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Objectives

Compute cracking moment of a concrete beam

Compute stresses in cracked concrete beams

Given:

$f^{\text{'}}c=5,000$

$f_y=60$ksi

$E_s=29,000$ksi

Concrete unit weight, $w=150pcf$

Beam $A_s=()2$

The centroid of the reinforcing steel is located $3"$ above the bottom of the

beam.

The beam width, $b=16"$

The beam depth, $h=25"$

Find:

The moment in kip$-$ft required to crack the beam. Use a modulus of rupture,

$f_r=7\mathrm{.}5\sqrt[\phantom{2}]{f_c^{\text{'}}}$

Compute the maximum allowable moment in kip$-$ft$,$ using allowable stress

design and a factor of safety of $2\mathrm{.}0$ for both the concrete stress $)=(f^{\text{'}}d2$

and reinforcing steel stress $)=(\frac{f_y}{2}.$ Assume that the section is cracked

$($i$.$e$.$ concrete has zero tension stress$).$ Indicate if the maximum allowable

moment is controlled by concrete allowable stress or the steel allowable

stress. Use $E_c=33w^{1\mathrm{.}5}\sqrt[\phantom{2}]{f_c^{\text{'}}}$ where $E_c$ is in ksi, $w$ is in pef and $f_c^{\text{'}}$ is in psi