# 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 Ry = 239 MPa. γc1 = 1, γc2 = 1

Section Properties

D = 300 mm

B = 300 mm

tf = 15 mm

tw = 10 mm

A = 119.78 cm2

Ix = 20,410 cm4

Iy = 6,755 cm4

rx = 13.05 cm

ry = 7.51 cm

J = 76.5 cm4

## Validation

Check for Axial Force

Need to satisfy the following equation per Cl. 7.1.1:

 $N A n R y γ c ≤ 1$ (Eq. 5)

Thus, the ratio is $1 , 500 119.78 × 10 − 1 × 239 × 1 = 0.524 < 1$

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

$λ x = k x l r x = 1.0 × 6.78 0.1305 = 51.94 < 120$
$λ y = k y l r y = 1.0 × 6.78 0.0751 = 90.28 < 120$

Thus, the ratio is 90.28 / 120 = 0.75

Check Cl. 7.1.3

$λ ¯ x = λ x R y E = 51.94 239 206 , 000 = 1.769$
$λ ¯ y = λ y R y E = 90.28 239 206 , 000 = 3.075$

Therefore, $λ ¯ = 3.075$

Need to satisfy the following equation:

 $N ϕ A R y γ c ≤ 1$ (Eq. 7)(
where
 ϕ = $0.5 δ − δ 2 − 39.48 × λ ¯ 2 λ ¯ 2$, per Eq. 8 δ = $9.87 ( 1 − α + β λ ¯ ) + λ ¯ 2$, per Eq. 9

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

$δ = 9.87 [ 1 − 0.04 + 0.14 ( 3.075 ) ] + ( 3.075 ) 2 = 23.18$
$ϕ = 0.5 23.18 − ( 23.18 ) 2 − 39.48 × ( 3.075 ) 2 ( 3.075 ) 2 = 0.549 < 7.6 λ ¯ 2 = 7.6 ( 3.075 ) 2 = 0.804$

Thus, the ratio is $1 , 500 0.549 × 119.78 × 10 − 1 × 239 × 1 = 0.955 < 1$

Check Cl. 7.3.2

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

$λ ¯ w = h e f t w R y E = 240 10 239 206 , 000 = 0.818$

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

$λ ¯ w < λ ¯ u w$, OK

Check Cl. 7.3.8

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

$λ ¯ f = b e f t f R y E = 130 15 239 206 , 000 = 0.295$

Since $λ ¯ = 3.075 > 2$, $λ ¯ u f = 0.36 + 0.10 λ ¯ = 0.668$ (per F.(37), Table 10)

$λ ¯ f < λ ¯ u f$, OK

## Results

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
$λ¯w$ 0.818 0.818 none
$λ¯uw$ 2.276 2.28 negligible
$λ¯f$ 0.295 0.295 none
$λ¯uf$ 0.668 0.668 none

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
****************************************
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 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