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Fooundations/footingsPart 2
Design of footing pad
In the previous lecture we have recognized that design of
footings consists from2 large areas: Geotechnical and Structural
(concrete.)In the previous lecture, we have recognized that design
of footings consists of 2
large areas: Geotechnical and Structural (concrete.) In the GEO
part, we arelooking usually for needed dimensions and contact area
sizes to ensure theerrorless transfer of the load from the
superstructure to the soil. The stressevoked by load should not
overrun the strength of the soil. We have recognizedthe big
influence of rigidity, plasticity or elasticity of the foundation
ground and ofthe foundation itself to this relationship. The
absolutely correct solution is almostimpossible. Therefore by non -
critical cases are very nice simplification used:The contact
pressure is constant on the so-called effective part Aef of the
totalcontact area AC. This is determined as the area, which
centroid is identicalthe location of the resultant of loading
forces. This principle is used also bystructural design very
frequently too, especially by the design of simple footingslike a
pad.
Flashback
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Footing pad (under a column) and strip under a wall (SUW)Common
rules for the GEO and structural Design!
EA pad is bent in both perpendicular directions x and y upwards!
The bottom fibres are in tension in both direction x, y by a pad
–see top scheme, left side. A strip under a wall (SUW) is bent
upwards in the direction x (perpendicular to the wall which is
stiff in its plane and prohibits bending of the strip in the wall
direction), only. SUW should be solved as a pad (strip) transversal
section with the breath of 1 m.This fact is valid both for
geotechnical and structural design!
The wall on the top of SUW can be of masonry or of reinforced
concrete. From it, we have in the structural analysis fixed or
hinged connection and relating shape of contact stress. – see figs.
(By hinged connection influence of M from the column is not
transferred to SUW the contact pressure is uniform by the whole
contact area.)
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Simplified model of compressive contact pressure distribution
used for the design of footing pads (principle in words→ see
previous lecture.) (slide repeated from previous lecture)
Vd is resulting vertical force of Nd , Zd
Vd= Nd + Zd
Zd Self-weight of the pad + backfill + relevant part of the
permanent load + variable load from the floor slab (If actual).
Nd Axial force from the superstructure (more loading cases
possible).
Md Bending moment in the foot of the actual column (more loading
cases possible).
Hd Horizontal (shear) force in the foot of the actual column
(more loading cases possible).
Aef Effective contact area
ed (e)= ( Md + Hd . H)/ (Nd + Zd)
Aef = (L-2 ed) . B !attention! B=B or B=1m Use the equivalent
values for Action and resistance! SUW always B= 1m!
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Design steps to determine pad dimensions (GEO)Condition of
reliability for ULS STR (pad sinking)
szd ≤ Rd has to be checked and fulfilled.
A) Design – proposal1. We know Md(i), Hd(i), Nd(i), Rd [index
(i) means for more
loading cases].
2. Zd and H (height) must be estimated3. Usually: H = approx.
(0,5-1,0)m, Zd = approx.
(0,1 -0,2 ) of max Nd (depends on Rd, too!)4. Plan shape of
designed pad must be estimated,
B=L or L = x. B, (x = 1 to 0,6, not less).5. Max ed should be
calculated (All forces can be
taken as (+) if Md and Hd act in the same direction.)
6. max ed (i)= max [( Md(i) + Hd(i) . H)/ (Nd (i) + Zd)] where
ed is the eccentricity in direction of L.
7. We presume sz= Rd witch is known from geo data and we can
write: Rd = (Nd + Zd) / ((L-2 ed) . L)
8. From this equation we can easy calculate L and in next step B
as minimum of plan dimensions.
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Determination of pad height h In the first step, we must choose
between
plain/under-reinforced concrete (PC) on one
side and reinforced concrete (RC) on the
opposite side. By PC is the angle an around
huge 60˚ due to different concepts of failure.
More details later. Even when we choose RC,
there's a lace space between two
recommended limits 30 and 45 degrees of an
angle. So, in the second step by RC pad
proposal, we have to choose angle a, because it is essential for
pad self-weight.
Pads with a close to 30 degrees save
concrete, but there is a risk of punching
failure, here. At least you need special
reinforcement and the cost-effectivity is
gone!? Pads with close to 45 degrees are
hard to punch - see later. determination of
pad height..
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B. Design – review (GEO)review for ULS - STR
1. Calculation of the correct self-weight of revived pad +
weight of the
backfill, flooring etc. (what existsTogether = Zd)
2. Calculation of deciding loading variants from the
superstructure
- max value of Nd(i) + corresponding Md(i) and Hd(i)- min value
of Nd(i) + corresponding Md(i) and Hd(i)- max value of Md(i) +
corresponding Hd(i) and Nd(i)- min value of Md(i) + corresponding
Hd(i) and Nd(i)- max value of Hd(i) + corresponding Md(i) and
Nd(i)- min value of Hd(i) + corresponding Md(i) and Nd(i)
By the review we respect all signs of used quantities!As safe
simplification comb. max INd(i) l + extreme Hd(i) + extreme Md(i)
can be used.
3. We find ed(i)= ( Md(i) + Hd(i) . H)/ (Nd(i) + Zd) (= e in the
figure).
4. we calculate szd (i) =(Nd(i) + Zd)/(B. (L-2ed(i)))
Conditionszd (i) ≤ Rd should be fulfilled for all extreme
combination of M, N and H. If it is fulfilled, the pad is
successfully
revived.
E
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Stability of a pad - ULS EQUA pad should not overturn and move
horizontally. There are some common rules:if max |ed(i)| ≤ 1/6 L,
overturning is impossible and no other check is necessary.if max
|ed(i)|≥ 1/6 L and ≤ 1/3 L,Stability against overturning (ULS EQU)
must be verified besides the main design sequence for the
condition:Mstb ≥ MdstMstb=[L/2 (Z’d + N’d)] . gstbgstb= 0,9
(depends on NA value), Z’d is Zd without backfill,N’d is Nd without
variable loadMdst=max [H . Hd(i) + Md(i)]Case |ed(i)|≥ 1/3 L is
prohibited!!
Don’t forget the influence of favourableand unfavourable load
action on the magnitude of internal forces and equal values of
coefficients gg and gq.
Stability against horizontal movement (ULS EQI)must be verified
separately by the condition:Hstb ≥ HdstHdst= Hd(i)Hstb= N’d . tgf
(extremely simplified)tgf is angle of the soil’s internal
friction
Another GEO controls E-EP
Notice: The pads of MSMB frames cannot over-turn due to the
principle of superstructure.
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Design of a pad and SUW as a structure = design of
reinforcement
It has been observed, that this clear fact is frequently ignored
in professional literature and instead of upwards pressure pz
contact/ground pressure sz is used. (Perhaps for higher simplicity
and higher safety.)
GEO designStructural design
First of all should be mentioned, that an only a part of contact
pressure sz is responsible for footing stress, only! Effective
(upward) pressure pz = sz – qz`, (pz sometimes is marked as pd.
Footing (pad) virtually „floats in the soil“ This is reason why the
self-weight of a pad cannot be count into loads causing stress.
Therefore it is not included in the upward pressure which stresses
the pad. Here qz = Zd
/(B . L) where Zd is self-weight of the pad body plus weight
of
the backfill. For safety is the backfill load sometimes omitted
(backfill can be excavated from some reason).
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Structural design of a footing pad and SUWAs the upward pressure
(by way of the reaction on the load action) acts in thedirection
bo�om→top, we can imagine a footing pad as a 3D double-sidedconsole
(cantilever) acting in an upside-down position and loaded with
theupward pressure pz. The column then represents support.In most
cases, we have to design footing/pad for (against ) two types
offailure Flexural failure design for flexure (bending). Punching
failure design for punching shear.
The pad works in two directions as double-sided console oriented
upside-down and isloaded with upward pressure pz. The deciding CSs
are stressed with flexure (bending)So, by ULS STR we presume acc.
to. EN 1992-1 following (known from basic course):
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Design for flexure (bending) E
The pad under load works in two perpendicular directions as 3D
double-sided console
oriented upside-down and loaded with upward pressure pz (see the
explanation two slides
back). The column and upper superstructure work like support in
this upside-down
concept. This concept is not obligatory, sometimes it is used
for a better idea. On the
following figures is the way of stressing by bending
demonstrated. The curvature and
cracks magnitude on the right fig is a little bit
exaggerated!!
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Determination of pad height h
The decision about usage of PC or
RC pad is usually done in GEO design
due to high differences in self-weight
between this two kinds of footing.
Commonly PC pad and PC SUW are
suitable to low loaded structureses
structures PC pad or Even when we
choose RC, there is a lace space
between 30 and 45 degrees of a
angle.
So in the second step by RC pad we
have to choose angle a and shape of the pad.
Pads with a close to 30 degrees
saves concrete, but there is a risk of
punching failure, here. At least you
need special reinforcement and the
cost- effectivity is gone. Pads with a
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Structural design sequence of a Footing pad (and SUW)Design of
the pad as a structure follows usually the GEO design. So we can
presume to have all the needed data collected and available. Even
the decision about the character of the pad must be done on the GEO
level. The reason is that the PC pad (for the same loading and soil
quality) is about three times heavier than the RC one. This fact
may have an important impact on the following structural design. In
the opposite way, we must be alert not to design a PC pad by
mistake in detailing. RC pad is a relatively massive structure. In
such a case the amount of reinforcement is mostly given from As,min
side, not from the static calculation, as it is common by the
majority of superstructure members. The most important and specific
rules are presented on the next slide. Possible shapes of pads and
position of the critical CS
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The only new thing you should know is how todefine effective
span internationally accepted semiempirical value:
lef = a + 0,15.hc sometime lef = a + 0,5. hc, is used. Fore
meaning of used quantities see figure on leftside. With this
knowledge we can expres actingflexural moment for 1 m of breath
with followingformula: MEd = - ½ ped . Lef
2 unit [kNm/m] - case a)With the same impact we can use formula
for totalbending moment (for the whole breath B):MEd = - ½ ped .
lef
2.B unit [kNm] - case b)Equivalent formula for resisting moment
is virtuallyequal for both cases a) and b)
MRd = Ast . fyd . (d-lx/2)
the difference is in the Ast.
Case a) you have by proposal calculated needed
sectional area of rfcmt for 1 m of breath only. So,
you have to make the review for 1 m of breath, too.Case b) you
have by proposal calculated sectionalarea of rfcmt for the whole
breath B. So you have tomake the review for whole breath B,
too.Finnaly– technique a) is suitable for SUWs,technique b) is
suitable for pads .desigbvte
Important limits by design of RC pad
As ≥ As,min --prior the review! As,min = 0,026 . fctm/fyk. bt
.d
but not less than: . 0,0013. bt . d
Where is d effective depth, hold trued = (d1 + d2)/2
for bt use booth B and L (check both directions x, y)!
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Detailing of footing pads (without punching shear
reinforcement)Concrete cover:for the surface in direct contact with
the soil (bottom) should be c ≥ 75 mmfor the surface with no direct
contact with the soil (sides, bottom with BCc ≥ 40 mmIF blinding
concrete is used, schould be count into Zd!max. distane of parallel
bars (beam or slab?)as ≤ 200 (300) mmSometimes is non-equivalent
distribution of bars in the plan recommended.Recommended f= 12 to
20 mm
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Special detailing - Anchoring of bars at the end of a pad.It is
relatively complicated, based on the strut and tie model.The
original theory is based on the elastic presumption of pd
distribution.There is no reason why not to keep the previous model
of the design with constantuniform distribution of pd of a part of
the contact area (Aef).Let us modify it. In the EN1992-1-1 can be
for anchoring seen:
This is strange!! For the designof the reinforcement commonlywe
use the presumption ofuniform distribution of upwardpressure on the
Aef. And nowfor the anchoring of the samerfcmt. we have to use
anotherpresumption?Here is something wrong in the Eurocode team.
Thus we will use the same presumption - see next page.
Do not use thispresumtion
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Detailing of rfcmt. in RC pad
issues 1 and 2 means the vertical reinforcement which connects
pad with a column cannot go through the bottom mesh-like rfcmt is
shown un the main scheme the figure left. Correct detailing is on
the enclosed figure below:
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The influence of the wall type (RC/masonry) is valid both for
the GEO and structural design. In both cases is strip under a wall
designed as 1 m breath strip/section. In the GEO part is designed
the breath of the strip in the direction „x“ perpendicularly to
wall. In the structural design, a partiof designed reinforcement in
the same direction.
For the main reinforcement with sectional area As/m
bars f 10 to 16 mm are usually used. For distributive
reinforcement bars f 8 to 12 mm as well. Should be
fulfilled As,dist ≥ 0,2 AS.
In the case of RC wall, reinforcement for wall strip connection
should be used - look at bottom figure
Similarity of a footing pad and SUW once more / detailing:
Main RFCMT Distributive RFCMT
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In calculated reinforcement must be in an effective position in
cross-section! By bended members it is the part of cross-section in
tension with the height (0,25 h).
Plain and slightly reinforced concrete foundations
What is it the “plain” and “slightly-reinforced”
concrete?Concrete with As = 0 is plain. (Concerns effective
zone.)Concrete with As < As,min is
slightly-reinforced.CriterionAs,min = 0,026 .fctm.bt . d/fyk, but
not less than: =0,0013. bt . dWhere d = (d1 + d2)/2(for bt in
calculations use booth B and L (dimensions of a footing in
directions x, y)!
From the point of view steel content in concrete we have
following two concrete materials
RC- reinforced concrete – amount of rfcmt is calculated from
static equilibrium conditions and detailing is used, too.
Plain and slightly reinforced cconcerte are virtually in the
same basket and these are used for less important structures. For
design simple or super simple empirical formulas and/or detaling i
are used, only.
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Axially loaded strip and pad footings may be designed and
constructed as plain concrete provided that acc. to EC2: Used is
one simple formula se next line
0,85 hf/a ≥ (3pd/ftd,pl)0,5
Where:
hf is the foundation depth
a is the projection from the column face (see figure)
pd is the design value of the upward
pressure (in the EC2 is mistakenly given ground
pressure)
fctd,pl is the design value of the concrete tensile strength
fctd,pl = act . fctd, where act is given in the N.A. act= 0,6 in
the CS.
The formula expresses relation between ten soil strangth
As a simplification the relation hf /a =2 may be used ⇒
a = cca 63°.
Plain concrete by footing is suitable first of all for low
loaded footings, especially for strips under a masonry walls. In
such cases is the breath bf the strip usually in the range of 50 to
80 cm.
a
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https://www.edisk.cz/stahni/27995/educationvideos_e7_10.zip_64.67MB.html/