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:
Need to satisfy the following equation from Cl. 8.2.3:
(Eq. 51) |
= | ||
= | ||
= | ||
= | ||
= |
Thus, the ratio is
Check for Stability
(Eq. 76) |
Per Cl. 8.4.6, the value is multiplied by δ.
where= | ||
= |
(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
STAAD.Pro Input
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
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MEMBER PROPERTY
1 UPTABLE 1 I_500
****************************************
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 PINNED
2 FIXED BUT FX MY MZ
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
MEMBER LOAD
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 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 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 <= 0,9*RS= 119.7E+03 TAUy=Qx/Af= 0.000E+00/ 138.0E-04= 0.00E+00 <= 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< 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