# V. AISI 2016 CS Compressive Strength

Verify the compressive strength of a cold-formed channel section with lips per the AISI S100 2016 specification.

## Details

A 10' long, simply supported beam is subjected to a 10 kip axial load (compression). The section used is a 362CS162-54, Grade 50 steel.

Section Properties

Taken from AISI Manual, Cold-Formed Steel Design - Vol. 1, 2017 Table I-2.

• Area, Ag = 0.422 in2
• Radius of gyration z axis, rz = 1.44in
• Radius of gyration y axis, ry = 0.605 in
• Distance from centroid to shear center, xo = -1.28 in
• Elastic section modulus y axis, Sfz = 0.482 in3
• Elastic section modulus z axis, Sfy = 0.142 in3
• Torsional constant, J = 0.000451 in4
• Warping constant, Cw = 0.457 in6
• j = 2.02 in

Material Properties

• E = 29,000 ksi
• G = 11,300 ksi
• Fy = 50 ksi

## Validation

The elastic flexural buckling stress about the z axis:
 (Eq. E2.1-1)

Polar radius of gyration of cross-section about shear center:

 (Eq. E2.2-4)
 $β = 1 - ( x o / r o ) 2 = 1 - ( -1.28 2.019 ) 2 = 0.598$ (Eq. E2.2-3)
 (Eq. E2.2-5)
 (Eq. E2.2-6)
The flexural-torsional buckling stress:
 $F cre = 1 2 β [ ( σ ez + σ t ) - ( σ ez + σ t ) 2 - 4 β σ ez σ t ]$ (Eq. E2.2-1)

The elastic global buckling stress about the z axis is the minimum of Fcre and Fcrez1; so Fcrez = 7.560 ksi.

The compressive stress capacity is:

 $λ cz = F y F cre = 50 7.560 = 2.572 > 1.5$ (Eq. E2-4)
 (Eq. E2-2)

The elastic flexural buckling stress about the y axis:

 (Eq. E2.1-1)

The elastic global buckling stress about the z axis is the minimum of Fcre and Fcrey1; so Fcrey = 7.275 ksi.

 $λ cy = F y F crey = 50 7.275 = 2.622 > 1.5$ (Eq. E2-4)
 (Eq. E2-2)

Global buckling about the Y axis governs.

Nominal capacity against global buckling:

Pn = AgFn = 0.422 × 6.380 = 2.692 kips

The available axial strength:

• LRFD: ϕcPn = 0.85 × 2.692 = 2.289 kips
• ASD: Pnc = 2.692 / 1.8 = 1.496 kips
Determine the compression capacity for local buckling interacting with yielding and global buckling as per E3:

The effective area, Ae, is equal to the gross area, Ag = 0.422 in2. By inspection, the local capacity, Pnℓ is equal to the global buckling capacity in this case.

• LRFD: ϕcPnℓ = 0.85 × 2.692 = 2.289 kips
• ASD: Pnℓc = 2.692 / 1.8 = 1.496 kips

Determine the compression capacity for distortional buckling as per E4:

The elastic distortional buckling stress, Fcrd = 149.8 ksi.

The elastic distortional buckling load, Pcrd = Ag × Fcrd = 0.422 × 149.8 = 63.21 kips.

 Py = Ag × Fy = 0.422 × 50 = 21.1 kips (Eq. E4.1-4)

 $λ d = P y P crd = 21.1 63.21 = 0.578 > 0.561$ (Eq. E4.1-3)
 $P nd = 1 - 0.25 P crd P y 0.6 P crd P y 0.6 P y$ (Eq. 4.1-2)

The available axial strength:

• LRFD: ϕcPnd = 0.85 × 21.08 = 17.91 kips
• ASD: Pndc = 21.08 / 1.8 = 11.71 kips

## Results

LRFD Local compression capacity (kips) 2.289 2.282 negligible
Distorional buckling capacity (kips) 17.91 17.914 negligible
Axial compression capacity (kips) 2.289 2.282 negligible
ASD Local compression capacity (kips) 1.496 1.491 negligible
Distorional buckling capacity (kips) 11.71 11.709 negligible
Axial compression capacity (kips) 1.496 1.491 negligible

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\US\AISI\AISI 2016 CS Compressive Strength.STD is typically installed with the program.

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 11-Jan-21
END JOB INFORMATION
INPUT WIDTH 79
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 10 0 0;
MEMBER INCIDENCES
1 1 2;
DEFINE MATERIAL START
ISOTROPIC STEEL
E 4.176e+06
POISSON 0.3
DENSITY 0.489024
ALPHA 6.5e-06
DAMP 0.03
G 1.6128e+06
TYPE STEEL
STRENGTH RY 1.5 RT 1.2
END DEFINE MATERIAL
MEMBER PROPERTY COLDFORMED AMERICAN
1 TABLE ST 362CS162-54
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 FIXED
2 FX 10
PERFORM ANALYSIS
UNIT INCHES KIP
PARAMETER 1
CODE AISI 2016
METHOD LRFD
FYLD 50 ALL
FU 58 ALL
FLX 0 ALL
TSA 0 ALL
TRACK 2 ALL
CHECK CODE ALL
PARAMETER 2
CODE AISI 2016
METHOD ASD
FYLD 50 ALL
FU 58 ALL
FLX 0 ALL
TSA 0 ALL
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  362CS162-54     LEN:  120.000     LOC:   0.000 |
| STATUS: PASS       RATIO:  0.545             REF: Sec. D3       LC:      1  |
|-----------------------------------------------------------------------------|
| DESIGN FORCES:                                                              |
|  Location:    0.000  Criteria:   Sec. D3              LC:           1       |
|  Fx:(T)      -10.000       Fy:         0.000          Fz:       0.000       |
|  Mx:           0.000       My:         0.000          Mz:       0.000       |
|-----------------------------------------------------------------------------|
| SECTION PROPERTIES:                                                         |
|  Ag:         0.42200       Az:     0.15191            Ay:     0.18916       |
|  Cz:         0.00000       Cy:     0.00000                                  |
|  Iz:         0.87300       Iy:     0.15400             J:     0.00045       |
|  Sz:         0.48166       Sy:     0.14141                                  |
|  Rz:         1.43830       Ry:     0.60409            Cw:     0.45700       |
|-----------------------------------------------------------------------------|
| MATERIAL INFO:                                                              |
|  Fy:    50.000        Fu:    58.000      E:  29000.000       G:  11200.000  |
|-----------------------------------------------------------------------------|
| DESIGN PROPERTIES:                                                          |
|  Member Length:   120.000   Lz:   120.000   Ly:   120.000   Lb:       0.000 |
| DESIGN PARAMETERS:                                                          |
|  Kz:   1.000    Ky:   1.000    NSF:  1.000                                  |
|-----------------------------------------------------------------------------|
| CRITICAL SLENDERNESS:                                                       |
|-----------------------------------------------------------------------------|
|  LC :     1   Actual :  198.645   Allowable :  300.000   Ratio :   0.662    |
|-----------------------------------------------------------------------------|
|  Section Dimension Check      |    Ratio     |    Limit     |     Status    |
|-----------------------------------------------------------------------------|
|  Radius To Thickness Ratio    |      1.500   |     10.000   |      PASS     |
|  Width To Thickness Ratio     |     23.710   |     60.000   |      PASS     |
|  Web Depth To Thickness Ratio |     59.046   |    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            |     1 |   0.00 |  -10.000 |   18.357 |0.545|Sec. D3    |
|   Yielding         |     1 |   0.00 |  -10.000 |   18.990 |0.527|Sec. D2    |
|   Rupture          |     1 |   0.00 |  -10.000 |   18.357 |0.545|Sec. D3    |
| Compression        |   -   |   -    |     -    |    2.282 |  -  |Sec. E2    |
|   Local Comp       |   -   |   -    |     -    |    2.282 |  -  |Sec. E3    |
|   Distortional     |   -   |   -    |     -    |   17.914 |  -  |Sec. E4    |
|   Axial Comp       |   -   |   -    |     -    |    2.282 |  -  |Sec. E2    |
| Bending            |   -   |   -    |     -    |    5.920 |  -  |Sec. F2    |
|   Major Local Bend |   -   |   -    |     -    |    5.924 |  -  |Sec. F3    |
|   Minor Local Bend |   -   |   -    |     -    |    6.239 |  -  |Sec. F3    |
|   Distortional     |   -   |   -    |     -    |   21.674 |  -  |Sec. F4    |
|   Major Sectional  |   -   |   -    |     -    |   21.674 |  -  |Sec. F2    |
|   Minor Sectional  |   -   |   -    |     -    |    6.364 |  -  |Sec. F2    |
|   LTB Major        |   -   |   -    |     -    |    5.920 |  -  |Sec. F2    |
| Shear              |   -   |   -    |     -    |    4.330 |  -  |Sec. G2    |
|   Major Shear (Z)  |   -   |   -    |     -    |    4.330 |  -  |Sec. G2    |
|   Minor Shear (Y)  |   -   |   -    |     -    |    5.081 |  -  |Sec. G2    |
| Interaction        |     1 |   0.00 |     -    |     -    |0.545|Eq. H1.1-1 |
|   (Bend+Ten) Int1  |     1 |   0.00 |     -    |     -    |0.545|Eq. H1.1-1 |
|-----------------------------------------------------------------------------|
42. PARAMETER 2
43. CODE AISI 2016
44. METHOD ASD
45. FYLD 50 ALL
46. FU 58 ALL
47. FLX 0 ALL
48. TSA 0 ALL
49. TRACK 2 ALL
50. 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  362CS162-54     LEN:  120.000     LOC:   0.000 |
| STATUS: PASS       RATIO:  0.817             REF: Sec. D3       LC:      1  |
|-----------------------------------------------------------------------------|
| DESIGN FORCES:                                                              |
|  Location:    0.000  Criteria:   Sec. D3              LC:           1       |
|  Fx:(T)      -10.000       Fy:         0.000          Fz:       0.000       |
|  Mx:           0.000       My:         0.000          Mz:       0.000       |
|-----------------------------------------------------------------------------|
| SECTION PROPERTIES:                                                         |
|  Ag:         0.42200       Az:     0.15191            Ay:     0.18916       |
|  Cz:         0.00000       Cy:     0.00000                                  |
|  Iz:         0.87300       Iy:     0.15400             J:     0.00045       |
|  Sz:         0.48166       Sy:     0.14141                                  |
|  Rz:         1.43830       Ry:     0.60409            Cw:     0.45700       |
|-----------------------------------------------------------------------------|
| MATERIAL INFO:                                                              |
|  Fy:    50.000        Fu:    58.000      E:  29000.000       G:  11200.000  |
|-----------------------------------------------------------------------------|
| DESIGN PROPERTIES:                                                          |
|  Member Length:   120.000   Lz:   120.000   Ly:   120.000   Lb:       0.000 |
| DESIGN PARAMETERS:                                                          |
|  Kz:   1.000    Ky:   1.000    NSF:  1.000                                  |
|-----------------------------------------------------------------------------|
| CRITICAL SLENDERNESS:                                                       |
|-----------------------------------------------------------------------------|
|  LC :     1   Actual :  198.645   Allowable :  300.000   Ratio :   0.662    |
|-----------------------------------------------------------------------------|
|  Section Dimension Check      |    Ratio     |    Limit     |     Status    |
|-----------------------------------------------------------------------------|
|  Radius To Thickness Ratio    |      1.500   |     10.000   |      PASS     |
|  Width To Thickness Ratio     |     23.710   |     60.000   |      PASS     |
|  Web Depth To Thickness Ratio |     59.046   |    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            |     1 |   0.00 |  -10.000 |   12.238 |0.817|Sec. D3    |
|   Yielding         |     1 |   0.00 |  -10.000 |   12.635 |0.791|Sec. D2    |
|   Rupture          |     1 |   0.00 |  -10.000 |   12.238 |0.817|Sec. D3    |
| Compression        |   -   |   -    |     -    |    1.491 |  -  |Sec. E2    |
|   Local Comp       |   -   |   -    |     -    |    1.491 |  -  |Sec. E3    |
|   Distortional     |   -   |   -    |     -    |   11.709 |  -  |Sec. E4    |
|   Axial Comp       |   -   |   -    |     -    |    1.491 |  -  |Sec. E2    |
| Bending            |   -   |   -    |     -    |    3.939 |  -  |Sec. F2    |
|   Major Local Bend |   -   |   -    |     -    |    3.941 |  -  |Sec. F3    |
|   Minor Local Bend |   -   |   -    |     -    |    4.151 |  -  |Sec. F3    |
|   Distortional     |   -   |   -    |     -    |   14.421 |  -  |Sec. F4    |
|   Major Sectional  |   -   |   -    |     -    |   14.421 |  -  |Sec. F2    |
|   Minor Sectional  |   -   |   -    |     -    |    4.234 |  -  |Sec. F2    |
|   LTB Major        |   -   |   -    |     -    |    3.939 |  -  |Sec. F2    |
| Shear              |   -   |   -    |     -    |    2.848 |  -  |Sec. G2    |
|   Major Shear (Z)  |   -   |   -    |     -    |    2.848 |  -  |Sec. G2    |
|   Minor Shear (Y)  |   -   |   -    |     -    |    3.343 |  -  |Sec. G2    |
| Interaction        |     1 |   0.00 |     -    |     -    |0.817|Eq. H1.1-1 |
|   (Bend+Ten) Int1  |     1 |   0.00 |     -    |     -    |0.817|Eq. H1.1-1 |
|-----------------------------------------------------------------------------|