NCCI_Design of Fixed Column Base Joints
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NCCI: Design of fixed column base joints SN043a-EN-EU
NCCI: Design of fixed column base joints This NCCI provides the rules for the design of fixed column base joints. The rules are limited to covering the design of symmetric un-stiffened base plate joints of I section columns subjected to normal force, shear force and moment about the column major axis. The design of a shear nib, if required, is covered by NCCI SN021. The rules given can be easily extended to bases of other types of column sections.
Contents
t n e m e e r g A e c n e c i L z i b l e e t S e h t f o s n o i t i d n o c d n a s m r e t e h t o t t c e j b u s s i t n e m u c o d s i h t f o e s U . d e v r e s e r s t h g i r l l a 9 t h 0 g 0 i 2 r y y p a o M c s 9 i 0 l a i n r o t e d a e t m a s i e r h C T
1.
Introduction
2
2.
Parameters
4
3.
Design model and limitations
5
4.
Design situation 1: Dimension a base plate for the loading at the base of a given column section
8
5.
Design situation 2: Determine the design resistances of a given base plate
12
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NCCI: Design of fixed column base joints SN043a-EN-EU
1.
Introduction
This NCCI covers the design of fixed bases of I section columns transmitting a normal force, a shear force and a moment. The rectangular base plate is welded to the column section in a symmetrical position so that it has projections beyond the column flange outer edges on all sides (see Figure 1.1). 1.1). Anchor bolts rows, normal to the column major axis, are symmetrically placed about the column minor axis. The base plate may be located eccentrically on the concrete foundation. In practice, the following two design situations are encountered: 1.
The column section and the concomitant design normal force, shear force and moment are known. The dimensions of the required base plate and anchor bolts are to be determined.
2.
The column section, base plate and foundation dimensions in a particular structure are known. It is required to check that the different combinations of axial force, shear force and moment that arise can be safely resisted.
The design procedures for these two situations are given in Sections 4 and 5 respectively. t n e m e e r g A e c n e c i L z i b l e e t S e h t f o s n o i t i d n o c d n a s m r e t e h t o t t c e j b u s s i t n e m u c o d s i h t f o e s U . d e v r e s e r s t h g i r l l a 9 t h 0 g 0 i 2 r y y p a o M c s 9 i 0 l a i n r o t e d a e t m a s i e r h C T
Noting, in particular, the importance of the intrinsic relationship between the values of the design moment and the concomitant normal force, the satisfactory determination of the fundamental characteristics of the joint components (i.e. grout/foundation bearing resistance, base plate area, base plat thickness, anchor bolt dimensions and anchor bolt positions) usually requires separate checking of all joint components for the concomitant forces and moments resulting from a number of different load combination cases acting on the structure. The shear force resistance of the base plate joint is either covered by SN037 and, if the friction resistance is insufficient, by SN043 SN043.. The shear force is not considered to have any effect of the joint resistance to a combination of a normal force and a moment. The stiffness of the base plate joint is obtained using SN045 SN045..
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1 5
2 3
4
d f
b p
bf
h p
t n e m e e r g A e c n e c i L z i b l e e t S e h t f o s n o i t i d n o c d n a s m r e t e h t o t t c e j b u s s i t n e m u c o d s i h t f o e s U . d e v r e s e r s t h g i r l l a 9 t h 0 g 0 i 2 r y y p a o M c s 9 i 0 l a i n r o t e d a e t m a s i e r h C T
hf
Key : 1. I section column 2. Base plate 3. Grout 4. Concrete foundation 5. Anchor bolt
Figure 1.1
Typical fixed column base plate joints
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NCCI: Design of fixed column base joints SN043a-EN-EU
2.
Parameters
Table 2.1
Parameters Definition
b eff
Effective width of a base plate T-stub in compression.
Definition As
Sectional area of an anchor bolt
c
Additional bearing width (measured from the column section perimeter) for a compression T-stub.
F t,Rd
e N
Effective normal load eccentricity expressed by the ratio, M Ed / N Ed , of the applied concomitant moment M Ed and axial load N Ed
F t,bond,Rd
Anchorage bond design resistance of an anchor bolt
Width, length and depth of the foundation.
F t,anchor,Rd
Design resistance of an anchor bolt in tension
b f, h f, d f
Design resistance in tension of an anchor bolt section
= min(F t,Rd: F t,bond,Rd) f yb
Yield strength of the anchor bolt.
F T,l,Rd
Design resistance in tension of the left-side anchor bolt row T-stub.
f yp
Yield strength of the base plate.
F T,r,Rd
Design resistance in tension of the right-side anchor bolt row T-stub.
F C,l,Rd
Design resistance in compression of the left-side compression flange T-stub. Design resistance in tension of the right-side compression flange T-stub.
f jd t n e m e e r g A e c n e c i L z i b l e e t S e h t f o s n o i t i d n o c d n a s m r e t e h t o t t c e j b u s s i t n e m u c o d s i h t f o e s U . d e v r e s e r s t h g i r l l a 9 t h 0 g 0 i 2 r y y p a o M c s 9 i 0 l a i n r o t e d a e t m a s i e r h C T
Design bearing strength of the foundation joint.
f cd
Design compressive strength of the concrete according to EN 1992-1-1.
F C,r,Rd
b fc, t fc, t wc , h c
Flange width, flange thickness web thickness and depth (height) of an I section column
LB
b p, h p, t p
Width, length and thickness of the base plate.
M Ed M j,Ed
Length of anchor bolt submitted to tensile elongation. Design moment applied by the column (positive if clockwise) to the base joint, in conjunction with N Ed.
b eff, l eff
Effective length of a T-stub in tension.
M j,Rd
Design resistance moment of the column base joint for a given effective eccentricity, e N = M Ed / N Ed of the normal load N Ed = N j,Rd
m, n, e
Tension T-stub geometric parameters
N Ed
Design normal force (positive if in tension) applied by the column to the base joint, in conjunction with the moment M Ed.
N j,Ed
γM0
Partial factor on the base plate bending resistance.
z
Lever arm between the left-side force and the right-side force induced on the column base to foundation joint.
z T,r
Distance of a right-side anchor bolt row from the column major axis.
z T,l
Distance of a left-side anchor bolt row from the column major axis.
z C,l
Distance of a left-side T stub centre of compression from the column major axis.
z C,r
Distance of a right-side T stub centre of compression from the column major axis.
N j,Rd
Design normal force resistance of the column base at an effective eccentricity of e N = M Ed / N Ed = M j,Rd / N j,Rd
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3.
Design model and limitations
3.1
Design model
The design model for a fixed column base plate joint for a combined normal force plus a moment about the major column axis is given in §6.2.8 of EN 1993-1-8. The most common load distributions in a fixed column base joint, shown in Figure 3.1 a), b) and c) respectively, are as follows:
Compression on both sides of the joint due to a dominant axial compression load combined with - either a clockwise moment - or an anticlockwise moment.
Tension on the left hand side and compression on the right hand side due to a dominant clockwise moment combined with - either a compressive axial load - or a tensile axial load (uplift) .
t n e m e e r g A e c n e c i L z i b l e e t S e h t f o s n o i t i d n o c d n a s m r e t e h t o t t c e j b u s s i t n e m u c o d s i h t f o e s U . d e v r e s e r s t h g i r l l a 9 t h 0 g 0 i 2 r y y p a o M c s 9 i 0 l a i n r o t e d a e t m a s i e r h C T
Compression on the left hand side and tension on the right hand side due to a dominant anticlockwise moment combined with - either a compressive axial load - or a tensile axial load (uplift).
In the design formulae given Table 6.7 of EN 1993-1-8 a distinction made between the latter two cases which permits the use of parameters, symbols and a sign convention which facilitate treating non symmetric joints subjected to multiple load cases. An additional load distribution case with tension on both sides of the joint ( Figure 3.1d)), for which an axial tensile load is dominant, completes the theoretical possibilities for the load distributions. While having tension throughout a fixed column base is uncommon in typical buildings, it could arise in vertical members of bracing sub-structures required to transmit high lateral loads, for instance in industrial buildings in which cranes operate or in buildings under significant seismic loading. A simplified mechanical model is adopted which considers that the possible reaction force on any one side of the joint can be either tension in a single anchor bolt row or compression on the foundation joint over a bearing area centred under the column flange. The design resistance of the critical joint component (T stub in compression or in tension) determines the design resistance moment acting in concomitance with the given normal force. The formulae given in Table 6.7 of EN 1993-1-8 are derived from the equilibrium between the applied moment - normal force combination and the reaction forces induced on the base plate. They cover each of the four possible and distinct load distribution scenarios for the basic configuration of column base plate joint shown in Figure 3.1.
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M
M N
a)
N
b) M
M N
t n e m e e r g A e c n e c i L z i b l e e t S e h t f o s n o i t i d n o c d n a s m r e t e h t o t t c e j b u s s i t n e m u c o d s i h t f o e s U . d e v r e s e r s t h g i r l l a 9 t h 0 g 0 i 2 r y y p a o M c s 9 i 0 l a i n r o t e d a e t m a s i e r h C T
c)
N
d)
Key : a)
Compression on both sides of the joint
b)
Compression on the right hand side and tension on the left hand side
c)
Compression on the left hand side and tension on the right hand side
d)
Tension on both sides of the joint (rare situation)
Figure 3.1
3.2
Load distribution
Resistance in bearing
For the compression side of a joint the 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. The design model assumes that the bearing resistance is provided by one or both of the column flange T-stubs in compression, depending on whether compression reigns over part or all of the column base plate respectively as shown in Figure 3.1. For a flange T-stub in compression the bearing stresses are assumed to be uniformly distributed over the T-stub area centred beneath the flange as shown in Figure 3.2. In the simplified approach given in EN 1993-1-8 for the design of column base joints transferring moment, no direct account is taken for any compression force that may be transferred through a column web T-stub in compression. In this NCCI, reference is made to SN037 for the design resistance of T-stubs in compression.
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3.3
Resistance in tension of an anchor bolt row
The design model for an anchor bolt row in tension is similar to that for a bolt row of an end plate connection transmitting moment. Therefore, the design approach is to ensure that the tensile force in the anchor bolt row does not exceed either of the following;
The design tensile resistance of the base plate tension T stub. This involves the consideration of the three basic tension T stub failure modes as identified in Table 6.2 of EN 1993-1-8. If relevant, the single mode replacing modes 1 and 2 shall be considered (see Table 6.2 EN 1993-1-8). The latter mode is possible if the prying effect disappears with the loss of contact between the base plate edge and the foundation because of anchor bolt elongation.
If necessary, i.e. for anchor bolt rows between the column flanges, the design resistance in tension of the column web component of the T stub.
The design approach is identical to that for a bolt row of an end plate except that when determining the resistance of the anchor bolt in tension one must also consider that the anchorage bond resistance may be more critical.
t n e m e e r g A e c n e c i L z i b l e e t S e h t f o s n o i t i d n o c d n a s m r e t e h t o t t c e j b u s s i t n e m u c o d s i h t f o e s U . d e v r e s e r s t h g i r l l a 9 t h 0 g 0 i 2 r y y p a o M c s 9 i 0 l a i n r o t e d a e t m a s i e r h C T
In the simplified mechanical model the resistance in tension is presented for the case of there being one anchor bolt row only. To permit the direct application of the design rules given for the case of anchor bolt rows on both sides of the column flange, it is recommended to use an equivalent single row having a total tensile resistance of the two rows acting together at the centroid. It is not recommended to consider that other rows than those about the column flanges contribute to the resistance of a fixed column base subjected to a moment combined with an axial load.
3.4
Limitations
The design rules provided are limited to applications for the types of un-stiffened column base plates shown in Figure 1.1 subjected to axial load in combination with moment acting about the column major axis only. The rules cover the case of two anchor bolts in a row. EN 1992-1-1 does not provide design rules for the bond anchorage resistance of plain bars. It is also believed also that the rules provided for the bends and hooks of the ribbed bars should not be applied to plain bars. No rules are given for the design of anchored bolts, such as with anchor plates or special heads. These issues may the subject of provisions in the National Annexes. In the present NCCI the design basic anchorage length of plain anchor bolts is taken as that for a ribbed bar divided by a factor of 2,25. This is in accordance with some existing national rules for reinforced concrete and with initial drafts for Eurocode 2. It is to be noted that, according to EN 1993-1-8 §6.2.6.12(5) that the yield strength of the steel for bent or hooked anchor bars should not exceed 300 N/mm².
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1 NEd 3
M Ed
2
la
F T,l
F C,r
zT,l
zC,r z 4 c
t fc
c
c
t fc
c
c
c
6 5
beff,c
beff,c
5
6
t n e m e e r g A e c n e c i L z i b l e e t S e h t f o s n o i t i d n o c d n a s m r e t e h t o t t c e j b u s s i t n e m u c o d s i h t f o e s U . d e v r e s e r s t h g i r l l a 9 t h 0 g 0 i 2 r y y p a o M c s 9 i 0 l a i n r o t e d a e t m a s i e r h C T
c
2
zT,l
zC,r
3
2
zT,l
zC,r
3
z z
Key: 1
Both the normal force and the moment applied by the column to the column base plate joint are shown acting in the positive sense as defined by EN 1993-1-8, i.e. tensile axial forces are positive and positive moments act clockwise.
2
Left-side of the base plate joint when the anchor bolts are in tension: the tensile force is resisted by the T stub formed by the base plate and the anchor bolt row.
3
Right side of the base plate joint when in compression: foundation joint offers bearing resistance on the underside of the base plate T stub which is acting in bending off the column flange.
4
Lever arm between the tension force in the anchor bolts and the compression force under the base plate.
5
Anchor bolts.
6
Compression T stub area.
Figure 3.2
Compression and anchor bolt tension induced by the normal force and moment
4. Design situation 1: Dimension a base plate for the loading at the base of a given column section 4.1
Choice of base plate type
It is recommended that the base plates be of the “long projection” type of sufficient width so as to allow having an anchor bolt row situated on the projection on each side of the column. This facilitates providing adequate compression resistance and, by increasing the lever arm between the compression and the tensile zones, reduces the mechanical resistance requirements on the anchor bolts in tension. Page 8
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In the following the dimensioning of a symmetric base plate joint is presented. A “long projection type of base is used, as shown in Figure 4.1, with anchor bolts with a single row on the extended part of the base plate or in two rows, one each side of the flange. Each row has two anchor bolts symmetrically placed about the column minor axis. hc
1
mx ex w
b p
3
t fc
1 e
m2
3
m b p
m
2
e
t n e m e e r g A e c n e c i L z i b l e e t S e h t f o s n o i t i d n o c d n a s m r e t e h t o t t c e j b u s s i t n e m u c o d s i h t f o e s U . d e v r e s e r s t h g i r l l a 9 t h 0 g 0 i 2 r y y p a o M c s 9 i 0 l a i n r o t e d a e t m a s i e r h C T
m2
e mx ex
m
m
e
3
Key: 1.
Column flange
2.
Column web
3.
Column base plate
Figure 4.1
4.2
Geometrical parameters for the tension T-stub
Choice of materials
It is necessary to choose the concrete class, the base plate steel and the anchor bolt class. For typical buildings, in some countries it has been usual practice to recommend class 4.6 anchor bolts while elsewhere class 8.8 plate ended anchors have become common. The base plate is not necessarily of the same steel grade as that of the column section.
4.3 Estimation of maximum compression and tension forces on the foundation Considering all the various combinations of axial load and moment ( N Ed, M Ed) at the column base, the following expressions provide estimates of the maximum compressive force and maximum tensile force acting on the foundation: -
max(F C,Ed ) compression: maximum value for F C,Ed =
-
max(F T,Ed ) tension: maximum value F T,Ed =
M Ed hc
− t fc
+
M Ed hc − t fc
−
N Ed
2
N Ed
2 Page 9
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Note: while the expressions above give the absolute values for the two forces, the sign of the axial load N Ed (positive if tensile, negative if compressive) is to be used in them. In order to simplify the notation N Ed , M Ed , N Rd , and M Rd are written for N j,Ed , M j,Ed , N j,Rd and M j,Rd respectively.
4.4 Dimension the base plate for the estimated maximum joint compression force To dimension the base plate, apply the procedure in Section 4 of SN037, assuming that the axial compressive load is. N j,Ed = 2 max(F C, Ed.)
A “long” projection base plate is chosen from the outset of the procedure. The values for the plate base plan dimensions ( b p, h p) and plate thickness ( t p) are obtained.
4.5 Dimension the base plate thickness and the anchor bolts for the estimated maximum joint tensile force 4.5.1 Axial tensile resistance of an anchor bolt t n e m e e r g A e c n e c i L z i b l e e t S e h t f o s n o i t i d n o c d n a s m r e t e h t o t t c e j b u s s i t n e m u c o d s i h t f o e s U . d e v r e s e r s t h g i r l l a 9 t h 0 g 0 i 2 r y y p a o M c s 9 i 0 l a i n r o t e d a e t m a s i e r h C T
Anchorage bond resistance and tensile section resistance of anchor bolts
When considering the failure modes of a T stub in tension the design tensile resistance of an anchor bolt in tension is to be taken as the least of the following two values:
Design bond anchorage resistance (assuming that good bond conditions pertain): o
o
Bolt diameter φ ≤ 32 mm: F t, bond,Rd
=
Bolt diameter φ > 32 mm: F t, bond,Rd
=
1 2,25
(πφ l b f bd ) ,
(132 − φ ) / 100 2,25
(πφ l b f bd ) .
Where l b is the basic anchorage length of the anchor bolt (starting from the bottom surface of the grout down into the foundation) and f bd is the design bond strength of the concrete (§8.4.2(2) of EN 1992-1-1). -
Note: EN 1992-1-1 provides design bond strengths for “ribbed” bars only. It is assumed in the present NCCI that the design value for a plain bar is the value given in §8.4 of EN 1992-1-1 (i.e. the design value for a ribbed bar of the same diameter in similar concrete and conditions) divided by 2,25. The relevant National Annex may provide guidance.
-
design tensile resistance of the anchor bolt section, F t,Rd
=
0,9 f ub As γ Mb,traction
Annex A of this NCCI gives the design bond anchorage resistance of often used diameters of class 4.6 anchor bolts as a function of the basic anchorage length for typical foundation concrete. A reduced anchorage depth into the foundation is required if bent or hooked anchor bolts are used. However the equivalent bond anchorage length for bends and hooks of plain bars is not Page 10
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provided by EN 1993-1-1 so that it is necessary to adopt other rules such as those in existing national standards or international recognised recommendations to provide them. The final choice of the anchor bolt details, in particular those concerning anchoring, usually requires knowledge of the foundation depth. The design resistance of a single anchor bolt F t, anchor, Rd is taken as: F t,anchor,Rd
= min [F t, bond, Rd ;
F t,Rd ]
Anchor bolt size
Assume that one anchor bolt row on the base plate projection will be adequate. To avoid anchor bolt failure (mode 3) the resistance of the anchor bolts of the chosen class must satisfy the following condition: 2F t,anchor,Rd ≥ max(F T,Ed)
t n e m e e r g A e c n e c i L z i b l e e t S e h t f o s n o i t i d n o c d n a s m r e t e h t o t t c e j b u s s i t n e m u c o d s i h t f o e s U . d e v r e s e r s t h g i r l l a 9 t h 0 g 0 i 2 r y y p a o M c s 9 i 0 l a i n r o t e d a e t m a s i e r h C T
As a first estimate, it is assumed that the full tensile resistance of the anchor bolt section can 0,9 f ub As be attained: F t,anchor,Rd = . The required bolt section is given as follows: γ M2 γ As ≥ F T,Ed ( M2 ) from which the bolt diameter can be obtained. 1,8 f ub Two rows of anchor bolts If one row of the anchor bolt size available is not adequate, decide to use two rows of anchor bolts (i.e. four anchor bolts of section As). The dimensioning of the bolt size becomes: As ≥ F T,Ed (
γ M2 3,6 f ub
)
The latter assumption about the anchor bolt tensile resistance needs to be checked when the final details of the bond anchorage lengths are established. Experience with standard foundation design and construction practice in a particular region will guide the designer in the choice of a suitable anchor bolt. If full anchorage for any given diameter and class of anchor bolt cannot be assured, it is necessary to adopt a lower resistance than the design tensile resistance of the section.
4.5.2 Design resistance of T-stub in tension with a two bolt anchor row Base plate thickness
The base plate thickness t p obtained for the compression design of the base plate may not be adequate. Based on the mode 1 resistance (full plastic mechanism) the following estimate of the plate thickness is obtained (see Figure 4.1 for the parameters): Page 11
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One anchor bolt row: t p
Two anchor bolt rows: t p
4.6
F T, Edγ M0
≥
f yp 2π
≥
F T, Edγ M0 f yp 4π
Check of the fixed base plate joint
Design resistance checks given in Section 5 below should be carried out, modifications being made if necessary to the base plate and/or anchor bolt dimensions.
5. Design situation 2: Determine the design resistances of a given base plate 5.1
Joint type
It is assumed below that the joint is symmetric with one row or two rows of anchor bolts (two per row) on each side of the joint (see Figure 5.1). t n e m e e r g A e c n e c i L z i b l e e t S e h t f o s n o i t i d n o c d n a s m r e t e h t o t t c e j b u s s i t n e m u c o d s i h t f o e s U . d e v r e s e r s t h g i r l l a 9 t h 0 g 0 i 2 r y y p a o M c s 9 i 0 l a i n r o t e d a e t m a s i e r h C T
Note: For a symmetric joint the distances z T,l = z T,r = z T and z C,l = z C,r = zC. c
t fc
c
c
t fc
c
c
c
beff,c
beff,c
c
zT,l
zT,l
zC,r
zC,r z
z
Figure 5.1
5.2
Compression and anchor bolt tension induced by the applied normal force and moment
Check the resistance of the anchor bolts
The design tensile resistance of an anchor bolt, F t,anchor,Rd, is obtained from 4.5.1 above: F t,anchor,Rd
5.3
= min[F t, bond,Rd ;
F t,Rd ]
Determine the axial compressive resistance
Refer to Section 5 of SN037 to provide the axial compressive resistance of the joint. This value is valid when the concomitant applied moment is zero. Page 12
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It provides a first indication of the possible ( N Ed , M Ed ) combinations that can be applied to the joint. It should be noted that if a part of the axial compression is transferred through a column web T-stub, the resistance obtained will exceed the sum of the resistances for the two column flange T-Stubs in compression. In the EN 1993-1-8 simplified model, the axial resistance in compression reduces to the latter value when the applied moment is zero. The resistance of each flange T-stub in compression is written here as F C,Rd .The axial compressive resistance is then given as: N C,Rd = -(2 F C,Rd) , the negative sign indicating that the load is compressive.
5.4
Determine the tensile axial load resistance
The resistance in tension of the anchor bolt rows on both sides of the joint are obtained. T stub effective lengths
t n e m e e r g A e c n e c i L z i b l e e t S e h t f o s n o i t i d n o c d n a s m r e t e h t o t t c e j b u s s i t n e m u c o d s i h t f o e s U . d e v r e s e r s t h g i r l l a 9 t h 0 g 0 i 2 r y y p a o M c s 9 i 0 l a i n r o t e d a e t m a s i e r h C T
The possible modes of failure of a T-stub in tension are shown schematically in Figure 5.2. The effective T stub length is as follows (see Figure 4.1 for the definition of the geometric parameters):
Outer anchor bolt row : o
o
Circular mechanism: leff,cp
= min[( 2π m); (π mx + w), (π mx + 2e)]
Non circular mechanism: leff,nc = min[0,5b p ; ( 4m + 1,25ex ); (e + 2mx
+ 0,625ex ); (0,5w + 2mx + 0,625ex )]
Mode 1 effective T-Stub length: leff,1
= min(leff,cp : leff,nc )
Mode 2 effective T-Stub length: leff,2
= leff,nc
Inner anchor bolt row o
o
Circular mechanism: leff,cp
= 2 π m
Non circular mechanism leff ,nc
= (4m + 1,25e)
Mode 1 effective T-Stub length: leff,1
= min(leff,cp : leff,nc )
Mode 2 effective T-Stub length: leff,2
= leff,nc
For the special mode indicated in Figure 5.2 e), the T stub length is that given above for mode 1.
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Ft
Ft
m
m
e
e
δ
Ft δ
n
n
a)
b)
Ft
Ft e)
δ
c)
d)
Key: a)
t n e m e e r g A e c n e c i L z i b l e e t S e h t f o s n o i t i d n o c d n a s m r e t e h t o t t c e j b u s s i t n e m u c o d s i h t f o e s U . d e v r e s e r s t h g i r l l a 9 t h 0 g 0 i 2 r y y p a o M c s 9 i 0 l a i n r o t e d a e t m a s i e r h C T
Full plastic mechanism (failure Mode 1),
b)
Partial plastic mechanism with anchor bolt failure (failure Mode 2),
c)
Anchor bolt failure (failure Mode 3),
d)
Web yielding in tension (failure Mode 4),
e)
Failure by flexural yielding of the flange in conjunction with separation of the base plate from the foundation due to anchor bolt elongation (the prying force becomes null). It replaces failure Modes 1 and 2
Figure 5.2
Possible failure modes for a T stub in tension
The special failure mode replacing mode 1 and mode 2 is possible only when the following condition on the anchor bolt length is met: ∗
L b > L b
=
8,8 As ⎡ m ⎤ leff,1
3
⎢ ⎥ ⎢⎣ t p ⎥⎦
Where the distance m is as shown in Figure 5.2 and the effective T stub length leff is determined above. T stub resistance in tension
Determine the resistance of the T stub in tension for the bolt row. The design resistance of a bolt row will be the least value for the failure modes shown in Figure 5.2. When considering the failure modes of a T stub in tension the design tensile resistance of an anchor bolt in tension is to be taken F t, anchor, Rd. The plastic hinge flexural resistance is given by: M pl,Rd
= lef f m pl,Rd = leff
t p2 f y
4γ M0
.
This value may be differ between mode 1 (with leff,1 ) and mode 2 (with leff,2 ). The value of the resistance of a T-stub in tension F t,Rd is taken as the least of the following resistances as relevant: Page 14
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NCCI: Design of fixed column base joints SN043a-EN-EU
=
4 M pl,Rd,1
-
Mode 1: Plastic mechanism: F t,1,Rd
-
Mode 2 : Mixed failure mode: F t,2,Rd
-
Mode 1-2: If the condition requiring adopting the special mode is met, the resistances for modes 1 and 2 are replaced by o
: F t,1/2,Rd
=
2 M pl,Rd,1 m
=
m
2 M pl,Rd,2 + 2nF t,anchor,Rd m+n
, n = min(e;1,25m)
.
= 2 F t,anchor,Rd
-
Mode 3 : Anchor bolt failure F t,3, Rd
-
Mode 4: Column web in tension for inner anchor bolt rows -: F t,wc,Rd
= beff,t,wct wc
f y,wc
γ M0
The resistance of all the anchor bolt rows present are calculated. The design resistance for the side in tension is taken as: F T,Rd = ∑F t,Rd t n e m e e r g A e c n e c i L z i b l e e t S e h t f o s n o i t i d n o c d n a s m r e t e h t o t t c e j b u s s i t n e m u c o d s i h t f o e s U . d e v r e s e r s t h g i r l l a 9 t h 0 g 0 i 2 r y y p a o M c s 9 i 0 l a i n r o t e d a e t m a s i e r h C T
The summation sign allows considering having either one bolt row on each side of the joint or two bolt rows on each side of the joint. Axial resistance in tension of the joint
The axial tensile resistance of the symmetric joint is given as follows: N T,Rd = 2 F T,Rd
Which is valid only when the concomitant moment is null.
5.5
Moment resistance
If the axial load is zero the moment resistance of the symmetric joint is given as the least of the following two values: M 0,Rd = min ( z F T,Rd : z F C,Rd), where the lever arm z = zT + zC
5.6
Case of a given load combination
When the check is limited to verifying that the joint can resist a given ( M Ed, N Ed) combination, the checks can be limited to the following steps: a) The distribution of stresses in the column section will provide a direct indication as to which load distribution reigns in the base plate joint. This information can be used to identify the load distribution case to be examined in table 6.7 of EN 1993-1-8. b) The effective eccentricity of the axial load is determined as e N
=
M Ed N Ed
for the applied
combination is ( M Ed, N Ed). It should be noted that the eccentricity value may be positive or negative depending on the signs of the forces and moments.
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c) The resistances of the bolt row T stubs in tension, F T,Rd, are obtained in 5.3 above. Because the joint is symmetric the design resistances on both sides in tension will be equal. (This calculation is not required if the entire section is in compression). d) The resistance of the column flange T stub in compression, F C,Rd can be obtained from 5.2 above, the value being taken as that for one column flange T-stub only. Because the joint is symmetric the design resistances on both sides in compression will be equal. (This calculation is not required if the entire section is in tension). e) The geometric parameters, in particular the various lever arms, are obtained as shown in Figure 5.1. Because of the joint symmetry z T,l = z T,r = z T and z C,l = z C,r = zC. f) From the distribution of stresses in the column identify the case to be examined. The M j,Rd moment resistance, applied simultaneously with the axial load, N Ed , is obtained by the direct application of the relevant formulae given in Table 5.1 (see table 6.7 of EN 1993-1-8). g) Check that the moment, M Ed and M Rd , are of the same sign and that M Ed
≤ M Rd . If
so, the joint is adequate to resist the load combination given. The formulae given in Table 5.1 are for symmetric joints and have been adapted from those in table 6.7 of EN 1993-1-8. t n e m e e r g A e c n e c i L z i b l e e t S e h t f o s n o i t i d n o c d n a s m r e t e h t o t t c e j b u s s i t n e m u c o d s i h t f o e s U . d e v r e s e r s t h g i r l l a 9 t h 0 g 0 i 2 r y y p a o M c s 9 i 0 l a i n r o t e d a e t m a s i e r h C T
Table 5.1
Checking the design moment resistance M Rd of fixed column bases
Loading
Lever arm z
Moment resistance M Rd
Left side in tension
z = zT,l + zC,r N Ed > 0 and
Right side in compression
z = zT + zC
Left side in tension
z = zT,l + zT,r N Ed > 0 and
Right side in tension z = zT + zT Left side in compression
The smaller of
z = zC,l + zC,r N Ed ≤ 0 and
Right side in compression
z = zC + zC
and
zC / e + 1 F T, Rd z zT / e + 1
and
− F C, Rd z zT / e + 1 − F C, Rd z zC / e + 1
zT / e − 1
e > zC,l
F T, Rd z zC / e − 1
N Ed ≤ 0 and
and
- zT,r < e ≤ 0
F T, Rd z
N Ed ≤ 0 and
and
e ≤ - zC,r
− F C, Rd z zT / e + 1
N Ed > 0 and
0 < e 0 is clockwise, N Ed > 0 is tension, e =
F T, Rd z
e ≤ - zT,r
The smaller of
Left side in compression
N Ed ≤ 0 and
0 < e 0 and
Right side in tension z = zC + zT
e > zT,l
- zC,r < e ≤ 0
− F C, Rd z zC / e − 1
M Ed N Ed
The formulae above are those for a symmetric joint so that: z T,l = z T,r = z T and z C,l = z C,r = zC If it is found that M Ed
≤ M Rd the joint is adequate.
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5.7
Interaction diagram for a column base joint
When the joint design resistance is attained under a combination ( M Ed, N Ed) the following holds: M Ed = M Rd N Ed = N Rd e=
M Ed N Ed
=
M Rd N Rd
All of the latter parameters can have both positive and negative values. By varying the value of the equivalent eccentricity within the range indicated for each loading situation (see Figure 3.1, Table 5.1 and Table 5.2), the limiting design condition is found to be a boundary plotted with, for instance, axial load N Rd on the vertical axis and moment M Rd on the horizontal axis (see Figure 5.3).
t n e m e e r g A e c n e c i L z i b l e e t S e h t f o s n o i t i d n o c d n a s m r e t e h t o t t c e j b u s s i t n e m u c o d s i h t f o e s U . d e v r e s e r s t h g i r l l a 9 t h 0 g 0 i 2 r y y p a o M c s 9 i 0 l a i n r o t e d a e t m a s i e r h C T
It is found that the boundary for the type of base plate joint treated here is made up of linear segments which can be plotted using the expressions between M Rd and N Rd given in Table 5.2. The diagram shown in Figure 5.3 is for the particular case of a symmetric joint with two bolt rows on each side for which it has been assumed that the distances from the column major axis to the centroids of the compression T stub area under a flange and of anchor bolt tension area, zC and zT respectively, are equal. When the latter distances are not equal, the enclosed area differs slightly from the diamond shape. The following type of interaction diagram is obtained. It allows rapid checking of any load combination applied to the base plate joint. All allowable load combinations fall on or within the surface defined by the boundaries corresponding to the relevant limiting design condition. (1) :
+N T.Rd
N Ed
(3) : +M0,Rd (4) : -M 0,Rd M Ed
(5)
(2) : -N C,Rd
Key:
1) Axial resistance in tension
4) Negative moment resistance
2) Negative moment resistance
5) Allowable M and N combination
3) Positive moment resistance
Figure 5.3
Fixed column base plate joint: Typical M-N interaction diagram
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Table 5.2
Interaction of design resistances NRd and MRd for fixed column bases
Loading
t n e m e e r g A e c n e c i L z i b l e e t S e h t f o s n o i t i d n o c d n a s m r e t e h t o t t c e j b u s s i t n e m u c o d s i h t f o e s U . d e v r e s e r s t h g i r l l a 9 t h 0 g 0 i 2 r y y p a o M c s 9 i 0 l a i n r o t e d a e t m a s i e r h C T
Lever arm z
Design moment resistance M Rd corresponding to N Rd
Left side in tension
0≤ NR d and e > zT
N Rd ≤ 0 and
Right side in compression
Compression side critical :
Compression side critical :
z
Dominant positive z = zT + zC moment with a tensile or compressive load (see figure 5.1)
M Rd
= − N C, Rd + N Rd zT
M Rd
= N T, Rd − N Rd zC
Both sides in tension
N Rd > 0 and 0 < e 0 and M Rd
- zT < e ≤ 0
= −( N T, Rd − N Rd )
z
2
0≤ NR d and e ≤ - zT
N Rd ≤ 0 and
Compression side critical :
Compression side critical :
z
M Rd
= N C,Rd − N Rd zT
M Rd
= − N T, Rd + N Rd zC
2 Tension side critical : z
2
N Rd ≤ 0 and z = 2 zC
z
e ≤ - zC
M Rd
0 < e 0 is clockwise, N Ed > 0 is tension, e =
M Ed N Ed
2
e > zC
z
M Rd
= N C, Rd − N Rd zT
M Rd
= − N T,Rd + N Rd zC
2 Tension side critical : z
2
N Rd ≤ 0 and M Rd
- zC < e ≤ 0 z
= −( N C, Rd − N Rd )
2
.
The values of N C,Rd and N T,Rd are obtained from 5.3 and 5.4 respectively. The formulae are for a symmetric joint so that: z T,l = z T,r = z T and z C,l = z C,r = z C
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Annex A: Design resistances of anchor bolts The reinforced concrete standard EN 1992-1-1 gives design rules for anchorage bond resistance for ribbed reinforcement bars only. No mention is made of anchor bolts or of ‘plain’ round bars, which is what most anchor bolts in use today are made of . It is assumed in the present NCCI that the design value for a plain bar is the value given in §8.4 of EN 1992-1-1 (i.e. the design value for a ribbed bar of the same diameter in similar concrete and conditions) divided by 2,25. The relevant National Annex may provide guidance on the design for anchorage bond of plain bars. The graphs below plot the basic anchorage bond length for class 4.6 and class 5.6 anchor bolts of various diameters against the design tensile resistance for typical foundation concrete classes. Tensile resistance F t,Anchor,Rd (kN) 110,0 100,0 90,0 t n e m e e r g A e c n e c i L z i b l e e t S e h t f o s n o i t i d n o c d n a s m r e t e h t o t t c e j b u s s i t n e m u c o d s i h t f o e s U . d e v r e s e r s t h g i r l l a 9 t h 0 g 0 i 2 r y y p a o M c s 9 i 0 l a i n r o t e d a e t m a s i e r h C T
80,0 M16 70,0
M18 M20
60,0
M22
50,0
M24 M27 M30
40,0
M33 M36
30,0 20,0 10,0 0,0 0
100
200
300
400
500
600
700
800
900
1000
Basic anchorage bond length (mm)
Figure A.1
Anchorage bond resistance and tensile resistance of anchor bolts – Steel 4.6 and concrete C20/25
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NCCI: Design of fixed column base joints SN043a-EN-EU
Tensile resistance F t,Anchor,Rd (kN) 150,0 140,0 130,0 120,0 110,0 M16
100,0
M18 90,0
M20
80,0
M22 M24
70,0
M27
60,0
M30 M33
50,0
M36
40,0 30,0 20,0 10,0 0,0 0
100
200
300
400
500
600
700
800
900
1000
Basic anchorage bond length (mm)
Figure A.2 t n e m e e r g A e c n e c i L z i b l e e t S e h t f o s n o i t i d n o c d n a s m r e t e h t o t t c e j b u s s i t n e m u c o d s i h t f o e s U . d e v r e s e r s t h g i r l l a 9 t h 0 g 0 i 2 r y y p a o M c s 9 i 0 l a i n r o t e d a e t m a s i e r h C T
Anchorage bond resistance and tensile resistance of anchor bolts – Steel 4.6 and concrete C30/37
Tensile resistance F t,Anchor,Rd (kN) 180,0 170,0 160,0 150,0 140,0 130,0 M16
120,0
M18
110,0
M20
100,0
M22
90,0
M24
80,0
M27 M30
70,0
M33
60,0
M36
50,0 40,0 30,0 20,0 10,0 0,0 0
100
200
300
400
500
600
700
800
900
1000
Basic anchorage bond length (mm)
Figure A.3
Anchorage bond resistance and tensile resistance of anchor bolts – Steel 4.6 and concrete C40/50
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Tensile resistance F t,Anchor,Rd (kN) 110,0 100,0 90,0 80,0 M16 70,0
M18 M20
60,0
M22 M24
50,0
M27 M30
40,0
M33 M36
30,0 20,0 10,0 0,0 0
100
200
300
400
500
600
700
800
900
1000
Basic anchorage bond length (mm)
Figure A.4 t n e m e e r g A e c n e c i L z i b l e e t S e h t f o s n o i t i d n o c d n a s m r e t e h t o t t c e j b u s s i t n e m u c o d s i h t f o e s U . d e v r e s e r s t h g i r l l a 9 t h 0 g 0 i 2 r y y p a o M c s 9 i 0 l a i n r o t e d a e t m a s i e r h C T
Anchorage bond resistance and tensile resistance of anchor bolts – Steel 5.6 and concrete C20/25
Tensile resistance F t,Anchor,Rd (kN) 150,0 140,0 130,0 120,0 110,0 M16
100,0
M18 90,0
M20
80,0
M22 M24
70,0
M27
60,0
M30 M33
50,0
M36
40,0 30,0 20,0 10,0 0,0 0
100
200
300
400
500
600
700
800
900
1000
Basic anchorage bond length (mm)
Figure A.5
Anchorage bond resistance and tensile resistance of anchor bolts – Steel 5.6 and concrete C40/50
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NCCI: Design of fixed column base joints SN043a-EN-EU
Tensile resistance F t,Anchor,Rd (kN) 180,0 170,0 160,0 150,0 140,0 130,0 M16
120,0
M18
110,0
M20
100,0
M22
90,0
M24
80,0
M27 M30
70,0
M33
60,0
M36
50,0 40,0 30,0 20,0 10,0 0,0 0
100
200
300
400
500
600
700
800
900
1000
Basic anchorage bond length (mm)
Figure A.6 Anchorage bond resistance and tensile resistance of anchor bolts – Steel 5.6 and concrete C40/50 t n e m e e r g A e c n e c i L z i b l e e t S e h t f o s n o i t i d n o c d n a s m r e t e h t o t t c e j b u s s i t n e m u c o d s i h t f o e s U . d e v r e s e r s t h g i r l l a 9 t h 0 g 0 i 2 r y y p a o M c s 9 i 0 l a i n r o t e d a e t m a s i e r h C T
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Quality Record RESOURCE TITLE
NCCI: Design of fixed column base joints
Reference(s) ORIGINAL DOCUMENT Name
Company
Date
Created by
Ivor Ryan
CTICM
06/02/2006
Technical content checked by
Alain Bureau
CTICM
06/02/2006
1. UK
G W Owens
SCI
07/04/06
2. France
A Bureau
CTICM
07/04/06
3. Sweden
B Uppfeldt
SBI
07/04/06
4. Germany
C Müller
RWTH
07/04/06
5. Spain
J Chica
Labein
07/04/06
G W Owens
SCI
18/08/06
Editorial content checked by Technical content endorsed by the following STEEL Partners:
t n e m e e r g A e c n e c i L z i b l e e t S e h t f o s n o i t i d n o c d n a s m r e t e h t o t t c e j b u s s i t n e m u c o d s i h t f o e s U . d e v r e s e r s t h g i r l l a 9 t h 0 g 0 i 2 r y y p a o M c s 9 i 0 l a i n r o t e d a e t m a s i e r h C T
Resource approved by Technical Coordinator TRANSLATED DOCUMENT This Translation made and checked by: Translated resource approved by:
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