# V. AISI 2016 CU Nominal Moment Capacity

Determine the nominal moment axial capacity of a simply-supported beam subject to a concentrated load at mid-span.

## Reference

Yu, Wei-Wen and Roger A. LaBoube. 2010 Cold-Formed Steel Design, Fourth Edition. Hoboken, NJ: Wiley. Example 4.3.

## Details

The member is a 10' simply-supported span subject to a 1 kip load applied at midspan. The section used is a CU_8X2_0.06 channel without lips. The member is laterally supported at the one-fourth points along the span.

Section properties:
• Depth: D = 8 in
• Width: B = 2 in
• Thickness: t = 0.06 in
• Inner radius: R = 3/32 in
• Area: A = 0.706 in2
• Moment of inertia about major axis: Ix = 6.129 in4
• Moment of inertia about minor axis: Iy = 0.229 in4
• Major axis section modulus: Sx = 1.532 in3
• Minor axis section modulus: Sy = 0.137 in3
• Torsional constant: J = 0.00085 in4
• Distance between centroid and shear center: x0 = -0.919 in
• Warping constant: Cw = 2.568 in6
Material properties:
• E = 29,500 ksi
• G = 11,300 ksi
• Fy = 33 ksi
• Fu = 58 ksi

## Validation

Elastic Critical Lateral-Torsional Stress

Per Cl. F2.1.1 of AISI S100-16:
$σ e y = π 2 × E ( K y × L y r y ) 2$
where
 $K y$ = Effective length factor for bending about y axis = 1 $L y$ = Unbraced length of member for bending about y axis = 30 in

So,

$C b = 12.5 × M max 2.5 M m a x + 3 M A + 4 M B + 3 M C$
where
 $M max$ = Absolute value of maximum moment in unbraced segment = 30 kip·in $M A$ = Absolute value of moment at quarter point of unbraced segment = 18.75 kip·in $M B$ = Absolute value of moment at mid-point of unbraced segment = 22.50 kip·in $M C$ = Absolute value of moment at three-quarter point of unbraced segment = 26.25 kip·in
 $C b = 12.5 × 30 2.5 × 30 + 3 × 18.75 + 4 × 22.5 + 3 × 26.25 = 1.25$ (Eq. F2.1.1-2)

The elastic buckling stress:

 (Eq. F2.1.1-1)

Calculate the nominal flexural strength, Fn, per Cl. F2.1 of S100-16:

Since ,

The nominal flexural strength:

 (Eq. F2.1-1)

Allowable flexural strength (ASD):

Design flexural strength (LRFD):

## Results

Table 1. AISI 2016 Cylindrical Tubular Section comparison
Flexural strength, ASD $M n e Ω b$ (in·kips) 30.278 30.278 none
Flexural strength, LRFD $ϕ b M n e$ (in·kips) 45.508 45.508 none

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

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 01-Jun-20
END JOB INFORMATION
INPUT WIDTH 79
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 10 0 0;
MEMBER INCIDENCES
1 1 2;
START USER TABLE
TABLE 1
UNIT INCHES KIP
CHANNEL
CU_8X2_0.06
0.706 8 0.06 2 0.06 6.129 0.229 0.00085 0.33 0.462 0.1143
END
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 AMERICAN
1 UPTABLE 1 CU_8X2_0.06
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 2 PINNED
1 CON GY -1
PERFORM ANALYSIS
PARAMETER 1
CODE AISI 2016
FYLD 33 ALL
METHOD LRFD
TRACK 2 ALL
LY 30 ALL
UNB 30 ALL
UNT 30 ALL
CHECK CODE ALL
PARAMETER 2
CODE AISI 2016
FYLD 33 ALL
METHOD ASD
TRACK 2 ALL
LY 30 ALL
UNB 30 ALL
UNT 30 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:UPT CU_8X2_0.06     LEN:  120.000     LOC:  60.000 |
| STATUS: PASS       RATIO:  0.895             REF: Sec. F3       LC:      1  |
|-----------------------------------------------------------------------------|
| DESIGN FORCES:                                                              |
|  Location:   60.000  Criteria:   Sec. F3              LC:           1       |
|  Fx:(C)        0.000       Fy:         0.500          Fz:       0.000       |
|  Mx:           0.000       My:         0.000          Mz:     -30.000       |
|-----------------------------------------------------------------------------|
| SECTION PROPERTIES:                                                         |
|  Ag:         0.70600       Az:     0.11430            Ay:     0.46200       |
|  Cz:         0.00000       Cy:     0.00000                                  |
|  Iz:         6.12900       Iy:     0.22900             J:     0.00085       |
|  Sz:         1.53225       Sy:     0.13713                                  |
|  Rz:         2.94641       Ry:     0.56953            Cw:     2.65754       |
|-----------------------------------------------------------------------------|
| MATERIAL INFO:                                                              |
|  Fy:    33.000        Fu:    58.000      E:  29000.000       G:  11300.000  |
|-----------------------------------------------------------------------------|
| DESIGN PROPERTIES:                                                          |
|  Member Length:   120.000   Lz:   120.000   Ly:    30.000   Lb:       0.000 |
| DESIGN PARAMETERS:                                                          |
|  Kz:   1.000    Ky:   1.000    NSF:  1.000                                  |
|-----------------------------------------------------------------------------|
| CRITICAL SLENDERNESS:                                                       |
|-----------------------------------------------------------------------------|
|  LC :     1   Actual :  210.701   Allowable :  300.000   Ratio :   0.702    |
|-----------------------------------------------------------------------------|
|  Section Dimension Check      |    Ratio     |    Limit     |     Status    |
|-----------------------------------------------------------------------------|
|  Width To Thickness Ratio     |     32.333   |     60.000   |      PASS     |
|  Web Depth To Thickness Ratio |    131.333   |    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            |   -   |   -    |     -    |   20.968 |  -  |Sec. D2    |
|   Yielding         |   -   |   -    |     -    |   20.968 |  -  |Sec. D2    |
|   Rupture          |   -   |   -    |     -    |   30.711 |  -  |Sec. D3    |
| Compression        |   -   |   -    |     -    |    3.623 |  -  |Sec. E3    |
|   Local Comp       |   -   |   -    |     -    |    3.623 |  -  |Sec. E3    |
|   Axial Comp       |   -   |   -    |     -    |    4.702 |  -  |Sec. E2    |
| Bending            |     1 |  60.00 |  -30.000 |   33.522 |0.895|Sec. F3    |
|   Major Local Bend |     1 |  60.00 |  -30.000 |   33.522 |0.895|Sec. F3    |
|   Minor Local Bend |   -   |   -    |     -    |    3.998 |  -  |Sec. F3    |
|   Major Sectional  |     1 |  60.00 |  -30.000 |   45.508 |0.659|Sec. F2    |
|   Minor Sectional  |   -   |   -    |     -    |    4.073 |  -  |Sec. F2    |
|   LTB Major        |     1 |  60.00 |  -30.000 |   42.559 |0.705|Sec. F2    |
| Shear              |     1 |   0.00 |    0.500 |    3.562 |0.140|Sec. G2    |
|   Major Shear (Z)  |   -   |   -    |     -    |    2.150 |  -  |Sec. G2    |
|   Minor Shear (Y)  |     1 |   0.00 |    0.500 |    3.562 |0.140|Sec. G2    |
| Interaction        |     1 |  60.00 |     -    |     -    |0.895|Eq. H1.1-2 |
|   (Bend+Ten) Int1  |     1 |  60.00 |     -    |     -    |0.659|Eq. H1.1-1 |
|   (Bend+Ten) Int2  |     1 |  60.00 |     -    |     -    |0.895|Eq. H1.1-2 |
|   (Bend+Comp)      |     1 |  60.00 |     -    |     -    |0.895|Eq. H1.2-1 |
|   (Bend+Shear) Z   |     1 |  60.00 |     -    |     -    |0.856|Sec. H2    |
|-----------------------------------------------------------------------------|
48. PARAMETER 2
49. CODE AISI 2016
50. FYLD 33 ALL
51. METHOD ASD
52. TRACK 2 ALL
53. LY 30 ALL
54. UNB 30 ALL
55. UNT 30 ALL
56. CHECK CODE ALL
STEEL DESIGN
NOTE # 1 ~ The assigned section for the member #     1
may not be a cold formed section.
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:UPT CU_8X2_0.06     LEN:  120.000     LOC:  60.000 |
| STATUS: FAIL       RATIO:  1.345             REF: Sec. F3       LC:      1  |
|-----------------------------------------------------------------------------|
| DESIGN FORCES:                                                              |
|  Location:   60.000  Criteria:   Sec. F3              LC:           1       |
|  Fx:(C)        0.000       Fy:         0.500          Fz:       0.000       |
|  Mx:           0.000       My:         0.000          Mz:     -30.000       |
|-----------------------------------------------------------------------------|
| SECTION PROPERTIES:                                                         |
|  Ag:         0.70600       Az:     0.11430            Ay:     0.46200       |
|  Cz:         0.00000       Cy:     0.00000                                  |
|  Iz:         6.12900       Iy:     0.22900             J:     0.00085       |
|  Sz:         1.53225       Sy:     0.13713                                  |
|  Rz:         2.94641       Ry:     0.56953            Cw:     2.65754       |
|-----------------------------------------------------------------------------|
| MATERIAL INFO:                                                              |
|  Fy:    33.000        Fu:    58.000      E:  29000.000       G:  11300.000  |
|-----------------------------------------------------------------------------|
| DESIGN PROPERTIES:                                                          |
|  Member Length:   120.000   Lz:   120.000   Ly:    30.000   Lb:       0.000 |
| DESIGN PARAMETERS:                                                          |
|  Kz:   1.000    Ky:   1.000    NSF:  1.000                                  |
|-----------------------------------------------------------------------------|
| CRITICAL SLENDERNESS:                                                       |
|-----------------------------------------------------------------------------|
|  LC :     1   Actual :  210.701   Allowable :  300.000   Ratio :   0.702    |
|-----------------------------------------------------------------------------|
|  Section Dimension Check      |    Ratio     |    Limit     |     Status    |
|-----------------------------------------------------------------------------|
|  Width To Thickness Ratio     |     32.333   |     60.000   |      PASS     |
|  Web Depth To Thickness Ratio |    131.333   |    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            |   -   |   -    |     -    |   13.951 |  -  |Sec. D2    |
|   Yielding         |   -   |   -    |     -    |   13.951 |  -  |Sec. D2    |
|   Rupture          |   -   |   -    |     -    |   20.474 |  -  |Sec. D3    |
| Compression        |   -   |   -    |     -    |    2.368 |  -  |Sec. E3    |
|   Local Comp       |   -   |   -    |     -    |    2.368 |  -  |Sec. E3    |
|   Axial Comp       |   -   |   -    |     -    |    3.073 |  -  |Sec. E2    |
| Bending            |     1 |  60.00 |  -30.000 |   22.303 |1.345|Sec. F3    |
|   Major Local Bend |     1 |  60.00 |  -30.000 |   22.303 |1.345|Sec. F3    |
|   Minor Local Bend |   -   |   -    |     -    |    2.660 |  -  |Sec. F3    |
|   Major Sectional  |     1 |  60.00 |  -30.000 |   30.278 |0.991|Sec. F2    |
|   Minor Sectional  |   -   |   -    |     -    |    2.710 |  -  |Sec. F2    |
|   LTB Major        |     1 |  60.00 |  -30.000 |   28.316 |1.059|Sec. F2    |
| Shear              |     1 |   0.00 |    0.500 |    2.344 |0.213|Sec. G2    |
|   Major Shear (Z)  |   -   |   -    |     -    |    1.414 |  -  |Sec. G2    |
|   Minor Shear (Y)  |     1 |   0.00 |    0.500 |    2.344 |0.213|Sec. G2    |
| Interaction        |     1 |  60.00 |     -    |     -    |1.345|Eq. H1.1-2 |
|   (Bend+Ten) Int1  |     1 |  60.00 |     -    |     -    |0.991|Eq. H1.1-1 |
|   (Bend+Ten) Int2  |     1 |  60.00 |     -    |     -    |1.345|Eq. H1.1-2 |
|   (Bend+Comp)      |     1 |  60.00 |     -    |     -    |1.345|Eq. H1.2-1 |
|   (Bend+Shear) Z   |     1 |  60.00 |     -    |     -    |1.287|Sec. H2    |
|-----------------------------------------------------------------------------|