# V. AISI 2016 CU Nominal and Local Axial Capacity

Determine the nominal axial capacity and local axial capacity of a 72-Inch-long member subjected to axial compression load.

## Details

The member is a 6' simply-supported span subject to a 1 kip axial load. The section used is a 800CU125-68 channel without lips.

Section properties:
• Depth: D = 8.25 in
• Width: B = 1.25 in
• Thickness: t = 0.0713 in
• Inner radius: R = 0.1069 in
• Area: A = 0.748 in2
• Moment of inertia about major axis: Ix = 6.0 in4
• Moment of inertia about minor axis: Iy = 0.0703 in4
• Torsional constant: J = 0.00127 in4
• Distance between centroid and shear center: x0 = -0.427 in
• Warping constant: Cw = 0.92 in6
Material properties:
• E = 29,500 ksi
• G = 11,300 ksi
• Fy = 50 ksi

## Validation

Section Dimension Checks

Width to thickness ratio:

Depth to thickness ratio:

Nominal Strength of Global Buckling

From Cl. E.2 of AISI S100-16:

$K y × L y r y = 1 × 72 0.307 = 234.9$
$β = 1 - x 0 r 0 2 = 1 - ( - 0.427 2.881 ) 2 = 0.978$
$F c r e T F = 1 2 × β × σ e x + σ t - ( σ e x + σ t ) 2 - 4 × β × σ e x × σ t$

Since: $F ( c r e ) T F > F c r e y$,

$λ c = F y F c r e = 3.104 > 1.5$

Allowable nominal axial strength (ASD):

Design nominal axial strength (LRFD):

Local Buckling Interacting with Lateral-Torsional Buckling

From Cl. E.3.1 of AISI S100-16:

Flange elements:

 $s = 1.28 × E F n = 1.28 × 29,000 4.551 = 102.2$ (Eq 1.3-7, Appendix 1 of AISI S100-16)
$W t = 15.03 < 0.328 × s = 33.51$

Therefore, calculation of the effective width is not required.

Web element:

$k = 4.0$
$λ = F n F c r = 4.551 8.553 = 0.729$
$ρ = 1 - 0.22 λ λ = 0.958$

Effective area,

Allowable local axial strength (ASD):

Design local axial strength (LRFD):

## Results

Table 1. AISI 2016 Cylindrical Tubular Section comparison
Allowable nominal axial strength, ASD $P n e Ω c$ (kips) 1.891 1.891 none
Allowable local axial strength, ASD $P n l Ω c$ (kips) 2.893 2.893 none
Design nominal axial strength, LRFD $ϕ b P n$ (kips) 1.830 1.830 none
Design local axial strength, LRFD $ϕ b P nl$ (kips) 2.801 2.800 negligible

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\US\AISI\AISI 2016 CU Nominal and Local axial Capacity.STD is typically installed with the program.

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 02-Jun-20
END JOB INFORMATION
INPUT WIDTH 79
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 6 0 0;
MEMBER INCIDENCES
1 1 2;
UNIT INCHES KIP
DEFINE MATERIAL START
ISOTROPIC STEEL
E 29000
POISSON 0.3
DENSITY 0.000283
ALPHA 6.5e-06
DAMP 0.03
TYPE STEEL
STRENGTH RY 1.5 RT 1.2
END DEFINE MATERIAL
MEMBER PROPERTY COLDFORMED AMERICAN
1 TABLE ST 800CU125-68
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 PINNED
2 FIXED BUT MY MZ
1 CON GX -1 0
1 CON GX 1 72
PERFORM ANALYSIS
PARAMETER 1
CODE AISI 2016
FYLD 50 ALL
METHOD LRFD
TRACK 2 ALL
CHECK CODE ALL
PARAMETER 2
CODE AISI 2016
FYLD 50 ALL
METHOD ASD
TRACK 2 ALL
CHECK CODE ALL
FINISH


      STAAD SPACE                                              -- PAGE NO.    3
STAAD.Pro CODE CHECKING - (AISI S100-16) [LRFD] (v1.0)
********************************************************
ALL UNITS ARE IN "INCH" AND "KIP " (U.N.O.)
|-----------------------------------------------------------------------------|
|  MEMBER:     1     SECTION:ST  800CU125-68     LEN:   72.000     LOC:   0.000 |
| STATUS: PASS       RATIO:  0.357             REF: Sec. E3       LC:      1  |
|-----------------------------------------------------------------------------|
| DESIGN FORCES:                                                              |
|  Location:    0.000  Criteria:   Sec. E3              LC:           1       |
|  Fx:(C)        1.000       Fy:         0.000          Fz:       0.000       |
|  Mx:           0.000       My:         0.000          Mz:       0.000       |
|-----------------------------------------------------------------------------|
| SECTION PROPERTIES:                                                         |
|  Ag:         0.74800       Az:     0.15284            Ay:     0.56281       |
|  Cz:         0.00000       Cy:     0.00000                                  |
|  Iz:         6.00000       Iy:     0.07030             J:     0.00127       |
|  Sz:         1.45455       Sy:     0.06552                                  |
|  Rz:         2.83221       Ry:     0.30657            Cw:     0.92000       |
|-----------------------------------------------------------------------------|
| MATERIAL INFO:                                                              |
|  Fy:    50.000        Fu:    58.000      E:  29000.000       G:  11300.000  |
|-----------------------------------------------------------------------------|
| DESIGN PROPERTIES:                                                          |
|  Member Length:    72.000   Lz:    72.000   Ly:    72.000   Lb:       0.000 |
| DESIGN PARAMETERS:                                                          |
|  Kz:   1.000    Ky:   1.000    NSF:  1.000                                  |
|-----------------------------------------------------------------------------|
| CRITICAL SLENDERNESS:                                                       |
|-----------------------------------------------------------------------------|
|  LC :     1   Actual :  234.858   Allowable :  200.000   Ratio :   1.174    |
|-----------------------------------------------------------------------------|
|  Section Dimension Check      |    Ratio     |    Limit     |     Status    |
|-----------------------------------------------------------------------------|
|  Radius To Thickness Ratio    |      1.499   |     10.000   |      PASS     |
|  Width To Thickness Ratio     |     15.032   |     60.000   |      PASS     |
|  Web Depth To Thickness Ratio |    110.710   |    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            |   -   |   -    |     -    |   32.538 |  -  |Sec. D3    |
|   Yielding         |   -   |   -    |     -    |   33.660 |  -  |Sec. D2    |
|   Rupture          |   -   |   -    |     -    |   32.538 |  -  |Sec. D3    |
| Compression        |     1 |   0.00 |   -1.000 |    2.800 |0.357|Sec. E3    |
|   Local Comp       |     1 |   0.00 |   -1.000 |    2.800 |0.357|Sec. E3    |
|   Axial Comp       |     1 |   0.00 |   -1.000 |    2.893 |0.346|Sec. E2    |
| Bending            |   -   |   -    |     -    |    2.913 |  -  |Sec. F3    |
|   Major Local Bend |   -   |   -    |     -    |   14.316 |  -  |Sec. F3    |
|   Minor Local Bend |   -   |   -    |     -    |    2.913 |  -  |Sec. F3    |
|   Major Sectional  |   -   |   -    |     -    |   65.455 |  -  |Sec. F2    |
|   Minor Sectional  |   -   |   -    |     -    |    2.948 |  -  |Sec. F2    |
|   LTB Major        |   -   |   -    |     -    |   14.311 |  -  |Sec. F2    |
| Shear              |   -   |   -    |     -    |    4.356 |  -  |Sec. G2    |
|   Major Shear (Z)  |   -   |   -    |     -    |    4.356 |  -  |Sec. G2    |
|   Minor Shear (Y)  |   -   |   -    |     -    |    6.107 |  -  |Sec. G2    |
| Interaction        |     1 |   0.00 |     -    |     -    |0.357|Eq. H1.2-1 |
|   (Bend+Comp)      |     1 |   0.00 |     -    |     -    |0.357|Eq. H1.2-1 |
|-----------------------------------------------------------------------------|
40. PARAMETER 2
41. CODE AISI 2016
42. FYLD 50 ALL
43. METHOD ASD
44. TRACK 2 ALL
45. CHECK CODE ALL
STEEL DESIGN
STAAD SPACE                                              -- PAGE NO.    5
STAAD.Pro CODE CHECKING - (AISI S100-16) [ASD ] (v1.0)
********************************************************
ALL UNITS ARE IN "INCH" AND "KIP " (U.N.O.)
|-----------------------------------------------------------------------------|
|  MEMBER:     1     SECTION:ST  800CU125-68     LEN:   72.000     LOC:   0.000 |
| STATUS: PASS       RATIO:  0.546             REF: Sec. E3       LC:      1  |
|-----------------------------------------------------------------------------|
| DESIGN FORCES:                                                              |
|  Location:    0.000  Criteria:   Sec. E3              LC:           1       |
|  Fx:(C)        1.000       Fy:         0.000          Fz:       0.000       |
|  Mx:           0.000       My:         0.000          Mz:       0.000       |
|-----------------------------------------------------------------------------|
| SECTION PROPERTIES:                                                         |
|  Ag:         0.74800       Az:     0.15284            Ay:     0.56281       |
|  Cz:         0.00000       Cy:     0.00000                                  |
|  Iz:         6.00000       Iy:     0.07030             J:     0.00127       |
|  Sz:         1.45455       Sy:     0.06552                                  |
|  Rz:         2.83221       Ry:     0.30657            Cw:     0.92000       |
|-----------------------------------------------------------------------------|
| MATERIAL INFO:                                                              |
|  Fy:    50.000        Fu:    58.000      E:  29000.000       G:  11300.000  |
|-----------------------------------------------------------------------------|
| DESIGN PROPERTIES:                                                          |
|  Member Length:    72.000   Lz:    72.000   Ly:    72.000   Lb:       0.000 |
| DESIGN PARAMETERS:                                                          |
|  Kz:   1.000    Ky:   1.000    NSF:  1.000                                  |
|-----------------------------------------------------------------------------|
| CRITICAL SLENDERNESS:                                                       |
|-----------------------------------------------------------------------------|
|  LC :     1   Actual :  234.858   Allowable :  200.000   Ratio :   1.174    |
|-----------------------------------------------------------------------------|
|  Section Dimension Check      |    Ratio     |    Limit     |     Status    |
|-----------------------------------------------------------------------------|
|  Radius To Thickness Ratio    |      1.499   |     10.000   |      PASS     |
|  Width To Thickness Ratio     |     15.032   |     60.000   |      PASS     |
|  Web Depth To Thickness Ratio |    110.710   |    200.000   |      PASS     |
|-----------------------------------------------------------------------------|
STAAD SPACE                                              -- PAGE NO.    6
STAAD.Pro CODE CHECKING - (AISI S100-16) [ASD ] (v1.0)
********************************************************
ALL UNITS ARE IN "INCH" AND "KIP " (U.N.O.)
|                                              - MEMBER:       1 (Contd.....) |
|                                                                             |
|-----------------------------------------------------------------------------|
| Limit States       | Load# |Location|  Demand  | Capacity |Ratio| Reference |
|--------------------|-------|--------|----------|----------|-----|-----------|
| Tension            |   -   |   -    |     -    |   21.692 |  -  |Sec. D3    |
|   Yielding         |   -   |   -    |     -    |   22.395 |  -  |Sec. D2    |
|   Rupture          |   -   |   -    |     -    |   21.692 |  -  |Sec. D3    |
| Compression        |     1 |   0.00 |   -1.000 |    1.830 |0.546|Sec. E3    |
|   Local Comp       |     1 |   0.00 |   -1.000 |    1.830 |0.546|Sec. E3    |
|   Axial Comp       |     1 |   0.00 |   -1.000 |    1.891 |0.529|Sec. E2    |
| Bending            |   -   |   -    |     -    |    1.938 |  -  |Sec. F3    |
|   Major Local Bend |   -   |   -    |     -    |    9.525 |  -  |Sec. F3    |
|   Minor Local Bend |   -   |   -    |     -    |    1.938 |  -  |Sec. F3    |
|   Major Sectional  |   -   |   -    |     -    |   43.549 |  -  |Sec. F2    |
|   Minor Sectional  |   -   |   -    |     -    |    1.962 |  -  |Sec. F2    |
|   LTB Major        |   -   |   -    |     -    |    9.522 |  -  |Sec. F2    |
| Shear              |   -   |   -    |     -    |    2.866 |  -  |Sec. G2    |
|   Major Shear (Z)  |   -   |   -    |     -    |    2.866 |  -  |Sec. G2    |
|   Minor Shear (Y)  |   -   |   -    |     -    |    4.018 |  -  |Sec. G2    |
| Interaction        |     1 |   0.00 |     -    |     -    |0.546|Eq. H1.2-1 |
|   (Bend+Comp)      |     1 |   0.00 |     -    |     -    |0.546|Eq. H1.2-1 |
|-----------------------------------------------------------------------------|