$1$

The $4-$span beam with dimensions $300mm700mm$ as shown Figures $1(a)$ to $1(c)$ is an indeterminate beam subjected to three different load cases. Analyse the beam for the three loading cases using "Moment Distribution Method".

$($A$)$ Using modified stiffness factor method, determine the distribution factors for all joints.

$($B$)$ Calculate the fixed$-$end moments at all the supports.

$($C$)$ Determine the final member end moments by using Moment Distribution Method with modified stiffness factor. $[$The calculation is considered complete when each of the balancing moments $($distribution moments$)$ is less than $0\mathrm{.}2kNm.$

$($D$)$ Draw the free$-$body diagrams for the beam.

$($E$)$ Determine the reaction forces at all supports.

$($F$)$ Draw the shear force diagram envelope diagram for all the three load cases.

$($G$)$ Draw the bending moment envelope or all the three load cases.