Homework $4$

Note: please put the lecture code for the lecture on Feb$-28$ in your solution beside your name.

In today's lecture, we have showed the design process for $A_{41},$ the tension reinforcement area, for section

$1$ of the floor beam $AB$ to resist the positive bending moment $M_{s1}$ as shown in the moment diagram $M_v.$

We also know that the beam section close to the column $B$ is subjected to the maximum negative moment

$M_s=-145k-$ft$,$ which means for beam section B$,$ the tension zone is in the top of the section while the

compression zone is in the bottom of the section, as indicated below. You can simply regard beam section

$B,$ which resists negative bending moment $M_s,$ as a singly reinforced rectangular beam section because

above the N$.$A$.,$ all concrete cracks and only the tension reinforcement $A_n$ can provide tension force. But

$A_s$ is unknown and we need to design for it$.$

Please follow the exact procedure shown in today's lecture to compute $A_{na}.$ You can review lecture notes,

or view recorded video, or study the Example $5-4$ in Chapter $5$ of our textbook to find hint.

Given:

$M_a=-145k-t.$

$f_c^{\text{'}}=4$ksi

$f_y=60$ksi

Compute: $A_{as}$