V. AISI 2016 Zee Section
Determine the axial strength and flexural strength of a cold-formed zee section without lips according to AISI S100 2016 Specification using the LRFD method.
Details
The member is a simply-supported, 2m span. The member is subject to a uniform load of 60 lbs/ft. The section used is an 8ZU 12.5x105.
Section Properties
- Depth of section, d = 8 in
- Width of section, b = 1.25 in
- Thickness, t = 0.105 in
- Fillet radius, r = 0.188 in
- Area, A = 1.059 in2
- Moment of inertia major axis, Izz = 7.88 in4
- Moment of inertia minor axis, Iyy = 0.120 in4
- Section modulus major axis, Zzz = 1.97 in3
- Section modulus minor axis, Zyy = 0.096 in3
- Torsion constant, J = 0.004 in4
- Warping constant, Cw = 1.546 in6
- Radius of gyration about major axis:
- Radius of gyration about minor axis:
- Polar radius of gyration:
Material Properties
- E = 29,000 ksi
- G = 11,300 ksi
- Fy = 36 ksi
Design Forces
- Mz = 3.975 ft·k
- Vy = 0.197 kips
Validation
Section Dimension Checks
Radius to thickness ratio:
Width to thickness ratio:
Depth to thickness ratio:
Calculate Axial Strength
Along Z axis:
Fcrex is the lesser of σx and σt ; Fcrex = 14.37 ksi
Along Y axis:
Fcrey is the lesser of σy and σt ; Fcrey = 5.244 ksi
Design nominal axial strength (LRFD):
Calculate Bending Strength
Major axis nominal moment capacity:
Mz = Sz × Fy = 1.97 × 36 = 70.92 in·kips
Major axis ultimate moment capacity:
Minor axis nominal moment capacity:
My = Sy × Fy = 0.096 × 36 = 3.456 in·kips
Minor axis ultimate moment capacity:
Lateral-Torsional Buckling Strength
For singly symmetric sections bent about the axis of symmetry:
where
= |
For Fcre < 0.56Fy = 0.56 × 36 = 20.16, Fn = Fcrez .
Mne = Fn × Sf = 7.283 × 1.97 = 14.35 in-k
Design nominal lateral-torsional buckling strength (LRFD):
Result Type | Reference | STAAD.Pro | Difference | Comments |
---|---|---|---|---|
Ultimate axial strength (kips) | 4.140 | 4.130 | negligible | |
Major axis bending strength (in·kips) | 63.83 | 63.828 | negligible | |
Minor axis bending strength (in·kips) | 3.110 | 3.110 | none | |
Lateral-torsional buckling strength (in·kips) | 12.92 | 12.914 | negligible |
STAAD.Pro Input File
The file C:\Users\Public\Public Documents\STAAD.Pro 2023\Samples \Verification Models\09 Steel Design\US\AISI\AISI 2016 Zee Section.STD is typically installed with the program.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 08-Mar-21
END JOB INFORMATION
INPUT WIDTH 79
UNIT INCHES KIP
JOINT COORDINATES
1 0 0 0; 2 78.74 0 0;
MEMBER INCIDENCES
1 1 2;
DEFINE MATERIAL START
ISOTROPIC STEEL
E 29000
POISSON 0.3
DENSITY 0.000283
ALPHA 6.5e-06
DAMP 0.03
G 11200
TYPE STEEL
STRENGTH RY 1.5 RT 1.2
END DEFINE MATERIAL
MEMBER PROPERTY COLDFORMED AMERICAN
1 TABLE ST 8ZU1.25X105
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 PINNED
2 FIXED BUT FX MY MZ
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
MEMBER LOAD
1 UNI GY -0.004
PERFORM ANALYSIS
PARAMETER 1
CODE AISI 2016
AXIS 1 ALL
METHOD LRFD
TRACK 2 ALL
CHECK CODE ALL
FINISH
STAAD.Pro Output
STAAD.Pro CODE CHECKING - (AISI S100-16) [LRFD] (v1.0) ******************************************************** ALL UNITS ARE IN "INCH" AND "KIP " (U.N.O.) |-----------------------------------------------------------------------------| | MEMBER: 1 SECTION:ST 8ZU1.25X105 LEN: 78.740 LOC: 39.370 | | STATUS: PASS RATIO: 0.994 REF: Sec. F2 LC: 1 | |-----------------------------------------------------------------------------| | DESIGN FORCES: | | Location: 39.370 Criteria: Sec. F2 LC: 1 | | Fx:(C) -0.000 Fy: -0.000 Fz: -0.000 | | Mx: 0.000 My: -0.000 Mz: -3.100 | |-----------------------------------------------------------------------------| | SECTION PROPERTIES: | | Ag: 1.06000 Az: 0.20107 Ay: 0.77857 | | Cz: 0.00000 Cy: 0.00000 | | Iz: 7.88000 Iy: 0.12000 J: 0.00389 | | Sz: 1.97000 Sy: 0.09600 | | Rz: 2.72653 Ry: 0.33646 Cw: 1.55000 | |-----------------------------------------------------------------------------| | MATERIAL INFO: | | Fy: 36.000 Fu: 58.000 E: 29000.000 G: 11200.000 | |-----------------------------------------------------------------------------| | DESIGN PROPERTIES: | | Member Length: 78.740 Lz: 78.740 Ly: 78.740 Lb: 0.000 | | DESIGN PARAMETERS: | | Kz: 1.000 Ky: 1.000 NSF: 1.000 | |-----------------------------------------------------------------------------| | CRITICAL SLENDERNESS: | |-----------------------------------------------------------------------------| | LC : 1 Actual : 234.023 Allowable : 300.000 Ratio : 0.780 | |-----------------------------------------------------------------------------| | Section Dimension Check | Ratio | Limit | Status | |-----------------------------------------------------------------------------| | Radius To Thickness Ratio | 1.786 | 10.000 | PASS | | Width To Thickness Ratio | 9.119 | 60.000 | PASS | | Web Depth To Thickness Ratio | 70.619 | 200.000 | PASS | |-----------------------------------------------------------------------------| STAAD SPACE -- PAGE NO. 4 STAAD.Pro CODE CHECKING - (AISI S100-16) [LRFD] (v1.0) ******************************************************** ALL UNITS ARE IN "INCH" AND "KIP " (U.N.O.) | - MEMBER: 1 (Contd.....) | | | |-----------------------------------------------------------------------------| | Limit States | Load# |Location| Demand | Capacity |Ratio| Reference | |--------------------|-------|--------|----------|----------|-----|-----------| | Tension | - | - | - | 34.344 | - |Sec. D2 | | Yielding | - | - | - | 34.344 | - |Sec. D2 | | Rupture | - | - | - | 46.110 | - |Sec. D3 | | Compression | - | - | - | 4.127 | - |Sec. E3 | | Local Comp | - | - | - | 4.127 | - |Sec. E3 | | Axial Comp | - | - | - | 4.130 | - |Sec. E2 | | Bending | 1 | 0.00 | -3.091 | 3.110 |0.994|Sec. F2 | | Major Local Bend | 1 | 39.37 | -0.237 | 12.927 |0.018|Sec. F3 | | Minor Local Bend | 1 | 39.37 | -3.091 | 3.275 |0.944|Sec. F3 | | Major Sectional | 1 | 39.37 | -0.237 | 63.828 |0.004|Sec. F2 | | Minor Sectional | 1 | 0.00 | -3.091 | 3.110 |0.994|Sec. F2 | | LTB Major | 1 | 39.37 | -0.237 | 12.914 |0.018|Sec. F2 | | Shear | 1 | 0.00 | -0.157 | 4.126 |0.038|Sec. G2 | | Major Shear (Z) | 1 | 0.00 | -0.157 | 4.126 |0.038|Sec. G2 | | Minor Shear (Y) | 1 | 0.00 | 0.012 | 14.838 |0.001|Sec. G2 | | Interaction | 1 | 39.37 | - | - |0.240|Eq. H1.1-2 | | (Bend+Ten) Int1 | 1 | 39.37 | - | - |0.049|Eq. H1.1-1 | | (Bend+Ten) Int2 | 1 | 39.37 | - | - |0.240|Eq. H1.1-2 | | (Bend+Comp) | 1 | 39.37 | - | - |0.240|Eq. H1.2-1 | | (Bend+Shear) Z | 1 | 39.37 | - | - |0.049|Sec. H2 | |-----------------------------------------------------------------------------|