Approximate Analysis of Statically Indeterminate Structures - Examples

A three-story frame has lateral loads of $15\text{ kN}$ at the roof, $25\text{ kN}$ at the third floor, and $30\text{ kN}$ at the second floor. Find the story shear in the first story.

A one-story, two-bay regular frame has two exterior columns and one interior column. Total story shear is $40\text{ kN}$. Under the classical $1:2:1$ portal shear assumption, find the column shears.

An exterior column in a portal-method model carries shear $V=12\text{ kN}$ and has story height $h=4.0\text{ m}$. Assuming an inflection point at mid-height, find the magnitude of the end moment.

A two-story one-bay frame carries $20\text{ kN}$ at the roof and $40\text{ kN}$ at the second floor. Under a symmetric portal assumption, determine each column shear in each story.

A frame has one transfer story with a very deep transfer girder, a sudden reduction in column count, and unequal bay widths. Should the standard $1:2:1$ portal shear rule be treated as a reliable primary analysis?

Three equal-area columns are located at $x=0$, $6$, and $14\text{ m}$. Find the centroidal axis location.

Using the column group from Example 6, let the overturning moment at the story cut be $M=600\text{ kN}\cdot\text{m}$ and all column areas be equal. Determine the column axial forces from $P_i=Mx_i/\sum x_j^2$, where $x_i$ is measured from the centroid.

Columns at $x=0$, $6$, and $14\text{ m}$ have relative areas $A$, $2A$, and $A$. Find the column-group centroid.

A portal-method girder span is $8.0\text{ m}$. Under the adopted lateral-load approximation, locate the assumed zero-moment point.

A portal hand check gives a first-story interior column shear of $22\text{ kN}$, while a verified elastic frame model gives $25\text{ kN}$. Compute the percent difference relative to the rigorous model.

Two frames have the same eight-story height. Frame A is wide with many comparable bays and strong floor diaphragms; Frame B is very slender and its lateral response is dominated by overturning with large axial-force variation in exterior columns. Which classical approximation is more behaviorally aligned with each frame?