V. SNiP SP16 2017 - I section with UDL
Design an I section subjected to a uniform distributed load per the SP 16.13330.2017 code.
Details
A 5m long, simply supported beam has a European HD320X127 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 Stability
So, the stability of the beam is not ensured per Cl. 8.4.4.b. Check per Cl 8.4.1 needs to be performed.
Check for Lateral-Torsional Buckling
Use an effective length of 10 m.
Need to satisfy the following equation:
(Eq. 69) |
(Eq. G.4) |
Since 0.1 < α < 40, from Table G.1:
(Eq. G.4) |
Thus, the ratio is
Check for Combined Flexure & Shear
Need to satisfy the following equation:
(Eq. 44) |
= | ||
= | ||
= |
Thus, the ratio is
Check for Deflection
The maximum member deflection is limited to l / 200 = 0.025 m
Thus, the ratio is 0.0128 / 0.025 = 0.51
Results
Result Type | Reference | STAAD.Pro | Difference | Comments |
---|---|---|---|---|
Ratio of Flexure (Eq. 41) | 0.63 | 0.63 | none | |
Ratio of Shear (Eq. 42) | 0 | 0 | none | |
Ratio of LTB (Eq. 69) | 0.67 | 0.67 | none | |
Ratio of Combined Shear & Flexure (Eq. 44) | 0.55 | 0.55 | none | |
Deflection (m) | 0.0128 | 0.01281 | negligible | |
Deflection Ratio | 0.51 | 0.51 | none |
STAAD.Pro Input
The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\Russia\SNiP SP16 2017 - I section with UDL.std is typically installed with the program.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 1-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 EUROPEAN
1 TABLE ST HD320X127
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
PARAMETER 1
CODE RUSSIAN
CMN 8 ALL
CMM 6 ALL
GAMM 2 ALL
LY 10 ALL
LZ 10 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 I HD320X127 PASS SP cl.8.2.1(41) 0.63 1 0.000E+00 3.125E+02 0.000E+00 2.500E+00 1 I HD320X127 PASS SP cl.8.2.1(42) 0.00 1 0.000E+00 3.125E+02 0.000E+00 2.500E+00 1 I HD320X127 PASS SP cl.8.2.1(44) 0.55 1 0.000E+00 3.125E+02 0.000E+00 2.500E+00 1 I HD320X127 PASS SP cl.8.4.1 0.67 1 0.000E+00 3.125E+02 0.000E+00 2.500E+00 1 I HD320X127 PASS DISPL 0.51 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 = 1.61E-02 Net Area = 1.61E-02 x-axis y-axis Moment of inertia (I) : 308.E-06 924.E-07 Section modulus (W) : 193.E-05 616.E-06 First moment of area (S) : 107.E-05 470.E-06 Radius of gyration (i) : 138.E-03 757.E-04 Effective Length : 1.00E+01 1.00E+01 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/( 1.93E-03* 235.0E+03* 1.10E+00= 6.28E-01=<1 F.(44) 0.87/(Ry*GammaC)*SQRT(SIGMx^2+3*TAUxy^2)= 0.87/( 235.0E+03* 1.10E+00)*SQRT(-162.2E+03^2+3* 0.000E+00^2)= 5.46E-01=<1 TAUxy/(Rs*GammaC)= 0.000E+00/( 136.3E+03* 1.10E+00)= 0.00E+00=<1 LAMBDA_b=(Lef/b)*SQRT(Ry/E)= ( 100.0E-01/( 3.000E-01))*SQRT( 235.0E+03/ 206.0E+06)= 1.126E+00 SIGMA_x=Mx/(Wc*GammaC)= 312.5E+00/( 192.6E-05* 110.0E-02)= 1.475E+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* 1.463E+01+(0.76-0.02* 1.463E+01)* 1.002E+00)* 1.000E+00* 1.262E+00 = 1.092E+00< LAMBDA_b= 1.126E+00 **Warning- Stability of the beam is not ensured according to cl. 8.4.4 b) F.(69) Mx/(FIb*Wcx*Ry*GammaC)= 312.5E+00/( 9.36E-01* 1.93E-03* 235.0E+03* 1.10E+00)= 6.70E-01=<1 LIMIT SPAN/DEFLECTION (DFF) = 200.00 (DEFLECTION LIMIT= 0.025 M) SPAN/DEFLECTION = 390.4E+00 (DEFLECTION= 1.281E-02M) LOAD= 1 RATIO= 0.512 LOCATION= 2.500