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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
written 7.8 years ago by gravatar for teamques10 teamques10 ★ 70k •   modified 3.9 years ago

Subject : Structural Analysis 1

Topic : Deflection of beam

Difficulty : High

enter image description here
structural analysis
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written 7.8 years ago by gravatar for teamques10 teamques10 ★ 70k •   modified 7.6 years ago

1. Support reaction calculation:

$ \sum M_A=0(\circlearrowright+ve)\\ 50\times4-V_B\times5.5=0\\ \boxed{V_B=36.36\ kN}(\uparrow)\\ \\ \sum F_Y=0(\uparrow +ve)\\ V_A-50+36.36=0\\ \boxed{V_A=13.64}(\uparrow)$


2. Draw BMD$[\circlearrowright|\circlearrowleft+ve]$

$ B.M_A=0\\ B.M_C=13.64\times2=27.28\ kNm\\ B.M_D=36.36\times1.5=54..54\ kNm\\ B.M_B=0$

enter image description here


3. Draw $\frac{M}{EI}$ diagram

enter image description here


4. Draw conjugate beam and consider $\frac{M}{EI}$ diagram as loading on the beam

enter image description here


$ \sum M_A=0(\circlearrowright+ve)\\ \left( \frac{1}{2}\times2\times\frac{27.28}{EI} \right) \left( …

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