lood Sustom moves fitom fo: Jeovant | to eft on 30 rmetras. ~ Find tho moxi \s A ghecers af Spoxy TALYN SF ata Seaton TBv0 Fram eh end. 6 — cox zo - ioa ‘a ven 4 \ >) ny. i rs tay mee —_ Ta Tes cause , = = oo = 85 Nova Wi fem C snd ‘oreing Wiz Overy @ =m We. BO > € Move. Wa frown @ omd. bret Ms avere = ee _ Pra 19-6 Move We from Q amd bring W4 Oven g = We xia = 60- G Fosm conden er) Mos 4+Ve, SF at Q ohn sige Load - _ i plane. at e, ONE NS 
