Question

An overhang beam with negligible weight is loaded as shown. Knowing that the flexural rigidity of the beam is El = 100 x 106 Nm?, (a) derive the elastic curve for section AB of the beam and (b) determine the slope at supports A and B. 10 KN 5 kN/m АР M = 40 kN-m B 4 m - 2 m (a) V = (b) ӨА = = Ob =

Answer 1

FBD 4m da Lokalm Qoka skallm loka prodhimb dy Rt tum Eam Equivalent load for UDL = (5x4)= Lokalm at 4m = 2m from A t MA=O (Hinge support cannot resist moment) (2042) - (R2 4) +(1086) – 46 =0 R18 = 15kN -02 20+10 = RA +RB Efy (=1) 30 RA +15 RA =15KN Joka jha skallm lokn A day 40km 15kn 15 kn K .im kam we can By using Double- Integration Method ).. Ely" = M₂ find out the required. Hati X 5 kulm roka A pecado al 40 kNm 4- 15kn 15kn Let x-x plane is at a distance of am from Mi My 5x(4-2)² -15 04-) + 10 (6-2)-40 n 2 :: Moment fouala wel تک EI [ word Ely's Me y ña (5 Cucoio 13 05-12-20 FI [ SCHat 451-40] slope y'= Sy" dx + C, deflection y= (Sy dx. dx + C, att og er det eneste som har [ sa - 400] + C / ti ( tas nesto posto de 2004 y' 5x(4- yo + 5a FI 3 y = [ 4 ฯ at a=0 y=0 a = 4, y =0 deflation yer- + cutes] } supports as no fon *** + 0-0+0+] (-5) os a [0 + +46- 5 24 ET C = -53.333 20(16) 3 140 3 (= so → slope Equation @ => y = → y y'a quadt 52-4 2-40 + Ti [<< 400 g- 202 + $02-0 Deflection Equation of AB 2-0 A y Contro] x 26.666 8 lo Force variables are in kal "FI=108 alm2 26. 666 = 105 kNm2 165 2.667x10-4rad © =)9= 4 B 2 y'al 0+ Şx16 -(1064) +50 [-40] los = -48104 and B