in today's video we're going to design the bottom reinforcement of a concrete beam in a very
quick fast rapid high speed turbo way and if you like the video you want to see more videos
like this one make sure you like share subscribe to the channel and hit the bell notification
having said that let's get started we're going to design
this bridging beam which is the exercise 7 of my new free ebook called 10 resolved exercises
i wish i knew in my first month into structural engineering and it's free of costs for you my
friends and you can download the pdf from my website there's a link in the description below
so just go to i'll show you here just go to my homepage of the website scroll down
and enter your email enter your name and i will email you a link so you can download the pdf
okay back to the concrete beam we know our factored bending moment that we need to design the beam for
which is a hundred kilonewtons meters we're gonna use 20 mpa concrete 50 millimeters cover i will
try n16 bars at first see if that works i would suggest using bars between 12 and 32 millimeters
if you go over 32 the bar starts to get really heavy and you will need big blokes to carry them
the cross-section dimensions are given to us but if you need to estimate a good rule
of thumb for the depth of a simply supported reinforced concrete beam is span divided by 13
and the width of the beam i'll show you how you can work that out later in this video the
width of the beam is 350 millimeters the depth is 400 millimeters the effective depth of the beam
which is the distance from the extreme compression fiber to the centroid of the bottom bars and that
works out to be the total depth of the beam minus the cover minus diameter of the ligs
minus half of the diameter of the bottom bars that works out to be 330 millimeters now that we have
all the data we need we're going to determine the required area of tension reinforcement and
to do so we're gonna use this ninja formula below here which is the area of steel equals to moment
divided by phi times fsy times 0.9 d in case you're asking yourself where did you get this
formula from it is only a practical derivation of this formula here which you might have seen when
you studied singly reinforced concrete beam so the problem with this formula is that we don't know a
because a is a function of the area of steel which is exactly what we are trying
to figure out and if you use this formula you would have to resolve a quadratic quadratic
quadratic quadratic equation which i don't like it no one likes it i know you don't
don't lie to me anyway some mastermind found out that d minus a divided by 2
equals approximately zero point zero point nine d and that's how this formula was created
and we're gonna double check this in the end okay don't worry we're not gonna just blindly rely on
this formula we need to double check that so let's plug the numbers into this equation and we get the
area of steel is approximately 793 millimeters millimeter squared that means we need 4 N16
bars and 4 N16 bars will give us a total area of 804 millimeter squared let's say for example
instead of n16 you had to use n20 bars you would have to go back here and change the effective
depth and redo this calculation okay that was pretty much a less than a minute calculation
okay and it is pretty it's quite accurate so you don't dare to say my video is a click
bait okay that was less than a minute you just needed to apply this formula is simple very
simple before we proceed we're going to calculate the minimum steel reinforcement for this beam so
that we make sure that the minimum is less than 804 we're just going to calculate this minimum
steel reinforcement according to as according to this formula in as3600 clause 18.1.6.1 and
the minimum steel reinforcement for this beam is 182 millimeters squared which is way less than 800
804 before we are okay before we keep going let's check if 4 and 16 bars will
fit in our beam you can either draw these in cad or you can manually calculate it to manually
calculate it you need to know that the spacing in between bars is 1.5 times the aggregate size
and the aggregate size is usually 20 millimeters you need to know the side cover you need to know
the diameter of the ligs the diameter of the bars and the bend radius the bend radius is equal to
two times the lig's diameter okay so 350 which is the total width of the beam needs to be greater
than two times the side cover which is 50 15 each side plus two times the lig's diameter which is
one here one here plus four times the lig's diameter that is two times lig's diameter times
two because you've got two bend radius here plus four times four times the bottom bar's diameter
four times 16 plus three times three you've got one two three spacings in between bars three times
1.5 times 20 that is equal to 326 millimeters therefore we are okay all the bars fit nice and
neatly in our beam so remember that we said that we will double check our results and make sure
or phi mu is greater than 100 kilonewtons meters we're going to do this now now we have an area
of steel that we can calculate a remember before we didn't have a that's why we had to
use the ninja formula but now we have we have the area of steel and we can calculate
a we're just going to use this formula here to calculate a and we get that a is 70.03 millimeters
after that we need to work out c see if you can't remember is the neutral axis depth in the stress
when you calculate the stress the rectangular stress block concrete beam that is just a divided
by this factor which is 76.12 and then finally we need to work out our k which is the neutral axis
parameter and k must be less than 0.36 so we have an under reinforced concrete beam which
means the reinforcement will yield before the beam reaches the ultimate limit state in flexure
in most cases you should always design a concrete beam to be under reinforced so you have a ductile
failure if for any reason the beam fails it will give out signs so if the beam is
under reinforced and it's under reinforced you can tell when it's gonna fail because
it gives it gives out signs and everybody can simply run away no one's gonna die so
after that we're gonna calculate the final moment check which is pretty much the same
formula that we saw before rearranged to calculate phi mu we get that phi mu is 100.79 kilonewtons
mere which is greater than 100 kilonewtons meters therefore we are okay it passes no
one's gonna die the engineer is gonna get paid everybody um goes home happy and that's it