Name:

Homework Assignment #$6$

Due Date:

Compression Steel $($Doubly Reinforced Beam$)$

Problem $1)$ Problem $5-28($page $148,$ McCormac and

Brown, $9^{th}$ Ed$.)$

$($a$)$ What is the nominal moment capacity, $M_n,$ if the

compression steel ${(}^{A_s^{\text{'}}})$ is ignored.

$($b$)$ Determine the neutral axis $($c$)$ and the depth of the

Whitney stress block $($ of the doubly reinforced beam,

using trial$-$and$-$error method.

$($c$)$ Determine the neutral axis $($c$)$ using quadratic equation

and compare the answer to part $($b$)$

$($d$)$ Check the strain in compression steel ${(}^{{}_s})$ and state

whether the compression steel has yielded?

$($e$)$ Calculate the strain in tension steel $({}_t)$ and determine if

the reduction factor $()$ is equal to $0\mathrm{.}9[$refer to figure $3\mathrm{.}5,$

page $72,$ McCormac and Brown, $9^{th}$ Ed$.]$

$($f$)$ Calculate the nominal moment capacity $($including

compression steel$),{?}^{M_n},$ compare that to answer in part

$($a$).$ Calculate the design moment, $M_n.$

Design for Negative Moments

Problem $2)$ Design a continuous interior T$-$beam having

center$-$to$-$center span of $40$ ft to carry $140$ psf of live load

plus its self$-$weight and slab weight $($assume $150$ pcf for the

density of concrete$).$ Ignore the contribution of

compression steel. $($refer to Figure $2$ of this assignment$).$

Use ACI coefficients $($Table $14\mathrm{.}1,$ p$.440,$ McCormac and

Brown, $9^{th}$ Ed$)$

$($a$)$ Determine effective flange width, if the center$-$to$-$

center spacing of the beams is $12$ ft $.$

$($b$)$ Calculate factored positive moment at the mid span

and factored negative moment at the support.

$($c$)$ Determine the number of #$8$ bars required to carry the

positive moment at mid span $($Section B$-$B$\text{'}).$ Calculate

the final design positive moment.

$($d$)$ Determine the number of #$8$ bars required to carry the

negative moment at the support $($Section A$-$A$\text{'}).$

Calculate the final design negative moment.