Question

Problem 11. Determine the reaction at the roller support and the deflection at point C (Fig. 7). 1 1 1 1 1 1 0 w L/2— A L /2 Fig. 7. Problem 11

Answer 1

draw the free body as shown in the given diagram of the system figure below - A MA Ant A717171 42. it42 - Resoleve te for along horizonted direction, En zo 9 Anzo Resolve the force along vertical direction {Fyzo Ay + (wit)-(wond) + By to Ayz - by — celebrate the moment about point a EMA 20 Ayollar (6 + y por esta razo

MAF By XL - we - 6 draw the free body diagram of the beam section C o<n<42) as shown in Ho given figure belo Colccelate the momond about the section 1 Axe 1 EMC co A nl 7999777 Tv M. Ma el conem , J- Ayensa Ay Ma Mat on 2 I + Ayx from the bending moment equation, EI dy = M = Cาพ - Mot ann taus taya Integrate the above equation EI dy 2 Homes In = Maation ** | 022 ) + ( Ay 22) ter ne

ETY = exy = mana + ( w ) + ( Ayrs) tanta MA 22 + Gat G @ Wherel G C are constanes - stands Apply the boundary condition in reg © c d - VA - 2 trên G+ N o 20+0tota a con Apply the second boundary at azo, y zo condition EI y = Max2 + cont + Ayna e tante 29 10=0 to 40 40 +G C =0 и from eq a- EI dy = mas t on tag x m2 Ő Tā to oln at 2-4 slope of beam Ac is

EI dy an en dit mo($)+(3 (49")+(9 (30) from ed @- Ely = MARE t cont + 999 Ay nan 29 AA ALAM pred nz 4 to find the deflection of be Ac. Mann Сот 4 - PM 29. .....77U egy = manat come to Ayat 070 (+14+ ) C:1946 (457 enya amat (+)2 + (0)2 (61+ pen CE117 Similarly for the sea a section CA draw to ABD as . shown below- th-> >

Calculate the moment about polat C. [Meto Ր Դ Ր Ր, (Agen) - Ma - wel from the moment eg... EINA EM = Ayrtma tolm-41 - Intl Integrate the above equation 2 times Er dy - Ayrt mar twe Chile ո ո ր ծ ո Ղ Ո Ո Ո Ր Դ Ի Ր Ր Ր Ր Ր Ր Ր Ր Ր Ր Ո n.112 tonta Appl Apply in bundang condinion ine, the bounda Ո condinon in

of mal gz0. foom en 6 - AAAAAA LLLLOOOOOOOOOOO Age of Modern (1-12 ans tek to co – tool toe Aye & tmal 21 4 w 69 7G- er dy clyn Sino at n=42 of both beam, slope and deflection cn and As are equal. from eg © ¢ © C3z wit ouoca 48 192

Similarly at az 42 deflection of Ac and CA ane que from og @ to- M a 13 ]2+ lo ltt my n (13 my (2 tl "+ + Ca li lt ca. 3 put cas 1n abouc expression - . (4= wet 768 I put the wall of Go to in eg 6 All timone (4) + (- tool to co XL - GL2

testy 14-4334 + 423 ) = 0 ogla - O Cool 768 17 GL 64 The moment, at point A is- MA = By XL - W2 LOLL 644 69 at point C. Find the deflection from ea @_ saya tahan () + 6)6)(4+ (319)

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