Q$2\mathrm{.}5$

$30$ MARKS

The concrete beam shown below supports the specified dead load of $24k\frac{N}{m}($including self weight of the beam$)$ and specified live load of $30k\frac{N}{m}.$ The concrete strength of the beam is $30$ MPa and the yield strength of the reinforcement is $400$ MPa. Max. aggr. size $=25mm.$

Cross section $($the shaded area is the cross$-$section of the beam that you are designing$)$:

Elevation $($the T$-$beam under consideration is between two columns$)$

$\mathrm{.}5$ No$.30$ bars

Note: Beam under consideration is an interior span of a continuous beam

$($a$)$ Draw the bending moment envelope using approximate bending moment coefficients given in CSAA$23\mathrm{.}3$:$24.$

$($b$)$ Draw the shear force envelope using approximate bending moment coefficients given in CSAA$23\mathrm{.}3$:$24.$

$($c$)$ Determine the maximum factored positive moment, factored negative moment, and factored shear for the beam.

$($d$)$ Compute the effective flange width at midspan.

$($e$)$ Compute the factored moment resistance for both the positive and negative moment regions, respectively. Check if $A_s>A_{s,\text{m}\text{i}\text{n}}$ and if the steel is yielding. Neglect the contribution of the compression reinforcement in the flexural strength calculation.