# V. EC3 - Pipe Section with Conc Load

Verify the adequacy of a circular hollow section used as a beam subject to concentrated loads per EN 1993-1-1:2005 (no national annex used).

## Details

The member is a 6 m long beam with pinned ends. The beam supports 10kN concentrated loads at the third points. The steel is grade S275. The section is a European 114.3X8CHS.

Section Properties

• A = 26.7 cm2
• Outer diameter = 114.3 mm
• t = 8 mm
• Iz = Iy = 379 cm4
• Zz = Zy = 90.6 cm3
• Cw = 0 cm6

Partial safety factors:

ΓM0 = 1.0

ΓM1 = 1.0

ΓM2 = 1.25

## Validation

Section Classification

$ε = 235 f y = 235 275 = 0.924$

As per Table 5.2:

d / t = 114.3 / 8 = 14.3 < 50×ε2 = 50 (0.924)2 = 42.7

Hence, this is a Class 1 section.

Slenderness Ratio

The slenderness ratio = kL / r = 1 × 6,000 / 37.68 = 159.3

Axial Tension

Determine axial tension capacity per Cl. 6.2.3.

The tensile capacity is the minimum of Npl,Rd and Nu,Rd, thus: Nt,Rd = 567.1 kN.

No axial tension in section, so by observation no need to check ratio.

Axial Compression

Determine axial compression capacity per Cl. 6.2.4 for a Class 1 section.

Next, check the flexural buckling resistance per Cl. 6.3.1.3:

$N b,Rd = χ × A × f y / γ M1$

From Table 6.1: the imperfection factor, ɑ = 0.21.

$ƛ = A × f y / N cr = L cr / i × λ 1$
where
 Lcr = 6,000 mm i = 37.68 mm λ1 = 93.9×ε = 93.9 × 0.924 = 86.8

ƛ = 1.834

$Ф = 0.5 [ 1 + ɑ ( ƛ - 0.2 ) + ƛ 2 ] = 0.5 [ 1 + 0.21 ( 1.834 - 0.2 ) + ( 1.834 ) 2 ] = 2.354$
$χ = 1 Ф + Ф 2 - ƛ 2 = 0.2611$

The compression capacity is the minimum of Nc,Rd and Nb,Rd, thus: Nc,Rd = 191.7 kN.

No axial compression in section, so by observation no need to check ratio.

Bending Capacity

Maximum bending moment in the section (center third of span): MEd = 20.0 kN·m.

Check for bending capacity per Cl. 6.2.5:

For a Class 1 section:

Ratio per Eq. 6.12: MEd / Mc,Rd = 20.0 / 24.92 = 0.803

Shear Capacity

Maximum shear in the section: VEd = 10 kN

Check for shear capacity per Cl. 6.2.6 for plastic design (Class 1):

Ratio per Eq. 6.17: VEd / Vc,Rd = 10.0 / 26.9 = 0.037

Lateral Torsional Buckling

$M c r = C 1 π 2 E I ( k L ) 2 [ ( k k w ) 2 I w I z + ( k L ) 2 G I t π 2 E I z + ( C 2 Z g ) 2 − C 2 Z g ]$
where
 C1 = 1.0 C2 = 1.0 $π 2 E I y k L 2$ = 213,000 $k k w 2 I w I y$ = 0 $k L 2 G I T π 2 E I y$ = 2,806,000 C2Zg = 1.0×114.3 / 2 = 57.15

Therefore,

For CHS sections, χLT = 1.0.

Ratio per Eq. 6.12: MEd / Mb,Rd = 20.0 / 24.92 = 0.803

## Results

Table 1. Comparison of results
Section Class Class 1 Class 1 none
Slenderness Ratio 159.3 159.3 none
Tension Capacity (kN) 567.1 567.1 none
Compression Capacity (kN) 191.7 191.7 none
Moment Capacity (kN·m) 24.92 24.9 negligible
Shear Area (cm2) 17.0 16.99 negligible
Shear Capacity (kN) 269.9 269.9 none
MB (kN·m) 24.92 24.9 negligible
Ratio per Cl. 6.2.5 0.803 0.803 none
Ratio per Cl. 6.2.6 (Y) 0.037 0.037 none
Ratio per Cl. 6.3.2 LTB 0.803 0.803 none

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\Europe\EC3 - Pipe Section with Conc Load.std is typically installed with the program.

The following design parameters are used:
• Use Cl. 6.3.2.2 to determine χLT: MTH 1
• The values of C1 1.0 and C2 1.0 are specified.
• The values of Fy and Fu are specified directly using PY 275000 and FU 295000.
STAAD PLANE
START JOB INFORMATION
ENGINEER DATE 07-May-21
END JOB INFORMATION
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 6 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 114.3X8CHS
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 2 PINNED
1 CON GY -10 2
1 CON GY -10 4
PERFORM ANALYSIS
PARAMETER 1
CODE EN 1993-1-1:2005
C1 1 ALL
C2 1 ALL
CMM 5 ALL
MTH 1 ALL
FU 295000 ALL
PY 275000 ALL
TRACK 2 ALL
CHECK CODE ALL
PRINT MEMBER PROPERTIES ALL
FINISH


                         STAAD.PRO CODE CHECKING - EN 1993-1-1:2005
********************************************
NATIONAL ANNEX - NOT USED
PROGRAM CODE REVISION V1.14 BS_EC3_2005/1
STAAD PLANE                                              -- PAGE NO.    3
ALL UNITS ARE - KN   METE (UNLESS OTHERWISE Noted)
FX            MY             MZ       LOCATION
=======================================================================
1 ST   114.3X8CHS  (EUROPEAN SECTIONS)
PASS     EC-6.2.5           0.803         1
0.00            0.00          20.00        2.00
=======================================================================
MATERIAL DATA
Modulus of elasticity    =  205 kN/mm2
Design Strength  (py)    =  275  N/mm2
SECTION PROPERTIES (units - cm)
Member Length =    600.00
Gross Area =   26.70          Net Area =   26.70
z-axis          y-axis
Moment of inertia        :      379.000         379.000
Plastic modulus          :       90.600          90.600
Elastic modulus          :       66.317          66.317
Shear Area               :       16.998          16.998
Radius of gyration       :        3.768           3.768
Effective Length         :      600.000         600.000
DESIGN DATA (units - kN,m)   EUROCODE NO.3 /2005
Section Class            :   CLASS 1
GM0 :  1.00          GM1 :  1.00          GM2 :  1.25
z-axis          y-axis
Slenderness ratio (KL/r) :        159.3          159.3
Compression Capacity     :        191.7          191.7
Tension Capacity         :        567.1          567.1
Moment Capacity          :         24.9           24.9
Reduced Moment Capacity  :         24.9           24.9
Shear Capacity           :        269.9          269.9
BUCKLING CALCULATIONS (units - kN,m)
Lateral Torsional Buckling Moment       MB =   24.9
co-efficients C1 & K : C1 =1.000 K =1.0, Effective Length= 6.000
Lateral Torsional Buckling Curve :
Compression buckling curves:     z-z:  Curve a   y-y:  Curve a
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       0.803     1     0.0     10.0     0.0    20.0     0.0
EC-6.2.6-(Y)   0.037     1     0.0     10.0     0.0     0.0     0.0
EC-6.3.2 LTB   0.803     1     0.0     10.0     0.0    20.0     0.0
Torsion has not been considered in the design.
_________________________
************** END OF TABULATED RESULT OF DESIGN **************