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FOUNDATIONS FOR COLUMNS (SPREAD FOOTING) DESIGN
4. Foundations for cast in situ reinforced concrete columns
Types of foundation for reinforced concrete columns reinforced concrete foundation – elastic foundation fig. 4.1. a
stepped foundation (plain concrete block and reinforced concrete block) - stiff
foundation fig. 4.1. b
TBF
> 2 0 c m
NAS
> 2 0 c m
NAS
Cuzinet de beton armat
Bloc de beton simplu
TBF
a. b.
Fig. 4. 1. a) Elastic foundation; b) stiff foundation
Criteria:
a) If the bearing layer is encountered at the surface we choose the first variant
b) Groundwater level : if is high – elastic foundations
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c) Load’s magnitude
High loads – elastic foundations
Low loads (
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Fig. 4. 3. Stiff foundation for one column
a. Determine the plain concrete block dimensions
The dimensions in plane of the foundation bottom are determined in order to
undertake the effect of the design actions, which acts on the foundation bottom, to be less or
equal with the design resistance of the bearing layer:
Vd ≤ Rd (4.1)
In order to evaluate the bearing capacity of the bearing layer, beside the geotechnical
parameters we need the values of the surface in plane of the foundation bottom (B x L). For
this reason, in order to verify the condition (4.1) it is imposed to know the estimative
dimension of the surface in plane for the foundation bottom. These can be adopted for one of
the following variant:
- Adopt some dimensions based on the experience or similar projects;
- Aproximative calculation, of initial sizing, based on acceptable pressures. For
this stage we can assume the base conventional pressures or plastic pressures
from STAS 3300/2 – 85 or NP 112 – 04.
Fig. 4. 4.
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B L p
N B
undede p B
N p
B L B
L
b
a
B
L
conv
Ed
conv Ed
ef
,8.0
2.1
,8.02.1
4.12.1
2
Ed fd Ed d
conv
N G N V
p
2.1
8.0
acc
accd
ef
p
pBxL
Vp
The following steps should be done for initial sizing:
a. Initial sizing
(4.4)
(4.5)
where: Gfd – design weight of the foundation, and the sustained soil
( f md fd D L BG )
It is considered a reduced value for the acceptable pressures of the bearing layer (0,8
conv p ) in order to take into account the corrections effect (depth and width).
(4.6)
(4.7)
(4.8)
The height of the concrete block is provided by the condition that at any point of the
dangerous sections of the plain concrete block there should be no tensile stress. This
condition is satisfied by adopting the height of the concrete block according to fig. 4.6.
The following relation should be satisfied:
tg≥tgadm. (4.9)
Values for tgadm are given in table 4.5. This relation should also be satisfied for
stepped foundation (fig.4.6.). The condition should be satisfied in all directions.
Tab. 4.5. Values for tgadm
For intermediate values of acceptable pressures, the corresponding value of the
closest superior effective pressure is to be used.
pacc (kPa)tgadm
C4/5 C8/10
200 1,15 1,05
250 1,30 1,15
300 1,40 1,30
350 1,50 1,40
400 1,60 1,50
600 2,00 1,85
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Fig. 4. 5. Stepped foundation
Construction requirements:
Minimum height 400mm – block with one step ;
Where we have more than 2, max. 3 steps, whose height is 300mm; minimum height for
the lower step should be 400mm;
Concrete class is minimum C8/10; if in the concrete block there is any reinforcement used
to fix the reinforced block , the minimum concrete class should be C12/15;
The forces transmitted on the superior part of the foundation are equal with the forces
encountered at the column. For this reason the concrete class used in the reinforced block
should be the same class used for the column. A lower class can be used only if the
punching verification it is done locally.
b. Initial sizing for reinforced block
Normally the reinforced block shape is prismatic. In case where the console length (l)
is higher than 400 mm, it can be rectangular.
Minimum class C8/10 results from the condition of local compressive strength of
concrete in the bearing column section. (Rc RC block ≥0.7 Rc colou;n);
One step block:
65.05.0 B
b
L
l cc (4.10)
2-3 step block:
5.04.0 B
b
L
l cc.
In order to determine the reinforced concrete block, a particular condition should be
satisfied: the reinforced concrete block should not shear on the perimetral contour of the
column. The real behavior of the reinforced concrete block is better than the one resulted
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from the above condition, because the reinforced block cannot shear, if the block on which is
placed do no shear. For this reason the following condition should be satisfied:
- Hc≥300mm,
- 25,0c
c
l
H (4.11)
- tg≥2/3.
If: tg≥1 the reinforced concrete block does not require the shear check;
- Anchorage length should be satisfied lancoraj+250mm, where la is taken
according to SR EN 1992.
c. Check
Bearing resistance check is done in ultimate limit state GEO in design approach (CP2).
Loads on foundation bottom:
Vd=NEd+Gf , (4.12)
Gf = BxLxDxmed (4.13)
med=20…22kN/m3,
NEd – design value of actions at column base.
The following condition should be satisfied:
Vd≤Rd (4.14)
Where: Vd – design load on foundation bottom
Rd – bearing resistance of the soil.
Bearing capacity value of the soil:
' A
R p d ,
R
d
d A
R
A
R
'
' , 1 R (for CP 3) (4.15)
''' L B A Error! Objects cannot be created from editing field codes.; Error! Objects
cannot be created from editing field codes. (4.16)Characteristic eccentricities:
6/ BekB ; 6/ LekL Where:
A’ – reduced area for the surface in plane of the foundation ( '' B L ), p – design critical pressure, according to SR EN 1997-1 (STAS 3300/2-85 or NP
112-04)
The design value of the pressure is determined according to the site conditions anddrained or undrained conditions. Eccentricities are limited to maximum 1/6 from the
foundation bottom dimensions or 0.20 from the radius in the case of circular foundations.
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Values of critical pressure for bearing layer: :- Undrained conditions
')2('/ qi sbc A R cccud (4.17)Where:b- coefficient depending on the foundation base inclination;
s- coefficient depending on the foundation shape;
i - coefficient depending on the inclination of the load caused by the horizontalload H ;- Drained conditions :
i sb N Bi sb N qi sb N c A R qqqqccccd ''5.0'''/ (4.18)
d. Settlement calculation
This check is done for the serviceability limit state (SLS)
The value of partial safety factor for this limit state is equal to 1.
Verification according to EC7:Ed≤ Cd
The soil is divided into 3 elementary layers with the height h≤0.4B.
hi= thickness of one elementary layer
ad ef s s
i
i
med
zi
E
h s
100 ; 8.0
2
inf sup
zi zimed
zi
n z p 0 (4.19)
),(0 B
L
B
z f
gz z 2.0 (active area)
)( i f ii gz Dh
e. Reinforcement
The strength reinforcement at the bottom of the reinforced block it determined in order
to overcame the bending moment determined in the sections surrounding the column, by
loading the surface at the bottom of the reinforced block with the pressure ’s diagram on the
bottom of the block with the exterior loadings.
a. Strength reinforcement on the reinforced block bottom, type 1 and 2 are parallel to the
block sides (fig. 4.7)
Conditions to be satisfied:
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ømin≥10mm,
dmin≥100mm / dmax≤250mm (4.20)
pmin≥0,01% (OB37)
pmin≥0,075 (PC52), on each direction.
b. Superior reinforcement (fig. 4.8), type 3, assures the connection of the reinforced
block with the plain concrete block
Fig. 4. 6. Reinforcement for reinforced concrete block
If at the reinforced concrete block in the bottom part there is only compressive
stresses – is not necessary to calculate or to dispose any anchorage reinforcement
On the other side, when tensile stress appears, it is imposed to dispose the
anchorage reinforcement in order to overcome the tensile stresses.
Fig. 4. 7. Superior reinforcement
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cbaT 12
1
It is disposed from the eccentric compression check of the reinforced section on the
contact surface between the reinforced and plain concrete block.
Design concrete strength :
2
,2
cc
cuz cap st calc
l b
M R
(4.21)
where bc – width of reinforced block
- the reinforcement is disposed uniformly on the block sides , and the
reinforcement sides are prolonged with the minimum length of 15Φ.
In the case where large loads appear, the pressure distribution it is done according to
the figure, and in this case the reinforcement type 3 is going to overcome the tensile
tensions.
(4.22)
In this case an additional check is to be done, namely the check of negative moment
(M-) for the reinforced concrete block, which is loaded with the forces developed in the
anchorage reinforcement.
The reinforcement type 3 is disposed with a minimum amount of 2 bars. The
constructive conditions that need to be covered by this reinforcement are the same with the
one of calculated reinforcement.
b. Reinforcement for columns type 5, assures the connection of the reinforced concrete
block with the reinforced column (fig. 4.8). They result from the sizing/verification of
column. Have similar position, diameter and number of bars with the column. Minimum
3 stirrups are required for the vertical reinforcement. The longitudinal reinforcement
needs to be prolonged in the foundation on a min. distance of la+250mm.
The connective reinforcement needs to be set in place in the reinforced
concrete block before the concrete is poured.
The overlapping distance between the connective reinforcement and the
longitudinal reinforcement of the column is according to SR EN 1992. For the columns
with 4 reinforcements bars at the corners the overlapping is to be done in the same
section. For the columns that have more than 8 bars, the overlapping is to be done at
least in two sections. If we have high loads, the overlapping is to be done at the
basement level.
Where the overlapping is taking place more stirrups are to be placed. (≤10Φ).
c. Transversal reinforcement is used if tgβ
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4.3.3. Calculation of bending moments, for determining the strengthreinforcement for the bottom of the reinforced concrete block
The positive bending moments in the reinforced concrete block is done considering
fixed console in the section at the face of the column. (fig. 4.9).
It is recommended to use the approximate methods, from the pressures on the contactsurface between the reinforced and plain concrete block (the weight of the reinforced
concrete block is not taken into consideration).
lc
b c
y
y
x x
p1p2
pm
p0
lx
l y
MEdNEd
y
y
My
Fig. 4. 8. Bending moments in the reinforced concrete block
2
2 2
0 1 0 0 1 0
1 2
( )2 2
2 1( )
2 3 2 2 3
2
y y
y c y m c m
x x x x x c x x c
m
l l M l l p l p
l l l l M b l p p p l b p p p
p p p
(4.24) / (4.25)
Bending moments Mx şi My are calculated charging the right console, below the x axis , with
the pressure from the contact surface fig. 4.8.
Observations:
1. If p2
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2. When for high moments, the active area from the contact surface between the
reinforced-plain concrete blocks is lower than 70% from the bottom of R.C. block (lc*bc), the
design bending moments of the reinforcement are the bending moments of the columns on
both directions :
Mx=Mx,st (4.27)
My=My,st.
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f. Foundation beams
To reduce differential rotation of the foundation due to contact pressures present at
the foundation’s extremities; the adjacent foundations can be connected using foundation
beams (fig. 4.11). the solution is recommended in cases where differential rotations of the
foundations are expected, due to non-homogen stratification along the building.
Fig. 4. 9. Calculation scheme for foundation beams
Same solution is to be used for foundations having large eccentricities reported to the
columns. For this particular situation, considering the effect of reducing the eccentricity
of loads from the column do not result in an economical sizing of the foundation , at
eccentric foundation where horizontal forces are not taken by the superstructure. They
can be used to reduce differential settlements between the adjacent foundations,
assuring the absorption of moments induced by the no uniform settlements at the
foundation level.
Design of foundation beams is developed based on two hypothesis:
a. Foundation beams has a high stiffness related to column stiffness
kgr /kst=10…15. In this case the loads coming from the columns are transmitted by the
entire surface of the beam and of the foundation . (fig. 4.34).
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Fig. 4. 10. Calculation scheme for foundation beams
b. The foundation beam has a lower stiffness related to column stiffness
kgr /kst10, loads coming from the columns are transmitted only by the end section of
the beam. Design it is done starting from the calculation scheme fig. 4.13. Startingfrom an “imposed” value of eccentricity “e”, the resultant of reactive pressure for the
foundations is calculated.
,111
L
e N R
L
e N N R 122 (4.29)
By knowing the acceptable pressure of the bearing (pacc), foundation plan will be:
acc
f
p
G R A
11
1
,
acc
f
p
G R A
22
2
, (4.30)
Where Gf – includes foundation weight and a part of beam weight
Fig. 4. 1. Calculation scheme for foundation beams
By knowing the values in plane of the foundation bottom, the dimensions of foundation
can be established, in order to satisfy the initial geometrical dimensions and
eccentricity. In addition, the foundation verification is done according to ultimate limit
state, identically with the case of centric isolated foundation.
If the conditions required in the ULS are not satisfied , a new value for the eccentricity
„e” is chosen , and the calculations are repeated until the conditions for sizing for the in panefoundation surface is satisfied.
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Based on the foundation bottom, the cross section dimensions are to be determined.
Bending moment and shear force diagram is determine for the foundation beam in order to
obtain the required reinforcement quantity. (fig. 4.14). The reinforcement for the two
foundations is done according to the elastic isolated foundation indications.
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