V. EC3 Belgian NA - I Section with UDL
Calculate the bending capacity of a beam using an I section subject to a uniformly distributed load per the Belgian NA to EC3.
Details
The section is a HD320X127, Grade S275 steel. The member is a 5 m, fixed-fixed span subject to a 10 kN/m uniform load.
Validation
The critical moment is given by:
where= | ||
= | ||
= | ||
= | ||
= | ||
= | ||
= |
Therefore, Mcr = 1,712 kN·m
From the Belgian NA, λLT, 0 = 0.2, β = 1.0
So,
H/b = 320/300 = 1.067 < 2. So, from Table 6.5 of Eurocode 3, αLT = 0.34.
From Cl. 6.3.2.3 of Eurocode3:
ФLT = 0.5[1+αLT (λLT- λLT, 0) + β× λLT2] = 0.5[1 + 0.34×(0.589 - 0.2) +1 × 0.5882] = 0.739
So,
From Table 6.6 of the Eurocode 3, kc = 0.9
Modification factor:
, OK
If Cl. 6.3.2.2 is used to determine χLT:
H/b = 320/300 = 1.067 < 2. So, from Table 6.3 of Eurocode 3, αLT = 0.21.
ФLT = 0.5[1+αLT (λLT- 0.2) + λLT2] = 0.5[1+0.21×(0.588 - 0.2) +1×0.5882] = 0.713
Results
Result Type | Reference | STAAD.Pro | Difference | Comments |
---|---|---|---|---|
Moment capacity, Mckd (kN·m) | 591.0 | 591.0 | none | |
Critical moment, Mcr (kN·m) | 1,712 | 1,712.9 | negligible | |
Bending capacity, MB (kN·m) | 521.8 | 522.1 | negligible | |
Bending capacity, MB (kN·m) | 528.9 | 528.8 | negligible |
STAAD.Pro Input
The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\Europe\EC3 Belgian NA - I Section with UDL.std is typically installed with the program.
The following design parameters are used:
- The Belgian NA is specified using NA 8
- Fully fixed span: CMN 0.5
- Uniformly distributed load w/ fixed-fixed supports: CMM 2
- The value of C2 1.554 is specified
- The parameter KC instructs the program to calculate the value of kc
- A second design parameter set is used with MTH 1 to use Cl 6.3.2.2 to determine ФLT
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 14-Apr-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+08
POISSON 0.3
DENSITY 76.8195
ALPHA 1.2e-05
DAMP 0.03
END DEFINE MATERIAL
MEMBER PROPERTY EUROPEAN
1 TABLE ST HD320X127
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 2 FIXED
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
MEMBER LOAD
1 UNI GY -10
PERFORM ANALYSIS
PARAMETER 1
CODE EN 1993-1-1:2005
NA 8
C2 1.554 ALL
CMM 2 ALL
CMN 0.5 ALL
PY 275000 ALL
KC 0 ALL
TRACK 2 ALL
CHECK CODE ALL
PARAMETER 2
CODE EN 1993-1-1:2005
NA 8
MTH 1 ALL
CHECK CODE ALL
FINISH
STAAD.Pro Output
STAAD.PRO CODE CHECKING - NBN EN 1993-1-1:2005 ******************************************** NATIONAL ANNEX - NBN EN 1993-1-1 ANB : 2018 PROGRAM CODE REVISION V1.13 BS_EC3_2005/1 STAAD SPACE -- 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 0.040 1 0.00 0.00 20.83 0.00 ======================================================================= 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 : 4180.9 4180.9 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 = 522.1 co-efficients C1 & K : C1 =2.578 K =0.5, Effective Length= 5.000 Lateral Torsional Buckling Curve : Curve b Elastic Critical Moment for LTB, Mcr = 1712.9 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 SPACE -- 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 0.035 1 0.0 25.0 0.0 20.8 0.0 EC-6.2.6-(Y) 0.030 1 0.0 25.0 0.0 20.8 0.0 EC-6.3.2 LTB 0.040 1 0.0 25.0 0.0 20.8 0.0 Torsion and deflections have not been considered in the design. _________________________ ************** END OF TABULATED RESULT OF DESIGN ************** 39. PARAMETER 2 40. CODE EN 1993-1-1:2005 41. NA 8 42. MTH 1 ALL 43. CHECK CODE ALL STEEL DESIGN STAAD.PRO CODE CHECKING - NBN EN 1993-1-1:2005 ******************************************** NATIONAL ANNEX - NBN EN 1993-1-1 ANB : 2018 PROGRAM CODE REVISION V1.13 BS_EC3_2005/1 STAAD SPACE -- PAGE NO. 5 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 0.039 1 0.00 0.00 20.83 0.00 ======================================================================= 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 : 4180.9 4180.9 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 = 528.8 co-efficients C1 & K : C1 =2.578 K =0.5, Effective Length= 5.000 Lateral Torsional Buckling Curve : Curve a Elastic Critical Moment for LTB, Mcr = 1712.9 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 SPACE -- PAGE NO. 6 ALL UNITS ARE - KN METE (UNLESS OTHERWISE Noted) MEMBER TABLE RESULT/ CRITICAL COND/ RATIO/ LOADING/ FX MY MZ LOCATION =======================================================================