written 7.1 years ago by | • modified 3.2 years ago |
Subject : Structural Analysis 1
Topic : Deflection of beam
Difficulty : High
written 7.1 years ago by | • modified 3.2 years ago |
Subject : Structural Analysis 1
Topic : Deflection of beam
Difficulty : High
written 7.1 years ago by | • modified 7.0 years ago |
1. Support reaction calculation:
∑MA=0(↻+ve)50×4−VB×5.5=0VB=36.36 kN(↑)∑FY=0(↑+ve)VA−50+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
3. Draw MEI diagram
4. Draw conjugate beam and consider MEI diagram as loading on the beam
∑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)−V′B×5.5=05.5V′B=1EI[36.37+45.33+81.84+184.07]=1EI[347.61]V′B=347.615.5EI=63.20EIV′B=63.20EI
∑FY=0(↑+ve)V′A−(12×2×27.28EI)−(12×2×13.6EI)−(2×13.64EI)−(12×1.5×54.54EI)+63.20EIV′A=1EI[27.28+13.6+27.28+40.90−63.20]V′A=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[94.8−20.45]B.MD=74.35EI(↓)