V. EC3 French NA - I Section with Conc Load
Calculate the bending capacity of a beam subject to a concentrated load per the French NA to EC3.
Details
The section is a HD320X127, Grade S275 steel. The member is a 5 m, simply-supported span subject to a 30 kN concentrated load at midpsan.
Validation
The critical moment is given by:
where= | ||
= | ||
= | ||
= | ||
= | ||
= |
Therefore, Mcr = 1,416 kN·m
From the French NA, λLT, 0 = 0.2 + 0.1 ×b / h = 0.2 + 0.1 × 300 / 327 = 0.292, β = 1.0
So,
H/b = 320/300 = 1.067 < 2
αLT = 0.4 - 0.2 ×b / h × λLT2 = 0.4 - 0.2 ×300 / 327 × 0.6462 = 0.324
From Cl. 6.3.2.3 of Eurocode3:
ФLT = 0.5[1+αLT (λLT- λLT, 0) + β× λLT2] = 0.5[1 + 0.324×(0.646 - 0.292) +1 × 0.6462] = 0.766
So,
STAAD.Pro Input
The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\Europe\EC3 National Annex\French NA\EC3 French NA-I Section with Conc Load.std is typically installed with the program.
The following design parameters are used:
- The French NA is specified using NA 4
- Simply-supported span: CMN 1
- Simply-supported span with concentrated load at midspan: CMM 3
STAAD PLANE
START JOB INFORMATION
ENGINEER DATE 21-June-20
END JOB INFORMATION
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 5 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
END DEFINE MATERIAL
MEMBER PROPERTY EUROPEAN
1 TABLE ST HD320X127
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 2 PINNED
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
MEMBER LOAD
1 CON GY -30
PERFORM ANALYSIS
PARAMETER 1
CODE EN 1993-1-1:2005
NA 4
CMM 3 ALL
CMN 1 ALL
FU 295000 ALL
PY 275000 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH
STAAD.Pro Output
PAGE NO. 1 **************************************************** * * * STAAD.Pro CONNECT Edition * * Version 22.05.00.** * * Proprietary Program of * * Bentley Systems, Inc. * * Date= AUG 14, 2020 * * Time= 9: 1:39 * * * * Licensed to: Bentley Systems Inc * **************************************************** 1. STAAD PLANE INPUT FILE: EC3 French NA-I Section with Conc Load.STD 2. START JOB INFORMATION 3. ENGINEER DATE 21-JUNE-20 4. END JOB INFORMATION 5. INPUT WIDTH 79 6. UNIT METER KN 7. JOINT COORDINATES 8. 1 0 0 0; 2 5 0 0 9. MEMBER INCIDENCES 10. 1 1 2 11. DEFINE MATERIAL START 12. ISOTROPIC STEEL 13. E 2.05E+008 14. POISSON 0.3 15. DENSITY 76.8195 16. ALPHA 1.2E-005 17. DAMP 0.03 18. END DEFINE MATERIAL 19. MEMBER PROPERTY EUROPEAN 20. 1 TABLE ST HD320X127 21. CONSTANTS 22. MATERIAL STEEL ALL 23. SUPPORTS 24. 1 2 PINNED 25. LOAD 1 LOADTYPE NONE TITLE LOAD CASE 1 26. MEMBER LOAD 27. 1 CON GY -30 28. PERFORM ANALYSIS STAAD PLANE -- PAGE NO. 2 P R O B L E M S T A T I S T I C S ----------------------------------- NUMBER OF JOINTS 2 NUMBER OF MEMBERS 1 NUMBER OF PLATES 0 NUMBER OF SOLIDS 0 NUMBER OF SURFACES 0 NUMBER OF SUPPORTS 2 Using 64-bit analysis engine. SOLVER USED IS THE IN-CORE ADVANCED MATH SOLVER TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 2 TOTAL LOAD COMBINATION CASES = 0 SO FAR. 29. PARAMETER 1 30. CODE EN 1993-1-1:2005 31. NA 4 32. CMM 3 ALL 33. CMN 1 ALL 34. FU 295000 ALL 35. PY 275000 ALL 36. TRACK 2 ALL 37. CHECK CODE ALL STEEL DESIGN STAAD.PRO CODE CHECKING - NF EN 1993-1-1:2005 ******************************************** NATIONAL ANNEX - NF EN 1993-1-1/NA PROGRAM CODE REVISION V1.13 BS_EC3_2005/1 STAAD PLANE -- PAGE NO. 3 ALL UNITS ARE - KN METE (UNLESS OTHERWISE Noted) MEMBER TABLE RESULT/ CRITICAL COND/ RATIO/ LOADING/ FX MY MZ LOCATION ======================================================================= 1 ST HD320X127 (EUROPEAN SECTIONS) PASS EC-6.3.2 LTB 0.075 1 0.00 0.00 -37.50 2.50 ======================================================================= MATERIAL DATA Grade of steel = USER Modulus of elasticity = 205 kN/mm2 Design Strength (py) = 275 N/mm2 SECTION PROPERTIES (units - cm) Member Length = 500.00 Gross Area = 161.30 Net Area = 161.30 z-axis y-axis Moment of inertia : 30820.004 9239.001 Plastic modulus : 2149.000 939.100 Elastic modulus : 1926.250 615.933 Shear Area : 81.998 51.728 Radius of gyration : 13.823 7.568 Effective Length : 500.000 500.000 DESIGN DATA (units - kN,m) EUROCODE NO.3 /2005 Section Class : CLASS 1 Squash Load : 4435.75 Axial force/Squash load : 0.000 GM0 : 1.00 GM1 : 1.00 GM2 : 1.25 z-axis y-axis Slenderness ratio (KL/r) : 36.2 66.1 Compression Capacity : 4078.2 3045.5 Tension Capacity : 3426.0 3426.0 Moment Capacity : 591.0 258.3 Reduced Moment Capacity : 591.0 258.3 Shear Capacity : 1301.9 821.3 BUCKLING CALCULATIONS (units - kN,m) Lateral Torsional Buckling Moment MB = 502.6 co-efficients C1 & K : C1 =1.350 K =1.0, Effective Length= 5.000 Lateral Torsional Buckling Curve : Elastic Critical Moment for LTB, Mcr = 1416.0 Compression buckling curves: z-z: Curve b y-y: Curve c Critical Load For Torsional Buckling, NcrT = 13898.0 Critical Load For Torsional-Flexural Buckling, NcrTF = 13898.0 STAAD PLANE -- PAGE NO. 4 ALL UNITS ARE - KN METE (UNLESS OTHERWISE Noted) MEMBER TABLE RESULT/ CRITICAL COND/ RATIO/ LOADING/ FX MY MZ LOCATION ======================================================================= CRITICAL LOADS FOR EACH CLAUSE CHECK (units- kN,m): CLAUSE RATIO LOAD FX VY VZ MZ MY EC-6.2.5 0.063 1 0.0 15.0 0.0 -37.5 0.0 EC-6.2.6-(Y) 0.018 1 0.0 15.0 0.0 0.0 0.0 EC-6.3.2 LTB 0.075 1 0.0 15.0 0.0 -37.5 0.0 Torsion and deflections have not been considered in the design. _________________________ ************** END OF TABULATED RESULT OF DESIGN ************** 38. FINISH STAAD PLANE -- PAGE NO. 5 *********** END OF THE STAAD.Pro RUN *********** **** DATE= AUG 14,2020 TIME= 9: 1:40 **** ************************************************************ * For technical assistance on STAAD.Pro, please visit * * http://www.bentley.com/en/support/ * * * * Details about additional assistance from * * Bentley and Partners can be found at program menu * * Help->Technical Support * * * * Copyright (c) 1997-2017 Bentley Systems, Inc. * * http://www.bentley.com * ************************************************************