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.
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,
- Elastic section modulus,
- Radius of gyration,
- Plastic section modulus,
- HSS Torsional constant,
Section Classification
Flange in compression
Per Table B4.1a, Case 9, , 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):
Per Table B4.1b, Case20, , therefore flange is compact for bending.
Compression Capacity
| (Eq. E3-4) |
| (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) = Pn/Ωc = 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:
Fcr = 30 ksi
Nominal shear capacity:
The shear capacity:- The ultimate shear capacity (LRFD) = ϕcVn = 0.9 × 223.8 = 201.5 kips
- The allowable shear capacity (ASD) = Vn/Ωc = 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) = My/Ωb = 2,259 / 1.67 = 1,352 in·kips
Torsional Capacity
The critical stress, Fcr, is the larger of:
But shall not exceed:
Fcr = 30 ksi
Nominal torsional capacity:
The torsional capacity:- The ultimate torsional capacity (LRFD) = ϕcTn = 0.9 × 2,126 = 1,914 kips
- The allowable torsional capacity (ASD) = Tn/Ωc = 2,126 / 1.67 = 1,273 kips
Interaction Ratio for Bending and Compression
Check the interaction ratio for Load Case 1:
So use Eq. H1-1b for both methods: .
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 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 **** ************************************************************ * For technical assistance on STAAD.Pro, please visit * * http://www.bentley.com/en/support/ * * * * Details about additional assistance from * * Bentley and Partners can be found at program menu * * Help->Technical Support * * * * Copyright (c) Bentley Systems, Inc. * * http://www.bentley.com * ************************************************************