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Comparison of Eurocode EC3 and American AISC 360 to the design of large
span structures
Research · June 2015
DOI: 10.13140/RG.2.1.4404.4966
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A BRIEF COMPARISON BETWEEN THE EUROCODE 3 AND
AMERICAN AISC-360 IN THE DESIGN OF LARGE SPAN
STRUCTURES
Yann Steve Siewe Tchoussonnou
A report submitted to the Department of Civil Engineering,
Architecture and Building, Coventry University in partial fulfilment of the
requirements for a degree in
(Bachelor in Engineering of Civil Engineering).
-1-
ABSTRACT
This report is to compare the North American AISC-360 Standard to Eurocode 3. Conclusions show
that both codes of practice differ from each other in so many ways but not so drastically in many
situations as well and they both can give provision to very strong, effective and efficient designs.
-2-
Table of Contents
ABSTRACT ...................................................................................................................................................................... - 2 1.
Introduction .......................................................................................................................................................... - 5 Rationale ................................................................................................................................................................... - 5 AIM ............................................................................................................................................................................ - 6 Objectives.................................................................................................................................................................. - 6 Organisation of the Report ....................................................................................................................................... - 6 -
2.
AISC-360 ................................................................................................................................................................ - 8 ASD (Allowable Stress or Strength Design); .............................................................................................................. - 8 LRFD (Load and Resistance Factor Design) ............................................................................................................. - 10 Ultimate Limit States (Limit states of strength) ......................................................................................... - 10 Comparison of ASD VS LRFD ................................................................................................................................... - 12 -
3.
EUROCODE 3 ....................................................................................................................................................... - 14 -
4.
CROSS SECTION CLASSIFICATION ........................................................................................................................ - 16 -
5.
MATERIALS ............................................................................................................................................................ - 0 -
6.
TENSION DESIGN ................................................................................................................................................... - 1 -
7.
COMPRESSION DESIGN ......................................................................................................................................... - 1 -
8.
METHODOLOGY .................................................................................................................................................... - 3 The MODEL ............................................................................................................................................................... - 3 Model Parameters ................................................................................................................................................ - 1 Procedure .............................................................................................................................................................. - 3 -
9.
ANALYSIS ............................................................................................................................................................... - 5 Results ....................................................................................................................................................................... - 5 Analysis and Comparison of the results .................................................................................................................... - 5 -
10.
CONCLUSION ..................................................................................................................................................... - 6 -
11.
REFERENCES ...................................................................................................................................................... - 7 -
12.
APPENDIX .......................................................................................................................................................... - 8 APPENDIX A ........................................................................................................................................................... - 8 APPENDIX B 1 ........................................................................................................................................................ - 9 APPENDIX B2 ....................................................................................................................................................... - 16 -
-3-
LIST OF TABLES
Table 4.1: Classification Similarities
Table 4.2: Cross Section Classifications
Table 5.1: Steel Grade Properties
Table 5.2: Steel Grade Equivalences
Table 6.1 Shear Lag Factors U
Table 7.1: Cross Sectional Buckling Curves
Table A1: Combination factors for Imposed and Snow Loads on a Structure
Table A2: Partial Safety Factors
-4-
1. Introduction
Rationale
A building code is a legal ordinance put to practice by public bodies such as city councils, regional planning
commissions, states, federal agencies, establishing regulations governing building design and construction.
Building codes are designed and put to practice to protect public health safety and wellbeing of the
inhabitants of the region, city, state or country involved. (Merritt and Brockenbrough, 1999, pp. 6.1 – 6.2)
Most regions in the world have their own code of practice designed they use when it comes to the
construction industry and built environment. These codes of practice differ from each other in so many
aspects. Such codes may not be used in regions in which they were not designed for as it may bring about
conflicting National Standards unless it’s modified and published in a National Annex (A National Annex to
a Building Code are modifications made to a code to better serve in a particular region).
Euro codes are a set of harmonized technical rules developed by the European Committee for
Standardisation for the structural design of construction works in the European Union. (EN 1990:2002 E,
Euro code - Basis of Structural Design, CEN, November 29, 2001). Under the Public Procurement Directive,
the Member States (European Union member states) must accept designs to the Euro codes. When
published, the Euro codes will become the standard technical specification for all public works contracts:
where a contract for a public body contains a technical specification this should reference the appropriate
European Standards. (Euro codes: Frequently Asked Questions, N.D). In that light, Euro codes are therefore
the confirmed mandatory code of practice used in the European Union for Structural Design. The Structural
Euro code program comprises the following parts, each generally consisting of a number of sub-parts:
EN 1990: Basis of structural design, EN 1991: (Eurocode 1) Actions on structures, EN 1992: (Euro code 2)
Design of concrete structures, EN 1993: (Eurocode 3) Design of steel structures, EN 1994: (Eurocode 4)
Design of composite steel and concrete structures, EN 1995: (Eurocode 5) Design of timber structures, EN
1996: (Eurocode 6) Design of masonry structures, EN 1997: (Eurocode 7) Geotechnical design, EN 1998:
(Eurocode 8) Design of structures for earthquake resistance, EN 1999: (Eurocode 9) Design of aluminium
structures.
This research will concentrate on Eurocode 3 (Design of Steel Structures).
In the United States, structural steel is used in specification in accordance with the applicable specification
of ASTM (American Society of Testing and Materials). ASTM International, known until 2001 as the
American Society for Testing and Materials (ASTM), is an international standards organization that
develops and publishes voluntary consensus technical standards for a wide range of materials, products,
systems, and services. Amongst the codes specified by the ASTM, is the American Institute of Steel
Construction (AISC) the technical Institute established to serve the structural steel design and construction
industry. AISC developed Specification for Structural Steel buildings commonly abbreviated AISC 360.
(‘ASTM International’, 2015)
AISC gives provision to determine the nominal and available strengths of members, connections and other
components of steel building structures. AISC contains 2 design methods, the Allowable Stress Design
method and Load (ASD) and Resistance Factor Design method (LRFD). The former being in use for a very
long period before the latter was initiated as it’s modification.
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EC3 is made up of many parts further divided into subparts. With each part specific to a particular
structure type such as buildings, bridges, towers, silos etc. General rules and rules for buildings are
specified in Part 1 of EC3. This part is has 11 subparts meanwhile, AISC-360 is only an integral document.
( Şahin, 2011)
The design of large span structures have been increasing in the construction industry for the past decades
and large span structures ranging from bridges to buildings are being erected in all areas of the world.
These structures are constructed under codes of practices including Eurocode and AISC in the regions
where appropriate.
These codes (Euro code 3 and AISC-360) have some differences in design criteria. The differences between
them brings about a code being suitable over the other in the design of structural members or a code
designing weaker members than another. In that light, a brief comparative study of both codes is going to
be carried out stating the differences found in the use of the same large span structure with only static
loading applied to it with both codes used one after the other.
Knowledge of the information covered above is important as to properly compare these standards, it’s
important to know how they were formed and classified.
AIM
To Briefly Compile a Comparative Study between the American AISC-360 and the European EUROCODE 3
codes of practice.
Objectives






To briefly outline the differences between ASD and LRFD
To briefly outline the differences between Euro code 3 and AISC-360
To use a large span model on MIDAS Civil to perform beam comparative analysis
To analyse the model with Euro code and AISC 360
To interprete the results of the analysis
To compare the results obtained from both codes.
Organisation of the Report
The report will follow the following sequence.
Firstly will be the introduction chapter, this chapter will provide a very brief overview of the building standards
compared (AISC-360 and EC3),the bodies which govern them and the regions they serve.
Then the next chapter will be Literature review of AISCS-360, This chapter will briefly trace to development of AISC.
Also, ASD and LRFD is compared in this chapter. The development of safety factors and resistance factors and uses
of Load combinations. Differences and similarities shown and the preference for comparison with EC3 (LRFD) stated.
The next chapter is the literature review of Eurocode 3. This chapter will cover the development of partial safety
factors, load factors and reduction factors and its applications.
And then, is the methodology, in this section, a model is designed and analysed, under both codes of practice. ( The
focus here will only be to analyse and interpret the behaviour of the long span beam in the model ).
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Following the methodology chapter is the analysis chapter. The results obtained from MIDAS Civil analysis software
is discussed and explained in this chapter.
Thereafter, comes the conclusion of the report, here all the findings from all the chapters is clearly outlined.
References and Appendices constitute the end of the document.
-7-
2. AISC-360
ASD (Allowable Stress or Strength Design);
ASD is the design method historically used in the United States, most buildings in America are built using
this technique. This technique is based on pure elastic theory, with this method, the stresses produced
from all the Static (Dead and Live) Loads and Dynamic Loads should not exceed the stipulated allowable
Stress in the structural members and their connections. With this technique, the designer uses the
following load Combinations for design,
D+F
D+H+F+L+T
D + H + F + (Lr or S or R)
D + H + F + 0.75(L + T) + 0.75(Lr or S or R)
D + H + F ± (W or 0.7E)
D + H + F + (0.75W or 0.7E) + 0.75L + 0.75(Lr or S or R)
0.6D + W + H 0.6D ± (W or 0.7E)
(These are not all, just to name few)
Where
D = dead load,
E = earthquake load,
F = load due to fluids with well-defined pressures and maximum heights,
H = load due to lateral earth pressure, ground water pressure, or pressure of bulk materials,
L = live load due to occupancy,
Lr = roof live load,
S = snow load,
R = nominal load due to initial rainwater or ice, exclusive of the ponding contribution,
T = self straining load,
W = wind load,
Meanwhile during design and construction, uncertainties arise. A few common uncertainties include;
errors in design and construction, random behaviour of weather and nature, material properties
exceptions. These uncertainties in both load and capacity are taken care of by the application of a single
variable :-factor of safety (Ω). In this light, the load combinations mentioned above must satisfy the
following equation;
Fa≤ 𝐹n⁄Ω
Equation 1
-8-
Or more explicitly
𝐹𝑛
Ω
≥ Qd + Qt1 + Qt 2Eqn 2
Where
Fa = required strength,
Fn = nominal strength
Ω = safety factor
Fn/Ω = allowable strength
Qt1, Qt2 = Nominal transient load effects
Qd = Nominal dead load effect
γ = Load factor
The safety factor Ω is always greater than 1. For each type of observed type of failure, a
different factor of safety is employed. ASD does not directly tell us the factor of safety to
use in a particular situation.
-9-
LRFD (Load and Resistance Factor Design)
The specification of Structural Steel Buildings developed by the AISC (AISC-360) makes use of limit state
design. “A limit state is a condition that represents a boundary of structural usefulness beyond which the
structure ceases to fulfil its intended function.” (Vinnakota, 2005, pp. 125 – 125). A limit state may be the
point where a structural member actually completely or partially collapses as a result of instability and
fracture or the point where structural members starts forming a plasting hinge or plastic mechanism.
There two types of limit states; Ultimate limit states (Limit states of Strength) and Limit States of
Serviceability.
Ultimate Limit States (Limit states of strength) ;
This a condition checked at a point along the behaviour of a structural member found at the upper
section of of its elastic zone at about 15% lower than the elastic limit. Thereby Ultimate limit states is a
purely elastic condition which behaves very differently and not close to the behaviour at Ultimate point
(Ultimate point is a physically situation where there is excessive deformations and imminent collapse of
the member under analysis or the structure). Here are few limit states of strength ; buckling of a column,
formation of a plastic hinge, lateral buckling of a beam, frame instability but not limited to these. Because
limits states vary among members, the most concerning limit state is that with the lowest design strength.
Serviceability Limit States;
Is a check targeted to prove that under the application of characteristic (unfactored ) design loads and
loads due to other factors like settlements, temperature gradients or vibrations, the structural behaviour
falls in line and does not exceeds the design criteria. They are designed to ensure malfunctions and
discomfort due to visible undesired structural behaviour are avoided or scarcely occur. (McCormac, Jack C,
2008).
LRFD is the second design technique developed and used by the AISC alongside ASD. In the US, It is
another way of calling limit states design (LSD). LRFD is the most widely used design technique when
designing according to AISC. The AISC specification demands that safety factors should be applied to both
the nominal strengths or nominal resistance and service loads of the structural members and their
connections. With this technique, the designer uses the following load Combinations for design,
1.4(D + F)
1.2(D + F + T) + 1.6(L + H) + 0.5(Lr or S or R)
1.2D + 1.6(Lr or S or R) + (L or 0.8W)
1.2D + 1.0W + L + 0.5(Lr or S or R)
1.2D ± 1.0E + L + 0.2S + 0.9D + 1.6W + 1.6H
0.9D + 1.6 H ± (1.6W or 1.0E)
LC1
LC2
LC3
LC4
LC5
LC6
(The load symbols are same as the ASD symbols mentioned above)
With Load and Resistance factor Design Specifications, the design strength of each connection or
structural member cannot be less than the required strength based on factored nominal loads (Galambos
and Ravindra, 1976; Ellingwood et al., 1982). Uncertainties always exists in design and construction as
mentioned above. But the way LRFD handles these uncertainties is slightly differently from ASD as shown
below. The load combinations mentioned above must satisfy the following equation;
- 10 -
𝐹n≥∑ γiQi
Eqn 3
or more explicitly
Rnd Qdt1Qt1t 2Qt 2 Eqn4
where
Rn = Nominal resistance
= Resistance factor
(All other symbols same as defined above)
The right side ( ∑ γiQi) stands for the required strength. This is strength obtained from analysis of the
member or connection under factored loads with the combination used. All the different loads from
different sources are added together therefore the summation sign. Sometimes the load effects may
slightly deviate from nominal values of Qi obtained from nominal loads, load factors’ introduction takes
account of those deviations and other uncertainties and inaccuracies in Load determination. (Vinnakota,
2005, pp. 125 – 125)
The Left side (𝐹 n) is the design strength obtained from the observed member. The maximum resistance
factor can be is 1.0 but most at times less than 1.0.
- 11 -
Comparison of ASD VS LRFD




ASD had been in use for more than 70 years before designers thought of modifying or upgrading.
The Following brief comparison between ASD and LRFD will give some insights to their differences
and similarities.
With ASD, the whole uncertainty and variability in the loads and resistance is applied to the
nominal strength side of the equation where these factors of safety were not obtained from
analysis but from a combination of experience and experiments carried out throughout the years.
In ASD design philosophy, uncertainties are dealt with by using a single factor of safety Ω where
this lone variable takes care of uncertainties in both load and capacity. Whereas, in LRFD design,
uses load factors to handle uncertainties due to applied loads and a resistance factor to handle
uncertainties due to material unpredictable behaviour or construction. This therefore implies LRFD
is advantageous over ASD, because distributing different factors depending on load type as LRFD
does brings about a more effective design with lighter members.
Loads found under the same load combination are considered to have the same uncertainty or
variability; doing some substitutions on equation 3, we have
∑ Qi
≤ Fn /(
∑ Qi
≤ 𝐹n⁄Ω = Fa
Which is very identical to
Therefore
Ω=

From this illustration, we see that the factor of safety in ASD is a ratio of the load factor over the
resistance factor of LRFD(in cases where all the loads are found under the same load combination) for the
load combination considered.


With a live load to dead load ratio of 3, ASD will produce members of same structural integrity and
same member sizes as LRFD. But with a ratio different from 3, designs produced by ASD are either
less efficient or less reliable or both as compared to LRFD which is relatively more rational in its
designs.
In ASD, combined action of loads, is generally maintained under the member under consideration’s
yield load forces with the required strength Fa obtained from dividing the nominal strength Fn by
the safety factor Ω thereby reducing its capacity to a point below yielding. See figure below
- 12 -
Rn/ Ω = ASD Capacity
Rn = LRFD Capacity
Rn = Nominal Capacity
Figure 2.1
Source: 2006,2008 T. Bartlett
Quemoy
The figure above represents the Load displacement graph of a mild steel member. In LRFD, combined
action of loads is maintained under the load capacity which is equal to the product of the nominal strength
Rn and the resistance factor .



Both codes cannot be used in the same design, it’s either one or the other
There is no particular recommendation to which code to use. It’s all up to designer. Decisions are
generally made base on finance.
LRFD designs gets the most out of material strength, thereby should be a more economical
approach.
This report focuses only on comparing AISC-LRFD to Eurocode 3, ASD won’t be compared to
Eurocode 3.
- 13 -
3. EUROCODE 3
As earlier defined, Euro codes are a set of harmonized technical rules developed by the European
Committee for Standardisation for the structural design of construction works in the European Union. (EN
1990:2002 E, Euro code - Basis of Structural Design, CEN, November 29, 2001). In Europe, the Limit State
Design is enforced by the Euro codes. Euro codes are used in many (all) countries in the European Union
but little modifications may be made it but published as a National Annex ( For example; British Standards
is a UK National Annex to Euro code). “In the language of the Euro codes, ‘dead loads’ become ‘permanent
actions’, imposed loads, snow loads and wind loads are collectively called ‘variable actions’ and ‘load
combinations’ becomes ‘combinations of actions’”. (David Brown, SCI Deputy Director) . As with the AISCLRFD design technique, Euro code 3 utilises limit state designs as well. This involves the use of partial safety
factors (γm). Here, the strength (Characteristic Strength) is divided by partial safety factor(s) and
compared to the design loads.
According to BS EN 1990 Basis of Structural Design, clause A1.2.1(1), the maximum allowed number of
variable actions are two, therefore, the designers need to make the decision which two variable loads
should be considered. Four limit states are considered in this same volume, these are EQU, STR, GEO and
FAT which stand for Equilibrium, Strength, Ground and Fatigue respectively. The most widely considered
by designers are equilibrium(EQU) when observing overturning and sliding and strength (STR) of the
members and frames. (Brown, no date)
Combination of Actions is determined in 2 ways: the first being;
∑j≥1 γG,j Gk,j+ γpP + γQ,1Qk,1 +∑𝑖≥1 γQ,iψ0,iQk
Eqn 5
Where;
G stands for permanent actions
P stands for prestressing (Which is of no interest to this report as it’s steel being studied)
Q1 stands for the variable variable action
Q stands for all the rest of the variable actions summed up
γp stands for the partial factor multiplied to
the Prestressing Actions
γQ stands for the partial factor multiplied to the variable actions
γG stands for the partial factor multiplied to the Permanent Action
ψ0 stands for Combination Factor
ξ stands for Reduction factor (see below)
- 14 -
the second being;
∑j≥1 γG,j Gk,j + γpP + γQ,1 ψ0Qk,1 +∑𝑖≥1 γQ,iψ0,iQk,i
∑j≥1 ξγG,j Gk,j + γpP + γQ,1Qk,1 +∑𝑖≥1 γQ,iψ0,iQk,i
Eqn 6
Eqn7
Notice the difference between Equation 6 and 7 to Equation 5 and between each other (Equations 3
& 4). That is the addition of a reduction factor (ξ) to Permanent Actions in Equation 7 and the addition
of a combination factor (ψ0 ) in Equation 6.
Equations 6 and 7 are the most widely used of the three equations. When designing according to
Eurocode for Ultimate Limit States (ULS),Equations 6 and 7 can be computed to find out the worst
case. For example, considering only one case in each load category; (For Values of ψ, see Appendix
A1)
Dead Load:
Gk = 9KN
Imposed Load: Qk,1 = 11KN
Snow Load:
Qk,2 = 6KN
(Random values used only for demonstration)
And applying all two Equations (6, 7);
1.35Gk + 1.50ψ0Qk,1 + 1.50ψ0Qk,2
= 1.35 x 9 + 1.50 x 0.7 x 11 + 1.50 x 0.5 x 6 = 28.15KN (Illustration of Eqn 6)
And
ξ1.35G + 1.5Q
k
k,1
+ 1.5 ψ0Qk,2
= 0.925 x 1.35 x 9 + 1.5 x 11 + 1.5 x 0.5 x 6 = 32.24KN
(Illustration of Eqn 7)
From the results above, that member or connection should be designed considering an Ultimate load
of 32.24KN.
- 15 -
4. CROSS SECTION CLASSIFICATION
AISC-360 and EC3 both have member section classifications for local buckling. The Seismic Provisions for
Structural Steel Buildings (AISC-341) is an extra document which defines a member classification;
seismically compact. AISC-360 has 3 section classifications namely; compact, non- compact and slender.
EC3 member cross section classification is Class1, Class 2, Class 3 and Class 4. The following observation
should be made about the similarities in these cross section classifications.
Table 4.1: Classification Similarities
AISC 360
Seismically
Compact
EC3
Class 1
Non-Compact
Class 2
Compact
Class 3
Slender
Class 4
Description
These are sections which can develop their plastic moment capacity
but still have quite an amount of rotation capacity.
These are sections which can develop their plastic moment capacity
but still have rather limited amount of rotation capacity due to local
buckling.
These are sections where the plastic moment capacity’s development
may be prevented by local buckling when extreme compression
fibre stresses reach yield strength.
These are sections where a member’s (plate) local buckling will occur
before the yield stress attained.
Table 4.2 below shows the ratio of the limits of EC3 to AISC-360. From that table, it can be seen that there
is no drastic difference between the limits in both codes.
Little differences in width thickness ratios also exist as in AISC-360, the flange slenderness is determined by
using half the flange width whereas in EC3, it’s determined by using the only the outstanding section of the
flange.
- 16 -
Table 4.2: Cross Section Classifications
Source: (Şahin, 2011)
Where
𝐸
E(Elasticity Modulus) = 210GPa
𝐴 = √𝐹
𝑦
Fy (Yield Strength) = 235 or 275 or
355 MPa
- 17 -
5. MATERIALS
When designing according to AISC-360 or Eurocode 3, there is a choice of material to be made. EC3 has
great variety of steel grades which has various strengths, chemical and Mechanical properties. These steel
grades have equivalences in AISC-360.
In table 5.1 below are some steel grades, equivalences and properties.
Varieties of steel grades utilised by EC3 include S195, S235, S275, S355, S420, S460 etc. . Those utilised by
AISC-360 are A36, A53, A283C, A570 Grade 40, A572 Grade 50 etc. However, the most widely used in the
construction industry of these are S235, S275, S355 and A283C, A572 Grade 40 and A572 Grade 50 . Their
properties are illustrated in table 5.1 below.
Table 5.1: Steel Grade Properties
Mechanical Properties
Chemical Properties
Steel Grade
Yield Strength
(MPa)
Tensile Strength
(MPa)
S235
235
S275
C%
Max
Mn%
Max
P%
Max
S%
Max
Si%
Max
360
0.22
1.60
0.05
0.05
0.05
275
370
0.25
1.60
0.04
0.05
0.05
S355
355
460
0.23
1.60
0.05
0.05
0.05
A283C
205
380
0.24
0.90
0.04
0.05
0.4
A570 Gr. 40
275
380
0.25
0.90
0.035 0.04
0.4
A572 Gr. 50
355
460
0.23
1.35
0.04
0.4
0.05
C = Carbon, Mn = Manganese, P = Phosphorous, S = Sulphur Si = Silicon
From the table above, it is observed that steel grades utilised under Eurocode 3 have very close equivalences in
AISC-360 as;
Table 5.2: Steel Grade Equivalences
EC3
AISC-360
S235
A283C
S275
A570Gr40
S355
A572Gr50
-0-
6. TENSION DESIGN
“AISC-360 and EC3 both consider Tensile yielding in the gross section and tensile rupture in the net
section as the two primary limit states for tension members,” Serkan Sahin,2011 .
The following equations show how the nominal resistance of members to tensile yielding and tensile
rupture strengths are obtained;
F n = Ag F y
Eqn 6.1
Fn = 0.9AnFu
Eqn 6.2
Fn= UAnFu
Eqn 6.3
Where
Fn = Nominal Axial Strength
Ag = Gross Area
Fy = Yield Stress
An = Net Area
Fu = Tensile Strength
U = Shear Lag Factor
Equation 6.1 above shows how Tensile yielding strength is calculated for both AISC-360 and EC3.
Equation 6.2 shows how tensile fracture strength is calculated for EC3 and
Equation 6.3 shows how tensile fracture strength is obtained for AISC-360.
Both equations look quite similar, the major difference is how the shear lag factor is obtained In EC3, the
tensile fracture capacity is common reduced by 10% regardless whether all cross sectional members are
connected or not. The coefficient of the Shear lag factor 0.9 may be replaced with a reduction factor which
can be any number between 0.4 and 0.7 for unsymmetrically connected members. In AISC-360, 1.0 is the
shear lag factor utilised when the tension load is transmitted directly to the cross sectional members.
Shear lag factors falling in the region of 0.6 to 0.9 may replace the 1.0 shear lag factor when dealing with Lsections, HSS or I-sections. See Table 6.1 below for more details
Table 6.1 Shear Lag Factors U
Member Description
Shear Lag Factor
Tension members where tension load is transmitted directly to the cross
sectional members
Tension members where tension load is not transmitted to all cross
sectional members
Tension members where tension load is transmitted by transverse welds to
some cross sectional members
Single Angles
With 4 or more fasteners per line in direction
of loading
With 2 or 3 fasteners per line in direction of
loading
U=1.0
U = 1-ɇ⁄𝑙
U=1
An = Area of directly connected
members
U = 0.80
U = 0.60
Source: Sahin 2011
ɇ = connection eccentricity, l = length of connection
-1-
7. COMPRESSION DESIGN
AISC-360 and EC3 both address reduction in Capacity with the use of a non-dimensional slenderness for flexural
buckling. In AISV-360, there is a single column strength curve whereas in EC3, there are 5 distinct curves (a0, a, b,
c, d) making EC3 more elaborate and specific over AISC-360. Flexural torsional buckling, lateral torsional
buckling, flexural buckling are analysed using reduction factors.
For both EC3 and AISC-360, the valid equation is
Fn = AgFy
Where
Eqn 7.1
 = reduction factor
In AISC-360, the reduction factor  = 0.658FB when FB≤1.5
 = 0.877/2FB when FB ≥ 1.5
FB
= sq root ( AgFy/Pcr = KL/r. sq root. (Fy/E)
Eqn
7.2
In EC3, c = 1/ F + sq root(2 – 2FB )
Where  = 0.5[ 1 +  ( FB – 0.2) + 2FB
An imperfection coefficient  is utilised by EC3 to identify suitable column strength curves to use.
Table 7.1 below shows buckling curves and types of cross sections associated with.
Figure 2 shows the comparison between AISC-360 curve and EC3 curves.
-1-
Table 7.1: Cross Sectional Buckling Curves
Source : EC3
-1-
Figure 7.1 : Reduction Factors for Flexural Buckling for EC3
Source : Sahin,2011
Figure 7.2
-2-
8. METHODOLOGY
The MODEL
To compare the difference in member behaviours of the application of the different on structural steel
long span structures, a model structure was created using the analysis software MIDAS CIVIL. After the
model was generated, all loads (static; dead loads and live loads).
The Model was first designed under EC3 specifications and analysed and then designed under AISC
specifications and tested.
The reason a long span structure was chosen is because in some cases, the difference between steel
members and their equivalents or close to equivalents in other design specifications are not too large and
easily illustrated. To better appreciate these differences, long span structures are the ideal structures to be
analysed.
Figure 6.1: Structural Model for Analysis
(This model was created portraying an Airport Terminal in Dusseldorf Airport Weeze)
The model’ to be analysed is only the frame because in most long span structures like Airport Terminals,
the structural frame is built and all other structures are built in the frame as separate short span
-3-
structures, one floor or two floors with its own support system independent from the overall structural
frame.
The independent short span structures under is not the point of interest in this paper so will not be
designed or analysed. Only the external structures is analysed as it has the long span members which are
the point of interest.
Model Parameters
As only the frame is analysed, the only loads to be considered are;
Dimensions of the structure
Roof Self Weight = 0.12 KN/m2
Span = 30m
Roof Variable Action = 0.2 KN/m2
Width = 8m
Height = 15m
Design Action Determination (to Eurocode 3)
To obtain the design action of a steel beam,
Self Weight of Steel is taken into account by the software
Self Weight of Roof = 0.12 KN/m2 x 10m = 1.2KN/m
Snow Action = 0.5 KN/m2
Gk = 1.2KN/m
Qk1 = 0.2KN/m2 x 10m = 2KN/m
Qk2 = 0.5 KN/m2 x 10m = 5 KN/m
ULS Design
 1.35Gk + 1.50ψ0Qk,1 + 1.50ψ0Qk,2
= 1.35 x 1.2 KN/m +1.5 x 0.7 x 2 KN/m + 1.5 x 0.5 x 5KN/m
= 7.47 KN/m
Or

ξ1.35Gk + 1.5Qk,1 + 1.5 ψ0Qk,2
= 0.925 x 1.35 x 1.2 KN/m + 1.5 x 2 KN/m + 1.5 x 0.5 x 5 KN/m
-1-
= 8.249 KN/m
(Refer to Appendix A2 for values of Combination factors and partial Safety Factors)
Thereby, 8.249 KN/m was considered as the design Action. (Remember, Partial factors of safety,
combination factors and reduction factor were all introduced in the designs to handle uncertainties in
practice. So shouldn’t be ignored)
Assumptions




Acceleration due to gravity was assumed to be 9.8 m/s
The design software used here takes into account the beam’s self weight when running it’s analysis
or checks.
The model was assumed to less than or equal to 1000m above sea level. Hence the combination
factor 0.5 for Snow Actions.
No Live Action like occupancy loading was considered on this model because the external frame
with no internal members are analysed thereby, the only live action considered is the roof life load.
( This Assumption applies to Design to AISC below, only roof life load Lr is considered, there is no
live load L)
Design Load Determination [to AISC-360 (LRFD)]
LRFD uses load combinations, in this case, only 3 load cases apply to the model; Dead Load, Live Load,
Snow Load. The load combination which the largest output is LC3;
1.2D + 1.6(Lr or S or R) + (L or 0.8W)
D = 1.2 KN/m
Lr = 2 KN/m
S = 5KN/m
 1.2D + 1.6(Lr or S or R) + (L or 0.8W)
= 1.2 (1.2 KN/m) + 1.6 ( 5 KN/m)***
=
9.44 KN/m
*** Lr or S or R means the biggest of the load cases which in this situation is Snow Load S = 5 KN/m
NB: The metric units KN/m is consistent throughout the report but it doesn’t reflect real life situation, it’s
only for direct comparison, the North American AISC uses the Imperial unit system.
Materials
The model was designed using Steel S355 (yield strength 355 N/mm2), and A572 Grade 50 steel. (See procedure
below)
-2-
Sections
For analysis and comparison purposes, the same section used for the Model’s Eurocode Design was used
for the AISC-LRFD design. With reasons being;
Two sections utilised by two different standards might have different dimensions as different widths,
depths, second moment of areas etc. which could considerably alter comparison results.
Procedure


The beams and columns were first created, then their material properties were applied to them.
(See figure 6.1 above)
Then ULS Design Action(EC3) determined above was applied to the model as thus
Figure 6.3: E C3 Design Action Applied
-3-


The analysis was done on the software and results obtained.
Thereafter, Design loads(AISC-LRFD) determined above were applied to the structure as thus
Figure 6.4: AISC-360 Design Load Applied
.
-4-
9. ANALYSIS
Results
After the successful computer analysis of the model. A steel code check was run by the software on the
Model under Codes. The results generated are reported as
Appendix B 1: 457x152x82 BEAM DESIGN TO EUROCODE 3
Appendix B2 : WIDE Flange W24x62 Beam Design to AISC-360
Analysis and Comparison of the results
These results are compared below;
EC3
AISC-LRFD
Ratio
Slenderness (l/i),
(l/r)
241.7
228.2
0.9
Shear Resistance
0.039
0.036
0.9
Combined Resistance
0.138
0.483
0.3
Moment Resistance about
Major Axis
0.138
0.68
0.2
Slenderness is calculated the same way under both codes. L/I and L/r for EC3 and AISC-360 respectively.
The combined resistance of EC3 is only 30% of the combined resistance In the AISC, therefore, under the
same characteristic load, at serviceable limit states, AISC 360 designed members .
From this, in axial tension, beams under EC3 will likely buckle around the same period .
-5-
10. CONCLUSION
The following conclusions were drawn after the analysis if the results.
In EC3, uncertainties are used to handle the same type of uncertainties involved in construction sector
but are employed in different ways. Partial safety factors might be looked at as the inverse of resistance
factors. Typical values for partial safety factors are 1.0 for buckling mode and yielding, and for fracture
limit states 1.25.
From the determination of design loads for both EC3 and AISC-360 in Chapter 7, it should be noted that
due to code difference (in factors applied), AISC-360 had a larger design load compared to EC3.
Nevertheless, this is not an observation which can be observed every time. AISC360 determines its design
load the loads with a few combination factors and designing for the worst case (the maximum), in that
light, the design load might be higher or lower than design by EC3 with the application of the same
characteristic load whereas EC3 has set formulae employed for design.
In calculating the tensile capacity of members, the difference is the calculation of the shear lag factor U.
EC3 has a fixed shear lag factor 0.9, while in AISC360, shear lag factors vary and are calculated in different
ways. A brief demonstration of that is shown in figure 6.1.
EC3 gives provision to five separate curves ( ao, a, b, c and d) when defining the reduction in capacity in
compression members meanwhile AISC-360 gives provision to only one curve (column strength curve).
Nevertheless, the single strength curve provided by AISC-360 gives a higher capacity value than curve b,c
and d provided by EC3. With a very limited use for design purposes, curve a0, is the only curve which gives
higher capacities compared to the single AAISC-360 curve.
Materials in EC3 and AISC-360 have very close equivalents which mechanical and chemical properties
very similar to each other. Details on this are tabulated in figure 5.1 and 5.2.
Ratio of Slenderness of AISC-360 to EC3 was very to close 1 (this number might not be the most accurate
as only one case was studied in this case, with more case studies, range small range might be concluded
rather than a fixed number). Both codes estimate ratio of slenderness the same way, thereby, for the same
characteristic load, beams designed under both codes might buckle around the same period.
-6-
11. REFERENCES
Şahin, S. (2011) ‘A comparative study of AISC-360 and EC3 strength limit states’, International Journal of
Steel Structures. Springer, 11(1), pp. 13–27. doi: 10.1007/S13296-011-1002-x.
EN 1990:2002 E, Eurocode - Basis of Structural Design, CEN, November 29, 2001
European Council Directive 89/106/EEC
Eurocodes: Frequently Asked Questions (no date). Eurocodes: Frequently Asked Questions. Available at:
http://www.standardsforhighways.co.uk/tech_info/eurocodes/faq.htm
‘ASTM International’ (2015) Wikipedia. Wikipedia. Available at:
http://en.wikipedia.org/wiki/ASTM_International (Accessed: 10 April 2015).Merritt, F. and Brockenbrough, R.
(1999) Structural Steel Designer’s Handbook. 3rd edn. United Kingdom: McGraw-Hill Publishing Co.
Roberts], B. [Compiler J. (2010) Extracts from the Structural Eurocodes for Students of Structural Design: PP
1990 2010. BSI Standards.
Duncan, C. (2005) ‘The 2005 AISC Specification for Structural Steel Buildings: An Introduction’, Structures
Congress 2005. doi: 10.1061/40753(171)162.
Naoum, S. (2012) Dissertation research and writing for construction students. 3rd edn. New York: Taylor &
Francis.
Transportation Development Centre (no date). Government of Canada; Transport Canada; Policy Group.
Available at: http://www.tc.gc.ca/tdc/summary/14000/14063e.htm (Accessed: 10 February 2015)
Chen, W. F. and Zhou, S. P. (1987) ‘Design of beam-columns using allowable stress design and load and
resistance factor design’, Engineering Structures, 9(3), pp. 201–209. doi: 10.1016/0141-0296(87)90016-2.
What are the advantages of LRFD over ASD design in Steel Structures? (no date). Bayt.com. Available at:
http://www.bayt.com/en/specialties/q/24758/what-are-the-advantages-of-lrfd-over-asd-design-in-steelstructures/ (Accessed: 26 March 2015).
Vinnakota, R. (2005) Behavior and LRFD of Steel Structures. Maidenhead: McGraw-Hill Higher Education.
Steel Construction Manual Fourteenth Edition. AISC. 2011. pp. 16.1–246. ISBN 1-56424-060-6.
McCormac, Jack C. (2008). Structural Steel Design (Google books (preview)) (4th ed.). Upper Saddle River,
NJ: Pearson Prentice Hall. ISBN 978-0-13-221816-0
Bulleit, William M. “Uncertainty in Structural Engineering”. Practice Periodical on Structural Design and
Construction. American Society of Civil Engineers (ASCE), February 2008, pp 24 –30.
Brown, D. (no date) ‘Loads and ULS Load combinations to the Eurocodes.’
Draycott, T. and Bullman, P. (2009) Structural elements design manual: working with Eurocodes.
Amsterdam: Butterworth-Heinemann.
-7-
12. APPENDIX
APPENDIX A
A1. Combination factors for Imposed and Snow Loads on a Structure

Action


Imposed Loads in buildings
Category A :Domestic and Residential
0.7
0.5
0.3
Category B: Office Areas
Category C: Congregation Areas
Category D: Shopping Areas
0.7
0.7
0.7
0.5
0.7
0.7
0.3
0.6
0.6
1
0.9
0.8
Category F: Traffic Area, Vehicle Weight<30KN
Category G: Traffic Area, 30<Vehicle Weight>160
0.7
0.7
0.7
0.5
0.6
0.3
Category H: Roofs
0.7
0
0
Snow Loads on Buildings
Altitude H≤1000m above sea level
0.5
0.2
0
0.7
0.6
0.5
0.2
0.2
0
Category E: Storage areas
Altitude H>1000m above sea level
Wind Loads on Buildings
Source; Table NA A1.1 of UK National Annex to EC0
A2: Partial Safety Factors
Limit State
ULS
SLS
Source: EC1
Partial Safety factor for Permant Actions
Gk
Partial Safety Factors for variable Actions
Qk
G = 1.35
Q
Q = 1.00
G = 1.00
-8-
APPENDIX B 1
UB 457x152x82 Design to Eurocodes
*. PROJECT
:
*. MEMBER NO =
45, ELEMENT TYPE = Beam
*. LOADCOMB NO =
1, MATERIAL NO =
1, SECTION NO =
1
*. UNIT SYSTEM : kN, m
*. SECTION PROPERTIES : Designation = UB 457x152x82
Shape
= I - Section. (Rolled)
Depth
=
0.465, Top F Width =
Web Thick =
0.011, Top F Thick =
0.154, Bot.F Width =
0.154
0.019, Bot.F Thick =
0.019
Area = 1.05000e-002, Avy = 5.92789e-003, Avz = 5.48653e-003
Ybar = 7.67500e-002, Zbar = 2.32550e-001, Qyb = 8.33135e-002, Qzb = 2.94528e-003
Wely = 1.55900e-003, Welz = 1.49000e-004, Wply = 1.80200e-003, Wplz = 2.36000e-004
Iyy = 3.62500e-004, Izz = 1.14400e-005, Iyz = 0.00000e+000
iy = 1.86000e-001, iz = 3.31000e-002
J = 8.95000e-007, Cwp = 5.70000e-007
*. DESIGN PARAMETERS FOR STRENGTH EVALUATION :
Ly = 8.00000e+000, Lz = 8.00000e+000, Lu = 8.00000e+000
Ky = 1.00000e+000, Kz = 1.00000e+000
*. MATERIAL PROPERTIES :
Fy = 3.55000e+005, Es = 2.10000e+008, MATERIAL NAME = S355
*. FORCES AND MOMENTS AT (1/2) POINT :
Axial Force
Shear Forces
Fxx = 0.00000e+000
Fyy = 0.00000e+000, Fzz = 0.00000e+000
Bending Moments My = 8.82000e+001, Mz = 0.00000e+000
End Moments
Myi = 0.00000e+000, Myj = 0.00000e+000 (for Lb)
Myi = 0.00000e+000, Myj = 0.00000e+000 (for Ly)
Mzi = 0.00000e+000, Mzj = 0.00000e+000 (for Lz)
*. Sign conventions for stress and axial force.
-9-
- Stress : Compression positive.
- Axial force: Tension positive.
======================================================================================
[[[*]]] CLASSIFY LEFT-TOP FLANGE OF SECTION (BTR).
======================================================================================
( ). Determine classification of compression outstand flanges.
[ Eurocode3:05 Table 5.2 (Sheet 2 of 3), EN 1993-1-5 ]
-. e
= SQRT( 235/fy ) = 0.81
-. b/t = BTR = 3.78
-. sigma1 = 56581.821 KPa.
-. sigma2 = 56581.821 KPa.
-. BTR < 9*e ( Class 1 : Plastic ).
======================================================================================
[[[*]]] CLASSIFY RIGHT-TOP FLANGE OF SECTION (BTR).
======================================================================================
( ). Determine classification of compression outstand flanges.
[ Eurocode3:05 Table 5.2 (Sheet 2 of 3), EN 1993-1-5 ]
-. e
= SQRT( 235/fy ) = 0.81
-. b/t = BTR = 3.78
-. sigma1 = 56581.821 KPa.
-. sigma2 = 56581.821 KPa.
-. BTR < 9*e ( Class 1 : Plastic ).
======================================================================================
[[[*]]] CLASSIFY LEFT-BOTTOM FLANGE OF SECTION (BTR).
======================================================================================
( ). Determine classification of tension outstand flanges.
-. Not Checking the Section Classification.
======================================================================================
[[[*]]] CLASSIFY RIGHT-BOTTOM FLANGE OF SECTION (BTR).
======================================================================================
- 10 -
( ). Determine classification of tension outstand flanges.
-. Not Checking the Section Classification.
======================================================================================
[[[*]]] CLASSIFY WEB OF SECTION (HTR).
======================================================================================
( ). Determine Classification of bending Internal Parts.
[ Eurocode3:05 Table 5.2 (Sheet 1 of 3), EN 1993-1-5 ]
-. e
= SQRT( 235/fy ) = 0.81
-. d/t = HTR = 39.93
-. sigma1 = 51983.255 KPa.
-. sigma2 = -51983.255 KPa.
-. HTR < 72*e ( Class 1 : Plastic ).
======================================================================================
[[[*]]] APPLIED FACTORS.
======================================================================================
( ). Partial Factors (Gamma_Mi).
[ Eurocode3:05 6.1 ]
-. Gamma_M0 = 1.00
-. Gamma_M1 = 1.10
-. Gamma_M2 = 1.25
======================================================================================
[[[*]]] CHECK AXIAL RESISTANCE.
======================================================================================
( ). Check slenderness ratio of axial tension member (l/i).
[ Eurocode3:05 6.3.1 ]
-. l/i = 241.7 < 300.0 ---> O.K.
( ). Calculate parameters for combined resistance.
-. Lambda1 = Pi * SQRT(Es/fy) = 76.409
-. Lambda_bz = (KLz/iz) / Lambda1 = 3.163
( ). Calculate axial tensile resistance (Nt_Rd).
- 11 -
[ Eurocode3:05 6.2.3 ]
-. Nt_Rd = fy * Area / Gamma_M0 =
3727.50 kN.
( ). Check ratio of axial resistance (N_Ed/Nt_Rd).
N_Ed
0.00
-. ----- = --------------- = 0.000 < 1.000 ---> O.K.
Nt_Rd
3727.50
====================================================================================
[[[*]]] CHECK SHEAR RESISTANCE.
======================================================================================
( ). Calculate shear area.
[ Eurocode3:05 6.2.6, EN1993-1-5:04 5.1 NOTE 2 ]
-. eta = 1.2 (Fy < 460 MPa.)
-. r
= 0.0000 m.
-. Avy = Area - hw*tw
=
0.0059 m^2.
-. Avz1 = eta*hw*tw
=
0.0055 m^2.
-. Avz2 = Area - 2*B*tf + (tw + 2*r)*tf =
-. Avz = MAX[ Avz1, Avz2 ]
=
0.0049 m^2.
0.0055 m^2.
( ). Calculate plastic shear resistance in local-z direction (Vpl_Rdz).
[ Eurocode3:05 6.1, 6.2.6 ]
-. Vpl_Rdz = [ Avz*fy/SQRT(3) ] / Gamma_M0 =
( ). Shear Buckling Check.
[ Eurocode3:05 6.2.6 ]
-. HTR < 72*e/Eta ---> No need to check!
( ). Check ratio of shear resistance (V_Edz/Vpl_Rdz).
( LCB = 1, POS = J )
-. Applied shear force : V_Edz =
44.10 kN.
- 12 -
1124.52 kN.
V_Edz
44.10
-. ------- = --------------- = 0.039 < 1.000 ---> O.K.
Vpl_Rdz
1124.52
======================================================================================
[[[*]]] CHECK BENDING MOMENT RESISTANCE ABOUT MAJOR AXIS.
======================================================================================
( ). Calculate plastic resistance moment about major axis.
[ Eurocode3:05 6.1, 6.2.5 ]
-. Wply
=
-. Mc_Rdy =
0.0018 m^3.
Wply * fy / Gamma_M0 =
639.71 kN-m.
( ). Check ratio of moment resistance (M_Edy/Mc_Rdy).
M_Edy
88.20
-. ------ = --------------- = 0.138 < 1.000 ---> O.K.
Mc_Rdy
639.71
======================================================================================
[[[*]]] CHECK BENDING MOMENT RESISTANCE ABOUT MINOR AXIS.
======================================================================================
( ). Calculate plastic resistance moment about minor axis.
[ Eurocode3:05 6.1, 6.2.5 ]
-. Wplz
=
0.0002 m^3.
-. Mc_Rdz = Wplz * fy / Gamma_M0 =
83.78 kN-m.
( ). Check ratio of moment resistance (M_Edz/Mc_Rdz).
M_Edz
0.00
-. ------ = --------------- = 0.000 < 1.000 ---> O.K.
Mc_Rdz
83.78
======================================================================================
[[[*]]] CHECK LATERAL-TORSIONAL BUCKLING RESISTANCE.
======================================================================================
( ). Calculate lateral-torsional buckling resistance (Mb_Rd).
- 13 -
[ Eurocode3:05 6.1, 6.3.2 ]
-. Por
= 0.300
-. Gs
= Es / [ 2*(1+Por) ] =80769230.769 KPa.
-. Ncr
= Pi^2*Es*Izz / Lu^2 =
-. psi
= 0.000
-. C1
= 1.132
-. Mcr
370.48 kN.
= C1 * Ncr * SQRT [ (Cwp/Izz) + (Gs*Ixx)/Ncr ] =
207.56 kN-m.
-. Lambda_LT_bar = SQRT [ Wply*fy / Mcr ] = 1.756
-. Lambda_LT_bar0 = 0.200
-. Lambda_LT_bar = 1.756 > Lambda_LT_bar0 = 0.200
-. M_Ed/Mcr
= 0.425 > Lambda_LT_bar0^2 = 0.040
If Lambda_LT_bar > Lambda_LT_bar0 and M_Ed/Mcr > Lambda_LT_bar0^2,
Allowance for lateral-torsional buckling necessary.
-. Alpha_LT = 0.340
-. Phi_LT = 0.5 * { 1+Alpha_LT*(Lambda_LT_bar-0.2) + Lambda_LT_bar^2 } = 2.305
-. Xi_LT
= MIN [ 1 / {Phi_LT + SQRT(Phi_LT^2 - Lambda_LT_bar^2)}, 1.0 ] = 0.263
-. Mb_Rd
= Xi_LT*Wply*fy / Gamma_M1 =
153.05 kN-m.
( ). Check ratio of lateral-torsional buckling resistance (M_Edy/Mb_Rdy).
M_Edy
88.20
-. -------- = --------------- = 0.576 < 1.000 ---> O.K.
Mb_Rdy
153.05
======================================================================================
[[[*]]] CHECK INTERACTION OF COMBINED RESISTANCE.
======================================================================================
( ). Calculate Major reduced design resistance of bending and shear.
[ Eurocode3:05 6.2.8 (6.30) ]
-. In case of V_Edz / Vpl_Rdz < 0.5
-. My_Rd = Mc_Rdy =
639.71 kN-m.
( ). Calculate Minor reduced design resistance of bending and shear.
[ Eurocode3:05 6.2.8 (6.30) ]
- 14 -
-. In case of V_Edy / Vpl_Rdy < 0.5
-. Mz_Rd = Mc_Rdz =
83.78 kN-m.
( ). Check general interaction ratio.
[ Eurocode3:05 6.2.1 (6.2) ] - Class1 or Class2
N_Ed
M_Edy
M_Edz
-. Rmax1 = ------ + ------- + ------N_Rd
My_Rd
Mz_Rd
= 0.138 < 1.000 ---> O.K.
( ). Check interaction ratio of bending and axial force member.
[ Eurocode3:05 6.2.9 (6.31 ~ 6.41) ] - Class1 or Class2
-. n
= N_Ed / Npl_Rd = 0.000
-. a
= MIN[ (Area-2b*tf)/Area, 0.5 ] = 0.447
-. Alpha = 2.000
-. Beta = MAX[ 5*n, 1.0 ] = 1.000
-. N_Ed < 0.25*Npl_Rd
=
931.88 kN.
-. N_Ed < 0.5*hw*tw*fy/Gamma_M0 =
811.55 kN.
Therefore, No allowance for the effect of axial force.
-. Mny_Rd = Mply_Rd
=
639.71 kN-m.
-. Rmaxy = M_Edy / Mny_Rd = 0.138 < 1.000 ---> O.K.
-. N_Ed < hw*tw*fy/Gamma_M0 =
2866.97 kN.
Therefore, No allowance for the effect of axial force.
-. Mnz_Rd = Mplz_Rd
=
83.78 kN-m.
-. Rmaxz = M_Edz / Mnz_Rd = 0.000 < 1.000 ---> O.K.
-. Rmax2 = MAX[ Rmaxy, Rmaxz ] = 0.138 < 1.000 ---> O.K.
-. Rmax = MAX[ Rmax1, Rmax2 ] = 0.138 < 1.000 ---> O.K.
- 15 -
APPENDIX B2
WIDE Flange W24x62 Beam Design to AISC-360
PROJECT
:
*. MEMBER NO =
*. LOADCOMB NO =
45, ELEMENT TYPE = Beam
1, MATERIAL NO =
2, SECTION NO =
2
*. UNIT SYSTEM : kN, m
*. SECTION PROPERTIES : Designation = W24x62
Shape
= I - Section. (Rolled)
Depth
=
Web Thick =
0.603, Top F Width =
0.011, Top F Thick =
0.179, Bot.F Width =
0.179
0.015, Bot.F Thick =
0.015
Area = 1.17419e-002, Asy = 3.57298e-003, Asz = 6.58592e-003
Ybar = 8.94080e-002, Zbar = 3.01498e-001, Qyb = 1.13179e-001, Qzb = 3.99690e-003
Syy = 2.14671e-003, Szz = 1.60593e-004, Zyy = 2.50722e-003, Zzz = 2.57277e-004
Iyy = 6.45159e-004, Izz = 1.43600e-005, Iyz = 0.00000e+000
ry = 2.34442e-001, rz = 3.50520e-002
J = 7.11756e-007, Cwp = 1.23442e-006
*. DESIGN PARAMETERS FOR STRENGTH EVALUATION :
Ly = 8.00000e+000, Lz = 8.00000e+000, Lu = 8.00000e+000
Ky = 1.00000e+000, Kz = 1.00000e+000
*. MATERIAL PROPERTIES :
Fy = 3.44738e+005, Es = 1.99948e+008, MATERIAL NAME = A572-50
======================================================================================
[[[*]]] COMPUTE MOMENT MAGNIFICATION FACTORS AND MAGNIFIED MOMENTS.
======================================================================================
( ). Compute moment magnification factors(B1y,B1z).
-. If tension or bending member.
-. Assumed B1y = 1.00
-. Assumed B1z = 1.00
( ). Magnification factors for sidesway moments(B2y,B2z).
-. B2y = 1.00 (Default value)
-. B2z = 1.00 (Default value)
- 16 -
( ). Given factored axial forces and moments at <1/2>.
---------------------------------------------------------------Load Case
Pu
My
Mz
---------------------------------------------------------------DL
0.00
18.00
0.00
LL
0.00
25.20
0.00
DL+LL
0.00
WL or EL
43.20
0.00
0.00
45.00
0.00
---------------------------------------------------------------DL+LL+WL(EL)
0.00
88.20
0.00
---------------------------------------------------------------( ). Compute magnified moments.
-. Muy = B1y*My(DL+LL) + B2y*My(WL(EL)) =
88.20 kN-m.
-. Muz = B1z*Mz(DL+LL) + B2z*Mz(WL(EL)) =
0.00 kN-m.
( ). Factored max. shear forces.
-. Vuy =
0.00 kN.
-. Vuz =
0.00 kN.
======================================================================================
[[[*]]] CHECK AXIAL STRENGTH.
======================================================================================
( ). Check slenderness ratio of axial tension member (l/r).
[ AISC-LRFD2K Specification B7. ]
-. l/r = 228.2 < 300.0 ---> O.K.
======================================================================================
[[[*]]] CHECK FLEXURAL STRENGTH ABOUT MAJOR AXIS.
======================================================================================
( ). Compute plastic bending moment (Mp).
[ AISC-LRFD2K Specification F1.1. (F1-1) ]
-. Mp = MIN[ Fy*Zyy, 1.5*Fy*Syy ] =
864.33 kN-m.
( ). Compute limiting buckling moment (Mr).
[ AISC-LRFD2K Specification F1.1. (F1-7) ]
- For rolled shapes : Fr
= 10.0 ksi.
- 17 -
Fo = MIN[ Fyw, Fyf-Fr ] = 275790.3776 KPa.
-. Mr = Fo*Syy
=
592.04 kN-m.
-------------------------------------------------------------------------[*] Check Web Local Buckling (WLB).
-------------------------------------------------------------------------( ). Calculate limiting width-thickness ratios for WLB.
[ AISC-LRFD2K Specification B5.1 ]
-. Pu > 0. ---> Webs in flexural tension.
-. Lambda_p(Lp) = 3.76*SQRT[Es/Fy]
= 90.55
-. For equal flanges with flexure only
-. Lambda_r(Lr) = 5.70*SQRT[Es/Fy]
= 137.27
( ). Check width-thickness ratio of web (DTR).
[ AISC-LRFD2K Specification B5.1 ]
-. DTR = hc/tw = 52.47 < Lambda_p ---> COMPACT.
( ). Compute nominal flexural strength (Mn3).
[ AISC-LRFD2K Specification Appendix F1. (A-F1-1) ]
-. Mn3 = Mp =
864.33
-------------------------------------------------------------------------[*] Check Lateral-Torsional Buckling (LTB).
-------------------------------------------------------------------------( ). Compute limiting laterally unbrace length for plastic analysis (Lpd).
[ AISC-LRFD2K Specification F1.2d. (F1-17) ]
*. For moments cause single curvature (M1/M2 < 0).
-. M1 = MIN( |Myy_i|, |Myy_j| ) =
0.00 kN-m.
-. M2 = MAX( |Myy_i|, |Myy_j| ) =
0.00 kN-m.
[ 0.12+0.076(M1/M2) ]*Es*rz
-. Lpd = --------------------------- = 0.895 m.
Fy
( ). Compute limiting laterally unbrace length for full plastic bending
capacity (Lp).
- 18 -
[ AISC-LRFD2K Specification F1.2a. (F1-4) ]
1.76*rz
-. Lp = ------------ = 1.486 m.
SQRT[Fyf/Es]
( ). Compute limiting laterally unbraced length for inelastic lateraltorsional buckling (Lr).
[ AISC-LRFD2K Specification F1.2a. (F1-6)~(F1-9) ]
-. Gs = Es/(2(1+Poisson Ratio)) = 7.6903e+007 KPa.
-. FL = MIN[ Fyf-Fr, Fyw ] = 275790.3776 KPa.
pi
[ Es*Gs*J*Area ]
-. X1 = ----- SQRT[ -------------- ] = 1.1731e+007 KPa.
Syy
[
2
]
Cwp [ Syy ]^2
-. X2 = 4 ----- [ ----- ] =5.28889e-010 m^4/kN^2.
Izz [ Gs*J ]
-. X3 = SQRT{ 1 + SQRT[1+X2*FL^2] } = 2.72413
rz*X1
-. Lr = -------- X3 = 4.062 m.
FL
( ). Check laterally unbraced length (Lu).
[ AISC-LRFD2K Specification F1. ]
-. Lu = 8.000 m. > Lr (F1-6).
( ). Calculate bending coefficient (Cb).
[ AISC-LRFD2K Specification F1.2a. (F1-3) ]
-. Cb
= 1.000 (User defined or default value)
( ). Compute elastic buckling moment (Mcr)
[ AISC-LRFD2K Specification F1.2b. (F1-13) ]
-. Y1 = Cb*pi/Lu
-. Y2 = Es*Izz*Gs*J
=
0.39270 m^(-1).
= 157161.37596 kN^2-m^4.
-. Y3 = Izz*Cwp*[pi*Es/Lu]^2 = 109287.62171 kN^2-m^4.
-. Mcr = Y1*SQRT[ Y2+Y3 ]
=
202.71 kN-m.
( ). Compute nominal flexural strength (Mn1)
- 19 -
[ AISC-LRFD2K Specification F1.2b. (F1-12) ]
-. Mn1 = MIN[ Mcr, Mp ] =
202.71 kN-m.
-------------------------------------------------------------------------[*] Check Flange Local Buckling (FLB).
-------------------------------------------------------------------------( ). Calculate limiting width-thickness ratios for FLB.
[ AISC-LRFD2K Specification B5.1 ]
-. For Rolled Shapes
-. Lambda_p(Lp) = 0.38*SQRT[Es/Fy]
= 9.15
-. Lambda_r(Lr) = 0.83*SQRT[Es/(Fy-10)] = 22.35
( ). Check width-thickness ratio of flange (BTR).
[ AISC-LRFD2K Specification B5.1 ]
-. BTR = bf/2tf = 5.97 < Lambda_p ---> COMPACT.
( ). Compute nominal flexural strength (Mn2).
[ AISC-LRFD2K Specification Appendix F1. (A-F1-1) ]
-. Mn2 = Mp =
864.33 kN-m.
( ). Compute flexural strength about major axis (phiMny).
[ AISC-LRFD2K Specification F1.2. ]
-. Mny = MIN[ Mn1, Mn2, Mn3 ] =
202.71 kN-m.
-. Resistance factor for flexure : phi = 0.90
-. phiMny = phi*Mny =
182.44 kN-m.
( ). Check ratio of flexural strength (Muy/phiMny).
Muy
88.20
-. -------- = --------------- = 0.483 < 1.000 ---> O.K.
phiMny
182.44
======================================================================================
[[[*]]] CHECK INTERACTION OF COMBINED STRENGTH.
======================================================================================
( ). Check interaction ratio of combined strength.
[ AISC-LRFD2K Specification H1.1. ]
-. Pu/phiPn < 0.20 ---> Formula(H1-1b)
Pu
[ Muy
Muz ]
- 20 -
-. ComRat = --------- + [ -------- + -------- ]
2*phiPn [ phiMny
phiMnz ]
= 0.000 + [ 0.483 + 0.000 ]
= 0.483 < 1.000 ---> O.K.
======================================================================================
[[[*]]] CHECK SHEAR STRENGTH.
======================================================================================
( ). Check depth-thickness ratio of web (DTRw).
[ AISC-LRFD2K Specification Appendix F2.2. ]
-. Assumed kv = 5
-. Lambda_r = 1.10*SQRT[kv*Es/Fyw] = 59.24
-. DTRw = hc/tw = 52.47 < Lambda_r
( ). Calculate shear strength in local-z direction (phiVnz).
[ AISC-LRFD2K Specification Appendix F2.2. (A-F2-1) ]
-. Resistance factor for shear : phi = 0.90
-. Vn = 0.6*Fyw*Asz =
-. phiVnz = phi*Vn =
1362.25 kN.
1226.03 kN.
( ). Check ratio of shear strength (Vu/phiVn).
( LCB = 1, POS = J )
-. Applied shear force : Vuz =
Vuz
44.10 kN.
44.10
-. -------- = --------------- = 0.036 < 1.000 ---> O.K.
phiVnz
1226.03
- 21 -
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