V.SNiP SP16 2011 - I Section with Axial Load

Verify the design capaciy of an I section used in a column per the SP16.13330.2011 code.

Details

The column is 7.5 m tall with a pinned base and a roller (free to move vertically and rotate) at the top. The column has a 3,500 kN axial load. The section used is an HD320X127. Steel grade is S235.

E = 205,000 MPa
R_y = 235 MPa (yield strength)
γ_c1 = 1, γ_c2 = 1

Validation

Check for Axial Force

\frac{N}{A_{n} \times R_{y} \times γ_{c}} \leq 1

[Cl. 7.1.1, Eqn. 5]

\frac{3,500}{161 (10^{- 4}) \times 235 (10^{3}) \times 1.0} = 0.925 \leq 1 (OK)

\frac{N}{ϕ \times A \times R_{y} \times γ_{c}} \leq 1

[Cl. 7.1.3, Eqn. 7]

where

cross sectional area = 161 cm²

Slenderness ratios:

K_y = K_x = 0.75

λ_{x} = \frac{K_{x} L}{r_{x}} = \frac{0.75 \times 7.5}{0.138} = 40.76

λ_{y} = \frac{K_{y} L}{r_{y}} = \frac{0.75 \times 7.5}{0.0757} = 74.3

{\bar{λ}}_{x} = λ_{x} \sqrt{\frac{R_{y}}{E}} = 40.76 \sqrt{\frac{235}{205, 000}} = 1.38

{\bar{λ}}_{y} = λ_{y} \sqrt{\frac{R_{y}}{E}} = 74.3 \sqrt{\frac{235}{205, 000}} = 2.516

ϕ = 0.5 \frac{\partial - \sqrt{\partial^{2} + 39.48 \times {\bar{λ}}^{2}}}{{\bar{λ}}^{2}}

[Eqn. 8]

\partial = 9.87 \times (1 - α + β \times \bar{λ}) + {\bar{λ}}^{2}

[Eqn. 9]

where

α	=	0.04 (From Table 7)
β	=	0.09 (From Table 7)
$\bar{λ}$	=	2.516 (maximum slenderness ratio)

\partial = 9.87 \times [1 - 0.04 + 0.09 \times (2.516)] + {(2.516)}^{2} = 18.04

ϕ = 0.5 \frac{18.04 - \sqrt{{(18.04)}^{2} + 39.48 \times {(2.516)}^{2}}}{{(2.516)}^{2}} = 0.7385 < \frac{7.6}{{\bar{λ}}^{2}} = 1.2006 (OK)

\frac{N}{ϕ \times A \times R_{y} \times γ_{c}} = \frac{3, 500}{0.7385 \times 0.0161 \times 235 (10^{3}) \times 1.0} = 1.25 > 1

[Cl. 7.1.3, Eqn. 7]

Check Web Slenderness

h_{e f} = D - 4 T_{f} = 320 - 4 \times 20.5 = 238 mm

{\bar{λ}}_{w} = \frac{h_{e f}}{T_{w}} \sqrt{\frac{R_{y}}{E}} = \frac{238}{11.5} \sqrt{\frac{235}{205, 000}} = 0.700

{\bar{λ}}_{u w} = 1.2 + 0.35 \bar{λ} = 1.2 + 0.35 (2.516) = 2.08

[Table 9; Eqn. 24]

{\bar{λ}}_{w} < {\bar{λ}}_{u w} (OK)

Check Flange Slenderness

b_{e f} = \frac{1}{2} (B - 2 T_{w}) = \frac{1}{2} (300 - 4 \times 11.5) = 127 mm

{\bar{λ}}_{f} = \frac{b_{e f}}{T_{f}} \sqrt{\frac{R_{y}}{E}} = \frac{127}{20.5} \sqrt{\frac{235}{205, 000}} = 0.210

{\bar{λ}}_{u f} = 0.36 + 0.1 \bar{λ} = 0.36 + 0.1 (2.516) = 0.612

[Table 10; Eqn. 37]

{\bar{λ}}_{f} < {\bar{λ}}_{u f} (OK)

Results

Table 1. Comparison of results
Result Type	Reference	STAAD.Pro	Difference
Cl. 7.1.1	0.925	0.92	negligible
Cl. 7.1.3	1.25	1.25	none
${\bar{λ}}_{w}$	0.700	0.699	negligible
${\bar{λ}}_{u w}$	2.08	2.08	none
${\bar{λ}}_{f}$	0.210	0.209	negligible
${\bar{λ}}_{u f}$	0.612	0.611	negligible

STAAD.Pro Input File

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\Russia\SNiP SP16 2011 - I Section with Axial Load.std is typically installed with the program.

STAAD PLANE
START JOB INFORMATION
ENGINEER DATE 18-Mar-19
END JOB INFORMATION
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 0 7.5 0;
MEMBER INCIDENCES
1 1 2;
DEFINE MATERIAL START
ISOTROPIC STEEL
E 2.05e+008
POISSON 0.3
DENSITY 76.8195
ALPHA 1.2e-005
DAMP 0.03
TYPE STEEL
STRENGTH FY 253200 FU 407800 RY 1.5 RT 1.2
END DEFINE MATERIAL
MEMBER PROPERTY EUROPEAN
1 TABLE ST HD320X127
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 PINNED
2 FIXED BUT FY MZ
LOAD 1 LOADTYPE None  TITLE LOAD CASE 1
JOINT LOAD
2 FY -3500
PERFORM ANALYSIS
PARAMETER 1
CODE RUSSIAN 2011
KY 0.75 ALL
KZ 0.75 ALL
SGR 1 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH

STAAD.Pro Output

                       STAAD.PRO CODE CHECKING - (SP 16.13330.2011)   V2.0
                       ********************************************
   ALL UNITS ARE - KN METRE
   ========================================================================
   MEMBER     CROSS          RESULT/   CRITICAL COND/    RATIO/    LOADING/
              SECTION NO.      N             Mx            My      LOCATION
   ========================================================================
*     1  I      HD320X127     FAIL      SP cl.7.1.3      1.25         1
                          3.500E+03 C    0.000E+00    0.000E+00   0.000E+00
      1  I      HD320X127     PASS      SP cl.7.1.1      0.92         1
                          3.500E+03 C    0.000E+00    0.000E+00   0.000E+00
   MATERIAL DATA
      Steel                         = S235        EN10025-2
      Modulus of elasticity         = 206.E+06 kPa
      Design Strength (Ry)          = 235.E+03 kPa
   SECTION PROPERTIES (units - m, m^2, m^3, m^4)
      Member Length                 = 7.50E+00
      Gross Area                    = 1.61E-02
      Net Area                      = 1.61E-02
                                         x-axis      y-axis
      Moment of inertia (I)         :   308.E-06    924.E-07
      Section modulus (W)           :   193.E-05    616.E-06
      First moment of area (S)      :   107.E-05    470.E-06
      Radius of gyration (i)        :   138.E-03    757.E-04
      Effective Length              :   5.63E+00    5.63E+00
      Slenderness                   :   407.E-01    743.E-01
   DESIGN DATA (units -kN,m) SP16.13330.2011
      Axial force                   :   350.0E+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)= 350.0E+01/( 7.40E-01* 1.613E-02* 235.0E+03* 1.00E+00)= 1.25E+00>1 
      7.3 LAMBDA_w&amp;lt;=LAMBDA_uw= 6.99E-01&amp;lt;= 2.08E+00 OK
          LAMBDA_f&amp;lt;=LAMBDA_uf= 2.09E-01&amp;lt;= 6.11E-01 OK
      F.(5)  N/(An*Ry*GammaC)= 350.0E+01/( 1.61E-02* 235.0E+03* 1.00E+00)= 9.23E-01=&lt;1