V. AS4600 2018 - C Shear Check
Verify the shear strength of a cold-formed channel along the local z & y directions per the AS6400:2018 code.
Reference
-
Technical Committee BD-082. Cold-formed steel structures AS/NZS 4600:2018. Sydney, NSW. 2012.
- OneSteel Market Mills. Cold Formed Structural Hollow Sections & Profiles. Fourth Edition. 2003. p.46
Problem
A 6 m long, cantilever beam is subjected to an transverse load of 5 kN along the major axis and 10 kN along the minor axis. The section is an Duragal C300X90X8.0 channel. The material is steel with a fy = 400 MPa and fu = 450 MPa.
Section Properties
From reference #2:
- Depth, d = 300 mm
- Flange width, bf = 90 mm
- Thickness, t = 8.0 mm
- Inside corner radius, ri = 8.0 mm
Calculations
Along Z Direction
Shear force: Vz = 10 kN
Depth of flat portion of web, d1 = bf - tw - ri = 90 - 8.0 - 8.0 = 74 mm
Shear buckling coefficient, kv = 5.34
The slenderness ratio of the web:
Note: The STAAD input file uses a modulus value of
E = 205 MPa, which results in a slightly
higher permissible slender ratio of 52.31.
The nominal shear capacity per flange (web
in the z direction):
Vvz = 2×Vvs =
2(151.6) = 303.1 kN
Capacity ratio for shear along minor axis
Along Y Direction
Shear force: Vy = 5 kN
Depth of flat portion of web, d1 = d - 2tw - 2ri = 300 - 2(8.0) - 2(8.0) = 268 mm
Shear buckling coefficient, kv = 5.34
The slenderness ratio of the web:
The nominal shear capacity of the web:
Capacity ratio for shear along minor axis
Comparison
| Result Type | Reference | STAAD.Pro | Difference | Comments |
|---|---|---|---|---|
| Shear strength along minor axis, ϕVvz (kips) | 272.8 | 272.794 | negligible | |
| Ratio for shear along minor axis | 0.037 | 0.0367 | negligible | |
| Shear strength along major axis, ϕVvy (kips) | 494.0 | 493.978 | negligible | |
| Ratio for shear along major axis | 0.010 | 0.0101 | negligible |
STAAD.Pro Input File
The file C:\Users\Public\Public Documents\STAAD.Pro 2024\Samples\Verification Models\09 Steel Design\Australia\AS4600 2018 - C Shear Check.STD is typically installed with the program.
The following design parameters are used:
- The steel yield strength is directly specified:
FYLD 400000andFU 450000
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 29-June-24
END JOB INFORMATION
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 6 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
G 7.88462e+07
TYPE STEEL
STRENGTH RY 1.5 RT 1.2
END DEFINE MATERIAL
MEMBER PROPERTY 'AUSTRALIA COLD FORMED (ONESTEEL).DB3'
1 TABLE 'CHANNEL - DURAGAL' ST 'C300X90X8.0'
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 FIXED
LOAD 1 LOADTYPE Dead TITLE LOAD CASE 1
JOINT LOAD
2 FY -5 FZ -10
PERFORM ANALYSIS PRINT ALL
PARAMETER 1
CODE AS NZS 4600 2018
FYLD 400000 ALL
FU 450000 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH
STAAD.Pro Output
--------------------------------------------------------------------------------
***STAAD.PRO DESIGN RESULTS SUMMARY***
Code: AS/NZS 4600:2018 [v1.0]
All units are in kN-m unless otherwise noted
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
MEMBER: 1 PROFILE: C300X90X8.0
CRITICAL RATIO: 2.272E+1 | STATUS: FAIL | GOVERNING CRITERIA: STRENGTH
--------------------------------------------------------------------------------
STRENGTH:
Status: FAIL Ratio: 22.7 Loadcase: 1
Location: 0.0 Reference: Eq. 3.3.5(1)
Fx: 0.0 Fy: -5.00 Fz: -10.0
Mx: 0.0 My: 60.0 Mz: -30.0
--------------------------------------------------------------------------------
SECTION PROPERTIES:
Ag: 0.363E-02
Ix: 0.774E-07 Iy: 0.244E-05 Iz: 0.442E-04
Sy: 0.350E-04 Sz: 0.295E-03 Cw: 0.377E-07
--------------------------------------------------------------------------------
SLENDERNESS RATIO:
Ratio: 1.16 Actual: 231.425 Allowable: 200.000
Ky.Ly/ry: 231.425 Ky: 1.00 Ly: 6.00
Kz.Lz/rz: 54.4 Kz: 1.00 Lz: 6.00
--------------------------------------------------------------------------------
DIMENSIONAL:
Web depth to thickness ratio:
Ratio: 0.168 [PASS] Actual: 33.5 Allowable: 200.000
Width to thickness ratio:
Ratio: 0.154 [PASS] Actual: 9.25 Allowable: 60.0
Unstiffened width to thickness ratio:
Ratio: 0.154 [PASS] Actual: 9.25 Allowable: 60.0
--------------------------------------------------------------------------------
TENSION:
(Gross Section) Yielding:
Ratio: 0.0 Demand: 0.0 Capacity: 1.31E+03
Ref.: Eq. 3.2.1 LoadCase: 1 Section: 1
Intermediate results:
Nominal section capacity, Nt: 1.45E+03
(Net Section) Rupture:
Ratio: 0.0 Demand: 0.0 Capacity: 1.25E+03
Ref.: Eq. 3.2.1 LoadCase: 1 Section: 1
Intermediate results:
Net area, An: 0.363E-02
Nominal section capacity, Nt: 1.39E+03
--------------------------------------------------------------------------------
STAAD SPACE -- PAGE NO. 6
--------------------------------------------------------------------------------
***STAAD.PRO DESIGN RESULTS SUMMARY***
Code: AS/NZS 4600:2018 [v1.0]
All units are in kN-m unless otherwise noted
--------------------------------------------------------------------------------
***Contd. Member: 1 | Ratio: 2.272E+1 [F] | Profile: C300X90X8.0
COMPRESSION:
Member Capacity:
Ratio: 0.0 Demand: 0.0 Capacity: 102.263
Ref.: Cl. 3.4.1 LoadCase: 1 Section: 1
Intermediate results:
Nominal member capacity, Nc: 120.309
Effective area, Ae: 0.363E-02
Critical stress, fn: 3.31E+04
Flexural/torsional stress, foc: 3.78E+04
Section Capacity:
Ratio: 0.0 Demand: 0.0 Capacity: 1.18E+03
Ref.: Cl. 3.4.1 LoadCase: 1 Section: 1
Intermediate results:
Nominal section capacity, Ns: 1.39E+03
Effective area, Ae: 0.346E-02
--------------------------------------------------------------------------------
STAAD SPACE -- PAGE NO. 7
--------------------------------------------------------------------------------
***STAAD.PRO DESIGN RESULTS SUMMARY***
Code: AS/NZS 4600:2018 [v1.0]
All units are in kN-m unless otherwise noted
--------------------------------------------------------------------------------
***Contd. Member: 1 | Ratio: 2.272E+1 [F] | Profile: C300X90X8.0
FLEXURE:
(Local Z) Section Capacity:
Ratio: 0.283 Demand: -30.0 Capacity: 106.006
Ref.: Eq. 3.3.1(1) LoadCase: 1 Section: 1
Intermediate results:
Nominal section capacity, Ms: 117.784
Effective section modulus, Ze: 0.294E-03
(Local Z) Member Capacity:
Ratio: 0.596 Demand: -30.0 Capacity: 50.3
Ref.: Eq. 3.3.1(2) LoadCase: 1 Section: 1
Intermediate results:
Nominal member capacity, Mb: 55.9
Effective section modulus, Zc: 0.294E-03
Full unreduced section modulus, Zf: 0.295E-03
Critical moment, Mc: 56.0
Moment for section yielding, My: 117.867
Elastic buckling moment, Mo: 56.0
(Local Y) Section Capacity:
Ratio: 4.77 Demand: 60.0 Capacity: 12.6
Ref.: Eq. 3.3.1(1) LoadCase: 1 Section: 1
Intermediate results:
Nominal section capacity, Ms: 14.0
Effective section modulus, Ze: 0.350E-04
(Local Y) Member Capacity:
Ratio: 1.89 Demand: 60.0 Capacity: 31.7
Ref.: Eq. 3.3.1(2) LoadCase: 1 Section: 1
Intermediate results:
Nominal member capacity, Mb: 35.2
Effective section modulus, Zc: 0.120E-03
Full unreduced section modulus, Zf: 0.120E-03
Critical moment, Mc: 35.3
Moment for section yielding, My: 48.1
Elastic buckling moment, Mo: 39.5
Reduced Member Capacity:
Ratio: 0.333 Demand: -30.0 Capacity: 90.1
Ref.: Eq. 3.3.1(2) LoadCase: 1 Section: 1
Intermediate results:
Nominal member capacity, Mb: 100.117
Reduction factor, R: 0.850
--------------------------------------------------------------------------------
STAAD SPACE -- PAGE NO. 8
--------------------------------------------------------------------------------
***STAAD.PRO DESIGN RESULTS SUMMARY***
Code: AS/NZS 4600:2018 [v1.0]
All units are in kN-m unless otherwise noted
--------------------------------------------------------------------------------
***Contd. Member: 1 | Ratio: 2.272E+1 [F] | Profile: C300X90X8.0
SHEAR:
(Local Z) Shear Capacity:
Ratio: 0.367E-01 Demand: -10.0 Capacity: 272.794
Ref.: Cl. 3.3.4.1 LoadCase: 1 Section: 1
Intermediate results:
Nominal shear capacity, Vv: 303.104
Shear buckling coefficient, kv: 5.34
Depth of flat portion of web, d1: 0.740E-01
(Local Y) Shear Capacity:
Ratio: 0.101E-01 Demand: -5.00 Capacity: 493.978
Ref.: Cl. 3.3.4.1 LoadCase: 1 Section: 1
Intermediate results:
Nominal shear capacity, Vv: 548.864
Shear buckling coefficient, kv: 5.34
Depth of flat portion of web, d1: 0.268
--------------------------------------------------------------------------------
INTERACTION:
Flexure-Shear (Local Z):
Ratio: 0.802E-01
Ref.: Eq. 3.3.5(1) LoadCase: 1 Section: 1
Flexure-Shear (Local Y):
Ratio: 22.7
Ref.: Eq. 3.3.5(1) LoadCase: 1 Section: 1
Flexure-Tension (Reduced):
Ratio: 5.36
Ref.: Eq. 3.5.2(1) LoadCase: 1 Section: 1
Flexure-Tension (Unreduced):
Ratio: 5.04
Ref.: Eq. 3.5.2(2) LoadCase: 1 Section: 1
Flexure-Compression (Unreduced):
Ratio: 5.36
Ref.: Eq. 3.5.1(3) LoadCase: 1 Section: 1
--------------------------------------------------------------------------------