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

LOKN Free Body Diagrum Ay= Reaction force at a Byə Reaction force at a 5KN/ .B by A am -4 m >x MEYOKW By take Ay moment at B=0 Ayx4 = 54x4 +40 - 10x2 Ay = 15kN Bending moment Equitation for AB, Ma = Ayx - 5X4X2 MX = 15x – 5x? from EI cl?- 2. da² = Mx EI day - 15% - da? on 5x² in Hegoating EI dgn 1572 - 5x3 +C, 6 integrating EIY= 15m 5x 4 tGat (2 24 cotxo yzo EI (0)= 151073 - 5(0) 24 & C, 80+ G (2=0 at a=4m y=0 EZ (0)= 15814)3, -5643 t + GXY २५ C,= -26.666667

hence Equation af Elastic -26.666667 x x] Cure, for AB V-y = 1 [ 9573 - 5x4 and stole Equation for AB, ÉI [ 152 - 543 – 26-666667] 2 Y dy Q. तत्र ΕΙ for slope O A = dy at À put a=om 1 15X102_5(0)3 EI 2 6 dx/x=0 26.666667 kNm2 EI 261666667 X103 Nm? 100x106 N m2 & A.-2.6666667710-4 sad slope at for slope at B but 06 = dy mucho en l x=4m 15x42.5x42 6 5x4° -26.66667) २ 40 kN m2 EI = 40x103 Nm 100 x 100 Nm2 08= 4x10-49ad Slope at B