Question $1-$ T$-$Beams

a$)$ Determine the most economical reinforcement for a $T-$section that has:

Flange width $b=40in.$

Flange thickness $t=4in$

Web width bw$=10$ in$.$

Carrying a factored moment of $545K*ft$

Given: $fc=3$ksi and $fy=60$ksi

$(40$ marks$)$

Hint: First check if a is less than or greater than t to know which case governs or $a=t.$

b$)$ Provide a detail drawing of the beam you have designed.

$(15$ marks$)$

Question $2-$Shear in Beams

c$)$ Design and prove detail drawing of the shear reinforcement for the said beam you have designed of the span is $16$ ft and simply supported.