design model for simple column bases- axially loaded i section columns

NCCI: Design model for simple column bases- axially loaded I section columns SN037a-EN-EU

NCCI: Design model for simple column bases- axially loaded I section columns

This NCCI provides rules for determining either the design resistance or the required dimensions of base plates of simple columns, i.e. columns which are predominantly loaded in axial compression. While this NCCI is limited to covering symmetrical I section column bases, the rules given can be easily extended to bases of hollow section columns.

Contents

1. Introduction 2

2. Parameters 4

3. Design model 4

4. Design situation 1: Dimension a base plate 7

5. Design situation 2: Determine the design axial load resistance of a column base 10

6. Shear resistance of the base plate joint 11

7. References 12

Annex A Design bearing strength 13

NCCI: Design model for simple column bases- axially loaded I section columnsC

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1. Introduction This NCCI covers the design of simple bases of I section columns transmitting an axial compressive force and a shear force (i.e. a “pinned” column base). The rectangular base plate is welded to the column section in a symmetrically position so that it has projections beyond the column flange outer edges on all sides (see Figure 1.1). The base plate may be positioned eccentrically on the concrete foundation.

If not required to resist moment, it is usual practice in many countries to attach this type of column base to the concrete foundation by two anchor bolts symmetrically placed about the web on the column’s major axis. However in some countries, such as the UK, it may be required to have four anchor bolts in order to better ensure the stability of the column during erection. Anchor bolts provide resistance to any uplift forces which arise in the column and also, but only under certain conditions, may be used to provide resistance to shear at the column base.

The present NCCI does not cover

the design of anchor bolts,

the design of the column to base plate welds.

3 4

df

5

1

2

bf bb bfc

hc

hb

hf

c)

a)

c)

Key: 1. I section column 2. Base plate 3. Grout 4. Concrete foundation 5. Anchor bolt

Figure 1.1 Typical simple column bases and alternative positions of anchor bolts


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In practice, the following two design situations are encountered:

The column section and the axial design force are known. The dimensions of the required base plate are to be determined.

The column section, base plate and foundation dimensions are known. The design compressive resistance of the column base is required to be determined.

The design procedures for these two situations are given in Sections 4 and 5 respectively.

The basis of the design requires a value of the design strength for the foundation joint material (grout) beneath the base plate. A simple conservative value is given in Section 4 and a method to determine a more exact value which can be used in Section 5, taking account of the foundation dimensions and the enhancement of strength that can be realised by load dispersal into the foundation, is given in Annex A to this NCCI.

A simple column base may be assumed to be a “nominally pinned” joint in the global analysis of the frame. Noting that there are no criteria given in EN 1993-1-8 for the “nominally pinned” classification of column bases, it is possible that National Annexes provide information.


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2. Parameters The following are the parameters referred to in this NCCI (see Figure 3.1 and Figure 3.2):

Table 2.1 Parameters

Parameter Definition

α Ratio of the base plate width or lenght of the design distribution area within the foundation to the width or length of the base plate.

αcc Coefficient taking account of long term effects and unfavourable effects due to the manner of loading on the compressive strength of concrete (see EN 1992-1-1)

βj Foundation joint material coefficient.

γc Partial factor on the concrete compressive strength (see EN 1992-1-1).

γM0 Partial factor on the bending resistance of the base plate.

bp Width of the base plate.

bf Width of the foundation (corresponding to the column width).

bfc Width of the column section (width of the I section column flange).

beff Effective width of a base plate T-stub in compression.

c Additional bearing width (outside the column section perimeter).

df Depth of the foundation.

fyb Yield strength of the anchor bolt.

fyp Yield strength of the base plate.

fjd Design bearing strength of the foundation joint.

fcd Design compressive strength of the concrete according to EN 1992-1-1.

Parameter Definition

hf Length of the foundation (corresponding to the column depth).

hc Depth (height) of the column section.

hp Depth of the base plate.

tfc Column flange thickness.

leff Effective length of a base plate T-stub in compression.

twc Column web thickness.

tp Base plate thickness.

Ac0 Compression area under the base plate of dimensions bp and hp.

Ac1 Design distribution area (dimensions bc1, hc1) within the concrete foundation after diffusion beneath the base plate.

Cf,d Coefficient of friction between the base plate and the grout layer.

FRdu Concentrated design resistance for a base plate compressive area of Ac0, according to EN 1992-1-1.

Ff,Rd Design friction shear resistance.

Fv,Rd Design shear resistance of the column base plate joint.

Nj,Ed Design compressive axial load at the column base.

Nj,Rd Design compressive resistance of the column base.

Design shear force at the column base.

Vj,Ed

3. Design model 3.1 General The design model for the axial compression force is based on §6.2.5 and §6.2.8.2(1) of EN 1993-1-8. The basic design approach is to ensure that the bearing stresses under the base plate neither exceed the design bearing strength of the foundation joint material nor lead to excessive bending of the base plate.


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http://www.access-steel.com/discovery/linklookup.aspx?id=EC168



The design model assumes that the bearing resistance of a column base on its foundation is provided by three non-overlapping T-stubs in compression, one for each column flange and one for the column web, as shown in Figure 3.1. For each T-stub, the design bearing resistance is determined by multiplying its bearing area (length by width) by the strength of the foundation joint material.

The length and width of each T-stub depend on the dimensions of the relevant flange or web and on an “additional” bearing width, cantilevered from the T-stub stem as shown in Figure 3.2and Figure 4.1. While the theoretical value of the “additional” bearing width depends on the elastic bending resistance of the base plate and on the design strength of the foundation joint material, the effective total bearing area needs to be corrected if use of the latter width leads to overlapping of the individual T-stub bearing areas between the flanges.

bf bp bfc

hc

hp

hf

1 2

3

Key: 1. T-stub bearing area for left column flange 2. T-stub bearing area for right column flange 3. T-stub bearing area for column web

Figure 3.1 Column base and non overlapping T-stub bearing areas (see Figure 6.19 of EN

1993-1-8)

3.2 Base plate types There are two basic types of base plate identified in EN1993-1-8, ‘large projection’ base plates and ‘short projection’ base plates.

For the “large projection” base plate, the projection of the base plate beyond the column section perimeter is such that the design bearing width on each side of all three T-stubs is usually equal to the value of the “additional” width (c). A large projection base plate is illustrated in Figure 3.2a).

For the “short projection” base plate, the projection beyond both column flanges towards the base plate edges, while being less than the value of the “additional” width (c), is adequate to allow fillet welding of the flanges to the base plate. Usually, for the latter purpose, a width approximately equal to the column flange thickness is provided. A “short projection” base plate is illustrated in Figure 3.2b).


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3.3 Accounting for overlap Note that when some H-section columns are used with thick base plates, the flange T-stubs of “additional” bearing width c on the web side would overlap in the central area between the flanges as shown in Figure 3.2c) and Figure 3.2d). In such cases, since there would be no bearing area left for a web T- stub, the effective bearing area would be reduced to a simple rectangular area as follows:

“Short” projection base plate: Aeff. bearing = Ac0 = leff beff = hpbp

“Large” projection base plate: Aeff. bearing = Ac0 = leff beff = (hc+ c)(bfc + c) ≤ hpbp

hc

bfc

≈ tfc

tfc

≈ tfc hc

twc

c

leff = bp

≈ bfc + 2tfc

hp ≈ hc + 2 tfc

c

c

beff

c

tfc

bfc twc

c

leff ≤ bp

hp ≥ hc + 2c

c

c

c

beff

a) b)

hc

bfc

≈ tfc

tfc

≈ tfc hc

twc leff = bp

≈ bfc + 2tfc

hp ≈ hc + 2 tfc = beff

d)

hc – 2tfc ≤ 2c c

tfc

bfc twc

c

leff ≤ bp

c

c

hp ≥ hc + 2c= beff

c)

hc – 2tfc ≤ 2c

a) “Large projection” base plate bearing areas of non overlapping T-stubs

b) “Short projection” base plate bearing areas of non overlapping T-stubs

c) “Large projection” base plate bearing areas if “overlap” of T-stubs occurs

d) “Short projection” base plate bearing areas if “overlap” of T-stubs occurs

Figure 3.2 Area / dimensions of equivalent T–stubs in compression


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4. Design situation 1: Dimension a base plate If the column section and the axial compression force are given, the following procedure can be used to dimension the base plate.

Step 1: Choose the design strengths of the materials Base plate steel strength:

A design value for the yield strength of the base plate steel is adopted. ypf

Bearing strength of the foundation joint material (grout):

It is shown below that, in most practical cases, the value of the design bearing strength of the joint material can be taken as equal to that of the design concrete strength in compression, i.e.

= . jdf cdf Table 4.1provides typical design bearing strengths for typical concrete grades and foundation joint materials.

Table 4.1 Bearing strength for typical foundation concrete and foundation joint material

Concrete class fck 20 25 30 35 40 45

Bearing strength fjd (N/mm2)

13,3 16,7 20 23,3 26,7 30

More generally, the design bearing strength of the foundation joint material is given as:

cdjjd ff αβ=

Where:

jβ is the foundation joint coefficient, whose value is taken as 2/3,

c0c1 / AA=α accounts for the concrete bearing strength enhancement due to diffusion of the concentrated force within the foundation over the area Ac1 (see Annex A). In practice, the value of 1,5 is commonly used..

cdf is the design compressive strength of the foundation concrete.

With the above assumptions for the values of the coefficients jβ and α one obtains

cdfff )5,1)(3/2(cdjjd == αβ = , which is the basis for the design values given in cdf Table 4.1.

It is usual practice to use a concrete of medium strength for foundations and quality grout for the joint material in all cases.

For other concrete classes and assumptions, see Annex A.


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Step 2: Make a preliminary estimate of the base plate area A first estimate of the required base plate area is given by the larger of the following two values:

2

cd

Edj,

c fc0

1⎥⎦

⎤⎢⎣

⎡=

fN

bhA

c

cd

Edj,c0 f

NA =

Step 3: Choose the type of base plate

The choice of the base plate type is recommended to be as follows:

Ac0 ≥ 0,95 hcbfc adopt a “large projection” base plate,

Ac0 < 0,95 hcbfc adopt a “short projection” base plate.

Note: A large projection base plate may be adopted in all cases.

Step 4: Determine the additional bearing width

The value of the “additional” bearing width, c, is obtained by satisfying the relevant design bearing resistance condition as follows (see figures 3.2 and 4.1):

Design bearing resistance of a “short “ projection base plate:

Assuming the projections beyond the column flange edges to be equal to the column flange thickness tfc , the design bearing resistance is as follows:

Nj,Rd = fjd [2(bfc + 2 tfc)(c + 2 tfc) + (hc – 2 c – 2 tfc)(2 c + twc)]

Design bearing resistance of a “large” projection base:

Assuming the bearing width about the column perimeter to be equal to the additional bearing width c, the design bearing resistance is as follows:

Nj,Rd = fjd [2(bfc + 2 c)(2c + tfc) + (hc - 2 c – 2 tfc)(2 c + twc)]

Replacing Nj,Rd by Nj,Ed in the above expressions, the solution to the resulting quadratic equations for the unknown c takes the standard form:

A

ACBBc2

42 −±−= - for which positive solutions only are of interest.

Table 4.2 gives the expressions for the constants A, B and C , under the relevant “non overlapping T-stub” column.


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Table 4.2 Expressions of the parameters of the quadratic equation

“Short projection” base “Large projection” base Constant

Non overlapping T-stubs Non overlapping T-stubs T-stub overlap predicted

2 2 2 A

- (bfc– twc+ hc) +(2 bfc– twc+ hc) +(bfc + hc) B

+(Nj,Ed/2fjd) - (2bfctfc+4tfc2+0,5hctwc-tfctwc)

+ (bfctfc+0,5hctwc-tfctwc) -(Nj,Ed/2fjd)

+ (bfchc)/2 -(Nj,Ed/2fjd) C

Check for “overlapping” T-stubs

The value obtained above for the “additional” width c sometimes exceeds half the height of the column web, which is unacceptable as it implies having overlapping T-stubs bearing areas.

“Short projection” base plate: change to a “large projection” base plate and recalculate c.

“Large projection” base plate: recalculate c based on having the entire area between the column flanges in bearing in the design expression. The design condition for the “large projection” base plate then becomes:

Nj,Ed ≤ Nj,Rd = fjd [(bfc + 2 c)(hc + 2 c)]

The corresponding expressions for A, B and C to be used in the solution for c are given in the last column of Table 4.2.

Step 5: Determine the required minimum plan dimensions of the base plate

The final plan dimensions of the base plate are based on the following:

“Short projection” base plate:

bp ≥ (bfc + 2 tfc)

hp ≥ (hc + 2 tfc)

“Large projection” base plate:

bp ≥ (bfc + 2 c)

hp ≥ (hc + 2 c)

Step 6: Determine the minimum required base plate thickness The minimum required thickness of the base plate is obtained from the condition that the plate, assumed to act as a cantilever off the column perimeter, is not subject to more than its elastic design bending resistance under a uniform bearing pressure equal to fjd acting over the “additional” width c (see Figure 4.1). The value for the minimum required thickness is given by:

5,0

M0jd

ypp

)3( ⎥⎦⎤

⎢⎣⎡

≥

γff

ct


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tp

tfc

c tfc βc≤ c

≥ tfc

tp

tfc or twc

c tfc or twc

c

a) b)

a) “Short projection” base: column flange T-stub

b) Column web T-stub and “Large projection” base column flange T-stub

Figure 4.1 Uniform distribution of bearing stresses over the width of T-stubs in compression

5. Design situation 2: Determine the design axial load resistance of a column base

Step 1: Establish basic parameters and assumptions - Base plate steel grade: the value of fyp is required to be known.

- Dimensions of the base plate: tp , bp and hp are required to be known.

- Column section: tfc , twc , bfc and hc are required to be known.

- Foundation joint material: it is assumed that a value of jβ = 2/3 is justified.

- Foundation dimensions (df , bf , hf ) and base plate position parameters (eb, , eh).:

- If known, ⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟

⎟⎠

⎞⎜⎜⎝

⎛+⎟

⎟⎠

⎞⎜⎜⎝

⎛+= 3,21,21,

),max(1min

p

b

p

h

pp

f

be

he

bhdα

Where eb = (bf – bfc -2 tfc)/2 and eh = (hf – hc -2 tfc)/2.

- If not known, adopt 5,1=α

- Foundation concrete strength:

- If known, take fcd from table 4.1 (or table A.1)

- If not known, assume grade 20: fcd = 13,3 N/mm².

Step 2: Determine the design bearing strength

The design bearing strength is given by: cdjd 3/2 ff α=


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Step 3: Determine the value of the “additional” bearing width

The value is given by: 03 Mjd

ypp f

ftc

γ=

Step 4: Determine the design compressive resistance of the base plate “Short projection” base plate

If c ≤ (hc– 2 tfc)/2 the design resistance in compression is given by:

Nj,Rd = 2 Ffc,Rd + Fwc,Rd = fjd [2 (bfc + 2βc)(c + βc + tfc) + (hc – 2 c – 2 tfc) (2 c + twc)]

Note: The projection length βc (see figure 4.1) can be safely replaced by tfc. If c > (hc– 2 tfc)/2 the design resistance in compression is given by:

Nj,Rd = 2 Ffc,Rd = fjd (bphp) .

“Large projection” base plate

If c ≤ (hc– 2 tfc)/2 the design resistance in compression is given by:

Nj,Rd = 2 Ffc,Rd + Fwc,Rd = fjd [2 (bfc + 2 c)(2c + tfc) + (hc – 2 c – 2 tfc)(2 c + twc)]

If c > (hc– 2 tfc)/2 , (hc + 2 c) ≤ hp and (bc + 2 c) ≤ bp (overlapping) the design resistance in compression is given by:

Nj,Rd = 2 Ffc,Rd = fjd [ (bfc + 2 c)( hc + 2 c)]

Otherwise, the design resistance in compression is given by:

Nj,Rd = 2 Ffc,Rd = fjd [min((bfc + 2 c):bp)×min((hc + 2 c ): hp)]

6. Shear resistance of the base plate joint The design shear resistance is based on the friction resistance developed by the compressive load applied by the base plate on the joint material. It is given as (EN 1993-1-8 § 6.2.2(6)):

Fv,Rd = Ff,Rd

Where: Ff,Rd = Cf,d Nc,Ed

Nc,Ed is the column design compressive load and

Cf,d is the coefficient of friction between the base plate and the grout layer. A value of 0,2 is specified for sand-cement mortar. Otherwise tests in accordance with EN 1990 Annex D are required to determine the coefficient value for any other type of grout.

The design check is: Vc,Ed ≤ Fv,Rd


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7. References 1 Cost C1 “Column Bases in Steel Building Frames”

European Commission Brussels, Edited by Klaus Weynand RWTH Aachen , 1999.

2 Dewolf, J.T., Ricker,D.T. “Column Base Plates”, AISC Steel Design Guides Series, N°1, 1990.

3 “Joints in Steel Construction: Simple Connections” Publication P212, SCI/BCSA, 2002.

4 Lescouarc’h, Y. “Pinned column bases”, CTICM collection, 1982 (in French).


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Annex A Design bearing strength A.1 Influence of foundation dimensions on bearing strength The design bearing strength of the foundation joint (grout), fjd , depends on:

the degree of diffusion of the base plate load into the foundation

the compressive strength of the foundation concrete

relative strength and thickness of the grout (see 6.2.5(7) of EN 1993-1-8).

If the foundation dimensions are sufficiently large compared to those of the base plate, the bearing strength can be significantly greater than the concrete design strength in compression, since optimal diffusion of the load is possible (see Figure A.1 d)). If full diffusion is not possible the design bearing strength can be considerably less than the maximum bearing strength (see Figure A.1 a), b), and c)).

The maximum bearing strength corresponds to the situation when the ratio c0c1 / AA = 3,0 (the limiting condition given in EN1992-1-1 §6.7(2)).

Where

Ac1 is the distribution area (by uninterrupted diffusion within the foundation)

Aco is the base plate bearing area

When the ratio c0c1 / AA is at the maximum, the required base dimensions (width, depth and thickness) will be the smallest possible.

Although the theoretical minimum value for the c0c1 / AA ratio is unity, it is common practice to adopt a minimum of 1,5. This minimum corresponds to having uninterrupted foundation dimensions of bf = 1,5bp and hf = 1,5hp (see figure A.1 e)). To ensure that this distribution can be achieved, the foundation depth must satisfy the following:

df ≥ max[bfhf /(bf + hf) , 3bphp /(2bp + 2hp)]


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df

eh < hbhb 1

2eh

2

df < 2hb df < 2bb

df > 2hb df > 2bb

3hb or 3bb

1 Ac1 = 9 Ac0

hb or bb hb or bb

Ac0 ≤ Ac1 < 9 Ac0

2

df

eb < bb

bb 1

2eb

2

Ac0 ≤ Ac1 < 9 Ac0 a) b)

hb or bb 1

2

Ac0 ≤ Ac1 < 9 Ac0 c) d)

df

eb = 0,25bb or 0,25hb

bb or hb 1

0,5bb or 0,5hb

2

Ac1 = 2,25 Ac0 e)

Key: 1. Base plate bearing area Ac0 2. Foundation

Figure A.1: Distribution area in the foundation: effect of the base plate size and position

A.2 Maximum and minimum bearing strengths The design bearing strength of the foundation joint material is given as:

cdjjd ff αβ=

Where: jβ is the foundation joint coefficient, whose value is taken as 2/3,

c0c1 / AA=α is the coefficient which accounts for the concrete bearing strength enhancement due the diffusion of the concentrated force within the foundation,

is the design compressive strength of the foundation concrete. cdf

The use of the jβ = 2/3 coefficient value requires that the relevant conditions on the grout compressive strength (EN 1993-1-8 §6.2.5(7)) be met:


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If the grout thickness ≤ min (50 mm; 0,2 hp ; 0,2 bp), the grout compressive strength should be at least equal to 0,2 cdf

If the grout thickness > 50 mm, the grout compressive strength should be at least equal to cdf

The determination the value of the “bearing strength enhancement” coefficient α requires knowledge of the foundation dimensions, information which is rarely available at the stage the dimensions the column base plates are fixed.

If the foundation dimensions are known, the design bearing strength of the foundation joint can be calculated:

c0c1cdjjd / AAff β=

Where: α=c0c1 AA /

And: ⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟

⎟⎠

⎞⎜⎜⎝

⎛+⎟

⎟⎠

⎞⎜⎜⎝

⎛+= 3,21,21,

),max(1min

p

b

p

h

pp

f

be

he

bhdα

The following simplifying assumptions are made in this NCCI:

To permit a foundation joint material coefficient of βj = 2/3, the conditions on strength and thickness of the grout joint (see clause 6.2.5(7) of EN 1993-1-8) are met.

In order to simplify the determination of the bearing strength, it is acceptable to consider that the base plate area as a whole is in bearing. Taking Ac0 = bphp (instead of Ac0 = beffheff for a single T-stub) leads to a safe estimate of the bearing resistance of the joint and is consistent with assuming the base plate to be under axial loading only. When the foundation dimensions are known initially, but those of the base plate are not, it is recommended to take Ac0 = (bfc + 2 tfc)(hc + 2 tfc) as an initial estimate.

If the foundation dimensions are unknown, it is recognized that usual foundation sizes relative to that of the base plate justify α=c0c1 AA / ≥ 1,5. Taking α = 1,5, a design bearing strength of fjd = fcd is obtained ( )5,1)(3/2(cdjjd == ff αβ cdf = ). cdf

If the more conservative value for the design bearing strength of fjd = 2/3fcd is adopted it corresponds to having the foundation area, Ac1, equal to the base plate area, Ac0, which is rarely the case in typical building situations.

Design on the basis of a design bearing strength fjd greater than fcd is recommended only if there can be prior collaboration with the party responsible for the foundations.

The values of fcd and βj fcd for the different concrete classes are given in table A.1


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Table A.1: Concrete classes, concrete strengths and bearing resistances (N/mm2) for βj = 2/3

Concrete class fck 12 16 20 25 30 35 40 45 50 60 fcd = αcc fck / γc

γc=1,5 and αcc= 1,0 8 10,7 13,3 16,7 20 23,3 26,7 30 33,3 40

Min fjd:for α =1,0 cdcdjjd )3/2(0,1 fff == β 5,3 7,1 8,9 11,1 13,3 15,6 17,8 20 22,2 26,7

fjd for α =1,5 cdcdjjd 5,1 fff == β 8 10,7 13,3 16,7 20 23,3 26,7 30 33,3 40

Max. fjd for α =3,0 cdcdjjd 20,3 fff == β 16 21,4 26,6 33,4 40 46,6 53,4 60 66,6 80

Notes: Some countries may have national practice requirements on the minimum concrete grade to be used for the foundations. For example some countries now require that mass concrete foundations be of ≥ grade 20 and reinforced concrete foundations be of ≥ grade 25.

A.3 Estimate of base plate plan dimensions The base plate area is estimated as the largest of the following values:

2

cdj

Edj,

c1C0

1⎥⎥⎦

⎤

⎢⎢⎣

⎡=

fN

AA

βin which Ac1 ≈ α2 (hcbfc)

Foundation dimensions known:

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟

⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛+

+⎟⎟⎠

⎞⎜⎜⎝

⎛+

+= 3,21,21,2

1,2

1minp

b

p

h

fcc

f

fcc

f

be

he

tbd

thdα

Where eb = (bf – bfc -2 tfc)/2 and eh = (hf – hc -2 tfc)/2.

Foundation dimensions unknown: α = 1,5

cdj

Edj,c0 f

NA

αβ=

With βj = 2/3 and fcd from Table A.1.


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Quality Record RESOURCE TITLE NCCI: Design model for simple column bases- axially loaded I

section columns

Reference(s)

ORIGINAL DOCUMENT

Name Company Date

Created by Ivor Ryan CTICM 21/04/2005

Technical content checked by Alain Bureau CTICM March 2006

Editorial content checked by

Technical content endorsed by the following STEEL Partners:

1. UK G W Owens SCI 17/3/06

2. France A Bureau CTICM 17/3/06

3. Sweden A Olsson SBI 17/3/06

4. Germany C Müller RWTH 17/3/06

5. Spain J Chica Labein 17/3/06

Resource approved by Technical Coordinator

G W Owens SCI 11/7/06

TRANSLATED DOCUMENT

This Translation made and checked by:

Translated resource approved by:


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design model for simple column bases- axially loaded i section columns

Documents

column section

design model

design of simple bases

design resistance

type of column base

pinned column base

design situations

typical simple column