V. AS4100 1998 - Combined Section and Member In-Plane Capacity

Verify the bending capacity in major and minor axis bending, biaxial bending, and in-plane bending for a UC member subject an axial load per AS4100-1998.

Given

The member is 7 m long and part of a steel frame structure. The section is a 200UC52.2. The member is subject to an axial load of 143.9 kN.

Section Properties

• Depth of section, D = 206 mm
• Width of section, B = 204 mm
• Thickness of web, tw = 8 mm
• Thickness of flange, tf = 12.5 mm
• Area, Ag = 6,660 mm2
• Moment of inertia about major axis, Izz = 52.8 (10)6 mm4
• Moment of inertia about minor axis, Iyy = 17.7 (10)6 mm4
• Elastic section modulus about major axis, Zxx = 513 (10)3 mm3
• Elastic section modulus about minor axis, Zyy = 174 (10)3 mm3
• Plastic section modulus about major axis, Sxx = 570 (10)3 mm3
• Plastic section modulus about minor axis, Syy = 264 (10)3 mm3

Material Properties

• fy = 300 MPa (flange); fy = 320 MPa (web)

Validation

Combined Major Axis Section Moment Capacity

Nominal axial capacity:

Nominal section capacity:

The section is compact, so the alternate method is applicable.

$ϕ M rx = ϕ 1.18 M sx ( 1 - N ϕ N s ) ≤ ϕ M sx$

Combined Minor Axis Section Moment Capacity

Nominal section capacity: $ϕ M sy = ϕ S yy F y ≤ ϕ 1.5 Z yy F y$

The section is compact, so the alternate method is applicable.

$ϕ M ry = ϕ 1.19 M sy ( 1 - N ϕ N s ) 2 ≤ ϕ M sy$

Member In-plane Capacity Check

The section is compact, so the alternate method is applicable. The larger end moment = 111.1 kN·m and the smaller end moment = 108.1 kN·m.

$β mx = 108.1 111.1 = 0.973$
$ϕ M ix = ϕ M s { [ 1 - ( 1 + β m 2 ) 3 ] ( 1 - N ϕ N c ) + 1.18 ( 1 + 1 + β m 2 ) 3 ( 1 - N ϕ N c ) } ≤ ϕ M rx$

Comparison

Table 1. Comparison of results
Result Type Theory STAAD.Pro Difference Comment
Combined major axis section moment capacity (kN·m) 153.9 153.9 none
Combined minor axis section moment capacity (kN·m) 153.9 153.9 none
Menber in-plane capacity check (kN·m) 153.9 153.9 none

Tip: You can copy and paste this content directly into a .std file to run in STAAD.Pro.

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\Australia\AS4100 1998 - Combined Section and Member In-Plane Capacity.STD is typically installed with the program.

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 16-Apr-21
END JOB INFORMATION
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 0 7 0; 3 12 7 0; 4 12 0 0; 5 0 12 0; 6 12 12 0;
MEMBER INCIDENCES
1 1 2; 2 2 3; 3 3 4; 4 2 5; 5 3 6; 6 5 6;
DEFINE PMEMBER
1 PMEMBER 4
4 PMEMBER 5
6 PMEMBER 6
2 PMEMBER 7
5 PMEMBER 8
3 PMEMBER 9
DEFINE MATERIAL START
ISOTROPIC STEEL
E 2.05e+08
POISSON 0.3
DENSITY 76.8195
ALPHA 1.2e-05
DAMP 0.03
G 7.88462e+07
TYPE STEEL
STRENGTH RY 1.5 RT 1.2
END DEFINE MATERIAL
MEMBER PROPERTY AUSTRALIAN
4 5 TABLE ST UC150X30.0
1 3 TABLE ST UC200X52.2
6 TABLE ST UB250X25.7
2 TABLE ST UB310X40.4
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 4 FIXED
6 CON GY -40
2 CON GY -80
5 6 FY -20
2 3 FY -50
5 FX 10
2 FX 30
PERFORM ANALYSIS
PARAMETER 1
CODE AUSTRALIAN
TRACK 2 PMEMB 9
CHECK CODE PMEMB 9
FINISH


                    STAAD.Pro CODE CHECKING - (  AS4100-1998   ) V2.3
****************************************************
MEMBER DESIGN OUTPUT FOR PMEMBER     9
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   UC200X52.2               (AUSTRALIAN SECTIONS)
Governing Criteria: SLENDERNESS
Governing Ratio:   0.754  (PASS)
SECTION PROPERTIES
=====================================================================================
d:       206.0000 mm   bf:       204.0000 mm
tf:        12.5000 mm   tw:         8.0000 mm
Ag:      6660.0000 mm2   J:   325.0000E+03 mm4             Iw:   165.6820E+09 mm6
Iz:    52.8000E+06 mm4  Sz:   570.0000E+03 mm3 (plastic)   Zz:   512.6214E+03 mm3 (elastic)
rz:    89.0389E+00 mm
Iy:    17.7000E+06 mm4  Sy:   264.0000E+03 mm3 (plastic)   Zy:   173.5294E+03 mm3 (elastic)
ry:    51.5525E+00 mm
MATERIAL PROPERTIES
=====================================================================================
Material Standard        :  AS/NZS 3679.1
Residual Stress Category :  HR (Hot-rolled)
E (#)      :204999.984 MPa    [AS 4100 1.4]
G          : 80000.000 MPa    [AS 4100 1.4]
fy, flange :   300.000 MPa    [AS 4100 Table 2.1]
fy, web    :   320.000 MPa    [AS 4100 Table 2.1]
fu         :   440.000 MPa    [AS 4100 Table 2.1]
SLENDERNESS
=====================================================================================
Actual slenderness   : 135.784
Allowable slenderness: 180.000
STAAD SPACE                                              -- PAGE NO.    4
BENDING
=====================================================================================
Section Bending Capacity
Critical Load Case:     1*          Critical Ratio:   0.722
Critical Location:        0.000 m from Start.
Mz* =   111.0612E+00 KNm                      My* =     0.0000E+00 KNm
Z-Axis Section Slenderness: Compact           Y-Axis Section Slenderness: Compact
Zez =   570.0000E+03 mm3                      Zey =   260.2941E+03 mm3
ϕMsz =   153.9000E+00 KNm                     ϕMsy =    70.2794E+00 KN[AS 4100 5.2.1]
Member Bending Capacity
Critical Load Case:     1*          Critical Ratio:   0.722
Critical Location:        0.000 m from Start.
Crtiical Segment/Sub-segment:
Location (Type):   0.00 m(F )-  7.00 m(F )
Length:    7.00 m
Mz* =   111.0612E+00 KNm                      My* =     0.0000E+00 KNm
kt   =      1.00                         [AS4100 Table 5.6.3(1)]
kl   =      1.00                         [AS4100 Table 5.6.3(2)]
kr   =      1.00                         [AS4100 Table 5.6.3(3)]
le   =      7.00 m                       [AS4100 5.6.3]
αm   =     2.435                         [AS4100 5.6.1.1(a)(iii)]
Mo   =   154.9263E+00 KNm                [AS4100 5.6.1.1(a)(iv)]
αsz  =     0.570                         [AS4100 5.6.1.1(a)(iv)]
ϕMbz =   153.9000E+00 KNm (&lt;= ϕMsz)      [AS4100 5.6.1.1(a)]
SHEAR
=====================================================================================
Section Shear Capacity
Critical Load Case:     1*          Critical Ratio:   0.110
Critical Location:        0.000 m from Start.
Vy*  =    31.3075E+00 KN
ϕVvy  =   284.7744E+00 KN                [AS 4100 5.11.2]
ϕVvmy =   284.7744E+00 KN                [AS 4100 5.12.3]
Vz*  =     0.0000E+00 KN
ϕVvz  =   826.2000E+00 KN                [AS 4100 5.11.2]
ϕVvmz =   826.2000E+00 KN                [AS 4100 5.12.3]
STAAD SPACE                                              -- PAGE NO.    5
AXIAL
=====================================================================================
Section Compression Capacity
Critical Load Case:     1*          Critical Ratio:   0.269
Critical Location:        0.000 m from Start.
N*    =   143.8336E+00 KN
Ae    =     6.6600E+03 mm2               [AS 4100 6.2.3 / 6.2.4]
kf    =     1.000                        [AS 4100 6.2.2]
An    =     6.6600E+03 mm2
ϕNs   =     1.7982E+03 KN                [AS 4100 6.2.1]
Member Compression Capacity
Lz    =      7.00 m
Ly    =      7.00 m
Lez   =      7.00 m
Ley   =      7.00 m
αb    =      0.00                        [AS 4100 Table 6.3.3(1)/6.3.3(2)]
λn,z  =    86.121                        [AS 4100 6.3.3]
αa,z  =    18.714                        [AS 4100 6.3.3]
λ,z   =    86.121                        [AS 4100 6.3.3]
h ,z   =     0.237                        [AS 4100 6.3.3]
x ,z   =     1.175                        [AS 4100 6.3.3]
αc,z  =     0.637                        [AS 4100 6.3.3]
ϕNcz  = 0.1146E+4 KN                     [AS 4100 6.3.3]
λn,y  =   148.744                        [AS 4100 6.3.3]
αa,y  =    12.969                        [AS 4100 6.3.3]
λ,y   =   148.744                        [AS 4100 6.3.3]
h ,y   =     0.441                        [AS 4100 6.3.3]
x ,y   =     0.764                        [AS 4100 6.3.3]
αc,y  =     0.298                        [AS 4100 6.3.3]
ϕNcy  = 0.5353E+3 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    =     6.6600E+03 mm2
ϕNt   =     1.7982E+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:     1*          Critical Ratio:   0.722
Critical Location:        0.000 m from Start.
N* =   143.8336E+00 KN    Mz* =   111.0612E+00 KNm      My* =     0.0000E+00 KNm
ϕNs   =     1.7982E+03 KN                [AS 4100 8.3.1]
ϕMsz  =   153.9000E+00 KNm
ϕMsy  =    70.2794E+00 KNm
ϕMrz  =   153.9000E+00 KNm               [AS 4100 8.3.2]
ϕMry  =    70.2794E+00 KNm               [AS 4100 8.3.3]
Member Combined Capacity - In-plane
Critical Load Case:     1*          Critical Ratio:   0.722
Critical Location:        0.000 m from Start.
N* =   143.8336E+00 KN    Mz* =   111.0612E+00 KNm      My* =     0.0000E+00 KNm
ϕNcz  =     1.1463E+03 KN                [AS 4100 8.4.2.2]
ϕMiz  =   153.9000E+00 KNm               [AS 4100 8.4.2.2]
ϕNcy  =   535.3019E+00 KN                [AS 4100 8.4.2.2]
ϕMiy  =    70.2794E+00 KNm               [AS 4100 8.4.2.2]
Member Combined Capacity - Out-of-plane(compression)
Critical Load Case:     1*          Critical Ratio:   0.722
Critical Location:        0.000 m from Start.
N* =   143.8336E+00 KN    Mz* =   111.0612E+00 KNm      My* =     0.0000E+00 KNm
ϕMbz  =   153.9000E+00 KNm
ϕNcy  =   535.3019E+00 KN
ϕMozc =   153.9000E+00 KNm               [AS 4100 8.4.4.1]
Member Combined Capacity - Out-of-plane(tension)
Critical Load Case: N/A             Critical Ratio: N/A
Critical Location: N/A
Member Combined Capacity - Biaxial(compression)
Critical Load Case:     1*          Critical Ratio:   0.633
Critical Location:        0.000 m from Start.
N* =   143.8336E+00 KN    Mz* =   111.0612E+00 KNm      My* =     0.0000E+00 KNm
ϕMcz  =   153.9000E+00 KNm               [AS 4100 8.4.5.1]
ϕMiy  =    70.2794E+00 KNm               [AS 4100 8.4.5.1]
Member Combined Capacity - Biaxial(tension)
Critical Load Case: N/A             Critical Ratio: N/A
Critical Location: N/A
STAAD SPACE                                              -- PAGE NO.    7
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