# V. SNiP SP16 2017 - I section with biaxial moment

Design an I section subjected to uniform distributed loads in both major in minor axes per the SP 16.13330.2017 code.

## Details

A 6m long, simply supported beam has a European HE500A section. The beam is subjected to a uniform distributed load of 132.2 kN/m in the Y direction and 30 kN/m in the Z direction. The steel used has a modulus of elasticity of 206,000 MPa and a Ryn = 235 MPa. γm = 1.05, γc = 1

## Validation

Ry = Ryn/ γm = 223.8 MPa

Rs = 0.58×Ry/ γm = 129.8 MPa

Check for Flexure

Need to satisfy the following equation from Cl. 8.2.1:

 $MxIxnRyγcy±MyIynRyγcs±BωIωnRyγc≤1$ (Eq. 43)
where
 Mx = 132.2 (6)2 / 8 = 594.9 kN·m My = 30 (6)2 / 8 = 135 kN·m Bx = 0

Thus, the ratio is $M x I x n R y γ c y ± M y I y n R y γ c s ± B ω I ω n R y γ c = 1.62 > 1$

Check for Shear

Need to satisfy the following equation:

 $Q S I t w R s γ c ≤ 1$ (Eq. 42)
where
 Q = 0 kN

Thus, the ratio is 0.0 < 1

Check for Combined Flexure & Shear

Need to satisfy the following equation:

 $0.87 R y γ c σ x 2 − σ x σ y + σ y 2 + 3 τ x y 2 ≤ 1$ (Eq. 44)
where
 σx = Mx / Wx = 594.9 (10)3 / 3,550 = 167.6 MPa σy = My / Wy = 135 (10)3 / 691.1 = 195.3 MPa τxy = 0 MPa

Thus, the ratio is $0.87 223.8 × 1. ( 167.6 ) 2 - 167.6 × 195.3 + ( 195.3 ) 2 = 0.71 < 1$

Check for Stability

Check per Cl. 8.4.4. From Table 11 of SP 16.13330-2017:

$λ ¯ u b = [ 0.35 + 0.0032 b t + ( 0.76 − 0.02 b t ) b h ] R y ϕ x$
$λ ¯ u b = [ 0.35 + 0.0032 300 23 + ( 0.76 − 0.02 300 23 ) 300 490 ] 235 167.6 = 0.823$
$λ ¯ b = l e f b R y E 6 0.3 235 206,000 = 0.659 < λ ¯ u b$

So, the stability of the beam is ensured per Cl. 8.4.4.b. Check per Cl 8.4.1 is not required.

## Results

Check for Deflection

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

Thus, the ratio is 0.0267 / 0.03 = 0.89

Ratio of Flexure (Eq. 43) 1.62 1.62 none
Ratio of Shear (Eq. 42) 0 0 none
Ratio of Combined Shear & Flexure (Eq. 44) 0.71 0.71 none
Deflection (m) 0.0267 0.02675 negligible
Deflection Ratio 0.89 0.89 none

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\Russia\SNiP SP16 2017 - 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;
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 EUROPEAN
1 TABLE ST HE500A
****************************************
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 PINNED
*2 FIXED BUT FX MZ
2 FIXED BUT FX MY MZ
****************************************
1 UNI GY -132.2
1 UNI GZ 30
********************************
PERFORM ANALYSIS
***********************
PARAMETER 1
CODE RUSSIAN
ENSGR 1 ALL
GAMM 2 ALL
DFF 200 ALL
TRACK 2 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  I      HE500A       FAIL     SP cl.8.2.1(43)    1.62         1
0.000E+00      5.949E+02    1.350E+02   3.000E+00
1  I      HE500A       PASS     SP cl.8.2.1(42)    0.00         1
0.000E+00      5.949E+02    1.350E+02   3.000E+00
1  I      HE500A       PASS     SP cl.8.2.1(44)    0.71         1
0.000E+00      5.949E+02    1.350E+02   3.000E+00
1  I      HE500A        PASS         DISPL         0.89         1
0.000E+00      5.949E+02    1.350E+02   3.000E+00
MATERIAL DATA
Steel                         = S235       EN10025-2
Modulus of elasticity         = 206.E+06 kPa
Design Strength (Ry)          = 224.E+03 kPa
SECTION PROPERTIES (units - m, m^2, m^3, m^4)
Member Length                 = 6.00E+00
Gross Area                    = 1.98E-02
Net Area                      = 1.98E-02
x-axis      y-axis
Moment of inertia (I)         :   870.E-06    104.E-06
Section modulus (W)           :   355.E-05    691.E-06
First moment of area (S)      :   197.E-05    530.E-06
Radius of gyration (i)        :   210.E-03    724.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                       :   594.9E+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    1
CRITICAL CONDITIONS FOR EACH CLAUSE CHECK
F.(43)  (Mx*y)/(Ixn*Ry*GammaC)+(My*x)/(Iyn*Ry*GammaC)+
+(B*w)/(Iwn*Ry*GammaC)=
( 594.9E+00* 2.45E-01)/( 8.70E-04* 223.8E+03* 1.00E+00)+
( 135.0E+00* 1.50E-01/( 1.04E-04* 223.8E+03* 1.00E+00)+
( 0.000E+00* 2.50E-01)/( 5.64E-06* 223.8E+03* 1.00E+00)=
= 1.62E+00>1
F.(44)  0.87/(Ry*GammaC)*SQRT(SIGMx^2-SIGMx*SIGMy+SIGMy^2+3*TAUxy^2)=
0.87/( 223.8E+03* 1.00E+00)*SQRT(-167.6E+03^2--167.6E+03
*-195.3E+03+-195.3E+03^2+3* 0.000E+00^2)= 7.11E-01=&lt;1
TAUxy/(Rs*GammaC)= 0.000E+00/( 129.8E+03* 1.00E+00)= 0.00E+00=&lt;1
LAMBDA_b=(Lef/b)*SQRT(Ry/E)=
( 600.0E-02/( 3.000E-01))*SQRT( 223.8E+03/ 206.0E+06)= 6.592E-01
SIGMA_x=Mx/(Wc*GammaC)= 594.9E+00/( 355.0E-05* 100.0E-02)= 1.676E+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)* 1.000E+00* 1.156E+00
= 8.232E-01>=LAMBDA_b= 6.592E-01
Stability of the beam is ensured according to cl. 8.4.4 b)
Check according to cl. 8.4.1 is not required
LIMIT SPAN/DEFLECTION (DFF) =    200.00   (DEFLECTION LIMIT=      0.030 M)
SPAN/DEFLECTION = 224.3E+00 (DEFLECTION=  2.675E-02M)
LOAD=    1     RATIO=    0.892     LOCATION=    3.000