Objectives

To develop a column interaction diagram based on nominal loads and moments

To apply the ACI code required strength reduction factors to develop a design interaction diagram

Given:

The tied column shown

$f_y=60$ksi

$f_c^{\text{'}}=6\mathrm{.}0$ksi

$16-$ #$10$ bars as shown

The distance from the column face to the nearest row of vertical bars in either direction is $3".$

Find:

Develop a spreadsheet to graph the interaction diagram for nominal axial loads from $P_n=P_o$ to $P_n=0$ for bending about the strong axis. Include in the graph the ACI code limit on $P_n$ of $0\mathrm{.}80P_o.$

Apply the ACI strength reduction factors to graph the interaction diagram for design axial loads from $P_{n,\text{m}\text{a}\text{x}}$ to $P_n=0($pure bending$).$

Include in tabular form the values of $P_n,M_n,P_n,$ and $M_n$ at the following critical locations of the depth to the neutral axis, c :

$c=,$ i$.$e$.,$ pure axial load $)=(0$

$,c$ where the maximum nominal axial load per the ACI code, $P_n=P_{n,\text{m}\text{a}\text{x}}=0\mathrm{.}80P_o$

$,c_b$ at the balanced load where $$ starts its transition from $0\mathrm{.}65.$

$,c$ where $$ ends its transition to $0\mathrm{.}90.$

$c$ where $P_n=0($pure bending$)$

Provide enough intermediate points between the above required points on the graph to provide a reasonably smooth interaction graph.