EXAMPLE #$1$:

A $4-$course high masonry beam is constructed using $200mm$ units is made of normal weight grouted $($hollow$)$ concrete block $($Classification A$)$ having a $30$MPa specified compressive strength. Type $N$ mortar is used. In addition to the self$-$weight of the masonry beam of $3\mathrm{.}26k\frac{N}{m},$ a specified superimposed dead load of $4\mathrm{.}74k\frac{N}{m}$ and a specified live load of $6k\frac{N}{m}$ are applied on the beam. The beam has tension reinforcement at a specified depth of $690mm.$ The steel yield strength is $400$MPa. Given the block web intercept the continuity of the grout o the compression side.

Determine

$($a$)$ The self$-$weight of the masonry beam using the following two approaches:

i$.$ Table B$.1$ "Dead Loads for Masonry Construction"

ii$.$ Table $2-1$ "Properties of Standard Concrete Block Units" using concrete density of $2100k\frac{g}{m}3$ and grout density of $2350k\frac{g}{m}3.$

Note the tables are on page $74$ in course notes W$2020$

$($b$)$ A practical steel area

$($c$)$ The factored moment of resistance of the beam using the reinforcement from $($b$)$

$($d$)$ The maximum factored moment resistance

$($e$)$ The maximum span of the beam that can carry the load when cracking at midspan is initiated $($neglect the area of steel$)$ and when the factored moment of resistance at midspan is reached. Comment on your answer.