V. EC3 Belgian NA - Varying End Moments
Calculate the bending capacity of a beam using an I section subject to a concentrated load and varying end moments per the Belgian NA to EC3.
Details
The section is a HD320X127, Grade S275 steel. The member is a 5 m, simply-supported span subject to a 10 kN/m uniform load. The left support has a -10.0 kN·m moment applied and the right support has a 8.0 kN·m moment applied.
Validation
Moment capacity:
The critical moment is given by:
Therefore, Mcr = 1,541 kN·m
From the graph, C1 = 1.184, C2 = 0.17
Therefore, Mcr = 1,676 kN·m
Results
Result Type | Reference | STAAD.Pro | Difference | Comments |
---|---|---|---|---|
Moment capacity, Mckd (kN·m) | 591.0 | 591.0 | none | |
Critical moment, Mcr (kN·m) | 1,676 | 1,676.1 | negligible |
STAAD.Pro Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2024\Samples \Verification Models\09 Steel Design\Europe\EC3 Belgian NA - Varying End Moments-CMM8.std is typically installed with the program.
The following design parameters are used:
- The Belgian NA is specified using
NA 8
- Simply-supported span:
CMN 1.0
- Concentrated load with varying end moments:
CMM 8
- The parameter
MU 0.5
is used for the case with varying end moments - The value of
C2 0.17
is specified; based on calculation of μ
STAAD PLANE
START JOB INFORMATION
ENGINEER DATE 20-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 PINNED
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
MEMBER LOAD
1 CON GY -4
JOINT LOAD
2 MZ 8
1 MZ -10
PERFORM ANALYSIS
PARAMETER 1
CODE EN 1993-1-1:2005
NA 8 ALL
CMM 8 ALL
MU 0.5 ALL
C2 0.17 ALL
CMN 1 ALL
PY 275000 ALL
*KC 1 ALL
TRACK 2 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 V1.14 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 0.026 1
0.00 0.00 -14.00 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 : 109.573 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 : 1739.7 821.3
BUCKLING CALCULATIONS (units - kN,m)
Lateral Torsional Buckling Moment MB = 543.6
co-efficients C1 & K : C1 =1.184 K =1.0, Effective Length= 5.000
Lateral Torsional Buckling Curve : Curve b
Elastic Critical Moment for LTB, Mcr = 1676.1
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
CRITICAL LOADS FOR EACH CLAUSE CHECK (units- kN,m):
CLAUSE RATIO LOAD FX VY VZ MZ MY
EC-6.2.5 0.024 1 0.0 1.6 0.0 -14.0 0.0
EC-6.2.6-(Y) 0.003 1 0.0 -2.4 0.0 -13.0 0.0
EC-6.3.2 LTB 0.026 1 0.0 1.6 0.0 -14.0 0.0
Torsion has not been considered in the design.
_________________________
************** END OF TABULATED RESULT OF DESIGN **************