Exact Analysis of Indeterminate Structures: Displacement Methods - Examples

A prismatic member has $EI=24000\text{ kN}\cdot\text{m}^2$ and $L=6.0\text{ m}$. Find the near-end rotational stiffness when the far end is fixed.

Use the same member data as Example 1, but the far end is an ideal hinge. Find $K$.

Three members meeting at joint $J$ have rotational stiffnesses $K_1=12$, $K_2=18$, and $K_3=30$ in consistent units. Find their distribution factors.

At a joint, the algebraic unbalanced moment is $+50\text{ kN}\cdot\text{m}$. The connected members have distribution factors $0.20$, $0.30$, and $0.50$. Find the balancing corrections.

A moment-distribution correction of $-24\text{ kN}\cdot\text{m}$ is applied at the near end of a prismatic member whose far end is fixed. Find the classical carry-over correction.

A prismatic fixed-fixed beam has $w=18\text{ kN/m}$ and $L=5.0\text{ m}$. Find the magnitude of each fixed-end moment.

Member $AB$ has $EI/L=5000\text{ kN}\cdot\text{m/rad}$, no member load, no chord rotation, $\theta_A=0$, and $\theta_B=0.002\text{ rad}$. Find $M_{AB}$ using the lesson equation.

Using the same member and rotations as Example 7, find $M_{BA}$.

A frame column has length $L=4.0\text{ m}$. Its top joint translates $12\text{ mm}$ to the right relative to its base. Under the small-angle approximation, find the chord-rotation magnitude.

A rectangular frame has fixed bases and is subjected only to symmetric vertical loading. Geometry and stiffness are symmetric about the centerline. Should a lateral sway degree of freedom be expected in the symmetric idealization?

After several distribution cycles, the largest remaining joint correction is $0.08\text{ kN}\cdot\text{m}$ while final member moments are about $120\text{ kN}\cdot\text{m}$. Compute the correction as a percentage of that moment scale.