Problem $1$

Answer the following using the abdominal reinforcement rectangular beam below and the given conditions.

$300$

$.2-$D$25$

$35$

$4-$D$25$

Section of Figure $1($unit: mm$)$

Ja $=30$ MPa, a $=1,$ f $=600$ MPa A$,$ D$2=506\mathrm{.}7$ mm $($the cross$-$sectional area of one D$25$ reinforcing bar$)(])$ When no cracks have occurred and the reinforcing bar is not considered, the cross$-$sectional secondary moment $(/.$ Calculate $.$

$(2)$ Find the crack moment $($Me$)$ when reinforcing bars are not considered

$(3)$ When no crack occurs, calculate the cross section of the double$-$stringed rectangular beam converted into concrete and the position $($y$)$ of the neutral axis measured from the top of the beam. $(4)$ If no crack occurs and the reinforcing bar is considered, calculate the second moment $(/$y$)$ of the cross section for the converted cross section.

$(5)$ Find the crack moment $($Me$)$ when considering the converted cross$-$sectional area

$(6)$ When a crack occurs, convert the cross section of the abdominal reinforcement rectangular beam into concrete, draw the cross section, and calculate the position $($yo$)$ of the neutral axis measured from the top of the beam.

$(7)$ Calculate the cross$-$sectional secondary moment $(1$a$)$ for the crack cross$-$section. $($Considering reinforcement$)$

$1($: $mm)$

Problem $1$

$.$

$f_{ck}=30$MPa,$=1,f_y=600$MPa,$A_{s,D25}=506\mathrm{.}7m{m}^2($D$251)$

$(1),2(I_g).$

$(2)(M_{cr}).$

$(3)(y_0).$

$(4),2(I_{gt}).$

$(5)(M_{cr}).$

$(6)(y_0).$

$(7)2(I_{cr}).()$