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Using Conjugate Beam method find the vertical deflection at D and slope at A for the S.S beam loaded as shown in figure in terms of EI

Subject : Structural Analysis 1

Topic : Deflection of beam

Difficulty : High

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1 Answer
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1. Support reaction calculation:

MA=0(+ve)50×4VB×5.5=0VB=36.36 kN()FY=0(+ve)VA50+36.36=0VA=13.64()


2. Draw BMD[|+ve]

B.MA=0B.MC=13.64×2=27.28 kNmB.MD=36.36×1.5=54..54 kNmB.MB=0

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3. Draw MEI diagram

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4. Draw conjugate beam and consider MEI diagram as loading on the beam

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MA=0(+ve)(12×2×27.28EI)(23×2)+(12×2×13.6EI)(2+23×2)+(2×13.64EI)(2+22)+(12×1.5×54.54EI)(4+13×1.5)VB×5.5=05.5VB=1EI[36.37+45.33+81.84+184.07]=1EI[347.61]VB=347.615.5EI=63.20EIVB=63.20EI


FY=0(+ve)VA(12×2×27.28EI)(12×2×13.6EI)(2×13.64EI)(12×1.5×54.54EI)+63.20EIVA=1EI[27.28+13.6+27.28+40.9063.20]VA=45.86EI


5. QA in real beam = S.F @ A in conjugate beam.

S.FAL=0S.FAR=45.86EI()


6. yD in real beam = B.M @ D in conjugate beam

B.MD=63.20EI×1.5[12×1.5×54.54EI](13×1.5)=1EI[94.820.45]B.MD=74.35EI()

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