Moment Distribution Method — Worked Problems

A prismatic beam $AB$ is fixed against rotation at both ends, has $L=6$ m and a downward uniformly distributed load $w=12$ kN/m. Find the clockwise-positive member-end fixed-end moments.

A prismatic fixed–fixed beam of length 8 m carries a downward central load of 64 kN. Find the two FEMs.

A beam member has constant $EI=24{,}000$ kN·m$^2$ and $L=5$ m. Compute near-end rotational stiffness for (a) a fixed far end and (b) a hinged far end.

Three non-translating members meet at a free-to-rotate rigid joint $J$ with near-end stiffnesses $8$, $12$ and $20$ MN·m/rad. The algebraic unbalanced moment is $U=+40$ kN·m. Calculate the correcting increments.

Beam $BC$ carries $w=12$ kN/m over $L=6$ m. Its near end $B$ is rotationally connected to a rigid joint; physical end $C$ is a hinge. Find load-only moments before releasing $B$.

A continuous two-span beam has $AB=5$ m under $w=10$ kN/m and $BC=6$ m under $w=12$ kN/m. $A$ is fixed, $B$ rotationally continuous, and $C$ a hinge/roller. $EI$ is the same. Find all four final member-end moments.

Use the previous spans, loads and constant $EI$, but now both $A$ and $C$ are fixed against rotation. Find four member-end moments from one release of B.

A continuous beam $ABCD$ has three 4-m spans with identical $EI$; $A$ and $D$ are fixed, $B$ and $C$ are rotationally continuous. Only middle span $BC$ carries $w=12$ kN/m. Compute representative distribution cycles and final end moments.

A 4-m prismatic column with $EI=10{,}000$ kN·m$^2$ has both end rotations restrained and a prescribed lateral relative translation $\Delta=0.010$ m. Find the magnitudes of column end sway moments and shear. Do not treat this as a free-rotation frame result.

A moment-distribution cycle leaves residual joint moments $U_B=-0.08$ kN·m and $U_C=+0.12$ kN·m. The stated absolute joint-equilibrium tolerance is 0.10 kN·m. Decide whether another cycle is needed.