 # V. SNiP SP16 2017 - Eccentrically Compressed Tube Section

Design a column subject to axial compressive force and biaxial moment per the SP 16.13330.2017 code.

## Details

A 5 m tall, simply supported column has a TUB200X160X8 section. The column is subject to a 80 kN axial load along with a uniformly distributed load of 30 kN/m in the local X axis. The steel used has a modulus of elasticity of 206,000 MPa and a Ry = 562 MPa. γc = 1, γm = 1.05

Section Properties

D = 200 mm

B = 160 mm

t = 8 mm

A = 52.84 cm2

Ix = 2,975 cm4

Iy = 2,110 cm4

IT = 4,083 cm4

rx = 7.50 cm

ry = 6.32 cm

## Validation

Ry = Ryn/ γm = 561.9 MPa

Rs = 0.58×Ry/ γm = 325.9 MPa

Bending moment:

Mx = qx × L2 / 8 = 30 (5)2 / 8 = 93.75 kN·m

Design for Strength (Cl. 9.1.1)

$σ = N A n = 80 52.84 ( 10 ) − 1 = 14.54 < 0.1 R y = 56.19$

Ryn ≤ 440 N/mm2

τ = 0; i.e., < 0.5×Rs

So, as per Cl. 9.1.1, F.105 should not be checked. Rather F.106 needs to be checked.

 $N A n ± M x y I x n ± M y x I y n ± B ω I ω n R y γ c ≤ 1$ (F.(106) )
where
 y = D / 2 = 100 mm Bω = 0

So, the ratio is $14.54 + 93.75 ( 100 ) 2,975 × 10 -2 561.9 × 1 = 0.588 < 1$

Design for Stability (Cl. 9.2.2)

To satisfy F.109, mef ≤ 20, where:

 $m ef = η × m$ (F.110)
where
 e = M / N = 93.75 / 80 = 1.172 m m = $e × A W c = 1.172 × 0.00055 / 0.000319 = 20.20$

Thus, m > 20, so must review Section 8 for further checks.

Design for Stability for a Box Section (Cl. 9.2.10)

Check the stability of box bars with constant cross-section subject to compression on one or two main planes:

 $N ϕ ey × A × R y × γ c + M x c x × δ x W x ,min × R y × γ c$ (F.120)

As per this clause, for uniaxial bending in the plane of maximum stiffness (i.e., Ix > Iy, My = 0), ϕey should be replaced by ϕy.

 λx = Kx × L / rx = 1.0 (500) / 7.50 = 66.34 (Cl 10.4.1)

λy = Ky × L / ry = 1.0 (500) / 6.32 = 79.12

$λ _ x = λ x R y E = 66.64 561.9 206,000 = 3.480$
$λ _ y = λ y R y E = 79.12 561.9 206,000 = 4.132$

The conditional slenderness, $λ _$, is the larger of $λ _ x$ and $λ _ y$. Thus, $λ _ = 4.132$

From Table 7, ɑ = 0.03 and β = 0.06 for a tube cross-section.

 $δ = 9.87 ( 1 - ɑ + β × λ _ ) + λ _ 2 = 9.87 ( 1 - 0.03 + 0.06 × 4.132 ) + ( 4.132 ) 2 = 29.098$ (F.(9) )
$ϕ = 0.5 δ − δ 2 − 39.48 × λ _ 2 λ _ 2 = 0.476$

Note that per Cl. 7.1.3, for section type a, the maximum value of ϕ is given as $7.6 λ _ 2 = 7.6 ( 4.132 ) 2 = 0.445$ for conventional flexibility greater than 3.8. Thus, take ϕ = 0.445.

cx = 1.14 (Table E.1)

 $δ x = 1 + 0.1 N × λ _ x 2 A × R y = 1 + 0.1 × 80 × ( 3.480 ) 2 ( 10 ) 52.84 × 561.9 = 1.033$ ( F.122)

So the ratio for stability about x axis is:

 $80 ( 10 ) 1 0.445 ( 52.84 ) ( 561.9 ) ( 1.0 ) + 93.75 ( 10 ) 3 1.14 ( 1.03 ) ( 297.5 ) ( 561.9 ) ( 1.0 ) = 0.061 + 0.478 = 0.537$ (F.120)

Check for Flexure

 $M W n , m i n R y γ c ≤ 1$ [Eqn. 41 of SNiP SP16.13330.2011]
where
 Wn,min = Wx = 3,191.2 cm3 = 319.6(10)-6 m3

Check for Shear

By inspection, the shear at the maximum moment location is zero under a uniformly distributed load.

 $Q S I t w R s γ c ≤ 1$ [Eqn. 42 of SNiP SP16.13330.2011]
where
 Q = q.l/2 = 0 kN

Check for Combined Shear & Flexure

 $0.87 R y γ c σ x 2 - σ x σ y + σ y 2 + 3 τ x y 2 ≤ 1$ [Eqn. 44 of SNiP SP16.13330.2011]
where
 σx = M / Wx = 93.75×103 / 297.5= 315.1 MPa σy = 0 (No weak axis bending) τxy = QS / (I × tw) = 0 MPa

## Results

Ratio per Cl. 9.1.1 0.588 0.588 none
Ratio per Cl. 9.2.10 0.537 0.536 negligible
ϕy 0.445 0.445 none
δx 1.03 1.03 none
Ratio per Cl. 8.2.1 (41) 0.561 0.561 none
Ratio per Cl. 8.2.1 (42) 0 0 none
Ratio per Cl. 8.2.1 (44) 0.488 0.488 none
σx (MPa) 315.1 315.1 none

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\Russia\SNiP SP16 2017 - Eccentrically Compressed Tube Section.std is typically installed with the program.

The following design parameters are used:
• The partial coefficient, γm = 1.05, is specified by GAMMA 2.
• The steel grade of S590 (for tube sections) is specified by SGR 18.
• The stress strain state is indicated by TB 1.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 05-Jan-21
END JOB INFORMATION
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 0 5 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
TYPE STEEL
STRENGTH FY 253200 FU 407800 RY 1.5 RT 1.2
END DEFINE MATERIAL
****************************************
MEMBER PROPERTY RUSSIAN
1 TABLE ST TUB200X160X8
****************************************
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 PINNED
2 FIXED BUT FY MX MZ
****************************************
2 FY -80
1 UNI GX 30
*1 UNI GZ 2
********************************
PERFORM ANALYSIS
PRINT MEMBER PROP ALL
***********************
PARAMETER 1
CODE RUSSIAN
TB 1 ALL
GAMM 2 ALL
SGR 18 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH


                       STAAD.PRO CODE CHECKING - (SP 16.13330.2017)   V1.0
********************************************
ALL UNITS ARE - KN METRE
========================================================================
SECTION NO.      N             Mx            My      LOCATION
========================================================================
1  TUB    TUB200X160X8  PASS      SP cl.9.1.1      0.59         1
8.000E+01 C    9.375E+01    0.000E+00   2.500E+00
1  TUB    TUB200X160X8  PASS      SP cl.9.2.10     0.54         1
8.000E+01 C    9.375E+01    0.000E+00   2.500E+00
1  TUB    TUB200X160X8 PASS     SP cl.8.2.1(41)    0.56         1
8.000E+01 C    9.375E+01    0.000E+00   2.500E+00
1  TUB    TUB200X160X8 PASS     SP cl.8.2.1(42)    0.00         1
8.000E+01 C    9.375E+01    0.000E+00   2.500E+00
1  TUB    TUB200X160X8 PASS     SP cl.8.2.1(44)    0.49         1
8.000E+01 C    9.375E+01    0.000E+00   2.500E+00
MATERIAL DATA
Steel                         = C590       SP16.13330
Modulus of elasticity         = 206.E+06 kPa
Design Strength (Ry)          = 562.E+03 kPa
SECTION PROPERTIES (units - m, m^2, m^3, m^4)
Member Length                 = 5.00E+00
Gross Area                    = 5.28E-03
Net Area                      = 5.28E-03
x-axis      y-axis
Moment of inertia (I)         :   298.E-07    211.E-07
Section modulus (W)           :   298.E-06    264.E-06
First moment of area (S)      :   149.E-06    132.E-06
Radius of gyration (i)        :   750.E-04    632.E-04
Effective Length              :   5.00E+00    5.00E+00
Slenderness                   :   666.E-01    791.E-01
DESIGN DATA (units -kN,m) SP16.13330.2017
Axial force                   :   800.0E-01
x-axis      y-axis
Moments                       :   937.5E-01    0.000E+00
Shear force                   :   0.000E+00    0.000E+00
Bi-moment                     :   0.000E+00 Value of Bi-moment not being entered!!!
Stress-strain state checked as:   Class    1
CRITICAL CONDITIONS FOR EACH CLAUSE CHECK
F.(106) (N/A+Mx*y/Ix+My*x/Iy+B*w/Iw)/(Ry*GammaC)=
( 800.0E-01/ 5.3E-03+ 937.5E-01* 1.00E-01/ 2.98E-05+ 0.000E+00* 8.00E-02/
2.11E-05+ 0.000E+00* 0.00E+00/ 0.00E+00)/( 561.9E+03* 1.00E+00)
= 5.88E-01=&lt;1
F.(120)  N/(FIy*A*Ry*GammaC)+Mx/(cx*DELx*Wx,min*Ry*GammaC)=-800.0E-01/( 4.45E-01* 5.28E-03* 561.9E+03*1.00E+00)+-937.5E-01/( 1.14E+00* 1.03E+00* 297.5E-06* 561.9E+03*1.00E+00)=5.36E-01=&amp;lt;1
m_x =20.8E+00>20.
F.(41)  M/(Wn,min*Ry*GammaC)= 937.5E-01/( 2.98E-04* 561.9E+03* 1.00E+00= 5.61E-01=&lt;1
F.(44)  0.87/(Ry*GammaC)*SQRT(SIGMx^2+3*TAUxy^2)=
0.87/( 561.9E+03* 1.00E+00)*SQRT(-315.1E+03^2+3* 0.000E+00^2)=
4.88E-01=&lt;1
TAUxy/(Rs*GammaC)= 0.000E+00/( 325.9E+03* 1.00E+00)= 0.00E+00=&lt;1