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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

E

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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/