Question

Question 11 15 pts Consider the beam below. Note the directions for X and X2. El is constant. A) List 2 boundary conditions and 2 continuity conditions that will help you solve for the deflection equation. B) Use the method of integration to determine the deflection at "C". (Hint: use your boundary conditions first, it will help simplify the equations). Your answer will be a function of El. Upload your work as ONE pdf file at the end of the exam. IOKN.M 3 1.5m Зm < x2 Upload Choose a File

Answer 1

(A) Boundry conditions: (2) deflection at Alya)=0 (l) deflection at B (YB) = 0 Continuity conditions:- (i) slope just before C (y'(-) = slope just after (ly'ct) (i) deflection just before cly(-) = deflection just after c (yet) 10Krom B A 3 RB 1:5 BA _6 9 EF=0 RAT R₂ = 0 RA = -RB EMA=0 ) RB X 4-5 - 10 RB-2-222 kN) from i RA -2.222 KN -RB (up to c) Solving from left, Mp, RA'x, standard moment -cus nature equation day dx² EI m 50 dy mx, RAX dx² EI EI

on integrating eq) SRAZ, da RAK? + a EI dy da, 2 slope cet c (x=1-5) = yć (15) +G y = RA On on integrating eq (i) RAx} +Gx, + 6 EI Y = (r) using boundry condition (1), at x, 20, Ya 3) C=0 RAXI + Ga EI Y= deflection at C (x, 21-5) = yo BA (15) + G (IS) EI Ye = R (vi) 6

Now, solving from right RB • X2 Lupto c) Mas Maz Reille daze EI ΕΣ 2 EI dy 2 y slope at on integrating eq (ii) (26. dez des Roxe + C - (viii) dz c (2 = 3) = yé gc = Re (37 +63 (ix) equating equalion (iv) and (x) [continuity eq i] BA (15P+= 89 (33+ G-C = 2.22249 - (- 2.222 x 2.25 G C = 12.5 on integrating cq (Viti) + G & t Cu (x ) 3 El y= G 2 RB X + C3 X using boundry condition ), at d = 0, YB 20 & Cyzo ЕТУ Bergy deflection at C (22= 3) = ye EI Ye = (x11) Ro (3) +G(3)

equating eq (vi) and (xii) [continuity eq il RA(15) + 6(1.5) RB (3) + (3) 3 3 6 G-2G = 7.5 (xii) solving equation (x) and iii) G= 19.5 = 7.5 Putting value of G in eq ci) (1.5} El Ye = 6 and Asii) solving eq. (x) G= 14.5 =75 putting value of Ca in eq (xii) 3 EIG RB (3) + 513) 3. Y = 25x10² m unht for y is decided by considering EI units in N-m? ΕΣ