Question

Question 3: (8 Marks) Apply Moment Area Theorems and Conjugate Beam Method to determine the slope and deflection at points B and C of the beam (Figure 3). El constant. 20 kN 400 kNm 15m 10 m Figure 3

Answer 1

zokn 4ookm lom M/81 diagram Conjugate beam with lo In Conjugate beam shear Pore gives plage of real bean at that point In CB 8.M giver deflection of real beam at that point · SF3 = * (7 .) x15 = 325 tentunya -- Plops at B= Sesonde BM0 = 4x x 15* (-3x13) - 400 x 15 - - 675cm (tales) : Deflection at B= - Shop = 1925-(Nm S.fc²8250 + 400 x ETER ET ... slope at C= 14250 BM 5-2 Port x 15 x(10*3x15) - we - Home Koning Deflection et co - 2000 ET uring Marient Area thony i EI og = Area of the diagram Who HR B = x to content is a festa de = A2 = Moment by Areas of M diagram blo AdB about it =-** X 15 (19) - z ISY LE = -67 oc = Aree of a diagram blow Ad C= 8280 & 400 x 10 = 12250 de Az = Moment of hore of m diagram blow the about a --x 15 (10+10)- 4 x 25*%£-force - - Please Ceine Rating - ET

X--- 1 *Most Important Sign Convention used: Right of the section downward force tve Left of the section upward force tve' Similarly Right of section upward force tve left of section downward forcel-ve Mor Bendling Moment: B.M due to downward forces taken as-ve B.M Olue to upward forces taken as tve cox) Sagging Moment is taken as the Hogging Moment is taken as -ve.