 # V. SNiP SP16 2017 - CLASS 2 UPT I section

Check the capacity of a user-provided table I section subject to biaxial moment per the SP 16.13330.2017 code.

## Details

A 6m, simply supported beam uses a welded, built-up I section. The section is defined as Class 2 (elasto-plastic). The flanges are 300 mm × 23 mm; the total section depth is 490 mm; the web thickness is 12 mm. The steel used has a modulus of elasticity of 206,000 MPa and a Ryn = 235 MPa. γm = 1.025. γc = 1.0

The member is subjected to uniformly distributed loads of 150 kN/m in the Y direction and 30 kN/m in the Z direction.

## Validation

Ry = Ryn/ γm = 229.3 MPa

Rs = 0.58×Ry/ γm = 133.0 MPa

Section Properties

Check for Flexure

Ratio of area of the flange to the area of the web:

$AfAw=300×23(490−2×23)12=1.295$

Need to satisfy the following equation from Cl. 8.2.3:

 $MxcxβWxn,min⁡Ryγc+MycyβWyn,min⁡Ryγc≤1$ (Eq. 51)
where
 Mx = 150 (6)2 / 8 = 675 kN·m My = 30 (6)2 / 8 = 135 kN·m β = 1 per Eq. 52, as Qx = Qy = 0, and therefore τx = τy = 0 cx = 1.0611 (from Table E.1) cy = 1.47 > 1.15, thus use 1.15

Thus, the ratio is $6751.061×1×3,431×(10)−3×229.3×1+1351.15×1×690.4×(10)−3×229.3×1=1.55>1$

Check for Stability

$λ ¯ b = l e f b R y E = 6 0.3 229.3 206 , 000 = 0.667$
 $λ ¯ u b = [ 0.35 + 0.0032 b t + ( 0.76 − 0.02 b t ) b h ] × δ R y ϕ x$ (Eq. 76)

Per Cl. 8.4.6, the value $λ ¯ u b$ is multiplied by δ.

where
 δ = $1 − 0.6 ( c 1 x − 1 ) / ( c x − 1 )$ c1x = is the larger of $M x W x n R y γ c = 675 3 , 431 × ( 10 ) − 3 229.3 × 1 = 0.858 , or β c x = 1.061$, so =1.061
$δ = 1 − 0.6 1 1 = 0.4$
 $λ ¯ u b = [ 0.35 + 0.0032 300 23 + ( 0.76 − 0.02 300 23 ) 300 490 − 23 ] × 0.4 229.3 196.7 = 0.308 < λ ¯ b$ (Eq. 73)

So, the stability of the beam is not ensured per Cl. 8.4.4.b.

Check for Deflection

The maximum member deflection is limited to l / 200 = 0.03 m

Thus, the ratio is 0.0279 / 0.03 = 0.93

## Results

Ratio for flexure (Eq. 51) 1.55 1.55 none
Deflection (m) 0.0279 0.02785 negligible
Deflection ratio 0.93 0.93 none

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\Russia\SNiP SP16 2017 - CLASS 2 UPT I section with biaxial moment.std is typically installed with the program.

STAAD SPACE
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 6 0 0;
MEMBER INCIDENCES
1 1 2;
START USER TABLE
TABLE 1
UNIT METER KN
WIDE FLANGE
I_500
0.019128 0.49 0.012 0.3 0.023 0.000840544 0.000103564 2.68914e-06 -
0.00588 0.0092
END
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
1 UPTABLE 1 I_500
****************************************
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 PINNED
2 FIXED BUT FX MY MZ
1 UNI GY -150
1 UNI GZ 30
PERFORM ANALYSIS
********************************
PARAMETER 1
CODE RUSSIAN
TRACK 2 ALL
DFF 200 ALL
TB 2 ALL
STP 2 ALL
SGR 9 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  B I    I_500         FAIL      SP cl.8.2.3      1.55         1
0.000E+00      6.750E+02    1.350E+02   3.000E+00
1  B I    I_500         PASS         DISPL         0.93         1
0.000E+00      6.750E+02    1.350E+02   3.000E+00
MATERIAL DATA
Steel                         = C255       SP16.13330
Modulus of elasticity         = 206.E+06 kPa
Design Strength (Ry)          = 229.E+03 kPa
SECTION PROPERTIES (units - m, m^2, m^3, m^4)
Member Length                 = 6.00E+00
Gross Area                    = 1.91E-02
Net Area                      = 1.91E-02
x-axis      y-axis
Moment of inertia (I)         :   841.E-06    104.E-06
Section modulus (W)           :   343.E-05    690.E-06
First moment of area (S)      :   191.E-05    525.E-06
Radius of gyration (i)        :   210.E-03    736.E-04
Effective Length              :   6.00E+00    6.00E+00
Slenderness                   :   0.00E+00    0.00E+00
DESIGN DATA (units -kN,m) SP16.13330.2017
Axial force                   :   0.000E+00
x-axis      y-axis
Moments                       :   675.0E+00    135.0E+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    2
CRITICAL CONDITIONS FOR EACH CLAUSE CHECK
F.(51)  Mx/(Cx*beta*Wxn,min*Ry*GammaC)+My/(Cy*Wyn,min*Ry*GammaC)=
675.0E+00/( 1.06E+00* 1.00E+00* 3.43E-03* 229.3E+03* 1.00E+00)+
135.0E+00/( 1.15E+00* 6.90E-04* 229.3E+03* 1.00E+00)=
1.55E+00>1
TAUx=Qy/Aw= 0.000E+00/ 532.8E-05= 0.00E+00 &lt;= 0,9*RS= 119.7E+03
TAUy=Qx/Af= 0.000E+00/ 138.0E-04= 0.00E+00 &lt;= 0,5*RS= 664.9E+02
LAMBDA_b=(Lef/b)*SQRT(Ry/E)=
( 600.0E-02/( 3.000E-01))*SQRT( 229.3E+03/ 206.0E+06)= 6.672E-01
SIGMA_x=Mx/(Wc*GammaC)= 675.0E+00/( 343.1E-05* 100.0E-02)= 1.967E+05 kPa
LAMBDA_ub=(0.35+0.0032*b/t+(0.76-0.02*b/t)*b/h)*delta*SQRT(Ry/SIGMA_x)=
=(0.35+0.0032* 1.304E+01+(0.76-0.02* 1.304E+01)* 6.424E-01)* 4.000E-01* 1.079E+00
= 3.076E-01&lt; LAMBDA_b= 6.672E-01
**Warning- Stability of the beam is not ensured according to cl. 8.4.4 b)
LIMIT SPAN/DEFLECTION (DFF) =    200.00   (DEFLECTION LIMIT=      0.030 M)
SPAN/DEFLECTION = 215.4E+00 (DEFLECTION=  2.785E-02M)
LOAD=    1     RATIO=    0.928     LOCATION=    3.000