STAAD.Pro EN 1993-1-1:2005 Implementation: Elastic Verification of Cross Sectional Resistance

STAAD.Pro EN 1993-1-1:2005 Implementation: Elastic Verification of Cross Sectional Resistance

STAAD.Pro EN 1993-1-1:2005 Implementation: Elastic Verification of Cross Sectional Resistance:

Introduction:

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 thorough 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 dealt
with 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 SPACE
START JOB INFORMATION
ENGINEER DATE 26-Oct-11
END JOB INFORMATION
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 3 0 0;
MEMBER INCIDENCES
1 1 2;
DEFINE MATERIAL START
ISOTROPIC STEEL
E 2.05e+008
POISSON 0.3
DENSITY 76.8195
ALPHA 1.2e-005
DAMP 0.03
TYPE STEEL
STRENGTH FY 253200 FU 407800 RY 1.5 RT 1.2
END DEFINE MATERIAL
MEMBER PROPERTY EUROPEAN
1 TABLE ST IPE100
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 2 PINNED
DEFINE REFERENCE LOADS
LOAD R1 LOADTYPE None  TITLE Dead Load
SELFWEIGHT Y -1 LIST ALL
LOAD R2 LOADTYPE None  TITLE Live Load
MEMBER LOAD
1 UNI GY -5
END DEFINE REFERENCE LOADS
LOAD 1 LOADTYPE None  TITLE Dead Load + Live Load
REFERECE LOAD
R1 1.35 R2 1.5
PERFORM ANALYSIS
PARAMETER 1
CODE EN 1993-1-1:2005
UNL 1 ALL
GM2 1.1 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH

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 ran, 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 1
CODE EN 1993-1-1:2005
UNL 1 ALL
GM2 1.1 ALL
TRACK 2 ALL
TOR 1 ALL
CHECK 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 inthiscase.

Afurthernoteontheinteractionchecks:

Asafurthernotetotheinteractionchecks,theEN1993-1-1:2005codepermitsinclause6.2.1(7)aconservativeformoftheinteractionequation(Equation6.2)formembersofclass1,2or3whichissubjectedtoacombinationofaxialandbendingforcesasbelow.

STAAD.ProImplementationofEquation6.2:

STAADusesequation6.2tocheckforthecrosssectionalinteractionofsectionsclassifiedas1,2and3asanalternativetochecksforclause6.2.9.1(class1andclass2)and6.2.9.2(class3).Theclauses6.2.9areinvokedforthecrosssectionalinteractionchecksbydefault.Ifonewishestoinvoketheconservativechecksperequation6.2–clause6.2.1(7),hewillneedtospecifytheELBparameteras1.ThedefaultvalueofELBis0,whichinvokesclause6.2.9checks.

ExampleontheuseoftheELBparameter:

Thefollowingisthegeometry,analysisanddesigninputofacolumnthatcarries500tonsofaxialloadand20ton-metremomentabouttheminoraxisand50ton-metermomentaboutthemajoraxis.Thecolumnheightis5metresandhaveasectionofUC356X406X634.

STAADSPACE
STARTJOBINFORMATION
ENGINEERDATE26-Oct-11
ENDJOBINFORMATION
INPUTWIDTH79
UNITMETERKN
JOINTCOORDINATES
1000;2050;
MEMBERINCIDENCES
112;
DEFINEMATERIALSTART
ISOTROPICSTEEL
E2.05e+008
POISSON0.3
DENSITY76.8195
ALPHA1.2e-005
DAMP0.03
TYPESTEEL
STRENGTHFY253200FU407800RY1.5RT1.2
ENDDEFINEMATERIAL
MEMBERPROPERTYBRITISH
1TABLESTUC356X406X634
CONSTANTS
MATERIALSTEELALL
SUPPORTS
1FIXED
LOAD1LOADTYPENone  TITLEFactoredDeadLoadandLiveLoad
JOINTLOAD
2FY-5000MX200MZ500
PERFORMANALYSIS
PARAMETER1
CODEEN1993-1-1:2005
TRACK2ALL
CHECKCODEALL
FINISH

IfyouruntheSTAADinputfile,youwillhavethefollowingdatafromtheoutputfile:

   DESIGNDATA(units-kN,m)   EUROCODENO.3/2005
      SectionClass            :   CLASS1
      SquashLoad              :  17372.00
      Axialforce/Squashload  :     0.288
      GM0:  1.00          GM1:  1.00          GM2:  1.25

So,thesectionisclassifiedasClass1.So,withouttheexistenceoftheELBparameterintheparameterblock,thedefaultvalueofELBwillbeinvokedwhichis0,andthus–asthesectionissubjectedtocombinedaxialandbending,itwillbeexpectedthatclause6.2.9.1tobeinvoked.  Lookingatthesummaryofthecodecheckintrack2output,wegetthefollowing.

Theseconditeminthelistofthecodechecksshowsthatclause6.2.9.1hasbeenchecked.

Now,letuschangetheparameterblocktoincludetheELBparameterandspecifyitas1.

PARAMETER1
CODEEN1993-1-1:2005
TRACK2ALL
ELB1ALL
CHECKCODEALL

Itwillbeexpectedthatthemoreconservativechecktoequation6.2–clause6.2.1(7)willbeinvokedinlieuofclause6.2.9.1.

Lookingatthesummaryofcodecheckedclauseswhenthefileisrunaftermakingtheabovementionedchanges,thefollowingisobserved.

CRITICALLOADSFOREACHCLAUSECHECK(units-kN,m):
 
    CLAUSE        RATIO  LOAD     FX       VY      VZ      MZ      MY
   EC-6.3.1.1       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-6.3.2LTB   0.164    1        5000.0     0.0     0.0   -500.0   200.0
    Torsionanddeflectionshavenotbeenconsideredinthedesign.

Theseconditeminthelistindicatesthatclause6.2.1(7)iscodecheckednow,whenELB1hasbeenspecified.

References:

1.EN1993-1-1:2005,DesignofSteelStructures-GeneralRulesandRulesforBuildings

2.Designer'sGuidetoEurocode3:DesignofSteelBuildingsEN1993-1-1,-1-3and-1-8,2ndEdition,L.GardnerandD.A.Nethercot,ICEPublishing

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