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V. AISC 360-16 Tapered Tube Section

Verify the axial compression capacity, flexure capacity, and interaction ratio of a tapered tube section member per both the LRFD and ASD methods of the AISC 360-16 code.

Details

A 5' × 5' portal frame consists of W12x72 columns and a steel tapered member for the beam.

The following load cases are evaluated:
  1. A uniformly distributed load of -2.25 k/in along the beam in the global Y direction.
  2. Lateral loads at the top of the left column of 50 kips in the global X direction and 25 kips in the global Z direction (out of plane).
  3. A concreted torque of 0.75 in·kips at mid-span of the beam.
Material Properties
  • E = 29,000 ksi
  • Fy = 50 ksi

Validation

Design Forces

By inspection, the right end of the beam (shallowest overall depth) governs under the symmetric loads present. The following design loads are used from the STAAD.Pro analysis are then used:
  • Mz = 505.66 in·kips
  • Fy = 67.2 kips
  • Fx = 10.23 kips

Section Properties

The section at the right end (OD = 10 in.) has the following properties:

  • Inner diameter, ID = 9 in.
  • Area, Ag = (π/4)(OD2 - ID2) = 14.92 in2
  • Form factor = 0.49 + 0.8 (t / OD) = 0.53
  • Shear area, Ay = 14.92(0.53) = 7.909 in2
  • Moment of inertia,
    I = π 64 ( OD 4 - ID 4 ) = 168.8  in 4
  • Elastic section modulus, S = π 32 ( OD 4 - ID 4 OD ) = 33.76  in 3
  • Radius of gyration, r = I A g = 168.8 14.92 = 3.363  in
  • Plastic section modulus, Z = OD 3 - ID 3 6 = 45.17  in 3
  • HSS Torsional constant, C = π 2 ( OD - t ) 2 t = 70.88  in 3

Section Classification

Flange in compression

λ = OD t = 10 0.5 = 20

Per Table B4.1a, Case 9, λ < λ r = 0.11 E F y = 63.8 , therefore flanges are non-slender for compression. The web is similarly non-slender for compression.

Flange in bending (use half the longer flange width as the outstanding width):

λ = OD t = 10 0.5 = 20

Per Table B4.1b, Case20, λ < λ r = 0.07 E F y = 40.6 , therefore flange is compact for bending.

Compression Capacity

k L r = 1.0 ( 60 ) 3.363 = 17.84 < 4.71 E F y = 4.71 29 , 000 50 = 113.4
F e = π 2 E ( k L r ) 2 = π 2 × 29,000 ( 17.84 ) 2 = 899.4  ksi (Eq. E3-4)
F y F e = 50 899.4 = 0.056 < 2.25
F crx = 0.658 F y F e F y = 0.658 ( 0.056 ) 50 = 48.85  ksi (Eq. E3-2)

Pn = Ag× Fcr = 14.92 × 48.85 = 729.0 kips (Eq. E3-1)

The axial capacity:
  • The ultimate compression capacity (LRFD) = ϕcPn = 0.9 × 729.0 = 656.1 kips
  • The allowable compression capacity (ASD) = Pnc = 729.0 / 1.67 = 436.5 kips

Shear Capacity

The distance from the maximum shear force (ends) to zero shear force (mid-span), Lv = L / 2 = 30 in.

The critical shear stress, Fcr, is the minimum of:

F cr1 = 1.60 E L v OD ( OD t ) 5 4 = 633.4  ksi
F cr2 = 0.78 E ( OD t ) 3 2 = 252.9  ksi
F cr3 = 0.6 F y = 30  ksi

Fcr = 30 ksi

Nominal shear capacity:

V n = F cr A g 2 = 223.8  kips
The shear capacity:
  • The ultimate shear capacity (LRFD) = ϕcVn = 0.9 × 223.8 = 201.5 kips
  • The allowable shear capacity (ASD) = Vnc = 223.8 / 1.67 = 134.0 kips

Calculate Bending Capacity

Bending capacity in plastic yielding:

Mp = Fy × Z = 50 × 45.17 = 2,259 in·kips < 1.6Fy × S = 1.6 (50) (33.76) = 2,701 in·kips

The bending capacity for flexural yielding:
  • The ultimate bending capacity (LRFD) = ϕbMy = 0.9 × 2,259 = 2,033 in·kips
  • The allowable bending capacity (ASD) = Myb = 2,259 / 1.67 = 1,352 in·kips

Torsional Capacity

The critical stress, Fcr, is the larger of:

F cr1 = 1.23 E L OD ( OD t ) 5 4 = 344.3  ksi
F cr2 = 1.23 E ( OD t ) 3 2 = 194.5  ksi

But shall not exceed:

F cr3 = 0.6 F y = 30  ksi

Fcr = 30 ksi

Nominal torsional capacity:

T n = F cr C = 2,126  in·kips
The torsional capacity:
  • The ultimate torsional capacity (LRFD) = ϕcTn = 0.9 × 2,126 = 1,914 kips
  • The allowable torsional capacity (ASD) = Tnc = 2,126 / 1.67 = 1,273 kips

Interaction Ratio for Bending and Compression

Check the interaction ratio for Load Case 1:

P r P c = 10.23 656.1 = 0.016 < 0.2  (LRFD)
P r P c = 10.23 436.5 = 0.023 < 0.2  (ASD)

So use Eq. H1-1b for both methods: P r 2 P c + ( M r x M c x + M r y M c y ) 1.0 .

0.016 2 + ( 505.7 2,033 + 0 2,033 ) = 0.257  (LRFD)
0.023 2 + ( 505.7 1,352 + 0 1,352 ) = 0.386  (ASD)

Results

Result Type Reference STAAD.Pro Difference Comments
LRFD Compression capacity (kips) 656.1 656.1 none  
Shear capacity (kips) 201.5 201.5 none  
Bending capacity (in·kips) 2,033 2,033 none  
Torsional capacity (in·kips) 1,914 1,914 none  
Interaction ratio 0.257 0.257 none  
ASD Compression capacity (kips) 436.5 436.5 none  
Shear capacity (kips) 134.0 134 none  
Bending capacity (in·kips) 1,352 1,352 none  
Torsional capacity (in·kips) 1,273 1,273 none  
Interaction ratio 0.386 0.386 none  

STAAD.Pro Input

The following design parameters are used:

  • The welded tapered member is specified using STP 2

The remaining parameters all use their default values.

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\US\AISC\AISC 360-16 Tapered Tube Section.STD is typically installed with the program.

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 13-Apr-21
END JOB INFORMATION
INPUT WIDTH 79
UNIT INCHES KIP
JOINT COORDINATES
1 0 0 0; 2 0 60 0; 3 60 60 0; 4 60 0 0;
MEMBER INCIDENCES
1 1 2; 2 2 3; 3 3 4;
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 AMERICAN
1 TABLE ST W12X72
3 TABLE ST W12X72
MEMBER PROPERTY
2 PRIS ROUND STA 12 END 10 THI 0.5
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 FIXED
4 FIXED
LOAD 1 LOADTYPE None  TITLE LOAD CASE 1
MEMBER LOAD
2 UNI GY -2.25
LOAD 2 LOADTYPE None  TITLE LOAD CASE 2
JOINT LOAD
2 FX 50 FZ 25
LOAD 3 LOADTYPE None  TITLE LOAD CASE 3
MEMBER LOAD
2 CMOM GX 0.75
PERFORM ANALYSIS
PRINT ANALYSIS RESULTS
PARAMETER 1
CODE AISC UNIFIED 2016
SLF 0.8 MEMB 2
FYLD 50 ALL
FU 60 ALL
METHOD LRFD
STP 2 MEMB 2
TRACK 2 MEMB 2
CHECK CODE MEMB 2
PARAMETER 2
CODE AISC UNIFIED 2016
SLF 0.8 MEMB 2
FYLD 50 ALL
FU 60 ALL
METHOD ASD
STP 2 MEMB 2
TRACK 2 MEMB 2
CHECK CODE MEMB 2
FINISH

STAAD.Pro Output

                                                                  PAGE NO.    1
             ****************************************************        
             *                                                  *        
             *           STAAD.Pro CONNECT Edition              *        
             *           Version  22.08.00.***                  *        
             *           Proprietary Program of                 *        
             *           Bentley Systems, Inc.                  *        
             *           Date=    OCT 19, 2021                  *        
             *           Time=    18:12:35                      *        
             *                                                  *        
             *  Licensed to: Bentley Systems Inc                *        
             ****************************************************        
     1. STAAD SPACE
INPUT FILE: AISC 360-16 Tapered Tube Section.STD
     2. START JOB INFORMATION
     3. ENGINEER DATE 13-APR-21
     4. END JOB INFORMATION
     5. INPUT WIDTH 79
     6. UNIT INCHES KIP
     7. JOINT COORDINATES
     8. 1 0 0 0; 2 0 60 0; 3 60 60 0; 4 60 0 0
     9. MEMBER INCIDENCES
    10. 1 1 2; 2 2 3; 3 3 4
    11. DEFINE MATERIAL START
    12. ISOTROPIC STEEL
    13. E 29000
    14. POISSON 0.3
    15. DENSITY 0.000283
    16. ALPHA 6.5E-06
    17. DAMP 0.03
    18. G 11200
    19. TYPE STEEL
    20. STRENGTH RY 1.5 RT 1.2
    21. END DEFINE MATERIAL
    22. MEMBER PROPERTY AMERICAN
    23. 1 TABLE ST W12X72
    24. 3 TABLE ST W12X72
    25. MEMBER PROPERTY
    26. 2 PRIS ROUND STA 12 END 10 THI 0.5
    27. CONSTANTS
    28. MATERIAL STEEL ALL
    29. SUPPORTS
    30. 1 FIXED
    31. 4 FIXED
    32. LOAD 1 LOADTYPE NONE  TITLE LOAD CASE 1
    33. MEMBER LOAD
    34. 2 UNI GY -2.25
    35. LOAD 2 LOADTYPE NONE  TITLE LOAD CASE 2
    36. JOINT LOAD
    37. 2 FX 50 FZ 25
    38. LOAD 3 LOADTYPE NONE  TITLE LOAD CASE 3
      STAAD SPACE                                              -- PAGE NO.    2
    39. MEMBER LOAD
    40. 2 CMOM GX 0.75
    41. PERFORM ANALYSIS
            P R O B L E M   S T A T I S T I C S
            -----------------------------------
     NUMBER OF JOINTS          4  NUMBER OF MEMBERS       3
     NUMBER OF PLATES          0  NUMBER OF SOLIDS        0
     NUMBER OF SURFACES        0  NUMBER OF SUPPORTS      2
           Using 64-bit analysis engine.
           SOLVER USED IS THE IN-CORE ADVANCED MATH SOLVER
   TOTAL      PRIMARY LOAD CASES =     3, TOTAL DEGREES OF FREEDOM =      12
   TOTAL LOAD COMBINATION  CASES =     0  SO FAR.
    42. PRINT ANALYSIS RESULTS
  ANALYSIS RESULTS                    
      STAAD SPACE                                              -- PAGE NO.    3
   JOINT DISPLACEMENT (INCH RADIANS)    STRUCTURE TYPE = SPACE
   ------------------
 JOINT  LOAD   X-TRANS   Y-TRANS   Z-TRANS   X-ROTAN   Y-ROTAN   Z-ROTAN
      1    1    0.00000   0.00000   0.00000   0.00000   0.00000   0.00000
           2    0.00000   0.00000   0.00000   0.00000   0.00000   0.00000
           3    0.00000   0.00000   0.00000   0.00000   0.00000   0.00000
      2    1    0.00162  -0.00665   0.00000   0.00000   0.00000  -0.00075
           2    0.07748   0.00168   0.25417   0.00541   0.00296  -0.00079
           3    0.00000   0.00000   0.00013   0.00000   0.00000   0.00000
      3    1    0.00033  -0.00659   0.00000   0.00000   0.00000   0.00069
           2    0.07448  -0.00168   0.07663   0.00255   0.00296  -0.00085
           3    0.00000   0.00000   0.00011   0.00000   0.00000   0.00000
      4    1    0.00000   0.00000   0.00000   0.00000   0.00000   0.00000
           2    0.00000   0.00000   0.00000   0.00000   0.00000   0.00000
           3    0.00000   0.00000   0.00000   0.00000   0.00000   0.00000
      STAAD SPACE                                              -- PAGE NO.    4
   SUPPORT REACTIONS -UNIT KIP  INCH    STRUCTURE TYPE = SPACE
   -----------------
 JOINT  LOAD   FORCE-X   FORCE-Y   FORCE-Z     MOM-X     MOM-Y     MOM Z
      1    1     10.23     67.81      0.00      0.00      0.00    -89.36
           2    -26.14    -17.09    -24.95  -1258.27     -1.62   1013.33
           3      0.00      0.00      0.00     -0.39     -0.00      0.00
      4    1    -10.23     67.19      0.00      0.00      0.00    108.13
           2    -23.86     17.09     -0.05   -241.73     -1.62    961.14
           3      0.00      0.00     -0.00     -0.36     -0.00      0.00
      STAAD SPACE                                              -- PAGE NO.    5
   MEMBER END FORCES    STRUCTURE TYPE = SPACE
   -----------------
   ALL UNITS ARE -- KIP  INCH     (LOCAL )
  MEMBER  LOAD  JT     AXIAL   SHEAR-Y  SHEAR-Z   TORSION     MOM-Y      MOM-Z
      1    1     1     67.81    -10.23     0.00      0.00      0.00     -89.36
                 2    -67.81     10.23     0.00      0.00      0.00    -524.44
           2     1    -17.09     26.14   -24.95     -1.62   1258.27    1013.33
                 2     17.09    -26.14    24.95      1.62    238.50     554.84
           3     1      0.00      0.00     0.00     -0.00      0.39       0.00
                 2      0.00      0.00    -0.00      0.00     -0.39       0.00
      2    1     2     10.23     67.81     0.00      0.00      0.00     524.44
                 3    -10.23     67.19     0.00      0.00      0.00    -505.66
           2     2     23.86    -17.09     0.05    238.50     -1.62    -554.84
                 3    -23.86     17.09    -0.05   -238.50     -1.62    -470.69
           3     2      0.00      0.00     0.00     -0.39     -0.00       0.00
                 3      0.00      0.00    -0.00     -0.36     -0.00       0.00
      3    1     3     67.19     10.23     0.00      0.00      0.00     505.66
                 4    -67.19    -10.23     0.00      0.00      0.00     108.13
           2     3     17.09     23.86     0.05     -1.62    238.50     470.69
                 4    -17.09    -23.86    -0.05      1.62   -241.73     961.14
           3     3      0.00      0.00     0.00     -0.00      0.36       0.00
                 4      0.00      0.00    -0.00      0.00     -0.36       0.00
   ************** END OF LATEST ANALYSIS RESULT **************
    43. PARAMETER 1
    44. CODE AISC UNIFIED 2016
    45. SLF 0.8 MEMB 2
    46. FYLD 50 ALL
    47. FU 60 ALL
    48. METHOD LRFD
    49. STP 2 MEMB 2
    50. TRACK 2 MEMB 2
    51. CHECK CODE MEMB 2
 PARAMETER 1       
      STAAD SPACE                                              -- PAGE NO.    6
                       STAAD.PRO CODE CHECKING - AISC 360-16 LRFD (V1.2)
                     *****************************************************
 ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted).
 ***NOTE : AISC 360-16 Design Statement for STAAD.Pro.
 *** AXIS CONVENTION ***:
 ========================
 The capacity results and intermediate results in the report follow the notations
 and axes labels as defined in the AISC 360-16 code.
 The analysis results are reported in STAAD.Pro axis convention and the AISC 360:16
 design results are reported in AISC 360-16 code axis convention.
   AISC Spec.      STAAD.Pro      Description
  ------------    -----------     -------------
       X               Z          Axis typically parallel to the sections principal major axis.
       Y               Y          Axis typically parallel to the sections principal minor axis.
       Z               X          Longitudinal axis perpendicular to the cross section.
 SECTION FORCES AXIS MAPPING: -
   AISC Spec.      STAAD.Pro      Description
  ------------    -----------     -------------
       Pz              FX         Axial force.
       Vy              FY         Shear force along minor axis.
       Vx              FZ         Shear force along major axis.
       Tz              MX         Torsional moment.
       My              MY         Bending moment about minor axis.
       Mx              MZ         Bending moment about major axis.
 *** DESIGN MESSAGES ***:
 =======================
    1. Section classification reported is for the cross section and loadcase that
       produced the worst case design ratio for flexure/compression Capacity results.     
    2. Results for any Capacity/Check that is not relevant for a section/loadcase
       based on the code clause in AISC 360-16 will not be shown in the report.     
    3. Bending results are reported as being �about� the relevant axis (X/Y), while 
       the results for shear are reported as being for shear forces �along� the axis.
       E.g : Mx indicates bending about the X axis, while Vx indicates shear along
       the X axis.
 *** ABBREVIATIONS ***:
 ======================
    F-T-B = Flexural-Torsional Buckling
    L-T-B = Lateral-Torsional Buckling
    F-L-B = Flange Local Buckling
    W-L-B = Web Local Buckling
    L-L-B = Leg Local Buckling
    C-F-Y = Compression Flange Yielding
    T-F-Y = Tension Flange Yielding
      STAAD SPACE                                              -- PAGE NO.    7
                       STAAD.PRO CODE CHECKING - AISC 360-16 LRFD (V1.2)
                     *****************************************************
 ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted).
 - Member :     2 
|-----------------------------------------------------------------------------|
|  Member No:        2       Profile:      PRISMAT             (AISC SECTIONS)|
|  Status:        PASS       Ratio:         0.334       Loadcase:        1    |
|  Location:     60.00       Ref:      Cl.G1                                  |
|  Pz:       10.23     C     Vy:       -67.19           Vx:      0.000        |
|  Tz:       0.000           My:        0.000           Mx:      505.7        |
|-----------------------------------------------------------------------------|
| SLENDERNESS                                                                 |
| Actual Slenderness Ratio    :     17.839                                    |
| Allowable Slenderness Ratio :    200.000            LOC  :    60.00         |
|-----------------------------------------------------------------------------|
| STRENGTH CHECKS                                                             |
| Critical L/C  :      1             Ratio     :        0.334(PASS)           |
|          Loc  :   60.00            Condition :    Cl.G1                     |
|-----------------------------------------------------------------------------|
| SECTION PROPERTIES  (LOC:    60.00, PROPERTIES UNIT: IN  )                  |
| Ag  :   1.492E+01     Axx :   7.909E+00     Ayy :   7.909E+00               |
| Ixx :   1.688E+02     Iyy :   1.688E+02     J   :   3.376E+02               |
| Sxx+:   3.376E+01     Sxx-:   3.376E+01     Zxx :   4.517E+01               |
| Syy+:   3.376E+01     Syy-:   3.376E+01     Zyy :   4.517E+01               |
| Cw  :   0.000E+00     x0  :   0.000E+00     y0  :   0.000E+00               |
|-----------------------------------------------------------------------------|
| MATERIAL PROPERTIES                                                         |
| Fyld:          50.000              Fu:          60.000                      |
|-----------------------------------------------------------------------------|
| Actual Member Length:        60.000                                         |
| Design Parameters                                            (Built-Up)     |
| Kx:    1.00  Ky:    1.00  NSF:    1.00  SLF:    0.80  CSP:   12.00          |
|-----------------------------------------------------------------------------|
| COMPRESSION CLASSIFICATION (L/C:      2 LOC:    60.00)                      |
|                            λ         λp        λr       CASE                |
| Flange: NonSlender      20.00       N/A      63.80     Table.4.1a.Case9     |
| Web   : NonSlender      20.00       N/A      63.80     Table.4.1a.Case9     |
|                                                                             |
| FLEXURE CLASSIFICATION     (L/C:      2 LOC:    60.00)                      |
|                            λ         λp        λr       CASE                |
| Flange: Compact         20.00      40.60    179.80     Table.4.1b.Case20    |
| Web   : Compact         20.00      40.60    179.80     Table.4.1b.Case20    |
|-----------------------------------------------------------------------------|
      STAAD SPACE                                              -- PAGE NO.    8
                       STAAD.PRO CODE CHECKING - AISC 360-16 LRFD (V1.2)
                     *****************************************************
 ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted).
                                                       - Member :     2 Contd.
|-----------------------------------------------------------------------------|
|                         CHECKS FOR AXIAL TENSION                            |
|-----------------------------------------------------------------------------|
| TENSILE YIELDING                                                            |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|              0.000       671.5       0.000     Cl.D2          1     60.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Nom. Ten. Yld Cap         : Pn     =  746.13     kip        Eq.D2-1        |
|-----------------------------------------------------------------------------|
| TENSILE RUPTURE                                                             |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|              0.000       537.2       0.000     Cl.D2          1     60.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Effective area            : Ae     =  11.938     in2        Eq.D3-1        |
|  Nom. Ten. Rpt Cap         : Pn     =  716.28     kip        Eq.D2-2        |
|-----------------------------------------------------------------------------|
|                         CHECKS FOR AXIAL COMPRESSION                        |
|-----------------------------------------------------------------------------|
| FLEXURAL BUCKLING X                                                         |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|              23.86       656.1       0.036     Cl.E3          2     60.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Effective Slenderness     : Lcx/rx =  17.839                Cl.E2          |
|  Elastic Buckling Stress   : Fex    =  899.40     ksi        Eq.E3-4        |
|  Crit. Buckling Stress     : Fcrx   =  48.850     ksi        Eq.E3-2        |
|  Nom. Flexural Buckling    : Pnx    =  728.97     kip        Eq.E3-1        |
|-----------------------------------------------------------------------------|
| FLEXURAL BUCKLING Y                                                         |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|              23.86       656.1       0.036     Cl.E3          2     60.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Effective Slenderness     : Lcy/ry =  17.839                Cl.E2          |
|  Elastic Buckling Stress   : Fey    =  899.40     ksi        Eq.E3-4        |
|  Crit. Buckling Stress     : Fcry   =  48.850     ksi        Eq.E3-2        |
|  Nom. Flexural Buckling    : Pny    =  728.97     kip        Eq.E3-1        |
|-----------------------------------------------------------------------------|
      STAAD SPACE                                              -- PAGE NO.    9
                       STAAD.PRO CODE CHECKING - AISC 360-16 LRFD (V1.2)
                     *****************************************************
 ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted).
                                                       - Member :     2 Contd.
|-----------------------------------------------------------------------------|
|                         CHECKS FOR SHEAR                                    |
|-----------------------------------------------------------------------------|
| SHEAR ALONG X                                                               |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|             0.5390E-01   201.5       0.000     Cl.G1          2     60.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Nom. Shear Along X        : Vnx    =  223.84     kip        Eq.G5-1        |
|  Crit. Stress Fcr Along X  : Fcrx   =  30.000     ksi        Eq.G5-2        |
|-----------------------------------------------------------------------------|
| SHEAR ALONG Y                                                               |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|              67.19       201.5       0.334     Cl.G1          1     60.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Nom. Shear Along Y        : Vny    =  223.84     kip        Eq.G5-1        |
|  Crit. Stress Fcr Along Y  : Fcrx   =  30.000     ksi        Eq.G5-2        |
|-----------------------------------------------------------------------------|
      STAAD SPACE                                              -- PAGE NO.   10
                       STAAD.PRO CODE CHECKING - AISC 360-16 LRFD (V1.2)
                     *****************************************************
 ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted).
                                                       - Member :     2 Contd.
|-----------------------------------------------------------------------------|
|                         CHECKS FOR BENDING                                  |
|-----------------------------------------------------------------------------|
| FLEX YIELDING (X)                                                           |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|              505.7       2033.       0.249     Cl.F8.1        1     60.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Nom Flex Yielding Along X : Mnx    =  2258.3     kip-in     Eq.F8-1        |
|-----------------------------------------------------------------------------|
| FLEX. YIELDING (Y)                                                          |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|             -1.617       2033.       0.001     Cl.F8.1        2     60.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Nom Flex Yielding Along Y : Mny    =  2258.3     kip-in     Eq.F8-1        |
|-----------------------------------------------------------------------------|
      STAAD SPACE                                              -- PAGE NO.   11
                       STAAD.PRO CODE CHECKING - AISC 360-16 LRFD (V1.2)
                     *****************************************************
 ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted).
                                                       - Member :     2 Contd.
|-----------------------------------------------------------------------------|
|                         CHECKS FOR AXIAL BEND INTERACTION                   |
|-----------------------------------------------------------------------------|
| COMBINED FORCES CLAU                                                        |
|                            RATIO      CRITERIA           L/C      LOC       |
|                            0.257      Eq.H1-1b            1       60.00     |
|                                                                             |
| Intermediate Results :                                                      |
|  Axial Capacity            : Pc     =  656.07     kip        Cl.H1.1        |
|  Moment Capacity           : Mcx    =  2032.5     kip-in     Cl.H1.1        |
|  Moment Capacity           : Mcy    =  2032.5     kip-in     Cl.H1.1        |
|-----------------------------------------------------------------------------|
      STAAD SPACE                                              -- PAGE NO.   12
                       STAAD.PRO CODE CHECKING - AISC 360-16 LRFD (V1.2)
                     *****************************************************
 ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted).
                                                       - Member :     2 Contd.
|-----------------------------------------------------------------------------|
|                         CHECKS FOR TORSION                                  |
|-----------------------------------------------------------------------------|
| TORSION CAPACITY                                                            |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|              238.5       1914.       0.125     Cl.H3.1        2     60.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Crit. Stress. Fcr         : Fcr    =  30.000     ksi        Cl.H3.1(a)     |
|  Nom. Strength             : Tn     =  2126.5     kip-in     Eq.H3-1        |
|-----------------------------------------------------------------------------|
    52. PARAMETER 2
    53. CODE AISC UNIFIED 2016
    54. SLF 0.8 MEMB 2
    55. FYLD 50 ALL
    56. FU 60 ALL
    57. METHOD ASD
    58. STP 2 MEMB 2
    59. TRACK 2 MEMB 2
    60. CHECK CODE MEMB 2
 PARAMETER 2       
      STAAD SPACE                                              -- PAGE NO.   13
                       STAAD.PRO CODE CHECKING - AISC 360-16 ASD (V1.2)
                     ****************************************************
 ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted).
 ***NOTE : AISC 360-16 Design Statement for STAAD.Pro.
 *** AXIS CONVENTION ***:
 ========================
 The capacity results and intermediate results in the report follow the notations
 and axes labels as defined in the AISC 360-16 code.
 The analysis results are reported in STAAD.Pro axis convention and the AISC 360:16
 design results are reported in AISC 360-16 code axis convention.
   AISC Spec.      STAAD.Pro      Description
  ------------    -----------     -------------
       X               Z          Axis typically parallel to the sections principal major axis.
       Y               Y          Axis typically parallel to the sections principal minor axis.
       Z               X          Longitudinal axis perpendicular to the cross section.
 SECTION FORCES AXIS MAPPING: -
   AISC Spec.      STAAD.Pro      Description
  ------------    -----------     -------------
       Pz              FX         Axial force.
       Vy              FY         Shear force along minor axis.
       Vx              FZ         Shear force along major axis.
       Tz              MX         Torsional moment.
       My              MY         Bending moment about minor axis.
       Mx              MZ         Bending moment about major axis.
 *** DESIGN MESSAGES ***:
 =======================
    1. Section classification reported is for the cross section and loadcase that
       produced the worst case design ratio for flexure/compression Capacity results.     
    2. Results for any Capacity/Check that is not relevant for a section/loadcase
       based on the code clause in AISC 360-16 will not be shown in the report.     
    3. Bending results are reported as being �about� the relevant axis (X/Y), while 
       the results for shear are reported as being for shear forces �along� the axis.
       E.g : Mx indicates bending about the X axis, while Vx indicates shear along
       the X axis.
 *** ABBREVIATIONS ***:
 ======================
    F-T-B = Flexural-Torsional Buckling
    L-T-B = Lateral-Torsional Buckling
    F-L-B = Flange Local Buckling
    W-L-B = Web Local Buckling
    L-L-B = Leg Local Buckling
    C-F-Y = Compression Flange Yielding
    T-F-Y = Tension Flange Yielding
      STAAD SPACE                                              -- PAGE NO.   14
                       STAAD.PRO CODE CHECKING - AISC 360-16 ASD (V1.2)
                     ****************************************************
 ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted).
 - Member :     2 
|-----------------------------------------------------------------------------|
|  Member No:        2       Profile:      PRISMAT             (AISC SECTIONS)|
|  Status:        PASS       Ratio:         0.501       Loadcase:        1    |
|  Location:     60.00       Ref:      Cl.G1                                  |
|  Pz:       10.23     C     Vy:       -67.19           Vx:      0.000        |
|  Tz:       0.000           My:        0.000           Mx:      505.7        |
|-----------------------------------------------------------------------------|
| SLENDERNESS                                                                 |
| Actual Slenderness Ratio    :     17.839                                    |
| Allowable Slenderness Ratio :    200.000            LOC  :    60.00         |
|-----------------------------------------------------------------------------|
| STRENGTH CHECKS                                                             |
| Critical L/C  :      1             Ratio     :        0.501(PASS)           |
|          Loc  :   60.00            Condition :    Cl.G1                     |
|-----------------------------------------------------------------------------|
| SECTION PROPERTIES  (LOC:    60.00, PROPERTIES UNIT: IN  )                  |
| Ag  :   1.492E+01     Axx :   7.909E+00     Ayy :   7.909E+00               |
| Ixx :   1.688E+02     Iyy :   1.688E+02     J   :   3.376E+02               |
| Sxx+:   3.376E+01     Sxx-:   3.376E+01     Zxx :   4.517E+01               |
| Syy+:   3.376E+01     Syy-:   3.376E+01     Zyy :   4.517E+01               |
| Cw  :   0.000E+00     x0  :   0.000E+00     y0  :   0.000E+00               |
|-----------------------------------------------------------------------------|
| MATERIAL PROPERTIES                                                         |
| Fyld:          50.000              Fu:          60.000                      |
|-----------------------------------------------------------------------------|
| Actual Member Length:        60.000                                         |
| Design Parameters                                            (Built-Up)     |
| Kx:    1.00  Ky:    1.00  NSF:    1.00  SLF:    0.80  CSP:   12.00          |
|-----------------------------------------------------------------------------|
| COMPRESSION CLASSIFICATION (L/C:      2 LOC:    60.00)                      |
|                            λ         λp        λr       CASE                |
| Flange: NonSlender      20.00       N/A      63.80     Table.4.1a.Case9     |
| Web   : NonSlender      20.00       N/A      63.80     Table.4.1a.Case9     |
|                                                                             |
| FLEXURE CLASSIFICATION     (L/C:      2 LOC:    60.00)                      |
|                            λ         λp        λr       CASE                |
| Flange: Compact         20.00      40.60    179.80     Table.4.1b.Case20    |
| Web   : Compact         20.00      40.60    179.80     Table.4.1b.Case20    |
|-----------------------------------------------------------------------------|
      STAAD SPACE                                              -- PAGE NO.   15
                       STAAD.PRO CODE CHECKING - AISC 360-16 ASD (V1.2)
                     ****************************************************
 ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted).
                                                       - Member :     2 Contd.
|-----------------------------------------------------------------------------|
|                         CHECKS FOR AXIAL TENSION                            |
|-----------------------------------------------------------------------------|
| TENSILE YIELDING                                                            |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|              0.000       446.8       0.000     Cl.D2          1     60.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Nom. Ten. Yld Cap         : Pn     =  746.13     kip        Eq.D2-1        |
|-----------------------------------------------------------------------------|
| TENSILE RUPTURE                                                             |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|              0.000       358.1       0.000     Cl.D2          1     60.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Effective area            : Ae     =  11.938     in2        Eq.D3-1        |
|  Nom. Ten. Rpt Cap         : Pn     =  716.28     kip        Eq.D2-2        |
|-----------------------------------------------------------------------------|
|                         CHECKS FOR AXIAL COMPRESSION                        |
|-----------------------------------------------------------------------------|
| FLEXURAL BUCKLING X                                                         |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|              23.86       436.5       0.055     Cl.E3          2     60.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Effective Slenderness     : Lcx/rx =  17.839                Cl.E2          |
|  Elastic Buckling Stress   : Fex    =  899.40     ksi        Eq.E3-4        |
|  Crit. Buckling Stress     : Fcrx   =  48.850     ksi        Eq.E3-2        |
|  Nom. Flexural Buckling    : Pnx    =  728.97     kip        Eq.E3-1        |
|-----------------------------------------------------------------------------|
| FLEXURAL BUCKLING Y                                                         |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|              23.86       436.5       0.055     Cl.E3          2     60.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Effective Slenderness     : Lcy/ry =  17.839                Cl.E2          |
|  Elastic Buckling Stress   : Fey    =  899.40     ksi        Eq.E3-4        |
|  Crit. Buckling Stress     : Fcry   =  48.850     ksi        Eq.E3-2        |
|  Nom. Flexural Buckling    : Pny    =  728.97     kip        Eq.E3-1        |
|-----------------------------------------------------------------------------|
      STAAD SPACE                                              -- PAGE NO.   16
                       STAAD.PRO CODE CHECKING - AISC 360-16 ASD (V1.2)
                     ****************************************************
 ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted).
                                                       - Member :     2 Contd.
|-----------------------------------------------------------------------------|
|                         CHECKS FOR SHEAR                                    |
|-----------------------------------------------------------------------------|
| SHEAR ALONG X                                                               |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|             0.5390E-01   134.0       0.000     Cl.G1          2     60.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Nom. Shear Along X        : Vnx    =  223.84     kip        Eq.G5-1        |
|  Crit. Stress Fcr Along X  : Fcrx   =  30.000     ksi        Eq.G5-2        |
|-----------------------------------------------------------------------------|
| SHEAR ALONG Y                                                               |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|              67.19       134.0       0.501     Cl.G1          1     60.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Nom. Shear Along Y        : Vny    =  223.84     kip        Eq.G5-1        |
|  Crit. Stress Fcr Along Y  : Fcrx   =  30.000     ksi        Eq.G5-2        |
|-----------------------------------------------------------------------------|
      STAAD SPACE                                              -- PAGE NO.   17
                       STAAD.PRO CODE CHECKING - AISC 360-16 ASD (V1.2)
                     ****************************************************
 ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted).
                                                       - Member :     2 Contd.
|-----------------------------------------------------------------------------|
|                         CHECKS FOR BENDING                                  |
|-----------------------------------------------------------------------------|
| FLEX YIELDING (X)                                                           |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|              505.7       1352.       0.374     Cl.F8.1        1     60.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Nom Flex Yielding Along X : Mnx    =  2258.3     kip-in     Eq.F8-1        |
|-----------------------------------------------------------------------------|
| FLEX. YIELDING (Y)                                                          |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|             -1.617       1352.       0.001     Cl.F8.1        2     60.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Nom Flex Yielding Along Y : Mny    =  2258.3     kip-in     Eq.F8-1        |
|-----------------------------------------------------------------------------|
      STAAD SPACE                                              -- PAGE NO.   18
                       STAAD.PRO CODE CHECKING - AISC 360-16 ASD (V1.2)
                     ****************************************************
 ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted).
                                                       - Member :     2 Contd.
|-----------------------------------------------------------------------------|
|                         CHECKS FOR AXIAL BEND INTERACTION                   |
|-----------------------------------------------------------------------------|
| COMBINED FORCES CLAU                                                        |
|                            RATIO      CRITERIA           L/C      LOC       |
|                            0.386      Eq.H1-1b            1       60.00     |
|                                                                             |
| Intermediate Results :                                                      |
|  Axial Capacity            : Pc     =  436.51     kip        Cl.H1.1        |
|  Moment Capacity           : Mcx    =  1352.3     kip-in     Cl.H1.1        |
|  Moment Capacity           : Mcy    =  1352.3     kip-in     Cl.H1.1        |
|-----------------------------------------------------------------------------|
      STAAD SPACE                                              -- PAGE NO.   19
                       STAAD.PRO CODE CHECKING - AISC 360-16 ASD (V1.2)
                     ****************************************************
 ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted).
                                                       - Member :     2 Contd.
|-----------------------------------------------------------------------------|
|                         CHECKS FOR TORSION                                  |
|-----------------------------------------------------------------------------|
| TORSION CAPACITY                                                            |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|              238.5       1273.       0.187     Cl.H3.1        2     60.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Crit. Stress. Fcr         : Fcr    =  30.000     ksi        Cl.H3.1(a)     |
|  Nom. Strength             : Tn     =  2126.5     kip-in     Eq.H3-1        |
|-----------------------------------------------------------------------------|
    61. FINISH
             *********** END OF THE STAAD.Pro RUN ***********         
               **** DATE= OCT 19,2021   TIME= 18:12:35 ****
         ************************************************************
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