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 R_y = 562 MPa. γ_c = 1, γ_m = 1.05

Section Properties

D = 200 mm

B = 160 mm

t = 8 mm

A = 52.84 cm²

I_x = 2,975 cm⁴

I_y = 2,110 cm⁴

I_T = 4,083 cm⁴

r_x = 7.50 cm

r_y = 6.32 cm

Validation

R_y = R_yn/ γ_m = 561.9 MPa

R_s = 0.58×R_y/ γ_m = 325.9 MPa

Bending moment:

M_x = q_x × L² / 8 = 30 (5)² / 8 = 93.75 kN·m

Design for Strength (Cl. 9.1.1)

σ = \frac{N}{A_{n}} = \frac{80}{52.84 {(10)}^{- 1}} = 14.54 < 0.1 R_{y} = 56.19

R_yn ≤ 440 N/mm²

τ = 0; i.e., < 0.5×R_s

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

\frac{\frac{N}{A_{n}} \pm \frac{M_{x} y}{I_{x n}} \pm \frac{M_{y} x}{I_{y n}} \pm \frac{B_{ω}}{I_{ω n}}}{R_{y} γ_{c}} \leq 1

(F.(106) )

where

y	=	D / 2 = 100 mm
B_ω	=	0

So, the ratio is $\frac{14.54 + \frac{93.75 (100)}{2,975 \times 10^{-2}}}{561.9 \times 1} = 0.588 < 1$

Design for Stability (Cl. 9.2.2)

To satisfy F.109, m_ef ≤ 20, where:

m_{ef} = η \times m

(F.110)

where

e	=	M / N = 93.75 / 80 = 1.172 m
m	=	$e \times \frac{A}{W_{c}} = 1.172 \times 0.00055 / 0.000319 = 20.20$

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:

\frac{N}{ϕ_{ey} \times A \times R_{y} \times γ_{c}} + \frac{M_{x}}{c_{x} \times δ_{x} W_{x,min} \times R_{y} \times γ_{c}}

(F.120)

As per this clause, for uniaxial bending in the plane of maximum stiffness (i.e., I_x > I_y, M_y = 0), ϕ_ey should be replaced by ϕ_y.

λ_x = K_x × L / r_x = 1.0 (500) / 7.50 = 66.34

(Cl 10.4.1)

λ_y = K_y × L / r_y = 1.0 (500) / 6.32 = 79.12

{\overline{λ}}_{x} = λ_{x} \sqrt{\frac{R_{y}}{E}} = 66.64 \sqrt{\frac{561.9}{206,000}} = 3.480

{\overline{λ}}_{y} = λ_{y} \sqrt{\frac{R_{y}}{E}} = 79.12 \sqrt{\frac{561.9}{206,000}} = 4.132

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

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

δ = 9.87 (1 - ɑ + β \times \overline{λ}) + {\overline{λ}}^{2} = 9.87 (1 - 0.03 + 0.06 \times 4.132) + {(4.132)}^{2} = 29.098

(F.(9) )

ϕ = 0.5 \frac{δ - \sqrt{δ^{2} - 39.48 \times {\overline{λ}}^{2}}}{{\overline{λ}}^{2}} = 0.476

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

c_x = 1.14 (Table E.1)

δ_{x} = 1 + \frac{0.1 N \times {\overline{λ}}_{x}^{2}}{A \times R_{y}} = 1 + \frac{0.1 \times 80 \times {(3.480)}^{2} (10)}{52.84 \times 561.9} = 1.033

( F.122)

So the ratio for stability about x axis is:

\frac{80 {(10)}^{1}}{0.445 (52.84) (561.9) (1.0)} + \frac{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

\frac{M}{W_{n, m i n} R_{y} γ_{c}} \leq 1

[Eqn. 41 of SNiP SP16.13330.2011]

where

W_n,min

W_x = 3,191.2 cm³ = 319.6(10)^-6 m³

\frac{93.75}{297.5 {(10)}^{-6} \times 561.9 \times 1.0} = 0.561 \leq 1 (OK)

Check for Shear

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

\frac{Q S}{I t_{w} R_{s} γ_{c}} \leq 1

[Eqn. 42 of SNiP SP16.13330.2011]

where

q.l/2 = 0 kN

\frac{Q S}{I t_{w} R_{s} γ_{c}} = 0 \leq 1 (OK)

Check for Combined Shear & Flexure

\frac{0.87}{R_{y} γ_{c}} \sqrt{σ_{x}^{2} - σ_{x} σ_{y} + σ_{y}^{2} + 3 τ_{x y}^{2}} \leq 1

[Eqn. 44 of SNiP SP16.13330.2011]

where

σ_x	=	M / W_x = 93.75×10³ / 297.5= 315.1 MPa
σ_y	=	0 (No weak axis bending)
τ_xy	=	QS / (I × t_w) = 0 MPa

\frac{0.87}{561.9 \times 1.0} \sqrt{{315.1}^{2}} = 0.488 \leq 1 (OK)

Results

Result Type	Reference	STAAD.Pro	Difference
Ratio per Cl. 9.1.1	0.588	0.588	none
Ratio per Cl. 9.2.10	0.537	0.536	negligible
ϕ_y	0.445	0.445	none
δ_x	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
σ_x (MPa)	315.1	315.1	none

STAAD.Pro Input

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, γ_m = 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
****************************************
LOAD 1 LOADTYPE None  TITLE LOAD CASE 1
JOINT LOAD
2 FY -80
MEMBER LOAD
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 Output

                       STAAD.PRO CODE CHECKING - (SP 16.13330.2017)   V1.0
                       ********************************************
   ALL UNITS ARE - KN METRE
   ========================================================================
   MEMBER     CROSS          RESULT/   CRITICAL COND/    RATIO/    LOADING/
              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