Verify the shear strength of an I section loaded in the
strong axis using the LRFD and ASD methods per AISC 360-16.
References
-
Steel Construction Manual, 15th Edition, American
Institute of Steel Construction, 2017
- Design Examples,
Version 15.0, American Institute of Steel Construction, 2017. pp G-3 -
G-4, Example G.1A
Details
From the reference:
determine the available shear strength and adequacy of an ASTM
A992 W24X62 with end shears of 48 kips from dead load and 145 kips from live
load.
The shear capacity values are evaluated from AISC Manual Table 2-4 and the
also calculated.
Validation
Area of the web used for shear is:
| Aw = dtw = 23.7 × 0.430 = 10.2 in2
| |
The nominal shear strength is:
| Vn = 0.6FyAwCv1 = 0.6
(50)(10.2)(1.0) = 306 kips
| |
LRFD
The shear strength is:
| ϕvVn = 1.00(306) = 306 kips
| |
The ultimate shear demand is:
| Vu = 1.2 (48) + 1.6 (145) = 289.6 kips
| |
ASD
The allowable shear is:
| Vn/Ωv = 306 / 1.5 = 204 kips
| |
Results
Table 1. Comparison of results
| Parameter
|
Hand Calculation
|
STAAD.Pro
|
Difference
|
Comments
|
| Shear capacity,
ϕvVn, Y axis (kips) LRFD
|
306
|
305.7
|
negligible
|
|
| Shear demand,
Vu, Y axis (kips) LRFD
|
289.6
|
289.6
|
none
|
The reference rounds this value to 290
kips.
|
| Shear capacity,
Vn/Ωvm, Y axis (kips) ASD
|
204
|
203.8
|
negligible
|
|
| Shear demand,
Va, Y axis (kips) ASD
|
193
|
193.0
|
none
|
|
STAAD Output
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. 5
STAAD.PRO CODE CHECKING - AISC 360-16 LRFD (V1.2)
*****************************************************
ALL UNITS ARE - KIP INCH (UNLESS OTHERWISE Noted).
- Member : 1
|-----------------------------------------------------------------------------|
| Member No: 1 Profile: ST W24X62 (AISC SECTIONS)|
| Status: FAIL Ratio: 1.009 Loadcase: 3 |
| Location: 24.00 Ref: Cl.F2.1 |
| Pz: 0.000 T Vy: 289.6 Vx: 0.000 |
| Tz: 0.000 My: 0.000 Mx: -6950. |
|-----------------------------------------------------------------------------|
| TENSION SLENDERNESS |
| Actual Slenderness Ratio : 34.863 |
| Allowable Slenderness Ratio : 300.000 LOC : 0.00 |
|-----------------------------------------------------------------------------|
| STRENGTH CHECKS |
| Critical L/C : 3 Ratio : 1.009(FAIL) |
| Loc : 24.00 Condition : Cl.F2.1 |
|-----------------------------------------------------------------------------|
| SECTION PROPERTIES (LOC: 24.00, PROPERTIES UNIT: IN ) |
| Ag : 1.820E+01 Axx : 8.307E+00 Ayy : 1.019E+01 |
| Ixx : 1.550E+03 Iyy : 3.450E+01 J : 1.710E+00 |
| Sxx+: 1.308E+02 Sxx-: 1.308E+02 Zxx : 1.530E+02 |
| Syy+: 9.801E+00 Syy-: 9.801E+00 Zyy : 1.570E+01 |
| Cw : 4.581E+03 x0 : 0.000E+00 y0 : 0.000E+00 |
|-----------------------------------------------------------------------------|
| MATERIAL PROPERTIES |
| Fyld: 50.000 Fu: 62.000 |
|-----------------------------------------------------------------------------|
| Actual Member Length: 48.000 |
| Design Parameters (Rolled) |
| Kx: 1.00 Ky: 1.00 NSF: 1.00 SLF: 1.00 CSP: 12.00 |
|-----------------------------------------------------------------------------|
| COMPRESSION CLASSIFICATION (L/C: 3 LOC: 48.00) |
| λ λp λr CASE |
| Flange: NonSlender 5.97 N/A 13.49 Table.B4.1a.Case1 |
| Web : Slender 50.05 N/A 35.88 Table.B4.1a.Case5 |
| |
| FLEXURE CLASSIFICATION (L/C: 3 LOC: 48.00) |
| λ λp λr CASE |
| Flange: Compact 5.97 9.15 24.08 Table.B4.1b.Case10 |
| Web : Compact 50.05 90.55 137.27 Table.B4.1b.Case15 |
|-----------------------------------------------------------------------------|
STAAD SPACE -- PAGE NO. 6
STAAD.PRO CODE CHECKING - AISC 360-16 LRFD (V1.2)
*****************************************************
ALL UNITS ARE - KIP INCH (UNLESS OTHERWISE Noted).
- Member : 1 Contd.
|-----------------------------------------------------------------------------|
| CHECKS FOR AXIAL TENSION |
|-----------------------------------------------------------------------------|
| TENSILE YIELDING |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| 0.000 819.0 0.000 Cl.D2 3 0.00 |
| |
| Intermediate Results : |
| Nom. Ten. Yld Cap : Pn = 910.00 kip Eq.D2-1 |
|-----------------------------------------------------------------------------|
| TENSILE RUPTURE |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| 0.000 846.3 0.000 Cl.D2 3 0.00 |
| |
| Intermediate Results : |
| Effective area : Ae = 18.200 in2 Eq.D3-1 |
| Nom. Ten. Rpt Cap : Pn = 1128.4 kip Eq.D2-2 |
|-----------------------------------------------------------------------------|
| CHECKS FOR AXIAL COMPRESSION |
|-----------------------------------------------------------------------------|
| FLEXURAL BUCKLING X |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| 0.000 726.0 0.000 Cl.E3 3 0.00 |
| |
| Intermediate Results : |
| Effective Slenderness : Lcx/rx = 5.2013 Cl.E2 |
| Elastic Buckling Stress : Fex = 10580. ksi Eq.E3-4 |
| Crit. Buckling Stress : Fcrx = 49.901 ksi Eq.E3-2 |
| Nom. Flexural Buckling : Pnx = 806.66 kip Eq.E7-1 |
|-----------------------------------------------------------------------------|
| FLEXURAL BUCKLING Y |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| 0.000 676.0 0.000 Cl.E3 3 0.00 |
| |
| Intermediate Results : |
| Effective Slenderness : Lcy/ry = 34.863 Cl.E2 |
| Elastic Buckling Stress : Fey = 235.48 ksi Eq.E3-4 |
| Crit. Buckling Stress : Fcry = 45.748 ksi Eq.E3-2 |
| Nom. Flexural Buckling : Pny = 751.08 kip Eq.E7-1 |
|-----------------------------------------------------------------------------|
| FLEXURAL-TORSIONAL-BUCKLING |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| 0.000 694.3 0.000 Cl.E4 3 0.00 |
| |
| Intermediate Results : |
| Elastic F-T-B Stress : Fe = 371.19 ksi Eq.E4-2 |
| Crit. F-T-B Stress : Fcr = 47.259 ksi Eq.E3-2 |
| Nom. Flex-tor Buckling : Pn = 771.39 kip Eq.E7-1 |
|-----------------------------------------------------------------------------|
STAAD SPACE -- PAGE NO. 7
STAAD.PRO CODE CHECKING - AISC 360-16 LRFD (V1.2)
*****************************************************
ALL UNITS ARE - KIP INCH (UNLESS OTHERWISE Noted).
- Member : 1 Contd.
|-----------------------------------------------------------------------------|
| CHECKS FOR SHEAR |
|-----------------------------------------------------------------------------|
| SHEAR ALONG X |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| 0.000 224.3 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 = 249.22 kip Eq.G6-1 |
|-----------------------------------------------------------------------------|
| SHEAR ALONG Y |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| 289.6 305.7 0.947 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 = 305.73 kip Eq.G2-1 |
|-----------------------------------------------------------------------------|
STAAD SPACE -- PAGE NO. 8
STAAD.PRO CODE CHECKING - AISC 360-16 LRFD (V1.2)
*****************************************************
ALL UNITS ARE - KIP INCH (UNLESS OTHERWISE Noted).
- Member : 1 Contd.
|-----------------------------------------------------------------------------|
| CHECKS FOR BENDING |
|-----------------------------------------------------------------------------|
| FLEXURAL YIELDING (X) |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| -6950. 6885. 1.009 Cl.F2.1 3 24.00 |
| |
| Intermediate Results : |
| Nom Flex Yielding Along X : Mnx = 7650.0 kip-in Eq.F2-1 |
|-----------------------------------------------------------------------------|
| FLEXURAL YIELDING (Y) |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| 0.000 705.7 0.000 Cl.F6.1 3 0.00 |
| |
| Intermediate Results : |
| Nom Flex Yielding Along Y : Mny = 784.09 kip-in Eq.F6-1 |
|-----------------------------------------------------------------------------|
STAAD SPACE -- PAGE NO. 9
STAAD.PRO CODE CHECKING - AISC 360-16 LRFD (V1.2)
*****************************************************
ALL UNITS ARE - KIP INCH (UNLESS OTHERWISE Noted).
- Member : 1 Contd.
|-----------------------------------------------------------------------------|
| CHECKS FOR AXIAL BEND INTERACTION |
|-----------------------------------------------------------------------------|
| COMBINED FORCES CLAUSE H1 |
| RATIO CRITERIA L/C LOC |
| 1.009 Eq.H1-1b 3 24.00 |
| |
| Intermediate Results : |
| Modification Fact. for Cb : Cbf = 1.0000 Eq.H1-2 |
| Axial Capacity : Pc = 819.00 kip Cl.H1.1 |
| Moment Capacity : Mcx = 6885.0 kip-in Cl.H1.1 |
| Moment Capacity : Mcy = 705.68 kip-in Cl.H1.1 |
|-----------------------------------------------------------------------------|
61. *********************************************
62. LOAD LIST 4
63. PARAMETER 2
64. CODE AISC UNIFIED 2016
65. METHOD ASD
66. *
67. TRACK 2 ALL
68. CHECK CODE ALL
PARAMETER 2
STAAD SPACE -- PAGE NO. 10
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. 11
STAAD.PRO CODE CHECKING - AISC 360-16 ASD (V1.2)
****************************************************
ALL UNITS ARE - KIP INCH (UNLESS OTHERWISE Noted).
- Member : 1
|-----------------------------------------------------------------------------|
| Member No: 1 Profile: ST W24X62 (AISC SECTIONS)|
| Status: FAIL Ratio: 1.011 Loadcase: 4 |
| Location: 24.00 Ref: Cl.F2.1 |
| Pz: 0.000 T Vy: 193.0 Vx: 0.000 |
| Tz: 0.000 My: 0.000 Mx: -4632. |
|-----------------------------------------------------------------------------|
| TENSION SLENDERNESS |
| Actual Slenderness Ratio : 34.863 |
| Allowable Slenderness Ratio : 300.000 LOC : 0.00 |
|-----------------------------------------------------------------------------|
| STRENGTH CHECKS |
| Critical L/C : 4 Ratio : 1.011(FAIL) |
| Loc : 24.00 Condition : Cl.F2.1 |
|-----------------------------------------------------------------------------|
| SECTION PROPERTIES (LOC: 24.00, PROPERTIES UNIT: IN ) |
| Ag : 1.820E+01 Axx : 8.307E+00 Ayy : 1.019E+01 |
| Ixx : 1.550E+03 Iyy : 3.450E+01 J : 1.710E+00 |
| Sxx+: 1.308E+02 Sxx-: 1.308E+02 Zxx : 1.530E+02 |
| Syy+: 9.801E+00 Syy-: 9.801E+00 Zyy : 1.570E+01 |
| Cw : 4.581E+03 x0 : 0.000E+00 y0 : 0.000E+00 |
|-----------------------------------------------------------------------------|
| MATERIAL PROPERTIES |
| Fyld: 50.000 Fu: 62.000 |
|-----------------------------------------------------------------------------|
| Actual Member Length: 48.000 |
| Design Parameters (Rolled) |
| Kx: 1.00 Ky: 1.00 NSF: 1.00 SLF: 1.00 CSP: 12.00 |
|-----------------------------------------------------------------------------|
| COMPRESSION CLASSIFICATION (L/C: 4 LOC: 48.00) |
| λ λp λr CASE |
| Flange: NonSlender 5.97 N/A 13.49 Table.B4.1a.Case1 |
| Web : Slender 50.05 N/A 35.88 Table.B4.1a.Case5 |
| |
| FLEXURE CLASSIFICATION (L/C: 4 LOC: 48.00) |
| λ λp λr CASE |
| Flange: Compact 5.97 9.15 24.08 Table.B4.1b.Case10 |
| Web : Compact 50.05 90.55 137.27 Table.B4.1b.Case15 |
|-----------------------------------------------------------------------------|
STAAD SPACE -- PAGE NO. 12
STAAD.PRO CODE CHECKING - AISC 360-16 ASD (V1.2)
****************************************************
ALL UNITS ARE - KIP INCH (UNLESS OTHERWISE Noted).
- Member : 1 Contd.
|-----------------------------------------------------------------------------|
| CHECKS FOR AXIAL TENSION |
|-----------------------------------------------------------------------------|
| TENSILE YIELDING |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| 0.000 544.9 0.000 Cl.D2 4 0.00 |
| |
| Intermediate Results : |
| Nom. Ten. Yld Cap : Pn = 910.00 kip Eq.D2-1 |
|-----------------------------------------------------------------------------|
| TENSILE RUPTURE |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| 0.000 564.2 0.000 Cl.D2 4 0.00 |
| |
| Intermediate Results : |
| Effective area : Ae = 18.200 in2 Eq.D3-1 |
| Nom. Ten. Rpt Cap : Pn = 1128.4 kip Eq.D2-2 |
|-----------------------------------------------------------------------------|
| CHECKS FOR AXIAL COMPRESSION |
|-----------------------------------------------------------------------------|
| FLEXURAL BUCKLING X |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| 0.000 483.0 0.000 Cl.E3 4 0.00 |
| |
| Intermediate Results : |
| Effective Slenderness : Lcx/rx = 5.2013 Cl.E2 |
| Elastic Buckling Stress : Fex = 10580. ksi Eq.E3-4 |
| Crit. Buckling Stress : Fcrx = 49.901 ksi Eq.E3-2 |
| Nom. Flexural Buckling : Pnx = 806.66 kip Eq.E7-1 |
|-----------------------------------------------------------------------------|
| FLEXURAL BUCKLING Y |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| 0.000 449.7 0.000 Cl.E3 4 0.00 |
| |
| Intermediate Results : |
| Effective Slenderness : Lcy/ry = 34.863 Cl.E2 |
| Elastic Buckling Stress : Fey = 235.48 ksi Eq.E3-4 |
| Crit. Buckling Stress : Fcry = 45.748 ksi Eq.E3-2 |
| Nom. Flexural Buckling : Pny = 751.08 kip Eq.E7-1 |
|-----------------------------------------------------------------------------|
| FLEXURAL-TORSIONAL-BUCKLING |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| 0.000 461.9 0.000 Cl.E4 4 0.00 |
| |
| Intermediate Results : |
| Elastic F-T-B Stress : Fe = 371.19 ksi Eq.E4-2 |
| Crit. F-T-B Stress : Fcr = 47.259 ksi Eq.E3-2 |
| Nom. Flex-tor Buckling : Pn = 771.39 kip Eq.E7-1 |
|-----------------------------------------------------------------------------|
STAAD SPACE -- PAGE NO. 13
STAAD.PRO CODE CHECKING - AISC 360-16 ASD (V1.2)
****************************************************
ALL UNITS ARE - KIP INCH (UNLESS OTHERWISE Noted).
- Member : 1 Contd.
|-----------------------------------------------------------------------------|
| CHECKS FOR SHEAR |
|-----------------------------------------------------------------------------|
| SHEAR ALONG X |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| 0.000 149.2 0.000 Cl.G1 4 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 = 249.22 kip Eq.G6-1 |
|-----------------------------------------------------------------------------|
| SHEAR ALONG Y |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| 193.0 203.8 0.947 Cl.G1 4 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 = 305.73 kip Eq.G2-1 |
|-----------------------------------------------------------------------------|
STAAD SPACE -- PAGE NO. 14
STAAD.PRO CODE CHECKING - AISC 360-16 ASD (V1.2)
****************************************************
ALL UNITS ARE - KIP INCH (UNLESS OTHERWISE Noted).
- Member : 1 Contd.
|-----------------------------------------------------------------------------|
| CHECKS FOR BENDING |
|-----------------------------------------------------------------------------|
| FLEXURAL YIELDING (X) |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| -4632. 4581. 1.011 Cl.F2.1 4 24.00 |
| |
| Intermediate Results : |
| Nom Flex Yielding Along X : Mnx = 7650.0 kip-in Eq.F2-1 |
|-----------------------------------------------------------------------------|
| FLEXURAL YIELDING (Y) |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| 0.000 469.5 0.000 Cl.F6.1 4 0.00 |
| |
| Intermediate Results : |
| Nom Flex Yielding Along Y : Mny = 784.09 kip-in Eq.F6-1 |
|-----------------------------------------------------------------------------|
STAAD SPACE -- PAGE NO. 15
STAAD.PRO CODE CHECKING - AISC 360-16 ASD (V1.2)
****************************************************
ALL UNITS ARE - KIP INCH (UNLESS OTHERWISE Noted).
- Member : 1 Contd.
|-----------------------------------------------------------------------------|
| CHECKS FOR AXIAL BEND INTERACTION |
|-----------------------------------------------------------------------------|
| COMBINED FORCES CLAUSE H1 |
| RATIO CRITERIA L/C LOC |
| 1.011 Eq.H1-1b 4 24.00 |
| |
| Intermediate Results : |
| Modification Fact. for Cb : Cbf = 1.0000 Eq.H1-2 |
| Axial Capacity : Pc = 544.91 kip Cl.H1.1 |
| Moment Capacity : Mcx = 4580.8 kip-in Cl.H1.1 |
| Moment Capacity : Mcy = 469.52 kip-in Cl.H1.1 |
|-----------------------------------------------------------------------------|
