V. EC3 French NA - Varying End Mom CMM8

Calculate the bending capacity of a beam using an I section subject to a concentrated load and varying end moments 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 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:

$M c r = C 1 π 2 E I ( k L ) 2 { ( k k w ) 2 I w I + ( k L ) 2 G I t π 2 E I + ( C 2 Z g ) 2 − C 2 Z g }$
where
 kw = k = 1 $π 2 E I y k L 2$ = 7,477,200 $k k w 2 I w I y$ = 22,394 $k L 2 G I t π 2 E I y$ = 23,737 C2Zg = 0.17×160 = 27.2
$μ = F L 4 M = 4 × 5 4 × 10 = 0.5 > 0$

From the graph, C1 = 1.184, C2 = 0.17

C2zg = 0.17×160 = 27.2

Therefore, Mcr = 1,676 kN·m

Results

Table 1.
Moment capacity, Mckd (kN·m) 591.0 591.0 none
Critical moment, Mcr (kN·m) 1,676 1,676.5 negligible

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\Europe\EC3 French NA-Varying End Mom CMM8.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 1.0
• 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 22-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+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
1 CON GY -4
2 MZ 8
1 MZ -10
PERFORM ANALYSIS
PARAMETER 1
CODE EN 1993-1-1:2005
NA 4
CMM 8 ALL
MU 0.5 ALL
C2 0.17 ALL
CMN 1 ALL
PY 275000 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH


                         STAAD.PRO CODE CHECKING - NF EN 1993-1-1:2005
********************************************
NATIONAL ANNEX - NF EN 1993-1-1/NA
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       0.027         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               :       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 =  516.2
co-efficients C1 & K : C1 =1.184 K =1.0, Effective Length= 5.000
Lateral Torsional Buckling Curve :
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   0.027     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 **************