STAAD.Pro EN 1993-1-1:2005 Implementation: Elastic Verification of Cross Sectional Resistance:
The EN 1993-1-1:2005 has very effective equations to determine the cross sectional resistance to a particular nature of force and to evaluate the safety of the sections for conditions arising due to interaction of these forces. These equations can be found in clause 6.2.3 through clause 6.2.10 of the code. One needs to determine the cross sectional classification before proceeding to use the aforementioned equations.
The interaction equations in the aforementioned clauses are especially effective because of the fact that they allow partially plastic interactions.
However, the code in the statement of clause 6.2.1(4) has allowed the elastic verification of the cross sectional resistance using a form of the famous equation representing the Von Mises yield criterion. The equation 6.1 – clause 6.2.1(5) of the code represents this form.
As mentioned by the code in clause 6.2.1(4), this equation can be used to verify the cross sectional resistance for all cross sectional classes provided effective cross sectional properties are used for class 4 sections. However, in clause 6.2.1(5) the code mentions that the above equation can be used unless other interaction equations from clause 6.2.8 through 6.2.10 apply. This means that we should use the more effective interaction equations in the aforementioned clauses if it applies.
Implementation of Elastic Verification of Cross Sectional Resistance in STAAD.Pro:
In STAAD.Pro, this equation has been implemented from the point of view of the torsional checks, because clause 6.2.7(5) optionally directs us to elastic verification as per the above equation as a part of the torsional checks. This equation check is made mandatory if torsion exists on the member as this is the only one equation that allows some sort of interaction of the torsion forces with the other existing forces on the member.
However, we can make the program check the Von Mises yield criterion irrespective of the fact of the existence or non- existence of torsion, by specifying the TOR parameter as 1. The program checks Equation 6.1 ignoring warping effects if torsion exists and if the TOR parameter is specified as 1.
The default value of the TOR parameter is 0, which means that the Von Mises yield criterion check will be invoked only in the existence of torsion. The topic of Elastic Verification of cross section during the existence of torsion is dealtwith in further details in the article STAAD.Pro EN 1993-1-1:2005 Implementation: Code Check for Torsion.
Example Model forcing the program to do the Von Misces Yield Criterion Check:
The following is the geometry, analysis and design input of a simply supported beam model of 3 metres length and having a section of IPE 100. The beam has lateral restraint to the compression flange at every one-third point along the span. The beam has selfweight as the dead load and a live load in form of a uniformly distributed load of 5 KN/m.
STAAD SPACESTART JOB INFORMATIONENGINEER DATE 26-Oct-11END JOB INFORMATIONINPUT WIDTH 79UNIT METER KNJOINT COORDINATES1 0 0 0; 2 3 0 0;MEMBER INCIDENCES1 1 2;DEFINE MATERIAL STARTISOTROPIC STEELE 2.05e+008POISSON 0.3DENSITY 76.8195ALPHA 1.2e-005DAMP 0.03TYPE STEELSTRENGTH FY 253200 FU 407800 RY 1.5 RT 1.2END DEFINE MATERIALMEMBER PROPERTY EUROPEAN1 TABLE ST IPE100CONSTANTSMATERIAL STEEL ALLSUPPORTS1 2 PINNEDDEFINE REFERENCE LOADSLOAD R1 LOADTYPE None TITLE Dead LoadSELFWEIGHT Y -1 LIST ALLLOAD R2 LOADTYPE None TITLE Live LoadMEMBER LOAD1 UNI GY -5END DEFINE REFERENCE LOADSLOAD 1 LOADTYPE None TITLE Dead Load + Live LoadREFERECE LOADR1 1.35 R2 1.5PERFORM ANALYSISPARAMETER 1CODE EN 1993-1-1:2005UNL 1 ALLGM2 1.1 ALLTRACK 2 ALLCHECK CODE ALLFINISH
As can be understood, this beam which is made up of an I section is not subjected to any torsional forces.
If one looks into the design parameters specified above, one will find that the TOR parameter has not been specified. Thus, the program will not check the yield criterion given by equation 6.1.
If the file is analyzed, the following is obtained for the summary of the clauses checked from the output file.
CRITICAL LOADS FOR EACH CLAUSE CHECK (units- kN,m): CLAUSE RATIO LOAD FX VY VZ MZ MY EC-6.2.5 0.934 1 0.0 0.0 0.0 -8.6 0.0 EC-6.2.6-(Y) 0.166 1 0.0 11.4 0.0 0.0 0.0 EC-6.3.2 LTB 1.068 1 0.0 0.0 0.0 -8.6 0.0 Torsion and deflections have not been considered in the design.
As can be seen, the program checks the bending moment clause, the shear clause and the clause to lateral torsional buckling. But it has not checked the yield criterion.
If the design parameter block is changed to the following :
PARAMETER 1CODE EN 1993-1-1:2005UNL 1 ALLGM2 1.1 ALLTRACK 2 ALLTOR 1 ALLCHECK CODE ALL
and run the file, we will obtain the following in the summary in the output file:
CRITICAL LOADS FOR EACH CLAUSE CHECK (units- kN,m): CLAUSE RATIO LOAD FX VY VZ MZ MY EC-6.2.5 0.934 1 0.0 0.0 0.0 -8.6 0.0 EC-6.2.6-(Y) 0.166 1 0.0 11.4 0.0 0.0 0.0 EC-6.3.2 LTB 1.068 1 0.0 0.0 0.0 -8.6 0.0
ADDITIONAL CLAUSE CHECKS FOR TORSION (units- kN,m): CLAUSE RATIO LOAD DIST FX VY VZ MZ MY MX EC-6.2.7(5) 1.134 1 1.5 0.0 0.0 0.0 -8.6 0.0 0.0
As can be seen, on addition of the TOR parameter and being specified as 1, the program now checks the yield criterion. The clause is mentioned as 6.2.7(5). As has been mentioned above, this clause refers back to equation 6.1. Though it is reported under the additional clause check for torsion, without the existence of torsional forces, the Von Misces Check has been done with plain longitudinal and shear stresses in this case.
A further note on the interaction checks:
As a further note to the interaction checks, the EN 1993-1-1:2005 code permits in clause 6.2.1(7) a conservative form of the interaction equation (Equation 6.2) for members of class 1, 2 or 3 which is subjected to a combination of axial and bending forces as below.
STAAD.Pro Implementation of Equation 6.2:
STAAD uses equation 6.2 to check for the cross sectional interaction of sections classified as 1, 2 and 3 as an alternative to checks for clause 126.96.36.199 (class 1 and class 2) and 188.8.131.52 (class 3). The clauses 6.2.9 are invoked for the cross sectional interaction checks by default. If one wishes to invoke the conservative checks per equation 6.2 – clause 6.2.1(7), he will need to specify the ELB parameter as 1. The default value of ELB is 0, which invokes clause 6.2.9 checks.
Example on the use of the ELB parameter:
The following is the geometry, analysis and design input of a column that carries 500 tons of axial load and 20 ton-metre moment about the minor axis and 50 ton-meter moment about the major axis. The column height is 5 metres and have a section of UC356X406X634.
STAAD SPACESTART JOB INFORMATIONENGINEER DATE 26-Oct-11END JOB INFORMATIONINPUT WIDTH 79UNIT METER KNJOINT COORDINATES1 0 0 0; 2 0 5 0;MEMBER INCIDENCES1 1 2;DEFINE MATERIAL STARTISOTROPIC STEELE 2.05e+008POISSON 0.3DENSITY 76.8195ALPHA 1.2e-005DAMP 0.03TYPE STEELSTRENGTH FY 253200 FU 407800 RY 1.5 RT 1.2END DEFINE MATERIALMEMBER PROPERTY BRITISH1 TABLE ST UC356X406X634CONSTANTSMATERIAL STEEL ALLSUPPORTS1 FIXEDLOAD 1 LOADTYPE None TITLE Factored Dead Load and Live LoadJOINT LOAD2 FY -5000 MX 200 MZ 500PERFORM ANALYSISPARAMETER 1CODE EN 1993-1-1:2005TRACK 2 ALLCHECK CODE ALLFINISH
If you run the STAAD input file, you will have the following data from the output file:
DESIGN DATA (units - kN,m) EUROCODE NO.3 /2005 Section Class : CLASS 1 Squash Load : 17372.00 Axial force/Squash load : 0.288 GM0 : 1.00 GM1 : 1.00 GM2 : 1.25
So, the section is classified as Class 1. So, without the existence of the ELB parameter in the parameter block, the default value of ELB will be invoked which is 0, and thus – as the section is subjected to combined axial and bending, it will be expected that clause 184.108.40.206 to be invoked. Looking at the summary of the code check in track 2 output, we get the following.
CRITICAL LOADS FOR EACH CLAUSE CHECK (units- kN,m): CLAUSE RATIO LOAD FX VY VZ MZ MY EC-220.127.116.11 0.333 1 5000.0 0.0 0.0 500.0 -200.0 EC-18.104.22.168 0.208 1 5000.0 0.0 0.0 -500.0 200.0 EC-6.3.3-661 0.550 1 5000.0 0.0 0.0 -500.0 200.0 EC-6.3.3-662 0.639 1 5000.0 0.0 0.0 -500.0 200.0 EC-6.3.2 LTB 0.164 1 5000.0 0.0 0.0 -500.0 200.0 Torsion and deflections have not been considered in the design.
The second item in the list of the code checks shows that clause 22.214.171.124 has been checked.
Now, let us change the parameter block to include the ELB parameter and specify it as 1.
PARAMETER 1CODE EN 1993-1-1:2005TRACK 2 ALLELB 1 ALLCHECK CODE ALL
It will be expected that the more conservative check to equation 6.2 – clause 6.2.1(7) will be invoked in lieu of clause 126.96.36.199.
Looking at the summary of code checked clauses when the file is run after making the above mentioned changes, the following is observed.
CRITICAL LOADS FOR EACH CLAUSE CHECK (units- kN,m): CLAUSE RATIO LOAD FX VY VZ MZ MY EC-188.8.131.52 0.333 1 5000.0 0.0 0.0 500.0 -200.0 EC-6.2.1(7) 0.582 1 5000.0 0.0 0.0 -500.0 200.0 EC-6.3.3-661 0.550 1 5000.0 0.0 0.0 -500.0 200.0 EC-6.3.3-662 0.639 1 5000.0 0.0 0.0 -500.0 200.0 EC-6.3.2 LTB 0.164 1 5000.0 0.0 0.0 -500.0 200.0 Torsion and deflections have not been considered in the design.
The second item in the list indicates that clause 6.2.1(7) is code checked now, when ELB 1 has been specified.
1. EN 1993-1-1:2005, Design of Steel Structures - General Rules and Rules for Buildings
2. Designer's Guide to Eurocode 3: Design of Steel Buildings EN 1993-1-1, -1-3 and -1-8, 2nd Edition, L. Gardner and D. A. Nethercot, ICE Publishing