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

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

Width to thickness ratio:

Depth to thickness ratio:

Calculate Axial Strength

Along Z axis:

$K x × L x r x = 1 × 78.74 2.728 = 28.86$

Fcrex is the lesser of σx and σt ; Fcrex = 14.37 ksi

$λ cz = F y F c r e x = 1.583 > 1.5$

Along Y axis:

$K y × L y r y = 1 × 78.74 0.337 = 233.7$

Fcrey is the lesser of σy and σt ; Fcrey = 5.244 ksi

$λ cy = F y F c r e y = 2.62 > 1.5$

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

$C b = 12.5 M max 2.5 M max + 3 M A + 4 M B + 3 M C = 1.136$

For singly symmetric sections bent about the axis of symmetry:

where
 Sf = the elastic section modulus for the unreduced section relative to the extreme compression fiber per AISI S100 2016. Hence, Sf = Sz .

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):

Table 1. Comparison of results
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

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\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
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 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    |
|-----------------------------------------------------------------------------|