Question

Structural Mechanics

03. Determine the maximum deflection in the beam AC. E = 20 kN/mmand I = 1600 x 106 mm". (6 Marks) 18 kN 2m 4m — в TICIT

Answer 1

To find the maximum deflection we use the double vintegration methode step (1) find the Mon at a distance & from support 'C' . 18kN 4m taking moment Equilibrium about point A. EMA=0 - ro REX 6 = 1882 Re=6kN) For Ma, cent the section between B4 C. 66N [Mm = 6x] w lah M Kом дар речі "с: bесaллaf Ком loading diagram of beam the maximum deflection occurs im blo B 4 C.

Step (2) Using the double Integration method: Es = Me - su Es e ox - 0 Integrating equation ☺ Worot. dn. we get Es een 632 +a cazarin [email protected] da, we get Egy a lehet G4 + ® Using the boundary conditions" (ed at razo yao cap at x=6m yao o= 623 + ax GX62 - 6823 E 6 put = 6 [65-36)

Putting the value of G A ce im Equation (21. El dimone + (-36) 1 & cat maximum deflection slope of the beam is zero te dy ao at maximum deflection * 0 - SM -36 on=VIZ = 3,464 m Hence at a = 3.464 m max. deflection occurs. thing Equation (3) ,4 a, se values, we get Ely = 628 - 368 at x = 3.464 m y is maximum EI = 20 kN/mm2 x 16008108mm4 = 324109 Kn-mm2 EI - 32000 KN-M2 Using the above values. 3covo Ymar = (3.464)9–36 (3.464) Hence the maximum deflection in beam Ac is 2.81 mm.