V. AISI 2016 Cylindrical Tubular Section

Determine the flexural strength of a closed cylindrical tubular member subjected to axial compression and bending moment according to AISI S100 2016 specification.

Reference

Cold-Formed Steel Design: AISI Manual. 2013 ed. Washington, D.C.: American Iron and Steel Institute, 2014. Example II-8.

Details

The member is a 10' simply-supported span. The section is a 8" diameter closed cylindrical tube with a wall thickness of 0.1".

Axial loads:

Dead load: P_DL = 7.5 kips
Roof live load: P_LR = 20 kips

Transverse loads:

Wind load: P_W = 50 kips (concentrated load at mid-span)

Section properties:

Area: A = 2.482 in²
Moment of inertia: I = 19.37 in⁴
Section modulus: S_f = 4.841 in³
Radius of gyration: $r = \sqrt{\frac{I}{A}} = 2.794 in.$

Material properties:

E = 29,500 ksi
G = 11,300 ksi
F_y = 42 ksi
F_u = 58 ksi

Validation

Design forces:

Governing load combination is DL + RLL + WL

Mu = 1.0 (5 kips) (120 in)/4 = 150 in·kips

Section Dimension Checks

Check the outside diameter to wall thickness ratio:

D / t = 8.0 / 0.1 = 80

{\frac{D}{t}}_{L i m i t} \frac{0.441 \times E}{F_{y}} = \frac{0.441 \times 29500}{42} = 310 > 80

Hence, OK.

Determine Axial Capacity

Determine the governing equation for F_n:

\frac{0.0714 \times E}{F_{y}} = \frac{0.0714 \times 29500}{42} = 50.2

\frac{0.318 \times E}{F_{y}} = \frac{0.318 \times 29500}{42} = 223

Since: $\frac{0.0714 \times E}{F_{y}} < \frac{D}{t} < \frac{0.318 \times E}{F_{y}}$

F_{n} = [0.970 + 0.020 \frac{E / {(F}_{y})}{\frac{D}{T}}] F_{y} = [0.970 + 0.020 \frac{29500 / 42)}{80}] 42 = 48.1 ksi

Determine Flexural Capacity

Nominal flexural strength (resistance) for yielding and global buckling:

M_{n e} = S_{f} \times F_{n} = 4.841 \times 48.1 = 233 in·kip

Allowable flexural strength (ASD):

\frac{M_{n e}}{Ω_{b}} = \frac{233}{1.67} = 140 in·kip

Design flexural strength (LRFD):

M_{n e} \times ϕ_{b} = 233 \times 0.95 = 221 in·kip

Results

Table 1. AISI 2016 Cylindrical Tubular Section comparison
Result Type	Reference	STAAD.Pro	Difference	Comments
Flexural strength, ASD $\frac{M_{n e}}{Ω_{b}}$ (in·kips)	140	139.481	negligible
Flexural strength, LRFD $ϕ_{b} M_{n e}$ (in·kips)	221	221.286	negligible

STAAD.Pro Input

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

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 06-Apr-20
END JOB INFORMATION
INPUT WIDTH 79
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 0 10 0;
MEMBER INCIDENCES
1 1 2;
UNIT INCHES KIP
DEFINE MATERIAL START
ISOTROPIC STEEL
E 29500
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 PIPE OD 8 ID 7.8
CONSTANTS
MATERIAL STEEL ALL
UNIT FEET KIP
SUPPORTS
2 FIXED BUT FY MX MZ
1 FIXED BUT MX MZ
UNIT INCHES KIP
LOAD 1 LOADTYPE Dead  TITLE LOAD CASE 1
MEMBER LOAD
1 CON GY 7.5 0
1 CON GY -7.5 120
LOAD 2 LOADTYPE Roof Live  TITLE LOAD CASE 2
MEMBER LOAD
1 CON GY 20 0
1 CON GY -20 120
LOAD 3 LOADTYPE Wind  TITLE LOAD CASE 3
MEMBER LOAD
1 CON GX 5
LOAD COMB 4 ULC D+0.45W+0.75L
1 1.0 3 0.45 2 0.75 
LOAD COMB 7 ULC, 1 DEAD + 1 ROOF LIVE
1 1.0 2 1.0 
LOAD COMB 8 ULC,  DEAD + 0.6 WIND
1 1.0 3 0.6 
PERFORM ANALYSIS
LOAD LIST 4 7 8
PARAMETER 1
CODE AISI 2016
METHOD LRFD
FYLD 42 ALL
TRACK 2 ALL
CHECK CODE ALL
PARAMETER 2
CODE AISI 2016
METHOD ASD
FYLD 42 ALL
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  PIP E           LEN:  120.000     LOC:  60.000 |
| STATUS: PASS       RATIO:  0.657             REF: Eq. H1.2-1    LC:      4  |
|-----------------------------------------------------------------------------|
| DESIGN FORCES:                                                              |
|  Location:   60.000  Criteria:   Eq. H1.2-1           LC:           4       |
|  Fx:(C)       22.500       Fy:         1.125          Fz:       0.000       |
|  Mx:           0.000       My:         0.000          Mz:     -67.500       |
|-----------------------------------------------------------------------------|
| SECTION PROPERTIES:                                                         |
|  Ag:         2.48186       Az:     1.24093            Ay:     1.24093       |
|  Cz:         0.00000       Cy:     0.00000                                  |
|  Iz:        19.36467       Iy:    19.36467             J:    38.72935       |
|  Sz:         4.84117       Sy:     4.84117                                  |
|  Rz:         2.79330       Ry:     2.79330            Cw:     0.00000       |
|-----------------------------------------------------------------------------|
| MATERIAL INFO:                                                              |
|  Fy:    42.000        Fu:    58.000      E:  29500.000       G:  11300.000  |
|-----------------------------------------------------------------------------|
| 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 :     4   Actual :   42.960   Allowable :  300.000   Ratio :   0.143    |
|-----------------------------------------------------------------------------|
      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            |   -   |   -    |     -    |   93.814 |  -  |Sec. D2    |
|   Yielding         |   -   |   -    |     -    |   93.814 |  -  |Sec. D2    |
|   Rupture          |   -   |   -    |     -    |  107.961 |  -  |Sec. D3    |
| Compression        |     7 |  10.00 |  -27.500 |   78.700 |0.349|Sec. E3    |
|   Local Comp       |     7 |  10.00 |  -27.500 |   78.700 |0.349|Sec. E3    |
|   Axial Comp       |     7 |  10.00 |  -27.500 |   79.259 |0.347|Sec. E2    |
| Bending            |     8 |  60.00 |  -90.000 |  181.828 |0.495|Sec. F3    |
|   Major Local Bend |     8 |  60.00 |  -90.000 |  181.828 |0.495|Sec. F3    |
|   Minor Local Bend |   -   |   -    |     -    |  181.828 |  -  |Sec. F3    |
|   CYL TUB Major    |     8 |  60.00 |   90.000 |  221.286 |0.407|Sec. F2.3  |
| Shear              |     8 |   0.00 |    1.500 |   29.708 |0.050|Sec. G2    |
|   Major Shear (Z)  |   -   |   -    |     -    |   29.708 |  -  |Sec. G2    |
|   Minor Shear (Y)  |     8 |   0.00 |    1.500 |   29.708 |0.050|Sec. G2    |
| Interaction        |     4 |  60.00 |     -    |     -    |0.657|Eq. H1.2-1 |
|   (Bend+Ten) Int1  |     8 |  60.00 |     -    |     -    |0.492|Eq. H1.1-1 |
|   (Bend+Ten) Int2  |     8 |  60.00 |     -    |     -    |0.495|Eq. H1.1-2 |
|   (Bend+Comp)      |     4 |  60.00 |     -    |     -    |0.657|Eq. H1.2-1 |
|   (Bend+Shear) Z   |     8 |  60.00 |     -    |     -    |0.498|Sec. H2    |
|-----------------------------------------------------------------------------|
    56. PARAMETER 2
    57. CODE AISI 2016
    58. METHOD ASD
    59. FYLD 42 ALL
    60. TRACK 2 ALL
    61. CHECK CODE ALL
 STEEL DESIGN    
   WARNING # 8 ~ The specified value of FU for member #     1 seems out of range.
                 Reset back to default value.
      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  PIP E           LEN:  120.000     LOC:  60.000 |
| STATUS: PASS       RATIO:  0.995             REF: Eq. H1.2-1    LC:      4  |
|-----------------------------------------------------------------------------|
| DESIGN FORCES:                                                              |
|  Location:   60.000  Criteria:   Eq. H1.2-1           LC:           4       |
|  Fx:(C)       22.500       Fy:         1.125          Fz:       0.000       |
|  Mx:           0.000       My:         0.000          Mz:     -67.500       |
|-----------------------------------------------------------------------------|
| SECTION PROPERTIES:                                                         |
|  Ag:         2.48186       Az:     1.24093            Ay:     1.24093       |
|  Cz:         0.00000       Cy:     0.00000                                  |
|  Iz:        19.36467       Iy:    19.36467             J:    38.72935       |
|  Sz:         4.84117       Sy:     4.84117                                  |
|  Rz:         2.79330       Ry:     2.79330            Cw:     0.00000       |
|-----------------------------------------------------------------------------|
| MATERIAL INFO:                                                              |
|  Fy:    42.000        Fu:    58.000      E:  29500.000       G:  11300.000  |
|-----------------------------------------------------------------------------|
| 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 :     4   Actual :   42.960   Allowable :  300.000   Ratio :   0.143    |
|-----------------------------------------------------------------------------|
      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            |   -   |   -    |     -    |   62.418 |  -  |Sec. D2    |
|   Yielding         |   -   |   -    |     -    |   62.418 |  -  |Sec. D2    |
|   Rupture          |   -   |   -    |     -    |   71.974 |  -  |Sec. D3    |
| Compression        |     7 |  10.00 |  -27.500 |   51.438 |0.535|Sec. E3    |
|   Local Comp       |     7 |  10.00 |  -27.500 |   51.438 |0.535|Sec. E3    |
|   Axial Comp       |     7 |  10.00 |  -27.500 |   51.804 |0.531|Sec. E2    |
| Bending            |     8 |  60.00 |  -90.000 |  120.977 |0.744|Sec. F3    |
|   Major Local Bend |     8 |  60.00 |  -90.000 |  120.977 |0.744|Sec. F3    |
|   Minor Local Bend |   -   |   -    |     -    |  120.977 |  -  |Sec. F3    |
|   CYL TUB Major    |     8 |  60.00 |   90.000 |  139.481 |0.645|Sec. F2.3  |
| Shear              |     8 |   0.00 |    1.500 |   19.545 |0.077|Sec. G2    |
|   Major Shear (Z)  |   -   |   -    |     -    |   19.545 |  -  |Sec. G2    |
|   Minor Shear (Y)  |     8 |   0.00 |    1.500 |   19.545 |0.077|Sec. G2    |
| Interaction        |     4 |  60.00 |     -    |     -    |0.995|Eq. H1.2-1 |
|   (Bend+Ten) Int1  |     8 |  60.00 |     -    |     -    |0.739|Eq. H1.1-1 |
|   (Bend+Ten) Int2  |     8 |  60.00 |     -    |     -    |0.744|Eq. H1.1-2 |
|   (Bend+Comp)      |     4 |  60.00 |     -    |     -    |0.995|Eq. H1.2-1 |
|   (Bend+Shear) Z   |     8 |  60.00 |     -    |     -    |0.748|Sec. H2    |
|-----------------------------------------------------------------------------|
    62. FINISH