V. AS4100 1998 - Bending Capacity for Non-compact Section
Verify the bending capacity for a non-compact section per AS4100-1998.
Given
The member is 8 m long simply-supported beam. The section is a 900WB218. The member is subject to major axis bending due to uniform dead load of 4.17 kN/m and live load of 8 kN/m as well as concentrated dead load of 104 kN and live load of 140 kN at mid-span.
Section Properties
- Overall depth of section, D = 910 mm
- Width of section, B = 350 mm
- Thickness of web, tw = 12 mm
- Thickness of flange, tf = 25 mm
- Area, Ag = 27,800 mm2
- Moment of inertia about major axis, Izz = 4,060 (10)6 mm4
- Moment of inertia about minor axis, Iyy = 179 (10)6 mm4
- Elastic section modulus about major axis, Zxx = 8.92 (10)6 mm3
- Elastic section modulus about minor axis, Zyy = 1.02 (10)6 mm3
- Plastic section modulus about major axis, Sxx = 9.96 (10)6 mm3
- Plastic section modulus about minor axis, Syy = 1.56 (10)6 mm3
- Torsion constant, J = 4.02 (10)6 mm4
- Warping moment, Iw = 35.05 (10)12 mm4
- Radius of gyration,
- Radius of gyration,
Material Properties
- E = 200,000 MPa
- G = 80,000 MPa
- fy = 360 MPa (flange); fy = 400 MPa (web)
Validation
Section Slenderness Check
Flange section slenderness parameter, , therefore the flange is non-compact.
Web section slenderness parameter, , therefore the web is non-compact.
Section Bending Capacity Major Axis
The plastic section capacity, Zcx , is the minimum of Sxx or 1.5×Zxx = 1.5(8.92 × 106) = 13.38 ×106 mm3 ; so Zcx = 9.96 ×106 mm3 .From Table 5.2 of AS 4100, λey = 115 and λep = 82.
For sections where , the effective section modulus is calculated as:
Section Bending Capacity Minor Axis
The plastic section capacity, Zcy is the minimum of Syy or 1.5×Zyy = 1.5(1.02 × 106) = 1.53 ×106 mm3 ; so Zcy = 1.53 ×106 mm3 .For sections where , the effective section modulus is calculated as:
Member Bending Capacity
Twist restraint factor,
From Table 5.6.3(2) of AS 4100, Load Height Factors, .
From Table 5.6.3(3) of AS 4100, Lateral Rotation Restraint Factors, .
Effective length of the member:
The slenderness reduction factor is then:
The moment shape factor is then:
The member moment capacity:
Comparison
Result Type | Theory | STAAD.Pro | Difference | Comment |
---|---|---|---|---|
Nominal section capacity major axis, Msx (kN·m) | 3,139 | 3,139 | none | |
Nominal section capacity major axis, Msy (kN·m) | 497.1 | 495.7831 | negligible | |
Member bending capacity, Mbx (kN·m) | 1,135 | 1,134.4 | negligible |
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2024\Samples \Verification Models\09 Steel Design\Australia\AS4100 1998 - Bending Capacity for Non-Compact section.std is typically installed with the program.
- The steel grade of Fy = 350 MPa is given by
SGR 8
(AS/NZS 3678 400). - The load height occuring at the top flange is specified by
LHT 1
.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 22-Mar-21
END JOB INFORMATION
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 8.00002 0 0;
MEMBER INCIDENCES
1 1 2;
DEFINE PMEMBER
1 PMEMBER 1
DEFINE MATERIAL START
ISOTROPIC STEEL
E 1.99947e+08
POISSON 0.3
DENSITY 76.8191
ALPHA 6.5e-06
DAMP 0.03
G 7.7221e+07
TYPE STEEL
STRENGTH RY 1.5 RT 1.2
END DEFINE MATERIAL
MEMBER PROPERTY AUSTRALIAN
1 TABLE ST WB900X218
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 PINNED
2 FIXED BUT FX MY MZ
LOAD 1 LOADTYPE Dead TITLE DEAD
MEMBER LOAD
1 UNI GY -4.17
1 CON GY -104
LOAD 2 LOADTYPE Dead TITLE LIVE
MEMBER LOAD
1 UNI GY -8
1 CON GY -140
LOAD COMB 3 COMBINATION LOAD CASE 3
1 1.2 2 1.5
PERFORM ANALYSIS
PARAMETER 1
CODE AUSTRALIAN 1998
LHT 1 PMEMB 1
SGR 8 PMEMB 1
TRACK 2 PMEMB 1
PBRACE TOP 0 P 1 P PMEMB 1
PBRACE BOTTOM 0 P 1 P PMEMB 1
CHECK CODE PMEMB 1
FINISH
STAAD Output
STAAD.Pro CODE CHECKING - ( AS4100-1998 ) V2.3
****************************************************
MEMBER DESIGN OUTPUT FOR PMEMBER 1
DESIGN Notes
------------
1. (*) next to a Load Case number signifies that a P-Delta analysis has not been performed for
that particular Load Case; i.e. analysis does not include second-order effects.
2. ϕ = 0.9 for all the calculations [AS4100 Table 3.4]
3. (#) next to Young's modulus E indicates that its value is not 200000 MPa as per AS4100 1.4.
DESIGN SUMMARY
=====================================================================================
Designation: ST WB900X218 (AUSTRALIAN SECTIONS)
Governing Load Case: 3*
Governing Criteria: AS-8.4.4.2
Governing Ratio: 0.710 (PASS)
SECTION PROPERTIES
=====================================================================================
d: 909.9999 mm bf: 350.0000 mm
tf: 25.0000 mm tw: 12.0000 mm
Ag: 27800.0000 mm2 J: 4.0200E+06 mm4 Iw: 35.0493E+12 mm6
Iz: 4.0600E+09 mm4 Sz: 9.9600E+06 mm3 (plastic) Zz: 8.9231E+06 mm3 (elastic)
rz: 382.1559E+00 mm
Iy: 179.0000E+06 mm4 Sy: 1.5600E+06 mm3 (plastic) Zy: 1.0229E+06 mm3 (elastic)
ry: 80.2424E+00 mm
MATERIAL PROPERTIES
=====================================================================================
Material Standard : AS 3678
Nominal Grade : 400
Residual Stress Category : HW (Heavily welded longitudinally)
E (#) :199947.000 MPa [AS 4100 1.4]
G : 80000.000 MPa [AS 4100 1.4]
fy, flange : 360.000 MPa [AS 4100 Table 2.1]
fy, web : 400.000 MPa [AS 4100 Table 2.1]
fu : 480.000 MPa [AS 4100 Table 2.1]
SLENDERNESS
=====================================================================================
Actual slenderness: 99.698
Allowable slenderness: 400.000
STAAD SPACE -- PAGE NO. 4
BENDING
=====================================================================================
Section Bending Capacity
Critical Load Case: 3* Critical Ratio: 0.257
Critical Location: 4.000 m from Start.
Mz* = -805.6343E+00 KNm My* = 0.0000E+00 KNm
Z-Axis Section Slenderness: Noncompact Y-Axis Section Slenderness: Noncompact
Zez = 9.6881E+06 mm3 Zey = 1.5302E+06 mm3
ϕMsz = 3.1390E+03 KNm ϕMsy = 495.7831E+00 KN[AS 4100 5.2.1]
Member Bending Capacity
Critical Load Case: 3* Critical Ratio: 0.710
Critical Location: 4.000 m from Start.
Crtiical Segment/Sub-segment:
Location (Type): 0.00 m(P )- 8.00 m(P )
Length: 8.00 m
Mz* = -805.6343E+00 KNm My* = 0.0000E+00 KNm
kt = 1.24 [AS4100 Table 5.6.3(1)]
kl = 1.40 [AS4100 Table 5.6.3(2)]
kr = 1.00 [AS4100 Table 5.6.3(3)]
le = 13.92 m [AS4100 5.6.3]
αm = 1.349 [AS4100 5.6.1.1(a)(iii)]
Mo = 1.1120E+03 KNm [AS4100 5.6.1.1(a)(iv)]
αsz = 0.268 [AS4100 5.6.1.1(a)(iv)]
ϕMbz = 1.1344E+03 KNm (<= ϕMsz) [AS4100 5.6.1.1(a)]
SHEAR
=====================================================================================
Section Shear Capacity
Critical Load Case: 3* Critical Ratio: 0.111
Critical Location: 0.667 m from Start.
Vy* = 224.0802E+00 KN
ϕVvy = 2.0266E+03 KN [AS 4100 5.11.2]
ϕVvmy = 2.0266E+03 KN [AS 4100 5.12.3]
Vz* = 0.0000E+00 KN
ϕVvz = 3.4020E+03 KN [AS 4100 5.11.2]
ϕVvmz = 3.4020E+03 KN [AS 4100 5.12.3]
STAAD SPACE -- PAGE NO. 5
AXIAL
=====================================================================================
Section Compression Capacity
Critical Load Case: 1* Critical Ratio: 0.000
Critical Location: 0.000 m from Start.
N* = 0.0000E+00 KN
Ae = 21.4645E+03 mm2 [AS 4100 6.2.3 / 6.2.4]
kf = 0.772 [AS 4100 6.2.2]
An = 27.8000E+03 mm2
ϕNs = 6.9545E+03 KN [AS 4100 6.2.1]
Member Compression Capacity
Lz = 8.00 m
Ly = 8.00 m
Lez = 8.00 m
Ley = 8.00 m
αb = 0.50 [AS 4100 Table 6.3.3(1)/6.3.3(2)]
λn,z = 22.073 [AS 4100 6.3.3]
αa,z = 8.186 [AS 4100 6.3.3]
λ,z = 26.166 [AS 4100 6.3.3]
h ,z = 0.041 [AS 4100 6.3.3]
x ,z = 6.660 [AS 4100 6.3.3]
αc,z = 0.957 [AS 4100 6.3.3]
ϕNcz = 0.6655E+4 KN [AS 4100 6.3.3]
λn,y = 105.125 [AS 4100 6.3.3]
αa,y = 16.742 [AS 4100 6.3.3]
λ,y = 113.496 [AS 4100 6.3.3]
h ,y = 0.326 [AS 4100 6.3.3]
x ,y = 0.917 [AS 4100 6.3.3]
αc,y = 0.457 [AS 4100 6.3.3]
ϕNcy = 0.3175E+4 KN [AS 4100 6.3.3]
ϕNc = N/A [AS 4100 6.3.3 / AS 4600 3.4.1(b)]
Section Tension Capacity
Critical Load Case: 1* Critical Ratio: 0.000
Critical Location: 0.000 m from Start.
N* = 0.0000E+00 KN
kt = 1.00 [User defined]
An = 27.8000E+03 mm2
ϕNt = 9.0072E+03 KN [AS 4100 7.2]
STAAD SPACE -- PAGE NO. 6
COMBINED BENDING AND AXIAL
=====================================================================================
Section Combined Capacity
Critical Condition: Cl 8.3.2
Critical Load Case: 3* Critical Ratio: 0.257
Critical Location: 4.000 m from Start.
N* = 0.0000E+00 KN Mz* = -805.6343E+00 KNm My* = 0.0000E+00 KNm
ϕNs = 6.9545E+03 KN [AS 4100 8.3.1]
ϕMsz = 3.1390E+03 KNm
ϕMsy = 495.7831E+00 KNm
ϕMrz = 3.1390E+03 KNm [AS 4100 8.3.2]
ϕMry = 495.7831E+00 KNm [AS 4100 8.3.3]
Member Combined Capacity - In-plane
Critical Load Case: N/A Critical Ratio: N/A
Critical Location: N/A
Member Combined Capacity - Out-of-plane(compression)
Critical Load Case: N/A Critical Ratio: N/A
Critical Location: N/A
Member Combined Capacity - Out-of-plane(tension)
Critical Load Case: 3* Critical Ratio: 0.710
Critical Location: 4.000 m from Start.
N* = 0.0000E+00 KN Mz* = -805.6343E+00 KNm My* = 0.0000E+00 KNm
ϕMbz = 1.1344E+03 KNm
ϕNt = 9.0072E+03 KN [AS 4100 8.4.4.2]
ϕMozt = 1.1344E+03 KNm [AS 4100 8.4.4.2]
Member Combined Capacity - Biaxial(compression)
Critical Load Case: N/A Critical Ratio: N/A
Critical Location: N/A
Member Combined Capacity - Biaxial(tension)
Critical Load Case: 3* Critical Ratio: 0.619
Critical Location: 4.000 m from Start.
N* = 0.0000E+00 KN Mz* = -805.6343E+00 KNm My* = 0.0000E+00 KNm
ϕMtz = 1.1344E+03 KNm [AS 4100 8.4.5.2]
ϕMry = 495.7831E+00 KNm [AS 4100 8.4.5.2]
STAAD SPACE -- PAGE NO. 7
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