Question

^{For the beam shown, use the Conjugate Beam Method to determine a) The deflection at F, b) The slopes on both sides of the hinge at C. 90 KN 160 kN.m E B с D F 2 m m 2 m 2 m 2 m EI = Constant}

Answer 1

Solution : Criven that :- Use Conjugate Beam Method. El=constant. 90KN 160KN.m E A DD -F С. f * zm 2.m 2m zm 2m DE - EL ola 7 it f 이 B > M diagram of Real Beam. E EL Menu 80 The Internal Roller → Consugate Beam AXK "B 2-4 -1.6 la E change and its loading 'FF Internal Hinge su ET Here se 2.x lood=40 20 80 EL Чо 50.4m 100 gia ox 910 207 2or

- Support Reaction of Real Beam in Ev=o V-90 +VE = 0 + VE 90 km-0 Emc=0 (Internal Hinge at C) (VE*4), -160 =0 VE = 160 = 40 kN (1) from equation ☺ go-40=50kN (^) A T Bending moment in Read Beam in (Right to Left of a ME OKNom ME =okarom .80KN.m MD, (D-Left) - Mc e (D-Rights = NEA2 = 40*2= 180 krom NEAR)-160 = (4042) -160 = To knom =180 knom (V*6) — 160 = (4046) -150 VE*8) -160-80*2) = (4048) – 160-180 Zoknim MB MA A

- Support Reaction of consugate Beam in tà* 0.4* ) - V + 6*16) + $*2*- W=0 V it + V VA 140 EL EME = 0 (Internal hinge at E) *2* -(3x0.4 2-867) + ($*** * * *6.533) +(+*24 * 5.233) -(444)-(* ( ** 2 * 2 * 1333) (+99.24 176.641 (+) EPA 706.564 YEI EL 176.641 EL 170 EI from equation o VE 140 .36.64 EL - ve Sign Shows assume direction of NA is wrong. Hence Vý' = 36.641 (1) ET

The deflection at "f' :- » Mour's and theoremia Deflection at any Point in given beam is equal to the Bending moment at that point in conjugate beanmi Hence (Srb. Bending Moment atronjugate Beam, Real Beam *7.333) - Limundo -(1204** *9-867) + (6*1.5** *2.55) + (112* ) -(1976.6.1. *6) -15*2*88774.667) + (*_*2** *3.333) - 73.282 Ant (ore Sign Shows = So EI Downward deflection)

The Slope on both sides of the hinge atc!- & Mour's 1st theorem in Slope at any point for a given beam is equal to the Shear forree at that point in conjugate beam. Hence Shear force at (Slope at left of 'C') left of Contugate Real Beam. Beain :-($w0:44 a) +(ful.com ) ($*2*) + 140 and (Slope at Right ofc) Shear force at ! Right of "c' conjugate (Real Beam Beam) 140 Ni' 140 140 EI 176.641 EL - 36.641 EI