Consider a rectangular reinforced concrete beam as shown in Figure $1.$ The beam is assumed

to be simply supported with an unsupported span of $25$ feet and is subject to the given

distributed loads. The concrete is normal$-$weight with a compressive strength $f_c^{\text{'}}=5,000,$

and the yield strength of the reinforcement $f_y=60$ksi.

a$.$ Determine the cracking moment, $M_{cr}$

b$.$ Determine the yield moment, $M_y$

c$.$ Compute the design moment strength $(M_n)$ of the beam using the proposed trial $A_s$:$3$#$8$

d$.$ Check whether the proposed reinforcement satisfies the minimum required area $(A_{s,\text{m}\text{i}\text{n}})$

for flexure per ACI $318-19$ provisions? Compute the strain in the tensile reinforcement

and state whether the section is tension$-$controlled or not.

e$.$ Draw the beam shear and moment diagrams noting the value and location of peak forces.

Compute the maximum factored moment demand $(M_u)$ per LRFD$.$ Check whether the

proposed tensile reinforcement is adequate to resist the maximum demand?

f$.$ Confirm what is the optimal tensile reinforcement $A_s$ required for beam to resist $M_u.$

$($a$)$

$($b$)3$ No$.8$ bars

$12$ in$.$

Figure $1.$ Reinforced Concrete Beam