Question

Question 2 [20 MARKS] Using virtual work theory, determine the reaction at supports C, A, and E for the frame shown in Figure 2. El =137500 kNm2 10 kN/m 7 D 10 m 5 m A E Figure 2

Question 2 [20 MARKS] Using virtual work theory, determine the reaction at supports C, A, and E for the frame shown in Figure 2. El =137500 kNm2 10 kN/m 7 D 10 m 5 m A E Figure 2

Answer 1

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DO! original structure can be dinintegrated sito structions, curing brinmpte I rupert the following two osition, taking f (since given to take Ay realondant. onie 9 Fig.nl 'Ay (a)

a nee fone to 199-21 Note- ve have wed only Ay redund ont because the Briginal, structure is having si determinacy, De = c 2 = 273-1-9-)) Thus, we only need extra Meantion Complete reaction forces will find the reaction Ay by finding the virtual me diep lauments Day of o the structures (a) and (6) and wing Compatibility determina - To find the displace the displacement SAYA Virtual Hethod. - from the virtual Hathod, we any diep lasement at A, DA - Mm da et will ccue EZ where H. Morrent at section at dit ame from origin in the stormnture with external loade cea) m- manert at sections distance form onigin is the structure with virtue load is wanit lood cie. (b).

JP 9-3 * For Aly in streatures (a) * To find t' of Structure (a) :- .P An 7x Cy By (Fig. 2) Elx=0 AntBr + G =P) (1) Efyzo = By-ly) -Gi). E Bending Moment at G, Mg. Me lide Cyxat Caxaco =) 16e --Cy] (10 Similarly, HE - Anx Ga so (from left hand Ano fin - Me o - Axxsat Bxx2a + By x26 - P x x = 0 (Bx t By : 2 32. 20

JP 9-3 * For Aly in streatures (a) * To find t' of Structure (a) :- .P An 7x Cy By (Fig. 2) Elx=0 AntBr + G =P) (1) Efyzo = By-ly) -Gi). E Bending Moment at G, Mg. Me lide Cyxat Caxaco =) 16e --Cy] (10 Similarly, HE - Anx Ga so (from left hand Ano fin - Me o - Axxsat Bxx2a + By x26 - P x x = 0 (Bx t By : 2 32. 20

ау From (2 с.). В Р (Р.) б) . . ) : 2 10-с.)-(- (s) - 2 , ) 2 s) 2 - 20 - 2 2. =) (cal 2 : 2 2, Р 3. - С.Р. Ч Then went My х ю be shown Р Осуух ба Осхе? < xide o Хуу? M, M2 1 < 2а

aboue figure culcan find the Mi-o 4 M22 - 3 P xa M₂ - - Prez My- o 4 2 - Now Momentum Estruture 6 with unit on virtual load at A is y-di- rection, A cie Ayala for the 5 a g TBY Су e tn. My 71 Smit - Bxt En Deri Ely, It By = Cy By - Cyst

- Pendling Moment at G =) (Exa-ly > MEO - 1x2a=Auxba :) An= 1 camit - Elco - Aux Sa Bux20 Byxa -lyse.. txser(ButB) x 2a-sa-o But By: (1.- 27 | Bu + By = -2 A Here, the direction dirution of reactions is the previness struction - Ca Hand should not confuled Pured with that. Putting in By- (-(x) = -1 s) By tla :-) 2y + Di Bulan Ilm- - Box B By-Bra cu nut some اوس (ر) V

-ار solving and Evi weget. - کے - 2 - 1/2 - 2 and Bra 3 - :(2) کے Bx 킁 رو 6) 2 =ر (= ( هر 2 ) - و) : ولا 2 This Moments, in com he thown as عن ۲۷3 mo هراز > 0 my <3<3 د ۱۰ و از > و 3 > > M, 0 20 21 >

1P9-8 M-? 6 mez m = 1 Zmou 2x my=xba.+ lilly = xy-da ms 3 - 35 - -3ns tha 2 2. me the dar This Day - som de Smmon for all the members, saleem My dose a fost (ma.Az dast - may. My day +{ms Ms dos My sosnaf og en todos ploma Ha).olm 10-30% (-LL-32) 22 -0 dom 3 ja - ZP

S. Um 10) elming sms)(-). 0 3 3 P 20 o -Pal 8 sa 3 my 22) Xoro day - Ilony-20) (-32 + 3 a) . Pas Safns'tts) oling x 2 2 1 ( 24"-42") -- DAS: So tell a 4+ ( - L a toto - DAY - SP 62 P. 22 12 I FI To find the dietaurant in stuntures by b) cic Day mom dx In de dr. IEI دارای o so se na tome da +2° + n).ens 4:22)

Polo yox 9 7 23 12/1/8 72 je 3 . DAB u 27 so + 149 To8 f 3 312e + 19-2a) 13e (Q-15 2 s) Day 49x 274 tik +213) The 24 2844 3 ET - Q? (24+ kr 132 + +28 362 36 . from compatibility, Ayx AACh & DAS 63P 82 Gor-0.760D

19-11 Now the structure will be E 20 — Р B > Ca Acy By A e An V Ay = o p or 0.77 P. { Fr=0 : AntBxt CutP =) -Ay t Bytly o :) Byr Cy = 0.77P Beresting Mount at Els are zero. o =) Anxbat Ayxaa. =) Axe - Ay = -0.20p ( "Ars 0.268) Ano

ГР /2 | че е c) Си Хоя Сухато = 2C 3-4 (м) ΣΗ. =) Antse Brxza + Ayxsa - By x2 + Pxaro О. 2 с/хла + Dax 2 + 0 72 хте - руха tpero Ba-By - 2-o75 Р. from - Baten = P-An. =) Butl-Cy) a Pto.2cp (hen i - 23 - fo.ap - B): 1.2 «Р 77 But By = 2.03P + Bя - Р --3-оP— (0) 2 Bя о 2-) : 097 Вх = -0.5-Р 2 (-) 0.52P = 1 By = 2.550 and Cy=-1.78P Cu = 1.88P

Then Therope) 1Pg13 becomes олара 7 (322pa) 1.sopa -1.56 le 29 <lg.19 Pa) HAPA e stop 11.89 ca se 0.52P A 0.268 Top Vo.72 P Bending Moment are shown, blue with black with =). #