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:
(Eq. 43) |
= | ||
= | ||
= |
Thus, the ratio is
Check for Shear
Need to satisfy the following equation:
(Eq. 42) |
= |
Thus, the ratio is 0.0 < 1
Check for Combined Flexure & Shear
Need to satisfy the following equation:
(Eq. 44) |
= | ||
= | ||
= |
Thus, the ratio is
Check for Stability
Check per Cl. 8.4.4. From Table 11 of SP 16.13330-2017:
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
STAAD.Pro Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2023\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
****************************************
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
MEMBER LOAD
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 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 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=<1 TAUxy/(Rs*GammaC)= 0.000E+00/( 129.8E+03* 1.00E+00)= 0.00E+00=<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