Problem $2$: $(35$ points$)$

Compute the design strength $(M_n)$ for the beam section shown in Figure $2.$ Use the following material properties:

$f_y=60,000$

$f_c^{\text{'}}=5,000$

Steel Young's Modulus $(E_s)=29,000$ksi

Fig. $2.$ Cross section of beam with location of top rebar

Page $\frac{2}{3}$

Problem $3$: $(20$ points$)$

Given the slab properties below, answer $($a$)$ through $($d$).$ Mark your answers to each subquestion clearly. Consider an $6$ inch thick slab, with #$4$ reinforcement bars spaced at $6$ inches on center. The slab span is $14$ feet, the service $($unfactored$)$ dead load on the slab is $85$ psf $($including self weight$)$ and the service $($unfactored$)$ live load is $80$ psf $.$ The concrete and reinforcing steel have the following properties:

$f_y=60,000$

Normal weight concrete

Interior exposure $($not exposed to weather or the ground$)$

$\frac{3}{4}$ inch aggregate

$f_c^{\text{'}}=5,000$

Steel Young's Modulus $(E_s)=29,000$ksi

Cite all locations that you are using within ACI $318.$

a$)$ Calculate the ultimate flexural demand on the slab

b$)$ Check that the reinforcement meets the minimum requirements for shrinkage reinforcement

c$)$ Calculate the design flexural strength of the slab $(M_n)$ and determine if the slab has enough capacity to resist the flexural demand calculated in $($a$)$

d$)$ Check that the reinforcement spacing meets the minimum and maximum requirements per ACI $318.$