V. AISC 360-16 Channel Section
Determine the capacities and interaction check ratio of a channel section per the AISC 360-16 code.
Reference
- Steel Construction Manual, 15th Edition, American Institute of Steel Construction, 2017 Table 1-5.
Details
The beam is a 15 feet (180 in.) long, simply supported member. The beam is subject to uniform dead load of 0.75 kip/ft and uniform live load of 1 kip/ft. A lateral-torsional buckling modification factor, Cb of 1.0 is assumed. The compression flange is braced against buckling at the third points.
The section used is a C15x50. The material is A36 steel.
Validation
Ultimate Load
Slenderness
Slenderness ratio: =
Compare this to the allowable tension slenderness ratio of 300 (note that no tension or compression is present in the member):
Section Classification
Compression elements
- Flange classification per Table B4.1a, Case 1:
thus, flanges are non-slender
- Web classification per Table B4.1a, Case 5:
thus, web is non-slender
Flexure elements
- Flange classification per Table B4.1b, Case 10:
thus, flanges are compact
- Web classification per Table B4.1b, Case 15:
thus, web is compact
Tension Capacity
- Tensile Yielding
Nominal tensile yield strength:
- Tensile Rupture
Effective area is equal to the net area, Ae = An = Ag = 14.7 in2 (no bolt holes)
Nominal tensile rupture strength:
Compression capacity
- Flexural buckling about the X axis:
the effective slenderness ratio about the local x axis (clause E2):
The elastic buckling stress:
Check that
Nominal compression capacity about the X axis:
- Flexural buckling about the Y axis:
the effective slenderness ratio about the local y axis (clause E2):
The elastic buckling stress:
Check that
Nominal compression capacity about the Y axis:
- Flexural torsional buckling: Channel section is singly symmetric:
- x0 = e0 + x = 0.583 + 0.490 = 1.382 in.
- y0 = 0
Euler buckling stress:
Elastic flexural torsional buckling stress:
Critical flexural torsional buckling stress:
Check that
Nominal compression capacity about the X axis:
Shear Capacity
- Shear along the X axis (
weak axis
shear)Take kv = 1.2 (clause G6)
Therefore, Cv2 = 1.0 per clause G2.2 and the nominal shear strength in the X direction:
- Shear along the Y axis (
strong axis
shear)Take kv = 5.34 (clause G2.1.b.2.i)
Therefore, Cv1 = 1.0 per eqn. G2-3 and the nominal shear strength in the Y direction:
Bending Capacity
- Flexural yielding about X axis
- Flexural yielding about Y axis
- Lateral torsional buckling about X axis:
The laterally unbraced length of the compression flange is 5 feet: Lb = 60 in.
For Lp < Lb < Lr :
Combined Interaction Check
Since Pr = 0, Pr / Pc = 0 < 0.2, equation H1-1b governs:
Results
Result Type | Reference | STAAD.Pro | Difference | Comments |
---|---|---|---|---|
Slenderness | 208.1 | 208.082 | negligible | |
Tensile Yielding (kips) | 476.3 | 476.3 | none | |
Tensile Rupture (kips) | 639.5 | 639.4 | negligible | |
Flexural Buckling About X axis (kips) | 447.6 | 447.6 | none | |
Flexural Buckling About Y axis (kips) | 76.70 | 76.70 | none | |
Flexural Torsional Buckling (kips) | 389.3 | 388.6 | negligible | |
Shear Capacity Along X Axis (kips) | 94.01 | 94.01 | none | |
Shear Capacity Along Y Axis (kips) | 208.8 | 208.8 | none | |
Flexural Yielding X Axis (ft·kips) | 185.0 | 185 | none | |
Flexural Yielding Y Axis (ft·kips) | 16.29 | 16.56 | negligible | |
Lateral Torsional Buckling About X Axis (ft·kips) | 177.7 | 177.7 | none | |
Interaction Ratio | 0.396 | 0.396 | none |
STAAD.Pro Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2024\Samples \Verification Models\09 Steel Design\US\AISC\AISC 360-16 Channel Section.STD is typically installed with the program.
The following design parameters are used:
- The value of
CB 1
is used for the lateral-torsional buckling modification factor, Cb of 1.0. - the value of
SGR 1
is used to specify ASTM A36 grade steel. - the value of
UNT 5
is used to specify the unsupported length of the top flange when in compression (positive bending) of 5 feet.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 24 Jan 2023
END JOB INFORMATION
INPUT WIDTH 79
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 15 0 0;
MEMBER INCIDENCES
1 1 2;
DEFINE MATERIAL START
ISOTROPIC STEEL
E 4.176e+06
POISSON 0.3
DENSITY 0.489024
ALPHA 6.5e-06
DAMP 0.03
TYPE STEEL
STRENGTH RY 1.5 RT 1.2
END DEFINE MATERIAL
MEMBER PROPERTY AMERICAN
1 TABLE ST C15X50
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 FIXED BUT MZ
2 FIXED BUT FX MZ
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
MEMBER LOAD
1 UNI GY -0.75
LOAD 2 LOADTYPE None TITLE LOAD CASE 2
MEMBER LOAD
1 UNI GY -1
LOAD COMB 3 COMBINATION LOAD CASE 3
1 1.2 2 1.6
PERFORM ANALYSIS
LOAD LIST 3
PARAMETER 1
CODE AISC UNIFIED 2016
CB 1 ALL
METHOD LRFD
SGR 1 ALL
TRACK 2 ALL
UNT 5 ALL
CHECK CODE ALL
FINISH
STAAD.Pro Output
STAAD.PRO CODE CHECKING - AISC 360-16 LRFD (V1.2)
*****************************************************
ALL UNITS ARE - KIP FEET (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. 4
STAAD.PRO CODE CHECKING - AISC 360-16 LRFD (V1.2)
*****************************************************
ALL UNITS ARE - KIP FEET (UNLESS OTHERWISE Noted).
- Member : 1
|-----------------------------------------------------------------------------|
| Member No: 1 Profile: ST C15X50 (AISC SECTIONS)|
| Status: PASS Ratio: 0.396 Loadcase: 3 |
| Location: 7.50 Ref: Cl.F2.2 |
| Pz: 0.000 T Vy: 0.000 Vx: 0.000 |
| Tz: 0.000 My: 0.000 Mx: -70.31 |
|-----------------------------------------------------------------------------|
| TENSION SLENDERNESS |
| Actual Slenderness Ratio : 208.082 |
| Allowable Slenderness Ratio : 300.000 LOC : 0.00 |
|-----------------------------------------------------------------------------|
| STRENGTH CHECKS |
| Critical L/C : 3 Ratio : 0.396(PASS) |
| Loc : 7.50 Condition : Cl.F2.2 |
|-----------------------------------------------------------------------------|
| SECTION PROPERTIES (LOC: 7.50, PROPERTIES UNIT: IN ) |
| Ag : 1.470E+01 Axx : 4.836E+00 Ayy : 1.074E+01 |
| Ixx : 4.040E+02 Iyy : 1.100E+01 J : 2.650E+00 |
| Sxx+: 5.387E+01 Sxx-: 5.387E+01 Zxx : 6.850E+01 |
| Syy+: 3.834E+00 Syy-: 1.293E+01 Zyy : 8.140E+00 |
| Cw : 4.913E+02 x0 : -1.447E+00 y0 : 0.000E+00 |
|-----------------------------------------------------------------------------|
| MATERIAL PROPERTIES |
| Fyld: 5184.000 Fu: 8351.999 |
|-----------------------------------------------------------------------------|
| Actual Member Length: 15.000 |
| Design Parameters (Rolled) |
| Kx: 1.00 Ky: 1.00 NSF: 1.00 SLF: 1.00 CSP: 1.00 |
|-----------------------------------------------------------------------------|
| COMPRESSION CLASSIFICATION (L/C: 3 LOC: 180.00) |
| λ λp λr CASE |
| Flange: NonSlender 5.72 N/A 15.89 Table.B4.1a.Case1 |
| Web : NonSlender 19.13 N/A 42.29 Table.B4.1a.Case5 |
| |
| FLEXURE CLASSIFICATION (L/C: 3 LOC: 180.00) |
| λ λp λr CASE |
| Flange: Compact 5.72 10.79 28.38 Table.B4.1b.Case10 |
| Web : Compact 19.13 106.72 161.78 Table.B4.1b.Case15 |
|-----------------------------------------------------------------------------|
STAAD SPACE -- PAGE NO. 5
STAAD.PRO CODE CHECKING - AISC 360-16 LRFD (V1.2)
*****************************************************
ALL UNITS ARE - KIP FEET (UNLESS OTHERWISE Noted).
- Member : 1 Contd.
|-----------------------------------------------------------------------------|
| CHECKS FOR AXIAL TENSION |
|-----------------------------------------------------------------------------|
| TENSILE YIELDING |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| -0.000 476.3 0.000 Cl.D2 3 0.00 |
| |
| Intermediate Results : |
| Nom. Ten. Yld Cap : Pn = 529.20 kip Eq.D2-1 |
|-----------------------------------------------------------------------------|
| TENSILE RUPTURE |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| -0.000 639.4 0.000 Cl.D2 3 0.00 |
| |
| Intermediate Results : |
| Effective area : Ae = 0.10208 ft2 Eq.D3-1 |
| Nom. Ten. Rpt Cap : Pn = 852.60 kip Eq.D2-2 |
|-----------------------------------------------------------------------------|
| CHECKS FOR AXIAL COMPRESSION |
|-----------------------------------------------------------------------------|
| FLEXURAL BUCKLING X |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| 0.000 447.6 0.000 Cl.E3 3 0.00 |
| |
| Intermediate Results : |
| Effective Slenderness : Lcx/rx = 34.335 Cl.E2 |
| Elastic Buckling Stress : Fex = 34961. kip/ft2 Eq.E3-4 |
| Crit. Buckling Stress : Fcrx = 4872.0 kip/ft2 Eq.E3-2 |
| Nom. Flexural Buckling : Pnx = 497.35 kip Eq.E3-1 |
|-----------------------------------------------------------------------------|
| FLEXURAL BUCKLING Y |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| 0.000 76.70 0.000 Cl.E3 3 0.00 |
| |
| Intermediate Results : |
| Effective Slenderness : Lcy/ry = 208.08 Cl.E2 |
| Elastic Buckling Stress : Fey = 951.90 kip/ft2 Eq.E3-4 |
| Crit. Buckling Stress : Fcry = 834.81 kip/ft2 Eq.E3-3 |
| Nom. Flexural Buckling : Pny = 85.221 kip Eq.E3-1 |
|-----------------------------------------------------------------------------|
| FLEXURAL-TORSIONAL-BUCKLING |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| 0.000 388.6 0.000 Cl.E4 3 0.00 |
| |
| Intermediate Results : |
| Constant : H = 0.93099 Eq.E4-8 |
| Euler Buckling Stress : Fez = 10990. kip/ft2 Eq.E4-7 |
| Elastic F-T-B Stress : Fe = 10667. kip/ft2 Eq.E4-3 |
| Crit. F-T-B Stress : Fcr = 4229.8 kip/ft2 Eq.E3-2 |
| Nom. Flex-tor Buckling : Pn = 431.79 kip Eq.E4-1 |
|-----------------------------------------------------------------------------|
STAAD SPACE -- PAGE NO. 6
STAAD.PRO CODE CHECKING - AISC 360-16 LRFD (V1.2)
*****************************************************
ALL UNITS ARE - KIP FEET (UNLESS OTHERWISE Noted).
- Member : 1 Contd.
|-----------------------------------------------------------------------------|
| CHECKS FOR SHEAR |
|-----------------------------------------------------------------------------|
| SHEAR ALONG X |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| 0.000 94.01 0.000 Cl.G1 3 0.00 |
| |
| Intermediate Results : |
| Coefficient Cv Along X : Cv = 1.0000 Eq.G2-9 |
| Coefficient Kv Along X : Kv = 1.2000 Cl.G6 |
| Nom. Shear Along X : Vnx = 104.46 kip Eq.G6-1 |
|-----------------------------------------------------------------------------|
| SHEAR ALONG Y |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| 18.75 208.8 0.090 Cl.G1 3 0.00 |
| |
| Intermediate Results : |
| Coefficient Cv Along Y : Cv = 1.0000 - |
| Coefficient Kv Along Y : Kv = 5.3400 Eq.G2-5 |
| Nom. Shear Along Y : Vny = 231.98 kip Eq.G2-1 |
|-----------------------------------------------------------------------------|
STAAD SPACE -- PAGE NO. 7
STAAD.PRO CODE CHECKING - AISC 360-16 LRFD (V1.2)
*****************************************************
ALL UNITS ARE - KIP FEET (UNLESS OTHERWISE Noted).
- Member : 1 Contd.
|-----------------------------------------------------------------------------|
| CHECKS FOR BENDING |
|-----------------------------------------------------------------------------|
| FLEXURAL YIELDING (X) |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| -70.31 185.0 0.380 Cl.F2.1 3 7.50 |
| |
| Intermediate Results : |
| Nom Flex Yielding Along X : Mnx = 205.50 kip-ft Eq.F2-1 |
|-----------------------------------------------------------------------------|
| FLEXURAL YIELDING (Y) |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| -0.000 16.56 0.000 Cl.F6.1 3 0.00 |
| |
| Intermediate Results : |
| Nom Flex Yielding Along Y : Mny = 18.402 kip-ft Eq.F6-1 |
|-----------------------------------------------------------------------------|
| LAT TOR BUCK ABOUT X |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| -70.31 177.7 0.396 Cl.F2.2 3 7.50 |
| |
| Intermediate Results : |
| Nom L-T-B Cap : Mnx = 197.39 kip-ft Eq.F2-2 |
| Mom. Distr. factor : CbX = 1.0000 Custom |
| Limiting Unbraced Length : LpX = 3.6009 ft Eq.F2-5 |
| coefficient C : Cx = 1.0736 Eq.F2-8b |
| Effective Rad. of Gyr. : Rts = 0.97350E-01 ft Eq.F2-7 |
| Limiting Unbraced Length : LrX = 19.539 ft Eq.F2-6 |
|-----------------------------------------------------------------------------|
STAAD SPACE -- PAGE NO. 8
STAAD.PRO CODE CHECKING - AISC 360-16 LRFD (V1.2)
*****************************************************
ALL UNITS ARE - KIP FEET (UNLESS OTHERWISE Noted).
- Member : 1 Contd.
|-----------------------------------------------------------------------------|
| CHECKS FOR AXIAL BEND INTERACTION |
|-----------------------------------------------------------------------------|
| COMBINED FORCES CLAUSE H1 |
| RATIO CRITERIA L/C LOC |
| 0.396 Eq.H1-1b 3 7.50 |
| |
| Intermediate Results : |
| Axial Capacity : Pc = 476.28 kip Cl.H1.1 |
| Moment Capacity : Mcx = 177.65 kip-ft Cl.H1.1 |
| Moment Capacity : Mcy = 16.562 kip-ft Cl.H1.1 |
|-----------------------------------------------------------------------------|