International International Journal of Steel Structures
March 2011, Vol 11, No 1, 13-27 DOI 10.1007/S13296-011-1002-x
www.sprin www.springer ger.co .com/jo m/journ urnal/ al/132 13296 96
A Comparative Study of AISC-360 and EC3 Strength Limit States Cem Topkaya1,* and Serkan Şahin2 1
Departmen Departmentt of Civil Civil Enginee Engineering, ring, Middle East Technical echnical University University,065 ,06531, 31, Ankara, Ankara, Turkey Turkey 2 MITENG MITENG,, Ankara, Ankara, Turkey Turkey
Abstract
A study has been undertaken to evaluate the similarities and differences between the steel building design specifications used in the United States and Europe. Expressions for nominal strength presented in the AISC-360 Specification and the Eurocode 3 Specification were compared for fundamental limit states. In particular, rules for cross-section classification, tension members, compression members, I-shaped members subjected to flexure, I-shaped members subjected to shear, and fasteners were studied. Results of the investigation revealed that, in general, both specifications provide nominal capacities that are close to each other. Significant differences were reported for some limit states such as flexure in I-shaped members with non-compact flanges, shear and lateral torsional buckling in I-shaped members, and bearing strength at bolt holes. In this paper, the details of the comparative study are presented along with observations that are useful for practicing engineers. Keywords: steel, specification, strength, limit state, building
1. Introduction Nowadays Nowadays design, design, fabrication, fabrication, and erection erection of steel structures may take place at different locations as a result of rapid globalization. Owners may require the use of widely accepted steel design codes regardless of the location where the structure is going to be built. Engineers are now faced with the challenge of being competent with several design specifications for a particular material type. Two of the widely used steel design specifications for buildings are the American and the European ones. In the United States, “Specification for Structural Steel Buildings (2005)” was developed by the American Institute of Steel Construction (AISC). This specification, hereafter referred to as the AISC-360 Specification, utilizes both Load and Resistance Factor Design (LRFD) and Allowable Strength Design (ASD) formats. In general, limit states that govern the design under a particular loading are given by the AISC-360 Specification and the nominal strength based on these limit states is either used in the LRFD or the ASD format. In the LRFD Note.-Di Note.-Discus scussio sion n open open until until August August 1, 2011. 2011. This This manuscri manuscript pt for this this paper paper was submi submitted tted for review review and and possib possible le publi publicati cation on on March March 25, 2010; approved on November 16, 2010. © KSSC and Springer 2011 *Corresponding author Tel: +90-312-210 5462; Fax: +90-312-210 7991 E-mail:
[email protected]
format, the nominal strength is multiplied by a resistance factor (φ (φ). The purpose of the resistance factor is to include the uncertainties in the material and geometric properties as well as the ones in modeling. Resistance factors of 0.75 and 0.9 are used for fracture and yielding/ instability limit states, respectively. In Europe, “Design of Steel Structures, EN 1993 (2003)” was developed by the European Committee for Standardization. This specification, hereafter referred to as the EC3 Specification, is based on limit state principles using partial safety factors (γ (γM). In general, the characteristic resistance is divided by a partial safety factor and then compared with the factored loads. The partial safety factors are used to account for the same types of uncertainties that were explained for the resistance factors (φ) in the AISC-360 Specification. In other words, partial safety factors (γ (γM) can be thought of as the inverse of resistance factors (φ (φ). The recommended γM values are 1.0 for yielding, 1.0 for buckling, and 1.25 for fracture limit states. Because Eurocodes are used in a number of different countries, each member state has the right to choose its own partial safety factors and publish these in a National Annex. The EC3 Specification refers to Annex D of EN 1990 Basis of Structural Design (2001) for determining the characteristic resistances. In addition, nominal values of material and geometric properties are adopted as characteristic values in design calculations. Because the characteristic values are replaced with the nominal ones, the characteristic resistance provided in the EC3 Specification is identical to the nominal resistance
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Cem Topkaya and Serkan Şahin / International Journal of Steel Structures, 11(1), 13-27, 2011
given in the AISC-360 Specification. Based on the above discussion, it is apparent that both the AISC-360 and the EC3 specifications utilize limit state principles with differing factors to account for uncertainties. A study has been undertaken with the following objectives; (i) put together the nominal strength expressions presented in both codes in a single document, (ii) to identify the similarities and the differences in calculated strengths, (iii) to facilitate rapid learning of either of the specifications with prior knowledge of the other. Because of the wide scope of specifications, only fundamental failure modes are considered in this paper. Resistance equations are directly compared with each other wherever possible. For cases where the treatment of specifications is entirely different, representative members were considered for comparison purposes.
The AISC-360 Specification is an integral document whereas the EC3 Specification consists of parts and subparts. In general, each part is focused on a particular structure type such as buildings, bridges, towers, silos, and etc. General rules and rules for buildings are specified in Part 1 of the EC3 Specification. This part is divided into 11 subparts. Among these, subparts 1.1 (General rules and rules for buildings (2003)), 1.5 (Plated structural elements (2004)), and 1.8 (Design of joints (2003)) are utilized in this paper.
The definitions for cross-sections in both specifications have similarities. Class 4 or slender cross-sections are those in which local buckling of the plate element(s) will occur before the attainment of yield stress. Class 3 or non-compact cross sections are those in which the stress in the extreme compression fiber can reach to the yield strength, but local buckling is liable to prevent the development of the plastic moment capacity. Class 2 or compact sections are those which can develop their plastic moment capacity, but have limited rotation capacity because of local buckling. Finally, Class 1 or seismically compact sections are those which can develop their plastic moment capacity and provide significant amount of rotation capacity. Limiting width-thickness ratios of stiffened and unstiffened elements for typical cases are summarized in Fig. 1 together with the ratio of the limits provided by the two specifications. According to this figure, the limits set by the two specifications are generally close to each other. Major differences arise for HSS members. In addition, the Class 3 or non-compact limits for flexure in flanges of rolled or built-up I-shapes differ significantly. It should also be emphasized that minor differences in the width-thickness ratio definitions are also present. For example, in the AISC-360 Specification, half of the flange width is used in determining the flange slenderness. In the EC3 Specification, however, only the outstanding portion of the flange that is measured from the toe of the fillet is used in calculations.
3. Materials
5. Design of Members for Tension
In the United States, structural steel material should conform to the standards set forth by the American Society for Testing and Materials (ASTM). Widely used structural steels are A36 ( F y=248 MPa (36 ksi), F u=400 MPa (58 ksi)), and A572 Gr50 or A992 ( F y=345 MPa (50 ksi), F u=448 MPa (65 ksi)). In Europe, structural steel material properties are documented in Euronorm EN 10025 (1994). Widely used structural steels are S235 ( F y=235 MPa (34 ksi), F u=360 MPa (52 ksi)), S275 ( F y=275 MPa (40 ksi), F u=430 MPa (62 ksi)), and S355 ( F y=355 MPa (51 ksi), F u=510 MPa (74 ksi)).
Both specifications consider tensile yielding in the gross section and tensile rupture in the net section as the two primary limit states for tension members. The nominal resistance of members to these limit states are calculated as follows:
2. Layout of the Specifications
4. Classification of Cross-sections Both specifications provide cross section classifications for local buckling. In the AISC-360 Specification crosssections are classified as compact, non-compact, and slender. In addition to the AISC-360 Specification requirements, the Seismic Provisions for Structural Steel Buildings (2005) (AISC-341) has an additional classification named as seismically compact. On the other hand, in the EC3 Specification sections are classified as Class 1 through Class 4.
P n= A g F y (yielding) (AISC-360 and EC3) P n=UAn F u (fracture) (AISC-360) P n=0.9 An F u (fracture) (EC3)
(1)
The fundamental difference between the two specifications comes from the way that the shear lag factor U is calculated. In the AISC-360 Specification, a shear lag factor of 1.0 is used if the tension load is transmitted directly to each of the cross sectional elements. An elaborate treatment is tabulated in the AISC-360 Specification for other types of connections. Separate rules are presented for I-section, L-shaped, and HSS members. Usually shear lag factors that range between 0.6 and 0.9 are found based on the recommended procedure. On the other hand, a less elaborate treatment for shear lag is given in the EC3 Specification. In general, a 10 percent reduction in tensile fracture capacity is considered even if all cross sectional elements are connected. Some specific rules for single angles connected by one leg and other unsym-
A Comparative Study of AISC-360 and EC3 Strength Limit States
15
Figure 1. Comparison of cross-section classifications.
metrically connected members are given in Part 1.8 Section 3.10.3 of the EC3 Specification. According to these rules, the 0.9 coefficient is replaced with a reduction factor that varies between 0.4 and 0.7. Both specifications favor the use of s2/4 g rule in determining the net area in staggered connections. In the AISC-360 Specification, the width of a bolt hole is taken 2 mm (1/16 in) greater than the nominal dimensions of the hole to account for damage in hole making process. No such damage allowance is recommended in the EC3 Specification.
6. Design of Members for Compression A single column strength curve is given in the AISC360 Specification whereas five separate curves are presented in the EC3 Specification. In general, both specifications use a non-dimensional slenderness for flexural buckling (λFB) to define the reduction in capacity. In Eurocode a unified approach has been adopted for various forms of member buckling. In other words, flexural buckling, torsional buckling, flexural-torsional buckling, and lateral torsional buckling are treated using
Cem Topkaya and Serkan Şahin / International Journal of Steel Structures, 11(1), 13-27, 2011
16
a unified set of reduction factors. The nominal axial strength for flexural buckling is computed as follows: P n=χ F y A g (AISC-360 and EC3)
(2)
The non-dimensional slenderness for flexural buckling, λFB, can be expressed as follows:
λ FB =
A g F y KL F y ----------- = ------- ----πr E P cr
(3)
The reduction factor (χ) has the following forms depending on the specification: 2
λ FB
χ = 0.658
Figure 2. Comparison of column strength curves.
------------- λ FB > 1.5 λ FB ≤ 1.5 χ = 0.877 2 λ FB
(AISC-360)
(4)
7. Design of Members for Flexure
2 χ = --------------1----------------- Φ = 0.5[ 1 + α(λ FB – 0.2) + λ FB ] 2 2 Φ + Φ – λ FB
(EC3)
compression.
(5)
An imperfection coefficient (α) to distinguish between different column strength curves is utilized in the EC3 Specification. For flexural buckling, five cases termed as a o, a, b, c, d are given for which the α values are 0.13, 0.21, 0.34, 0.49, and 0.76, respectively. The choice as to which buckling curve to adopt is dependent upon the geometry and material properties of the cross section and upon the axis of buckling. The rules for selecting the appropriate column strength curve are tabulated in the EC3 Specification. In general, curve “a o” is used for rolled I-shapes made up of high strength material (F y=460 MPa (67 ksi)). For steels with a yield strength in the range 235 MPa (34 ksi) to 420 MPa (61 ksi) curve “a” is used for major axis buckling of rolled I-shapes (tf 0.673
Cem Topkaya and Serkan Şahin / International Journal of Steel Structures, 11(1), 13-27, 2011
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h ⁄ t λ p = --------------w-------- ε = 28.4ε k σ
235 ---------------------------
F y( in MPa )
ψ=−1 and k =23.9 for doubly symmetric sections under pure bending (9) σ
According to the effective cross section shown in Fig. 3b, 40 percent of the effective compression area is adjacent to the compression flange, and the remaining 60 percent is adjacent to the elastic neutral axis of the cross section. Calculation of the effective section properties requires finding the location of the elastic neutral axis. From equilibrium of stress resultants, the following equation was derived to find the depth of the web under compression (bc): 2
[0.4ρt w+0.1ρ2t w−0.5t w] bc +[2 A f +ht w]bc−[ A f h+0.5h2t w]=0 (10) Depending on the geometrical properties, the second order equation can be solved for bc. After determining the value of bc the effective inertia ( I eff ) and the effective section modulus (S eff =I eff /bc) can be found. The nominal moment capacity is calculated as follows: M n=S eff F y (EC3)
(11)
The nominal moment capacities from both specifications were compared by considering doubly symmetric Ishaped members with different web dimensions. For all cases, 300 mm (11.81 in) by 20 mm (0.79 in) flanges were considered. The web height was varied between 500 mm (19.69 in) and 2000 mm (78.74 in) and the web thickness was varied between 5 mm (0.20 in) and 20 mm (0.79 in). A total of 89 sections were considered which had an average, maximum, and minimum shape factor of 1.16, 1.28, and 1.07, respectively. Nominal moment capacities of these sections were calculated according to both specifications. The capacities were normalized by the plastic moment capacity ( M p) and are presented in Fig. 4 for two different yield strength values. In addition, the ratio (EC3/AISC-360) of the capacities calculated using both specifications is also given in this figure. Analysis results reveal that the nominal moment capacity calculated using the EC3 Specification is lower than the ones calculated using the AISC-360 Specification for the web slenderness range between 70 and 250. The opposite is true for web slenderness values in excess of 250. The differences are more pronounced for non-compact (Class 3) web members. Capacity estimates are the same for web slenderness less than 70. The average, standard deviation, maximum, and minimum of the ratios for the 89 sections are 0.96, 0.05, 1.08, and 0.83, respectively when data points for both yield strengths are combined. 7.1.2. Members with compact webs (Class 1 or Class 2) The effects of flange slenderness were studied by considering compact web I-shaped members. Usually the
Figure 4. Comparison of nominal moment capacities for compact flange members.
flanges of built-up members are designed to be compact (Class 1 or Class 2). Non-compact or slender flanges may be used in some cases to reduce cost of steel framing. Each specification has a different treatment for the flange buckling problem. In the AISC-360 Specification, the limiting slenderness ratio for slender flanges is dependent on the web dimensions. In other words, the rotational restraint that is provided by the web to the flange is explicitly taken into account using a k c factor. In the EC3 Specification, however, the limiting flange slenderness ratios are not given as a function of the web slenderness. In order to make a fair comparison of the capacities given by both specifications, members with different flange and web slenderness ratios were considered herein. According to both specifications, a member can reach to its plastic moment capacity if the flanges are compact (Class 1 or Class 2). Therefore, Eq. 6 is valid for determining the nominal moment capacity of such members. Treatment of non-compact flanges is similar to the treatment on non-compact webs in both specifications. According to the AISC-360 Specification, the nominal moment capacity reduces linearly with an increase in the flange slenderness and varies between the plastic moment capacity ( M p) and the yielding moment considering residual stresses (0.7 M y). On the other hand, the nominal
A Comparative Study of AISC-360 and EC3 Strength Limit States
moment capacity is equal to the yield moment for Class 3 sections according to the EC3 Specification. The nominal moment capacity for members with noncompact flanges is determined as follows:
λ – λ λrf – λ pf
----- (AISC-360) M n = M p – (M p – 0.7 F yS x) ----------- pf M n=S x F y (EC3)
(12)
For slender flange members the AISC-360 Specification utilizes the elastic critical buckling moment approach. According to the AISC-360 specification the nominal moment capacity is calculated as follows: 0.9 Ek cS 4 x M n = -----------2--------- where k c = ------------- and h ⁄ t w λ
0.35
≤ k c ≤ 0.76 (13)
In the EC3 Specification, the post-buckling reserve strength approach is utilized. An effective cross-section shown in Fig. 3c is considered for this purpose. In this effective cross section, the outstanding portions of the compression flange are assumed to be ineffective. The nominal moment capacity for sections with Class 4 flanges is determined using the elastic section modulus (S eff ) of the effective cross section shown in Fig. 3c. The effective area of the compression flange and the nominal moment capacity are determined as follows: Ac,eff =beff t f =ρb f t f ρ=1.0 for
λ p ≤ 0.748
λ – 0.188 ρ = --- p---------2---------λ p
for
b ⁄ t λ p = ---------- f ----- f ------- ε = 28.4ε k σ
λ p > 0.748 235 ---------------------------
F y( in MPa )
k =0.43 for flanges under uniform compression σ
M n=S eff F y
(14)
A total of 264 cross-sections were analyzed to study the differences between the two specifications. The web of the sections was selected to be compact (Class 1 or Class 2). The web height varied between 500 mm (19.7 in) and 1000 mm (39.4 in) while the web thickness varied between 8 mm (0.31 in) to 20 mm (0.79 in). The resulting webs had a slenderness ratio that changed between 25 and 67. Based on these web slenderness ratios the k c factor changed between 0.49 and 0.76. Flange thickness values between 10 mm (0.39 in) and 20 mm (0.79 in) and flange width values between 300 mm (11.8 in) and 500 mm (19.7 in) were considered. The shape factor for these sections varied between 1.07 and 1.28 with an average of 1.15. Two different yield strength values were considered and the variations of the nominal capacity for these are
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given in Fig. 5. In this figure, the capacities calculated using the two specifications are given separately for clarity. In addition, the ratios (EC3/AISC-360) of the capacities are presented. Analysis results reveal that the nominal moment capacity based on the EC3 Specification is less than the one based on the AISC-360 Specification for flange slenderness values less than 20. These are sections that generally qualify as non-compact flange sections. For flange slenderness values greater than or equal to 20, significant differences are observed where the EC3 capacities are much higher than the AISC-360 ones. Contrary to previous analysis on web slenderness, the results are dependent on the yield strength. For F y=345 MPa (50 ksi) the difference between the EC3 and the AISC-360 capacities are more pronounced. It should be mentioned that the ratios are also dependent on the web slenderness. For slender web cases where the k c value is low, the AISC-360 capacities tend to be lower than the EC3 ones. As mentioned before, the primary difference between the two specifications arise from the fact that post-buckling capacity is considered in the EC3 Specification whereas the AISC-360 capacities are based on elastic buckling loads. 7.2. Lateral torsional buckling of compact I-shaped members The two specifications have differences in the treatment of lateral torsional buckling. The AISC-360 Specification identifies three regimes of buckling depending on the unbraced length of the member ( Lb). For a beam under uniform moment (C b=1) two threshold values for unbraced length namely L p and Lr are defined in the AISC-360 Specification. The L p value provides a dividing line between plastic (no lateral buckling) and inelastic buckling behavior. Similarly, the Lr value provides a dividing line between inelastic and elastic buckling behavior. According to the AISC-360 Specification, plastic moment capacity of a compact member can develop if the unbraced length is less than L p. The member’s capacity reduces linearly between M p and 0.7 M y if the unbraced length is between L p and Lr. If the unbraced length is greater than Lr, then elastic buckling is expected to occur and the capacity can be found using elastic critical buckling moment ( M cr). The following equations summarize the nominal moment capacity for lateral torsional buckling as per the AISC360 Specification:
M n= M p=ZF y when Lb ≤ L p
L – L M n = C b M p – (M p – 0.7S x F y)----b-------- p-- Lr – L p
≤ M p
when L p < Lb ≤ Lr 2
C bπ E
M n = M cr = S x-------------- Lb2
-r--ts--
J Lb 2 S xho rts
1 + 0.078---------- -----
Cem Topkaya and Serkan Şahin / International Journal of Steel Structures, 11(1), 13-27, 2011
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Figure 5. Comparison of nominal moment capacities for compact web members.
when Lb > Lr
L p = 1.76r y
E ---- F y
E J Lr = 1.95rts ------------- --------0.7 F y S x ho 2
I yC w
rts = -------------S x
reduction factor approach for all buckling problems is utilized in the EC3 Specification. The lateral torsional buckling problem is also treated by developing a reduction factor (χ LT ) expression. The nominal moment capacity for lateral torsional buckling can be found as:
1+
0.7 F y S x ho 1 + 6.76 -----------------------
E
J
2
M n = χ LT M p = χ LT ZF y The reduction factor (χLT) is defined as: (15)
As mentioned in the compression members section, a
χ LT = -------------------1---------------------- but χ LT ≤ 1.0 χ LT ≤ ---1-2--2 2 λ LT Φ LT + Φ LT – βλ LT
(16)
A Comparative Study of AISC-360 and EC3 Strength Limit States
21
2 Φ LT = 0.5[ 1 + α LT ( λ LT – λ LT,o) + βλ LT ]
λ LT =
M p
--------
M cr
(17)
First of all, no M cr expression is recommended in the EC3 Specification. Any rational analysis to determine M cr is acceptable. In this study, the elastic critical moment expression (Eq. 15) provided in the AISC-360 Specification was considered to be used in the EC3 Specification expressions. As shown in Eq. 17, the EC3 Specification approach requires three parameters namely, αLT, λLT,O, and β to be used. The αLT factor is dependent on the imperfections and its value is identical to the α factors given in the compression members section. The proper imperfection curve (i.e. type a, b, c, or d) and the values of λLT,O, and β are dependent on the country of use and are specified in the National Annex. On the other hand, a maximum value of 0.4 for λLT,O and a minimum value of 0.75 for β are recommended in the absence of a National Annex. The appropriate buckling curve as per the EC3 Specification recommendations is based on the depth to width ratio (d /b f ) of the member. For rolled I-sections, curve “b” is utilized for d /b f t w k v E
---- ------- 1.37
1.51
C v = ----------------------2- (AISC-360) y -h--- --F ---t w k -v- E 1.10
C v = ---------------- (EC3-NREP) h F y ---- --------
t w k v E
1.37
C v = ------------------------------------------- (EC3-REP) h F y 0.7 + 0.78 ---- --------
t w
k v E
(20) Note that C v factor is dependent on the plate buckling coefficient, k v, which is calculated as follows: 5.0
k v = 5.0 + -------------2- (AISC-360) (a ⁄ h ) k v = 5.34 + 4.0( h ⁄ a)
2
for a ⁄ h ≥ 1 (EC3)
k v = 4.0+ 5.34( h ⁄ a)
2
for a ⁄ h < 1 (EC3)
(21)
The k v factors presented in the two specifications are similar. In the EC3 Specification a more elaborate treatment is presented which is dependent on whether the
Figure 7. Comparison of shear resistances.
a/ h ratio is greater than or less than unity. The EC3 Specification equations for k v formed the basis of old AISC specifications. Over the years these two equations were replaced with a single one for simplicity. Two conclusions can be derived by examining Eq. 20. The behavior in the two regimes where λ is less than 1.37 is identical according to both specifications. Differences are observed, however, for the elastic buckling range (λ>1.37). It should be noted that for end panels the EC3 Specification presents two different cases depending on the boundary conditions. These cases which are shown in Fig. 7 are termed as rigid end post (REP) and non-rigid end post (NREP). The rigid end post (REP) is formed by providing a W-shape or two double sided stiffeners at the end. There are special requirements for the size of the stiffening elements. Basically the very end panel in between these stiffeners is designed as a short beam under the membrane forces produced by the web plate. Cases that do not satisfy the REP criteria are designed as non-rigid end post (NREP). When Eq. 20 is examined, it is evident that the decrease in capacity (V n) with the non-dimensional slenderness is quadratic in the AISC-360 Specification whereas it is linear in the EC3 Specification. A plot of C v as a function on the non-dimensional slenderness is given in Fig. 7. As
A Comparative Study of AISC-360 and EC3 Strength Limit States
expected the capacities based on the EC3 Specification are significantly higher than the ones for the AISC-360 Specification for λ>1.37. In addition, the REP case offers slightly higher capacities as compared to the NREP case. For cases with λ>1.1, the AISC-360 Specification presents the following equation for V n that takes into account the tension field action:
1 – C v V n = 0.6 F y AwC v + ----------------------------------- 1.15 1 + (a ⁄ h )2
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the AISC-360 Specification. Furthermore, more simplified and conservative rules are presented that are independent of the loading direction. Similarly, the EC3 Specification presents two methods namely, the Simplified Method, and the Directional Method. The simplified methods are compared in this paper. The nominal strength per length of a weld segment is calculated as follows:
Rn = 0.6 F EXX t e (AISC-360) (22)
In Fig. 7 the two specifications were compared for the cases where TFA is included in the calculations. The results are presented for stiffener spacing to web depth ratio (a/ h) of 0.5, 1.0, 1.5, 2.0, 2.5, and 3.0. Consideration of tension field action is not permitted for a member when a/ h>3.0. This case and the EC3-NREP case are also presented in this figure. Analysis results reveal that the capacity curve for a/ h=3.0 coincides with the EC3-NREP curve. It can be concluded that the EC3 Specification provides lower capacities when compared with the capacities calculated using TFA in the AISC-360 Specification. The opposite is true for the other cases. It is worthwhile to note that minor differences are present between the two specifications for calculating shear strength. The shear area definitions are different. In the AISC-360 Specification, the total depth is multiplied by the web thickness to determine the shear area. On the contrary, the area of the web and a small portion of the flange area is utilized in the EC3 Specification. Furthermore, the EC3 Specification presents rules for including the contribution of the flanges to the shear resistance. In addition, the plastic shear capacity can be increased by 20 percent according to the EC3 Specification and this increase is determined by the rules of the National Annex.
F Rn = --------u----t e (EC3)
β
(23)
3 w
The maximum of the resultant of all forces at every point of the weld group is considered for design purposes. In the EC3 Specification, the resistance is a function of the ultimate tensile strength ( F u) of the weaker part joined (i.e. base metal) whereas the AISC-360 Specification utilizes the electrode strength ( F EXX ) for this purpose. In addition, it is required to check the base metal separately in the AISC-360 Specification. The EC3 Specification utilizes a βw factor which depends on the yield strength of the base metal. Typical values of βw are 0.8, 0.85, 0.9, 1.0 for S235 ( F y=235 MPa (34 ksi)), S275 ( F y=275 MPa (40 ksi)), S355 ( F y=355 MPa (51 ksi)), S420 ( F y=420 MPa (61 ksi)) steels, respectively. The directional method presented in the AISC-360 Specification is based on dividing the weld group into segments and summing up the strength of each segment considering its orientation. For the weld groups loaded inplane the instantaneous center of rotation method is utilized. The methodology for welds loaded in-plane is rigorous and takes into account the deformability of the weld. On the contrary, the von Mises yield criterion is applied using the normal and shear stresses on the effective throat area in the EC3 Specification directional method.
9. Design of Welded Connections The American Welding Society (AWS (2004)) provisions are adopted in the AISC-360 Specification for the selection of matching weld (filler) metal for a particular base (parent) metal. In general, the ultimate strength, F EXX , of the weld metal is greater than that of the base metal. According to the EC3 Specification, any weld metal having strength properties equivalent or better than that specified for the base metal can be utilized. 9.1. Fillet welds Effective area for fillet welds is the effective length multiplied by the effective throat thickness (t e) according to the two specifications. The primary difference between the two specifications is on how the direction of loading is treated. In general, the strength of a weld depends on the direction of loading. Transversely loaded fillet welds are stronger compared to the longitudinally loaded fillet welds. The direction of loading is taken into account in
9.2. Complete joint penetration groove welds The provisions provided in the two specifications for complete joint penetration groove (butt) welds are identical. According to the provisions the limit states for the base metal apply for these types of connections.
10. Design of Bolted Connections In the United States, two types of bolt grades namely, A325 ( F y=634 MPa (92 ksi), F u=830 MPa (120 ksi)) and A490 ( F y=940 MPa (130 ksi), F u=1040 MPa (150 ksi)) are widely used. The AISC-360 Specification adopts the provisions of the Specification for Structural Joints Using ASTM A325 or A490 Bolts (2004). The EC3 Specification presents rules for the widely used bolt grades in Europe that are based on International Standardization Organization ISO-898 (1999) standard. Typical bolt grades are 4.6 ( F y=240 MPa (35 ksi), F u=400 MPa (58 ksi)), 5.6 ( F y= 300 MPa (44 ksi), F u=500 MPa (73 ksi)), 6.8 ( F y=480
24
Cem Topkaya and Serkan Şahin / International Journal of Steel Structures, 11(1), 13-27, 2011
MPa (70 ksi), F u=600 MPa (87 ksi)), 8.8 ( F y=640 MPa (93 ksi), F u=800 MPa (116 ksi)), and 10.9 ( F y=900 MPa (131 ksi), F u=1000 MPa (145 ksi)). It is apparent that the high-strength bolts A325 and 8.8 have identical strength properties while A490 and 10.9 possess the same strengths. According to the AISC-360 Specification provisions the center-to-center distance between the bolt holes should be 2.7d o (3d o preferred) where d o is the diameter of the bolt. A value of 2.2d o and 2.4d o is recommended in the EC3 Specification for the distance between bolts that are parallel and perpendicular to the application of the load, respectively. The minimum edge distance is determined based on the manufacturing process in the AISC-360 Specification. This distance should be at least 1.75d o and 1.25d o for plates with sheared and rolled edges, respectively. In the EC3 Specification a minimum edge distance of 1.2d o is recommended irrespective of the manufacturing process. According to the AISC-360 Specification all A325 and A490 bolts should be pre-tensioned unless the bolts are installed to the snug-tight condition which is permitted for the bearing-type connections and for some applications where loosening or fatigue due to vibration or load fluctuations are not design considerations. The slip critical connections can be designed based on a different criterion. These connections are designed to prevent slip either as a serviceability limit state or at the required strength limit state. Similarly the EC3 Specification presents design categories for the bolted connections. Design category “A” is for bearing-type connections under shear where the aforementioned bolt types can be utilized without pretension. Design categories “B” and “C” are for slip critical connections under shear, utilizing 8.8 or 10.9 bolts, and are designed for serviceability and strength limit state, respectively. Design categories “D” and “E” are for bolts under tension designed using no-pretension and with pre-tension, respectively. 10.1. Bolt strength under tension Tensile rupture along the threaded portion is considered as the ultimate limit state for bolts under the action of tensile forces according to both specifications. In the AISC-360 Specification the net area of the threaded portion is estimated by considering 75 percent of the gross area ( Ab) of the bolt. In the EC3 Specification, no specific equations or recommendations are presented and designers have to resort to manufacturers’ catalogs to determine the net area of the bolt ( As). The tensile capacity is determined as follows:
T n=0.75 F u Ab (AISC-360) T n=0.9 F u As (EC3)
(24)
According to Eq. 24 the primary difference between the two specifications is the use of a 0.9 factor in the EC3 Specification. This is similar to the use of this factor in
tension member provisions. 10.2. Bolt strength under shear Shear rupture along the threaded or unthreaded portion is considered as the ultimate limit state for bolts under the action of shear forces according to both specifications. In the AISC-360 Specification, equations were developed by taking into account the reduction of shear area due to the threads and the effect of having long connections with multiple bolts. In the EC3 Specification the net shear area through the threads needs to be calculated when the threads are in the shear plane. Furthermore, a reduction factor, βLF, is proposed for long connections. The shear capacity for high strength bolts (A325, A490, 8.8, and 10.9) is calculated as follows:
V n=0.5 F u Ab (AISC-360 threads excluded) (A325 (8.8), A490 (10.9)) V n=β LF 0.6 F u Ab (EC-3 threads excluded) (A325 (8.8), A490 (10.9)) V n=0.4 F u Ab (AISC-360 threads included) (A325 (8.8), A490 (10.9)) V n=β LF 0.6 F u As (EC-3 threads included) (A325 (8.8)) V n=β LF 0.5 F u As (EC-3 threads included) (A490 (10.9))
L – 15d
β LF = 1 – --- j---------------o- 0.75 ≤ β LF ≤ 1 200d o
(25)
If values of β LF =0.8 and As=0.8 Ab are assumed then it is evident that the provisions of the two specifications are identical for the threads excluded and the threads included (A325 (8.8)) cases. For the threads included (A490 (10.9)) case the EC3 Specification provides lower capacity values. It is evident from Eq. 25 that the EC3 specification has a more elaborate treatment that includes the connection length as well as the type of bolt material used. 10.3. Combined tension and shear in bearing type connections There are interaction equations provided in both specifications to assess the bolt capacity under combined actions. Although the main body of the AISC-360 Specification presents a single expression, the commentary to the AISC-360 Specification presents an additional expression. In the EC3 Specification, only one equation is given for the assessment. In order to make a fair comparison, the general form of the expressions with the reduction and the partial safety factors are given. The following expressions are utilized for the resistance of high strength bolts under combined actions: 2 u --T V u 2 ------ + -------- ≤ 1 (AISC-360) φT n φV n
u V u u --T T u --V ------ + -------- ≤ 1.3 -------- ≤ 1 ----- ≤ 1 φT n φV n φT n φ--V n
(AISC-360)
A Comparative Study of AISC-360 and EC3 Strength Limit States
u --------T V u ------------ + ------------- ≤ 1 (EC3) 1.4T n ⁄ γ M V n ⁄ γ M
Rb = k 1αd F ud ot (26)
It should be noted that the recommended values for φ and γ M are 0.75 and 1.25, respectively. The first of the AISC-360 Specification expressions is an ellipse and the second expression is a simplification of the first one which consists of three straight lines. The EC3 Specification also adopts the straight line approach. According to the second expression in the AISC-360 Specification the combined actions do not have an effect on each other if either T u
