Question

8k 3 k/ft -- c) Slope and vertical displacement at point D (use kN and m) a) Conjugate beam method (El is constant)

Answer 1

ANSWER:---

CONJUGATE BEAM METHOD:--- Conjugate beam is defined as the imaginary beam with the same dimensions (length) as that of the original beam but load at any point on the conjugate beam is equal to the bending moment at that point divided by EI.

The conjugate-beam method is an engineering method to derive the slope and displacement of a beam.

Given 8k skift 3 RA uft uft eft IRC using the Conjugate Beam method, find slope and Vertical displacement at pont D. Taking epopent about B about' right part of Beam Empo (Rex3) -(3x3 x 4) = 0 9 3Rc-36 RC = 12k Efyzo RA+Re = 8+ 3x8 = 32k (RATRE RA+ 12 = 32 RA= 32 - 12 RA = 20k Taking yompent about & Left part of the Beam RAX8 -8 xu+MA 20x8 - 32 160-32 MA МА MA = 128 LA Conjugate Beam Method :- slope at any point a Real Beam = shear at Don't in stear at Pont un conjugate Beam

in Real Beam deflection at any point Bording yomgest at the point 'Congregate som Bending onyert diagrams by pasts about pourt ist 160/er abler 126 fy - 37313 Em Labler To calculate Rc , Taking youport about B' Embo (R! x 8) + ( 2 4 60 x 8 x 8 x !) + 9 Y 2+1 2+2 x 32 xцx Ч+ Ee 3 F2 xdx 4 + 1 +96 없을 6656 + 15616 3k2 Rexo - 3 fer 8 RC = 8960/142 RICE 1120 JE 373.33 R2 Calculate Shear & Bexd hug yoment at pont d. Take Section at Dc of Beam.

3 49 helhen x=8ft, y=0 96 96 uft - Y= ax² y=axt uft then a= 2 96 = a (8) 94 64 kr kelton x=uft, y=? y = 96 x H)2 €264 24 Ez 96 373.3 Tuls ft hu Ely=0, VD-32 ab + 373.3 Ez ka &2 = 30qB Slope at point d' 301.3 EL

мь 0 - Mox(1) ) + R)-- 14932 T 32 128 Ez 1493' + 32 -12 - 13.97.2 Ez BM at any part as Conjugate Conjugate Beam an to deflection at that point in Real Beam equal