V. SNiP SP16 2017 - CLASS 2 Rolled I Section with Bi-Moment
Verify a rolled I section subjected to uniform distributed loads per the SP 16.13330.2017 code.
Details
A 6m long, simply supported beam has a UPT HE500A section. The beam is subjected to a uniform distributed load of 132.2 kN/m in the Y direction and a bi-moment of 10 kN·. The steel used has a modulus of elasticity of 206,000 MPa and a Ryn = 235 MPa. γm = 1.025, γc = 1
Section Properties
D = 490 mm
B = 300 mm
tf = 23 mm
tw = 12 mm
Ix = 84,054 cm4
Iy = 10,356 cm4
Wx = 3,431 cm3
Wy = 690.4 cm3
Validation
Ry = Ryn/ γm = 229.3 MPa
Rs = 0.58×Ry/ γm = 133.0 MPa
Check for Flexure
As this is a Class 2 section (elasto-plastic), it must satisfy equation 53 from Cl. 8.2.3:
(Eq. 53) |
= | ||
= | ||
= | ||
= |
Thus, the ratio is
Check for Stability
Check per Cl. 8.4.4. From Table 11 of SP 16.13330-2017:
Per Cl. 8.4.6, this value is multiplied by δ as indicated above, where:
(Eq. 76) |
= |
Therefore, since c1x = cx, δ = 1 - 0.6 = 0.4
So, the stability of the beam is not ensured per Cl. 8.4.4.b.
Results
Check for Deflection
The maximum member deflection is limited to l / 200 = 0.03 m
Thus, the ratio is 0.0129 / 0.03 = 0.429
STAAD.Pro Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2023\Samples \Verification Models\09 Steel Design\Russia\SNiP SP16 2017 - CLASS 2 Rolled I Section with Bi-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
UTP-HE-500-A
0.019128 0.49 0.012 0.3 0.023 0.000840544 0.000103564 2.68914e-06 -
0.00588 0.0092 0.3 0.023
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 RUSSIAN
1 UPTABLE 1 UTP-HE-500-A
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 PINNED
2 FIXED BUT FX MZ
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
MEMBER LOAD
1 UNI GY -132.2
PERFORM ANALYSIS
PARAMETER 1
CODE RUSSIAN
BMT 10 ALL
GAMM 1 ALL
SGR 9 ALL
GAMC2 1 ALL
GAMC1 1 ALL
GAMM 1 ALL
STP 2 ALL
TB 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 B I UTP-HE-500-A PASS SP cl.8.2.3 0.73 1 0.000E+00 5.949E+02 0.000E+00 3.000E+00 1 B I UTP-HE-500-A PASS DISPL 0.43 1 0.000E+00 5.949E+02 0.000E+00 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 Sectorial moment of inertia (Iw) : 564.E-08 [m^6] Sectorial section modulus (Ww) : 226.E-07 [m^4] Sectorial area (coordinate) (w) : 250.E-03 [m^2] DESIGN DATA (units -kN,m) SP16.13330.2017 Axial force : 0.000E+00 x-axis y-axis Moments : 594.9E+00 0.000E+00 Shear force : 0.000E+00 0.000E+00 Bi-moment : 100.0E-01 [kNm^2] Stress-strain state checked as: Class 2 CRITICAL CONDITIONS FOR EACH CLAUSE CHECK F.(53) Mx/(Cx*beta*Wxn,min*Ry*GammaC)+B/(Cw*Wyn,min*Ry*GammaC)= 594.9E+00/( 1.06E+00* 1.00E+00* 3.43E-03* 229.3E+03* 1.00E+00)+ 100.0E-01/( 2.92E+00* 6.90E-04* 229.3E+03* 1.00E+00)= 7.33E-01=<1 TAUx=Qy/Aw= 0.000E+00/ 532.8E-05= 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)= 594.9E+00/( 343.1E-05* 100.0E-02)= 1.734E+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* 1.150E+00 = 3.277E-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 = 466.0E+00 (DEFLECTION= 1.287E-02M) LOAD= 1 RATIO= 0.429 LOCATION= 3.000