HOMEWORK $6-$ SHORT COLUMNS $($Intermediate and final answers at bottom$)$

Reinforced Concrete Design

Instructions: Perform all necessary intermediate and final calculations to reach at all the results$/$answers of the

problems included in this assignment. Your calculations will need to be uploaded into the Homework $6$

Dropbox in Folio, to be indicated by the instructor. Additionally, you will be asked to answer multiple$-$choice

questions on most intermediate and final calculations.

PROBLEM $1$:

Consider a short tied square column $(12$in x $12$in$)$ with $3$ #$6$ bars on each of two opposite faces $($i$.$e$.,$ a total of

$6$ #$6$ bars$)$ and stirrups #$3.$ The material properties are: $f_c^{\text{'}}=6,000p,f_y=60$ksi,$E_s=29,000$ksi.

While calculating distances $d_1$ to $d_2,$ use exact numbers, not approximated ones. For such purpose, consider

the exact diameter of stirrups #$3,$ the exact radius of bar #$6$ and a minimum cover of $1\mathrm{.}5$ in$.$

Determine the below indicated points of the capacity interaction diagram $P_{n}v{M}_n$ and the reduced capacity

diagram $\frac{O}{P_n}v{M}_n.$ That is$,$ calculate the following points:

$(1)$ Maximum capacity in pure axial compression. In this case, provide $P_{no},P_{n(max)},P_{no}$ and $P_{n(max)}.$

$(2)$ Two pair of values $(M_n,P_n)$ and $(\frac{O}{M_n},\frac{O}{P_n})$ for $Z=0$

$(3)$ Two pair of values $(M_n,P_n)$ and $(\frac{O}{M_n},\frac{O}{P_n})$ for $Z=-2$

$(4)$ Maximum capacity in pure axial tension, $P_{nt}$ and $P_{nt}.$

The various solved examples presented in class, on the generation of Interaction Diagrams, should be used as

guides for all calculations required in this problem.

intermediate and final answers

for Z$=0$; phi Pn$=338$k and phi Mn$=71\mathrm{.}5$k$-$ft

for Z$=2$; phi Pn$=127\mathrm{.}5$k and phi Mn$=90\mathrm{.}1$k$-$ft

Tha nk you