A simply supported beam is shown below. This beam is subjected to a uniform factorec load $w_u$ of $40\mathrm{.}0t\frac{f}{m}$ over the entire span. No need to consider the possible movement of the load. Assume the load is applied on the top face of the beam. $f_c^{\text{'}}=280kg\frac{f}{c}{m}^2$ and $f_y=4200kg\frac{f}{c}{m}^2.$

$($a$)$ Determine the maximum factored shear the section can take. Use the simplified equation for $V_c.$ Assume no axial load and the beam is provided with the minimum amount of shear reinforcement. What design action can be taken if the maximum factored shear exceeds the maximum shear the section can take?

$($b$)$ Determine the maximum spacing of shear reinforcement for the beam section at the column face. Use the simplified equation for $V_c.$ If the condition of section $4\mathrm{.}4$ E of the lecture notes is satisfied, the reduction of factored shear should be considered. Assume the section takes no axial force.

$($c$)$ Determine the maximum spacing of shear reinforcement for the section $200$ cm from the face of the column. If the factored shear is small enough so that the shear reinforcement is not required according to the code, do not design shear reinforcement. In this case, check whether concrete shear strength is sufficient to resist the factor shear. Assume the section is subjected to a factored axial compression of $125$ tf $.$

$($d$)$ Set the spacing of the shear reinforcement to be $20$ cm $.$ Assume the beam is also subjected to a factored shear of $20$ tf along the $x$ direction of the section, which is perpendicular to the gravity direction. Assume the effective depth of the section along the $x$ direction is $80\%$ the overall depth in that direction. Check whether the section of $($b$)$ is safe under the factored biaxial shear. Assume the section takes no axial force.

$w_u=40t\frac{f}{m}$

Unit : cm