 # 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:

 $M W n , min ⁡ R y γ c ≤ 1$ (Eq. 41)
where
 M = 100 (5)2 / 8 = 312.5 kN·m Wn,min = Wx = 883 cm3

Thus, the ratio is $312.5 883 ( 10 ) − 3 × 235 × 1.1 = 1.37 > 1$

Check for Shear

Need to satisfy the following equation:

 $Q S I t w R s γ c ≤ 1$ (Eq. 42)
where
 Q = 0 kN

Thus, the ratio is 0.0 < 1

Check for Combined Flexure & Shear

Need to satisfy the following equation:

 $0.87 R y γ c σ x 2 − σ x σ y + σ y 2 + 3 τ x y 2 ≤ 1$ (Eq. 44)
where
 σx = M / Wx = 312.5 (10)3 / 883 = 353.9 MPa σy = 0 MPa τxy = 0 MPa

Thus, the ratio is $0.87 235 × 1.1 ( 353.9 ) 2 = 1.19 > 1$

Check for Stability

Check per Cl. 8.4.4. From Table 11 of SP 16.13330-2017:

 $λ ¯ u b = 0.35 + 0.0032 b t + ( 0.76 − 0.02 b t ) b h$ (Eq. 73)
 $λ ¯ u b = 0.35 + 0.0032 94.49 16.51 + ( 0.76 − 0.02 94.49 16.51 ) 0.2593 = 0.536$ (Eq. 73)
$λ ¯ b = l e f b R y E = 1.787 > λ ¯ u b$

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:

 $M x ϕ b W c x R y γ c ≤ 1$ (Eq. 69)
 $α = 1.54 I t I y ( l e f h ) 2 = 59.62$ (Eq. G.4)

Since α > 40, from Table G.1:

$ψ = 3.15 + 0.04 α − 2.7 ( 10 ) − 5 α 2 = 5.439$
 $ϕ 1 = ψ I y I x ( h l e f ) 2 E R y = 0.754$ (Eq. G.4)
$ϕ b = 0.7 ϕ 1 = 0.7 ( 0.754 ) = 0.528$

Thus, the ratio is $312.5 0.528 × 883 ( 10 ) − 3 × 235 × 1.1 = 2.60 > 1$

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

## Results

Ratio of Flexure (Eq. 41) 1.37 1.37 none
Ratio of Shear (Eq. 42) 0 0 none
Ratio of LTB (Eq. 69) 2.60 2.60 none
Ratio of Combined Shear & Flexure (Eq. 44) 1.19 1.19 none
Deflection (m) 0.0235 0.02348 negligible
Deflection Ratio 0.94 0.94 none

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\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
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 CODE CHECKING - (SP 16.13330.2017)   V1.0
********************************************
ALL UNITS ARE - KN METRE
========================================================================
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      2.60         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=&lt;1
F.(69)  Mx/(FIb*Wcx*Ry*GammaC)=
312.5E+00/( 5.28E-01* 8.83E-04* 235.0E+03* 1.10E+00)= 2.60E+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