V. AISI 2016 CU Nominal Moment Capacity
Determine the nominal moment axial capacity of a simply-supported beam subject to a concentrated load at mid-span.
Reference
Yu, Wei-Wen and Roger A. LaBoube. 2010 Cold-Formed Steel Design, Fourth Edition. Hoboken, NJ: Wiley. Example 4.3.
Details
The member is a 10' simply-supported span subject to a 1 kip load applied at midspan. The section used is a CU_8X2_0.06 channel without lips. The member is laterally supported at the one-fourth points along the span.
Section properties:
- Depth: D = 8 in
- Width: B = 2 in
- Thickness: t = 0.06 in
- Inner radius: R = 3/32 in
- Area: A = 0.706 in2
- Moment of inertia about major axis: Ix = 6.129 in4
- Moment of inertia about minor axis: Iy = 0.229 in4
- Major axis section modulus: Sx = 1.532 in3
- Minor axis section modulus: Sy = 0.137 in3
- Torsional constant: J = 0.00085 in4
- Distance between centroid and shear center: x0 = -0.919 in
- Radius of gyration about major axis:
- Radius of gyration about minor axis:
- Polar radius of gyration:
- Warping constant: Cw = 2.568 in6
Material properties:
- E = 29,500 ksi
- G = 11,300 ksi
- Fy = 33 ksi
- Fu = 58 ksi
Validation
Elastic Critical Lateral-Torsional Stress
Per Cl. F2.1.1 of AISI S100-16:where
- Effective length factor for bending about y axis = 1
- Unbraced length of member for bending about y axis = 30 in
=
=
So,
where
- Absolute value of maximum moment in unbraced segment = 30 kip·in
- Absolute value of moment at quarter point of unbraced segment = 18.75 kip·in
- Absolute value of moment at mid-point of unbraced segment = 22.50 kip·in
- Absolute value of moment at three-quarter point of unbraced segment = 26.25 kip·in
=
=
=
=
The elastic buckling stress:
Calculate the nominal flexural strength, Fn , per Cl. F2.1 of S100-16:
Since ,
The nominal flexural strength:
Allowable flexural strength (ASD):
Design flexural strength (LRFD):
Results
| Result Type | Reference | STAAD.Pro | Difference | Comments |
|---|---|---|---|---|
| Flexural strength, ASD (in·kips) | 30.278 | 30.278 | none | |
| Flexural strength, LRFD (in·kips) | 45.508 | 45.508 | none |
STAAD.Pro Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2024\Samples \Verification Models\09 Steel Design\US\AISI\AISI 2016 CU Nominal Moment Capacity.STD is typically installed with the program.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 01-Jun-20
END JOB INFORMATION
INPUT WIDTH 79
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 10 0 0;
MEMBER INCIDENCES
1 1 2;
START USER TABLE
TABLE 1
UNIT INCHES KIP
CHANNEL
CU_8X2_0.06
0.706 8 0.06 2 0.06 6.129 0.229 0.00085 0.33 0.462 0.1143
END
UNIT INCHES KIP
DEFINE MATERIAL START
ISOTROPIC STEEL
E 29000
POISSON 0.3
DENSITY 0.000283
ALPHA 6.5e-06
DAMP 0.03
TYPE STEEL
STRENGTH RY 1.5 RT 1.2
END DEFINE MATERIAL
MEMBER PROPERTY AMERICAN
1 UPTABLE 1 CU_8X2_0.06
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 2 PINNED
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
MEMBER LOAD
1 CON GY -1
PERFORM ANALYSIS
PARAMETER 1
CODE AISI 2016
FYLD 33 ALL
METHOD LRFD
TRACK 2 ALL
LY 30 ALL
UNB 30 ALL
UNT 30 ALL
CHECK CODE ALL
PARAMETER 2
CODE AISI 2016
FYLD 33 ALL
METHOD ASD
TRACK 2 ALL
LY 30 ALL
UNB 30 ALL
UNT 30 ALL
CHECK CODE ALL
FINISH
STAAD.Pro Output
STAAD.Pro CODE CHECKING - (AISI S100-16) [LRFD] (v1.0)
********************************************************
ALL UNITS ARE IN "INCH" AND "KIP " (U.N.O.)
|-----------------------------------------------------------------------------|
| MEMBER: 1 SECTION:UPT CU_8X2_0.06 LEN: 120.000 LOC: 60.000 |
| STATUS: PASS RATIO: 0.895 REF: Sec. F3 LC: 1 |
|-----------------------------------------------------------------------------|
| DESIGN FORCES: |
| Location: 60.000 Criteria: Sec. F3 LC: 1 |
| Fx:(C) -0.000 Fy: 0.500 Fz: -0.000 |
| Mx: 0.000 My: -0.000 Mz: -30.000 |
|-----------------------------------------------------------------------------|
| SECTION PROPERTIES: |
| Ag: 0.70600 Az: 0.11430 Ay: 0.46200 |
| Cz: 0.33000 Cy: 0.00000 |
| Iz: 6.12900 Iy: 0.22900 J: 0.00085 |
| Sz: 1.53225 Sy: 0.13713 |
| Rz: 2.94641 Ry: 0.56953 Cw: 2.65754 |
|-----------------------------------------------------------------------------|
| MATERIAL INFO: |
| Fy: 33.000 Fu: 58.000 E: 29000.000 G: 11300.000 |
|-----------------------------------------------------------------------------|
| DESIGN PROPERTIES: |
| Member Length: 120.000 Lz: 120.000 Ly: 30.000 Lb: 0.000 |
| DESIGN PARAMETERS: |
| Kz: 1.000 Ky: 1.000 NSF: 1.000 |
|-----------------------------------------------------------------------------|
| CRITICAL SLENDERNESS: |
|-----------------------------------------------------------------------------|
| LC : 1 Actual : 210.701 Allowable : 300.000 Ratio : 0.702 |
|-----------------------------------------------------------------------------|
| Section Dimension Check | Ratio | Limit | Status |
|-----------------------------------------------------------------------------|
| Width To Thickness Ratio | 32.333 | 60.000 | PASS |
| Web Depth To Thickness Ratio | 131.333 | 200.000 | PASS |
|-----------------------------------------------------------------------------|
STAAD SPACE -- PAGE NO. 4
STAAD.Pro CODE CHECKING - (AISI S100-16) [LRFD] (v1.0)
********************************************************
ALL UNITS ARE IN "INCH" AND "KIP " (U.N.O.)
| - MEMBER: 1 (Contd.....) |
| |
|-----------------------------------------------------------------------------|
| Limit States | Load# |Location| Demand | Capacity |Ratio| Reference |
|--------------------|-------|--------|----------|----------|-----|-----------|
| Tension | - | - | - | 20.968 | - |Sec. D2 |
| Yielding | - | - | - | 20.968 | - |Sec. D2 |
| Rupture | - | - | - | 30.711 | - |Sec. D3 |
| Compression | - | - | - | 3.623 | - |Sec. E3 |
| Local Comp | - | - | - | 3.623 | - |Sec. E3 |
| Axial Comp | - | - | - | 4.702 | - |Sec. E2 |
| Bending | 1 | 60.00 | -30.000 | 33.522 |0.895|Sec. F3 |
| Major Local Bend | 1 | 60.00 | -30.000 | 33.522 |0.895|Sec. F3 |
| Minor Local Bend | - | - | - | 3.998 | - |Sec. F3 |
| Major Sectional | 1 | 60.00 | -30.000 | 45.508 |0.659|Sec. F2 |
| Minor Sectional | - | - | - | 4.073 | - |Sec. F2 |
| LTB Major | 1 | 60.00 | -30.000 | 42.559 |0.705|Sec. F2 |
| Shear | 1 | 0.00 | 0.500 | 3.562 |0.140|Sec. G2 |
| Major Shear (Z) | - | - | - | 2.150 | - |Sec. G2 |
| Minor Shear (Y) | 1 | 0.00 | 0.500 | 3.562 |0.140|Sec. G2 |
| Interaction | 1 | 60.00 | - | - |0.895|Eq. H1.1-2 |
| (Bend+Ten) Int1 | 1 | 60.00 | - | - |0.659|Eq. H1.1-1 |
| (Bend+Ten) Int2 | 1 | 60.00 | - | - |0.895|Eq. H1.1-2 |
| (Bend+Comp) | 1 | 60.00 | - | - |0.895|Eq. H1.2-1 |
| (Bend+Shear) Z | 1 | 60.00 | - | - |0.856|Sec. H2 |
|-----------------------------------------------------------------------------|
48. PARAMETER 2
49. CODE AISI 2016
50. FYLD 33 ALL
51. METHOD ASD
52. TRACK 2 ALL
53. LY 30 ALL
54. UNB 30 ALL
55. UNT 30 ALL
56. CHECK CODE ALL
STEEL DESIGN
WARNING # 8 ~ The specified value of FU for member # 1 seems out of range.
Reset back to default value.
NOTE # 1 ~ The assigned section for the member # 1
may not be a cold formed section.
STAAD SPACE -- PAGE NO. 5
STAAD.Pro CODE CHECKING - (AISI S100-16) [ASD ] (v1.0)
********************************************************
ALL UNITS ARE IN "INCH" AND "KIP " (U.N.O.)
|-----------------------------------------------------------------------------|
| MEMBER: 1(*) SECTION:UPT CU_8X2_0.06 LEN: 120.000 LOC: 60.000 |
| STATUS: FAIL RATIO: 1.345 REF: Sec. F3 LC: 1 |
|-----------------------------------------------------------------------------|
| DESIGN FORCES: |
| Location: 60.000 Criteria: Sec. F3 LC: 1 |
| Fx:(C) -0.000 Fy: 0.500 Fz: -0.000 |
| Mx: 0.000 My: -0.000 Mz: -30.000 |
|-----------------------------------------------------------------------------|
| SECTION PROPERTIES: |
| Ag: 0.70600 Az: 0.11430 Ay: 0.46200 |
| Cz: 0.33000 Cy: 0.00000 |
| Iz: 6.12900 Iy: 0.22900 J: 0.00085 |
| Sz: 1.53225 Sy: 0.13713 |
| Rz: 2.94641 Ry: 0.56953 Cw: 2.65754 |
|-----------------------------------------------------------------------------|
| MATERIAL INFO: |
| Fy: 33.000 Fu: 58.000 E: 29000.000 G: 11300.000 |
|-----------------------------------------------------------------------------|
| DESIGN PROPERTIES: |
| Member Length: 120.000 Lz: 120.000 Ly: 30.000 Lb: 0.000 |
| DESIGN PARAMETERS: |
| Kz: 1.000 Ky: 1.000 NSF: 1.000 |
|-----------------------------------------------------------------------------|
| CRITICAL SLENDERNESS: |
|-----------------------------------------------------------------------------|
| LC : 1 Actual : 210.701 Allowable : 300.000 Ratio : 0.702 |
|-----------------------------------------------------------------------------|
| Section Dimension Check | Ratio | Limit | Status |
|-----------------------------------------------------------------------------|
| Width To Thickness Ratio | 32.333 | 60.000 | PASS |
| Web Depth To Thickness Ratio | 131.333 | 200.000 | PASS |
|-----------------------------------------------------------------------------|
STAAD SPACE -- PAGE NO. 6
STAAD.Pro CODE CHECKING - (AISI S100-16) [ASD ] (v1.0)
********************************************************
ALL UNITS ARE IN "INCH" AND "KIP " (U.N.O.)
| - MEMBER: 1 (Contd.....) |
| |
|-----------------------------------------------------------------------------|
| Limit States | Load# |Location| Demand | Capacity |Ratio| Reference |
|--------------------|-------|--------|----------|----------|-----|-----------|
| Tension | - | - | - | 13.951 | - |Sec. D2 |
| Yielding | - | - | - | 13.951 | - |Sec. D2 |
| Rupture | - | - | - | 20.474 | - |Sec. D3 |
| Compression | - | - | - | 2.368 | - |Sec. E3 |
| Local Comp | - | - | - | 2.368 | - |Sec. E3 |
| Axial Comp | - | - | - | 3.073 | - |Sec. E2 |
| Bending | 1 | 60.00 | -30.000 | 22.303 |1.345|Sec. F3 |
| Major Local Bend | 1 | 60.00 | -30.000 | 22.303 |1.345|Sec. F3 |
| Minor Local Bend | - | - | - | 2.660 | - |Sec. F3 |
| Major Sectional | 1 | 60.00 | -30.000 | 30.278 |0.991|Sec. F2 |
| Minor Sectional | - | - | - | 2.710 | - |Sec. F2 |
| LTB Major | 1 | 60.00 | -30.000 | 28.316 |1.059|Sec. F2 |
| Shear | 1 | 0.00 | 0.500 | 2.344 |0.213|Sec. G2 |
| Major Shear (Z) | - | - | - | 1.414 | - |Sec. G2 |
| Minor Shear (Y) | 1 | 0.00 | 0.500 | 2.344 |0.213|Sec. G2 |
| Interaction | 1 | 60.00 | - | - |1.345|Eq. H1.1-2 |
| (Bend+Ten) Int1 | 1 | 60.00 | - | - |0.991|Eq. H1.1-1 |
| (Bend+Ten) Int2 | 1 | 60.00 | - | - |1.345|Eq. H1.1-2 |
| (Bend+Comp) | 1 | 60.00 | - | - |1.345|Eq. H1.2-1 |
| (Bend+Shear) Z | 1 | 60.00 | - | - |1.287|Sec. H2 |
|-----------------------------------------------------------------------------|