V. SNiP SP16 2017 - Column in compression

Design a column per the SP 16.13330.2017 code.

Details

A 6.78 m tall, simply supported column has a Russian K2-30 section. The column is subject to a 1,500 kN axial load. The steel used has a modulus of elasticity of 206,000 MPa and a R_y = 239 MPa. γ_c1 = 1, γ_c2 = 1

Section Properties

D = 300 mm

B = 300 mm

t_f = 15 mm

t_w = 10 mm

A = 119.78 cm²

I_x = 20,410 cm⁴

I_y = 6,755 cm⁴

r_x = 13.05 cm

r_y = 7.51 cm

J = 76.5 cm⁴

Validation

Check for Axial Force

Need to satisfy the following equation per Cl. 7.1.1:

\frac{N}{A_{n} R_{y} γ_{c}} \leq 1

(Eq. 5)

Thus, the ratio is $\frac{1, 500}{119.78 \times 10^{- 1} \times 239 \times 1} = 0.524 < 1$

Check the slenderness per Cl. 10.4.1. Limit the slenderness to 120.

λ_{x} = \frac{k_{x} l}{r_{x}} = \frac{1.0 \times 6.78}{0.1305} = 51.94 < 120

λ_{y} = \frac{k_{y} l}{r_{y}} = \frac{1.0 \times 6.78}{0.0751} = 90.28 < 120

Thus, the ratio is 90.28 / 120 = 0.75

Check Cl. 7.1.3

{\bar{λ}}_{x} = λ_{x} \sqrt{\frac{R_{y}}{E}} = 51.94 \sqrt{\frac{239}{206, 000}} = 1.769

{\bar{λ}}_{y} = λ_{y} \sqrt{\frac{R_{y}}{E}} = 90.28 \sqrt{\frac{239}{206, 000}} = 3.075

Therefore, $\bar{λ} = 3.075$

Need to satisfy the following equation:

\frac{N}{ϕ A R_{y} γ_{c}} \leq 1

(Eq. 7)(

where

ϕ	=	$0.5 \frac{δ - \sqrt{δ^{2} - 39.48 \times {\bar{λ}}^{2}}}{{\bar{λ}}^{2}}$ , per Eq. 8
δ	=	$9.87 (1 - α + β \bar{λ}) + {\bar{λ}}^{2}$ , per Eq. 9

From Table 7, note 2, α = 0.04 and β = 0.14.

δ = 9.87 [1 - 0.04 + 0.14 (3.075)] + {(3.075)}^{2} = 23.18

ϕ = 0.5 \frac{23.18 - \sqrt{{(23.18)}^{2} - 39.48 \times {(3.075)}^{2}}}{{(3.075)}^{2}} = 0.549 < \frac{7.6}{{\bar{λ}}^{2}} = \frac{7.6}{{(3.075)}^{2}} = 0.804

Thus, the ratio is $\frac{1, 500}{0.549 \times 119.78 \times 10^{- 1} \times 239 \times 1} = 0.955 < 1$

Check Cl. 7.3.2

Design height of the cross-section wall, h_ef = 240 mm (Cl. 7.3.1)

{\bar{λ}}_{w} = \frac{h_{e f}}{t_{w}} \sqrt{\frac{R_{y}}{E}} = \frac{240}{10} \sqrt{\frac{239}{206, 000}} = 0.818

Since $\bar{λ} = 3.075 > 2$ , ${\bar{λ}}_{u w} = 1.20 + 0.35 \bar{λ} = 2.276 < 2.3$ (per F.(24), Table 9)

${\bar{λ}}_{w} < {\bar{λ}}_{u w}$ , OK

Check Cl. 7.3.8

Design width of the cross-section wall, b_ef = b/2 - 2×t_w = 130 mm

{\bar{λ}}_{f} = \frac{b_{e f}}{t_{f}} \sqrt{\frac{R_{y}}{E}} = \frac{130}{15} \sqrt{\frac{239}{206, 000}} = 0.295

Since $\bar{λ} = 3.075 > 2$ , ${\bar{λ}}_{u f} = 0.36 + 0.10 \bar{λ} = 0.668$ (per F.(37), Table 10)

${\bar{λ}}_{f} < {\bar{λ}}_{u f}$ , OK

Results

Result Type	Reference	STAAD.Pro	Difference
Ratio per Cl. 7.1.3	0.955	0.96	negligible
Ratio per Cl. 7.1.1	0.524	0.52	negligible
Ratio per Cl. 10.4.1C	0.75	0.75	none
${\bar{λ}}_{w}$	0.818	0.818	none
${\bar{λ}}_{u w}$	2.276	2.28	negligible
${\bar{λ}}_{f}$	0.295	0.295	none
${\bar{λ}}_{u f}$	0.668	0.668	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 - Column in compression.STD is typically installed with the program.

The following design parameters are used:

The slenderness for compression member is limited to 120 by the CMN 2 parameter.
The steel grade of S255B-1 (for K type sections) is specified by SGR 20.
The stress strain state is indicated by TB 1.

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 08/31/2020
END JOB INFORMATION
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 0 6.78 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 K2-30
****************************************
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 -1500
********************************
PERFORM ANALYSIS
PRINT MEMBER PROP ALL
*********************************
PARAMETER 1
CODE RUSSIAN
TRACK 2 ALL
TB 1 ALL
CMN 2 ALL
SGR 20 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  I      K2-30         PASS      SP cl.7.1.3      0.96         1
                          1.500E+03 C    0.000E+00    0.000E+00   0.000E+00
      1  I      K2-30         PASS      SP cl.7.1.1      0.52         1
                          1.500E+03 C    0.000E+00    0.000E+00   0.000E+00
      1  I      K2-30         PASS      SP cl.10.4.1C    0.75         1
                          1.500E+03 C    0.000E+00    0.000E+00   0.000E+00
   MATERIAL DATA
      Steel                         = C255B      SP16.13330
      Modulus of elasticity         = 206.E+06 kPa
      Design Strength (Ry)          = 239.E+03 kPa
   SECTION PROPERTIES (units - m, m^2, m^3, m^4)
      Member Length                 = 6.78E+00
      Gross Area                    = 1.20E-02
      Net Area                      = 1.20E-02
                                         x-axis      y-axis
      Moment of inertia (I)         :   204.E-06    675.E-07
      Section modulus (W)           :   136.E-05    450.E-06
      First moment of area (S)      :   751.E-06    342.E-06
      Radius of gyration (i)        :   131.E-03    751.E-04
      Effective Length              :   6.78E+00    6.78E+00
      Slenderness                   :   519.E-01    903.E-01
   DESIGN DATA (units -kN,m) SP16.13330.2017
      Axial force                   :   150.0E+01
                                         x-axis      y-axis
      Moments                       :   0.000E+00    0.000E+00
      Shear force                   :   0.000E+00    0.000E+00
      Bi-moment                     :   0.000E+00 Value of Bi-moment not being entered!!!
   CRITICAL CONDITIONS FOR EACH CLAUSE CHECK
      F.(7)  N/(FI*A*Ry*GammaC)= 150.0E+01/( 5.48E-01* 1.198E-02* 239.0E+03* 1.00E+00)= 9.55E-01=&lt;1
      7.3 cl. LAMBDA_w&amp;lt;=LAMBDA_uw= 8.18E-01&amp;lt;= 2.28E+00 OK
              LAMBDA_f&amp;lt;=LAMBDA_uf= 2.95E-01&amp;lt;= 6.68E-01 OK
      F.(5)  N/(An*Ry*GammaC)= 150.0E+01/( 1.20E-02* 239.0E+03* 1.00E+00)= 5.24E-01=&lt;1
      ULTIM. SLENDERNESS >= Lambda_y 120.0E+00 >= 902.8E-01