In today's video I'm going to be going over the theory behind the design of pad footings
and everything else you need to know to design them and then i'm going to record a second video
where we're going to go through an actual example together i hope you're as excited as i am and if
you liked the video and learn something new maybe consider sharing what you learned with
your buddies let's share the knowledge and make the world a better place to live in
let's begin by understanding the behavior of pad footings so the pad itself acts as a cantilever
loaded by the soil pressure eq and supported by the column to make it easier you can visualize
the pad as an upside down beam so if you have a beam fixed to a column the maximum bending moment
is at the face of the column like it happens in a cantilever beam and by looking at the deflection
shape notice that the bottom face is in tension therefore the need for bottom reinforcement
now let's have a look at the image on the right hand side the transfer of load from the column
to the footing is by a combination of end bearing of the column and the starter bars in the footing
what that means is that the column has to sit on the footing obviously and you need
bars sticking out of the footing to connect to the column reinforcement these bars sticking out
of the footings are called starter bars and they must extend into the footing a minimum distance
equal to the development length and they must extend into the column a minimum lap splice length
now if you have a look at the end of some bars you will notice that they've got a bend or cog and the
bars can be cogged to provide better anchorage and also reduce the tensile development length
and last but not least make sure you provide enough cover to the reinforcement
according to the concrete strength and exposure classification
in this next slide i put together some tables with compressive and tensile development length
which may at times govern the depth of the footing so let me run you through the theory behind here
if the column is subject only to compressive loads you will have compressive lap splice length
and compressive development length the compressive development length is shown
on this column as lsycb and the splice length for compression is equal to 40 times the bar diameter
for example if your starter bars are n16s you need the bars going into the footing at least
355 millimeters and lapping to the column reinforcement a minimum of
40 times 16 so 40 times 16 which is equal to 640 millimeters remember that cogs have no effect on
compressive developmental length in other words they won't help in this case however the bars
are often cogged to tie the starters to the reinforcement or if you have bending moment
in the footing which is my next point if you apply a bending moment to the structure some
bars will tend to pull out while others will tend to push that's when you have to take into account
the tensile development length which i show here in this column of the table as lsytb so again if
you're using n16 starters and they're subject to tension you need the bars going into the footing
at least 700 millimeters however if you cog the bar 70 70 millimeters or four times the bar
diameter this number can be halved so instead of 700 it would be 700 divided by two 350 millimeters
and i clouded this information here in addition to this the splice length is 1.25 times as lsytb
so the lapping the lapping between the status and the column reinforcement would be 1.25 times 350
let's calculate this here equal to 440 millimeters minimum additionally since the pad is calculated
as a being fixed to the column we also have tensile development length for the bottom
reinforcement which i show here on this table as a this distance a has to be minimum of these
values for instance if the bottom reinforcements if the bottom reinforcement is n20 the distance a
has to be 940 millimeters for straight bars or 500 millimeters for cogged bars okay remember
in the first slide that i said the maximum bending moment is at the face of the column yeah so i lied
no i'm joking um but the position of the critical section for the maximum bending moment will vary
according to the type of column or wall for example the critical section for a steel column
is midway between column face and edge of the base plate for mainstream walls or columns it is
midway between the center line and the face of the mainstream the mainstream wall or column so when
you're calculating the bending moment you take the distance to the critical section okay the actual
pressure distribution under a footing is not linear it depends on the stiffness of the footing
and the type of soil so for axially loaded footings in cohesionless sandy soils the very
pressure near edges is less than that near the center of the footing because sand along the edges
will flow sideways thus reducing the pressure on the other hand with footings bearing on clay soils
bearing pressure along the edges tend to be higher than the near the center of the footing
with clay soils lateral movement of the soil is restrained due to its cohesion so to make our
lives easier we assume uniform linear pressure distribution as we introduce moment in our
structure the bearing pressure distribution under the footing can be determined as the superposition
of the uniform bearing pressure due to the axial load n and the linearly varying pressure
due to the moment m as i show in this slide so basically um you're gonna add this pressure
with this pressure and you will have a new pressure distribution that takes into account
axial force and bending moment and we're gonna go over this process right now let's introduce
a little bit of matte that will help us figure out the ideal pressure distribution so let's
use the good old formula pressure equals force divided by area that means the pressure q equals
n which is the axial load divided by b l which is the area of the rectangle on the other hand if we
introduce moment to the equation we get or other good old formula stress equals m y divided by i
simplifying it pressure q due to moment equals moment divided by section modulus z
and since z equals b l squared divided by 6 and let's also assume that our moment m
is equal to a force n times an eccentricity e and if we substitute these values in this equation
we get 6 n e divided by b l squared then as i mentioned before we need to add both pressures
and we get to this last simplified form of equation from this equation you get that if
the eccentricity e is less than l divided by 6 both q1 and q2 are positive which means that
the footing is in direct contact with the soil over its full length if e equals l divided by six
the pressure distribution varies from zero to maximum q1 when e is greater than
l divided by six the pressure q2 theoretically is negative however you cannot have a tension under
the footing you cannot have a negative contact bearing pressure between the footing and the soil
so this is the type of situation you need to avoid okay so now you understand
the middle third rule that you see in all engineering books to determine the plan
dimensions of the footing in contact with the soil we use the allowable soil bearing pressure q given
by the geotech and the service loads which is the unfactor combination g plus q then we use the
ultimate limit state combination to get a factor design bearing pressure and we're going to use
this factored pressure to design the footing for bending and shear we design for bending moment at
the critical section for a one meter width of footing by using the equation m equal m equals
to q times a squared divided by two so let's understand this equation firstly what happens
here in this situation is that the pressures resisting the applied load causes the footing
to go into flexure and eventually fail under flexural action as a cantilever of distance a
if we multiply the pressure q by the area we get a force as a result so f equal f equals q times area
which is equal to q times b times a since moment is equal to force times distance the force f
times half of a results in the moment m and if we substitute b for one meter we get to this equation
you can estimate the area of reinforcement by using this simplified equation or you can
use charts or spreadsheets or whatever software that you use to design single reinforced beams
make sure you specify at least the minimum reinforcement required
according to the code in the country that you live in and and then you're
going to repeat the same process for the short direction if the pad is not square
the next step is the design for one-way shear the critical section for one way she is taking
a distance d from the face of the column and again the shear force is equal to the pressure q
times area for b equal equals to 1 meter v equals q times a minus d and since we usually don't have
shear reinforcement in pad footings the shear capacity has to be provided by the concrete
so shear force must be equal or smaller than the factored concrete shear capacity and if
it's not the depth of the footing will have to be increased and the shear capacity of the concrete
is given by this formula in as3600 if you remember when you're learning how to design a slab you had
to take into account the possibility of the column literally punching through the slab therefore you
had to design the slab for punching shear and this phenomenon also happens to pad footing
and the punching shear force is equal to the pressure times the area around the perimeter u
and the shear capacity for two way action is given by this simple expression here and just a heads
up this distance 0.5 d varies from code to code so double check this value in the standards of
your own country so i hope you enjoyed the video thanks for watching again and stay tuned for the
next video where we're gonna go through an actual example together and it's gonna make things more
clear if you didn't understand something in this video thanks again and see you next time