V. SNiP SP16 2017 - Channel section with UDL
Design an channel section subjected to a uniform distributed load per the SP 16.13330.2017 code.
Details
A 5m long, simply supported beam has an American C15X50 section. The beam is subjected to a uniform distributed load of 100 kN/m in the Y direction. The steel used has a modulus of elasticity of 206,000 MPa and a Ryn = 235 MPa. γc1 = 1.1, γc2 = 1.1
Validation
Ry = Ryn/ γm = 223.8 MPa
Rs = 0.58×Ry/ γm = 129.8 MPa
Check for Flexure
Need to satisfy the following equation:
(Eq. 41) |
= | ||
= |
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:
(Eq. 73) |
(Eq. 73) |
So, the stability of the beam is not ensured per Cl. 8.4.4.b. Therefore a check per Cl 8.4.1 needs to be made.
Check for Lateral-Torsional Buckling
Need to satisfy the following equation:
(Eq. 69) |
(Eq. G.4) |
Since α > 40, from Table G.1:
(Eq. G.4) |
Thus, the ratio is
Check for Deflection
The maximum member deflection is limited to l / 200 = 0.025 m
Thus, the ratio is 0.0235 / 0.025 = 0.94
STAAD.Pro Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2023\Samples \Verification Models\09 Steel Design\Russia\SNiP SP16 2017 - Channel section with UDL.std is typically installed with the program.
STAAD PLANE
START JOB INFORMATION
ENGINEER DATE 01-Sep-20
END JOB INFORMATION
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 5 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 AMERICAN
1 TABLE ST C15X50
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 -100
PERFORM ANALYSIS
PRINT MEMBER PROPERTIES ALL
PARAMETER 1
CODE RUSSIAN
CB 1 ALL
PY 235000 ALL
GAMC2 1.1 ALL
GAMC1 1.1 ALL
TB 1 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 [ C15X50 FAIL SP cl.8.2.1(41) 1.37 1 0.000E+00 3.125E+02 0.000E+00 2.500E+00 1 [ C15X50 PASS SP cl.8.2.1(42) 0.00 1 0.000E+00 3.125E+02 0.000E+00 2.500E+00 * 1 [ C15X50 FAIL SP cl.8.2.1(44) 1.19 1 0.000E+00 3.125E+02 0.000E+00 2.500E+00 * 1 [ C15X50 FAIL SP cl.8.4.1 2.52 1 0.000E+00 3.125E+02 0.000E+00 2.500E+00 1 [ C15X50 PASS DISPL 0.94 1 0.000E+00 3.125E+02 0.000E+00 2.500E+00 MATERIAL DATA Steel = User Modulus of elasticity = 206.E+06 kPa Design Strength (Ry) = 235.E+03 kPa SECTION PROPERTIES (units - m, m^2, m^3, m^4) Member Length = 5.00E+00 Gross Area = 9.48E-03 Net Area = 9.48E-03 x-axis y-axis Moment of inertia (I) : 168.E-06 458.E-08 Section modulus (W) : 883.E-06 617.E-07 First moment of area (S) : 561.E-06 667.E-07 Radius of gyration (i) : 133.E-03 220.E-04 Effective Length : 5.00E+00 5.00E+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 : 312.5E+00 0.000E+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.(41) M/(Wn,min*Ry*GammaC)= 312.5E+00/( 8.83E-04* 235.0E+03* 1.10E+00= 1.37E+00>1 F.(44) 0.87/(Ry*GammaC)*SQRT(SIGMx^2+3*TAUxy^2)= 0.87/( 235.0E+03* 1.10E+00)*SQRT(-354.0E+03^2+3* 0.000E+00^2)= 1.19E+00>1 TAUxy/(Rs*GammaC)= 0.000E+00/( 136.3E+03* 1.10E+00)= 0.00E+00=<1 F.(69) Mx/(FIb*Wcx*Ry*GammaC)= 312.5E+00/( 5.43E-01* 8.83E-04* 235.0E+03* 1.10E+00)= 2.52E+00>1 LIMIT SPAN/DEFLECTION (DFF) = 200.00 (DEFLECTION LIMIT= 0.025 M) SPAN/DEFLECTION = 213.0E+00 (DEFLECTION= 2.348E-02M) LOAD= 1 RATIO= 0.939 LOCATION= 2.500