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BE$8234-$ Questions for HBL $4($AY$23/24$ S$2)$ : $2\mathrm{.}5\%$

Topic : $3\mathrm{.}1-$ Moment Distribution Method $($Beam$)$

Figure $1$ shows a continuous beam ABCD. The relative moments of inertia of members are indicated on the diagram and all the members have the same elastic modulus $E.$

$($a$)$ Determine the stiffness $($K$)$ of each member of the beam in terms of $E$ and I.

$($b$)$ Calculate the initial fixed end moments in members $AB,BC$ and $CD.$

$($c$)$ Use the Moment Distribution Method to analyze the beam.

$($d$)$ Sketch the Bending Moment Diagram for the beam and indicate the bending moment values at the supports $A,B,C$ and $D.$

Figure $1$