Ejemplo Cimentación con Eurocódigo

7/30/2019 Ejemplo Cimentacin con Eurocdigo

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Design of footings 325

10.10.1 Pad footing on dry sand

Example 10.1 considers thedesign of a simplerectangular spread footingon dry sand, as shown inFigure 10.9. It adopts thecalculation method given inAnnex D of EN 1997-1.

In this example it isassumed that groundsurface is at the top of thefooting, i.e. the base of thefooting is 0.5m below ground level.

The loading is applied centrally to the footing and therefore eccentricity canbe ignored. Ground water is also not considered. The example concentrateson the application of the partial factors under the simplest of conditions. Inreality, the assessment of a footing would need to consider a number of othersituations before a design may be finalized.

Notes on Example 10.1

In order to concentrate on the EC7 rather than the geotechnical relatedissues a relatively simple problem has been selected which excludes theeffects of groundwater.

The formulas for bearing capacity factors and shape factors are those givenin Annex D. Other formulas could be used where they are thought to give abetter theoretical/practical model for the design situation being considered.

The suggested method in Annex D does not include depth factors whichare present in other formulations of the extended bearing capacity formula(e.g. Brinch-Hansen or Vesic). There has been concern in using these depthfactors as their influence can be significant and the reliance on the additionalcapacity provided by its inclusion is not conservative.

For Design Approach 1, DA1-2 is critical with a utilization factor of 97%

implying that the requirements of the code are only just met.

For Design Approach 2 the uncertainty in the calculation is coveredthrough partial factors on the actions and an overall factor on the calculatedresistance.

Figure 10.9. Pad footing on dry sand


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Example 10.1

Pad footing on dry sand

Verification of strength (limit state GEO)

Design situation

Consider a rectangular pad footing of length L 2.5m , breadth B 1.5m , and

depth d 0.5m , which is required to carry an imposed permanent action

VGk 800kN and an imposed variable action VQk 450kN , both of which

are applied at the centre of the foundation. The footing is founded on dry

sandn with characteristic angle of shearing resistance k 35 , effective

cohesion c'k 0kPa , and weight density k 18kN

m3

. The weight density of

the reinforced concrete is ck 25kN

m3

(as per EN 1991-1-1 Table A.1).

Design Approach 1

Actions and effects

Characteristic self-weight of footing is WGk ck Lu Bu du 46.9kN

Partial factors from SetsA1

A2

: G

1.35

1

and Q

1.5

1.3

Design vertical action: Vd G WGk VGk u Q VQku1818.3

1431.9

kN

Area of base: Ab L Bu 3.75m2

Design bearing pressure: qEd

Vd

Ab

484.9

381.8

kPa

Material properties and resistance

Partial factors from SetsM1

M2

:

1

1.25

and c

1

1.25

Design angle of shearing resistance is d tan1

tan k

35

29.3

Design cohesion is c'd

c'k

c

0

0

kPa


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Bearing capacity factors

For overburden: Nq e tan

d u

tan 45

d2

2

u

o

33.3

16.9

For cohesion: Nc Nq 1 cot d uo 46.1

28.4

For self-weight: N 2 Nq 1 tan d uo 45.2

17.8

o

Shape factors

For overburden: sq 1B

L

sin d u

o1.34

1.29

For cohesion: sc

sq Nqu 1 Nq 1

o1.35

1.31

For self-weight: s 1 0.3B

L

u 0.82 p

Bearing resistance

Overburden at foundation base is 'vk,b k du 9kPa

Partial factors from SetR1

R1

: Rv

1.0

1.0

From overburden qult1

Nq squ 'vk,bu o 402.8

196.9

kPa

From cohesion qult2

Nc scu c'du o 0

0

kPa

From self-weight qult3

N su kuB

2u

o500.7

197.5

kPa

Total resistance qult

1

3

i

qulti

o

903.5

394.4

kPa

Design resistance is qRd

qult

Rv

903.5

394.4

kPa


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Verification of bearing resistance

Utilization factor GEO,1

qEd

qRd

54

97

% q

Design is unacceptable if utilization factor is > 100%

Design Approach 2

Actions and effects

Partial factors from Set A1: G 1.35 and Q 1.5

Design action is Vd G WGk VGk u Q VQku 1818.3 kN

Design bearing pressure is qEd

Vd

Ab484.9kPa


Partial factors from Set M1: 1.0 and c 1.0


tan k

35


c'k

c0kPa


For overburden: Nq e tan d u

tan 45d

2

2

33.3

For cohesion: Nc Nq 1 cot d u 46.1For self-weight: N 2 Nq 1 tan d u 45.2

Shape factors


L

sin d u 1.34

For cohesion: sc

sq Nqu 1

Nq 1 1.35


L

u 0.82


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Bearing resistance

Partial factor from Set R2: Rv 1.4 rFrom overburden qult1

Nq squ 'vk,bu 402.8kPa

From cohesion qult2

Nc scu c'du 0kPa


N su kuB

2u 500.7kPa

Total resistance qult qult 903.5kPa

Design resistance is qRd

qult

Rv

645.3kPa



qEd

qRd75 % s


Design Approach 3

Actions and effects

Partial factors on structural actions, Set A1: G 1.35 and Q 1.5

Design vertical action Vd G WGk VGk u Q VQku 1818.3 kN

Design bearing pressure qEd

Vd

Ab484.9kPa


Partial factors from Set M1: 1.25 and c 1.25 t


tan k

29.3


c'k

c0kPa


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For overburden: Nq e

tan d u tan 45

d

2

2

u 16.9

For cohesion: Nc Nq 1 cot d u 28.4For self-weight: N 2 Nq 1 tan d u 17.8

Shape factors


L

sin d u 1.29

For cohesion: sc

sq Nqu 1

Nq 11.31


L

u 0.82

Bearing resistance

Partial factor from Set R2: Rv 1

From overburden qult1

Nq squ 'vk,bu 196.9kPa

From cohesion qult2

Nc scu c'du 0kPa


N su kuB

2u 197.5kPa

Total resistance qult qult 394.4kPa

Design resistance qRd

qult

Rv394.4kPa



qEd

qRd123% u



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Design of footings 331

The calculated utilization factor is 75% which would indicate thataccording to DA2 the footing is potentially over-designed.

Design Approach 3 applies partial factors to both actions and materialproperties at the same time.

The resultant utilization factor is 123% thus the DA3 calculation suggeststhe design is unsafe and re-design would be required.

The three Design Approaches give different assessments of the suitability ofthe proposed foundation for the design loading. Of the three approaches,DA1 suggests the footing is only just satisfactory whilst DA3 suggestsredesign would be required and DA2 may indicate that the footing isoverdesigned!

Which approach is the most appropriate cannot be determined althoughDA3 would appear unnecessarily conservative by providing significantpartial factors on both actions and material properties.

10.10.2 Eccentric pad footing on dry sand

Example 10.2 considers thedesign of a pad footing ondry sand, in which theimposed vertical load fromthe superstructure iseccentric to the centre of

the foundation, as shown inFigure 10.10.

Because the load iseccentric, the foundationsdesign is based on itseffective area. The foundations self weight (which acts through the centre ofthe footing) helps to reduce the eccentricity of the total load. Eccentric loadsshould be avoided whenever possible since they make the footing inefficient.

Figure 10.10. Eccentric pad footing on dry sand

Ejemplo Cimentación con Eurocódigo

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