"ANGLE" --- SINGLE STEEL ANGLE MEMBER ANALYSIS Program Description: "ANGLE" is a spreadsheet program written in MS-Excel for the purpose of analysis of a single steel subjected to major/minor axis bending, shear and axial forces. Program Environment: Microsoft Office Excel 2003 Creation Date: December 12th, 2008 Design References: This program is a workbook consisting of two (2) worksheets, described as follows: Worksheet Name Description Doc This documentation sheet ANGLE Single Steel Angle Member Analysis Revision 1.2: 3/31/09 - Fixed a couple negative/positive errors with Shear values and its summary. - Added an easy to review summary for the results. Program Assumptions and Limitations: 1. This spreadsheet program is intended to analyze and design a single angle member subjected to w/o Lateral-torsional restraint, (4) Unequal angle w/o Lateral-torsional restraint. 2. This program assumes, if load case 3 or 4 is used, bending will only be about the major axis. 3. The available angles, using yield stress of 36ksi, are either compact or noncompact but not sl the width-thickness ratios for compression elements of Table B4.1. 4. The steel yield and ultimate stresses are limited to 36 and 58 kips per square inch, respectiv 5. The Shear lag factor, U, is limited 0.6 per D3.3. 7. This program was not intended for design of angles subjected to torsion (moment in the Z-direc 8. This program contains numerous “comment boxes” which contain a wide variety of information inc explanations of input or output items, equations used, data tables, etc. (Note: presence o is denoted by a “red triangle” in the upper right-hand corner of a cell. Merely move the mo desired cell to view the contents of that particular "comment box".) 1. AISC Steel Construction Manual, 13th Ed. ACI 318R-05 2. AISC spreadsheet, "AISC_ShapesDatabase_v13.0-Current.xls" shear and axial loads in both the major and minor axis for 4 various loading cases: (1) Full restraint, (2) Equal angle w/ Lateral-torsional restraint at the point of maximum moment only, (3 6. The angle sizes and member properties are from AISC spreadsheet, AISC_ShapesDatabase_v13.0-Current.
shear and axial loads in both the major and minor axis for 4 various loading cases: (1) Full Lateral-torsional
restraint, (2) Equal angle w/ Lateral-torsional restraint at the point of maximum moment only, (3) Equal angle
6. The angle sizes and member properties are from AISC spreadsheet, AISC_ShapesDatabase_v13.0-Current.
information in lightly yellow highlighted boxes. Information required includes the following:
Input:1. Angle Size: predetermined sizes from AISC.2. Steel yield stess, Fy: 36ksi.3. Steel ultimate stress, Fu: 58ksi.4. Factored or Unfactored Axial load, Pu/Pa: Based on input of load development (see input #11), the max factored or unfactored compression/tension force is entered.5. Shear lag factor, U: Per Table D3.1 and D3.3.
tip is in compression or tension. If loads are reversive, the lateral-torsional buckling strength should be checked for both flanges.7. Factored or Unfactored shear in the direction of the y-axis, Vy/Vyu: Based on input of load development (see input #11), the max factored or unfactored shear is entered.
tip is in compression or tension. If loads are reversive, the lateral-torsional buckling strength should be checked for both flanges.9. Factored or Unfactored shear in the direction of the x-axis, Vx/Vxu: Based on input of load development (see input #11) the max factored or unfactored shear is entered.10. Angle Load Case: Determination of the member's restaint.11. Load combination: ASD or LRFD per ASCE Load Combinations and AISC Specifications Sections B3.3 & B3.4.
Output: To see the core formulas and organization of the calculations, unhide columns: I to AO.
Spreadsheet is protected but w/o password.1. Tension per D2 & D3.2. Compression per E3; E5 & E7 are N/A due to unavailable slender elements in angle list.3. Shear per G4 & G2.4. Combined flexural and axial forces per Eqn H1-1a & H1-1b.
Program Theory and Operation: The top of the spreadsheet screen allows for input of required
6. Factored or Unfactored bending moment about the x-axis, MRX: The (+/-) value determines is the angle
8. Factored or Unfactored bending moment about the x-axis, MRx: The (+/-) value determines is the angle
0 in-kip 1.00 3/8 IN. Flexural (per F10)Vx= 0 kips Comp Case= 2 CASE 1:
Angle Case= 3 YIELDING (angle tip is in tension)
Load Comb.= ASD 4 IN.
Analysis: LLB (angle tip is in compression)
AXIAL FORCE CAPACITY
Pr/Pc= 0.02
Tension Capacity= 61.65 kips
BENDING MOMENT CAPACTIY LTB (angle tip is in compression)
Mrx/Mcx= 0.98 < 1.0
38.80 in-kips
0.00 in-kips
SHEAR
19.40 kips
19.40 kips
0.00
0.77
COMBINED STRESS RATIOC.S.R.= 0.99
Compact:
COMMENTS:
Pnx=Pny=
CbY =
LL =
LS =
Kx eff.=
Ky eff.= Sx =
LBX.= Sy =
MRX= LBy.= Zx =
CbX = Zy =
MRy= CbY =
Mnx=
Mny=
b/tx=
b/ty=
Mnx=
Mny=
Mnx=
Mex1 =
Mcx= Mex2 =
Mcy= Mny=
Mey1 =
VRX= Mey2 =
VRY=
VRX/VCX=
VRY/VCY=
λP=< 1.0
KLx / rx =
KLy / ry =
Fex =
Fey =
B9
Steel Yield Stress
B10
Steel Ultimate Stress
E10
Strong Geometric Axis Effective Length Factor Type K value Fixed-Fixed 0.65 Fixed-Pinned 0.8 Pinned-Pinned 1.0 Fixed-Free 2.1 AISC Table C-C2.2
B11
Allowable or Ultimate Axial Force: Positive for Tension, Negative for Compression.
E11
Weak Geometric Axis Effective Length Factor Type K value Fixed-Fixed 0.65 Fixed-Pinned 0.8 Pinned-Pinned 1.0 Fixed-Free 2.1 AISC Table C-C2.2
B12
Shear Lag Factor: If welded, U=1.0. If 4 or more fasteners per line of direction of loading, U=0.8 If 2 or 3 fasteners per line in the direction of loading, U=0.6 Or, if fastened, can calculate: U=1-x/L See Table D3.1 of AISC Steel Construction Manual 13th Ed.
'Cb' is the lateral-torsional buckling modification factor for nonuniform moment diagrams about the X-axis (major axis) when both ends of the unsupported segment are braced . 'Cb' is determined as follows: Cb = [12.5Mmax/(2.5Mmax + 3MA + 4MB + 3 MC)] x Rm < 3.0 (F1.2) where: MA = absolute value of moment at quarter point of the unbraced segment. (in-kip) MB = absolute value of moment at centerline of the unbraced segment. (in-kip) MC = absolute value of moment at three-quarter point of the unbraced segment. (in-kip) Mmax = absolute value of maximum moment in the unbraced segment. (in-kip) Rm = 1.0, doubly symmetric members = 1.0, singly symmetric members subject to single curvature bending. = 0.5 + 2(Iyc/Iy)^2, singly symmetric members subject to reverse curvature bending. Iy = moment of inertia about the principal y-axis, in^4 Iyc = moment of inertia about the y-axis referred to the compression flange, or if reverse curvature bending referred to the smaller flange, in^4 Notes: 1. When computing 'Fbx' to be used in AISC Eqn. H1-1: a. For frames with sidesway (joint translation), then compute 'Cb' using above equation. b. For frames without sidesway (braced against joint translation), then use 'Cb' = 1.0. 2. In singly symmetric members subject to reverse curvature bending, the lateral-torsional buckling strength shall be checked for both flanges. The available flexural strength shall be greater than or equal to the maximum required moment causing compression within the flange under consideration. Cb is permitted to be taken as 1.0 in all cases. 3. For cantilever beams, 'Cb' may be conservatively assumed = 1.0.
B15
Weak Geometric Axis Effective Bending Moment Positive moment means compression at tip. Negative moment means tension at tip.
E15
'Cb' is the lateral-torsional buckling modification factor for nonuniform moment diagrams about the Y-axis (minor axis) when both ends of the unsupported segment are braced . 'Cb' is determined as follows: Cb = [12.5Mmax/(2.5Mmax + 3MA + 4MB + 3 MC)] x Rm < 3.0 (F1.2) where: MA = absolute value of moment at quarter point of the unbraced segment. (in-kip) MB = absolute value of moment at centerline of the unbraced segment. (in-kip) MC = absolute value of moment at three-quarter point of the unbraced segment. (in-kip) Mmax = absolute value of maximum moment in the unbraced segment. (in-kip) Rm = 1.0, doubly symmetric members = 1.0, singly symmetric members subject to single curvature bending. = 0.5 + 2(Ixc/Ix)^2, singly symmetric members subject to reverse curvature bending. Ix = moment of inertia about the principa lx-axis, in^4 Ixc = moment of inertia about the x-axis referred to the compression flange, or if reverse curvature bending referred to the smaller flange, in^4 Notes: 1. When computing 'Fbx' to be used in AISC Eqn. H1-1: a. For frames with sidesway (joint translation), then compute 'Cb' using above equation. b. For frames without sidesway (braced against joint translation), then use 'Cb' = 1.0. 2. In singly symmetric members subject to reverse curvature bending, the lateral-torsional buckling strength shall be checked for both flanges. The available flexural strength shall be greater than or equal to the maximum required moment causing compression within the flange under consideration. Cb is permitted to be taken as 1.0 in all cases. 3. For cantilever beams, 'Cb' may be conservatively assumed = 1.0.
B16
Weak Direction Shear Load
E16
SLENDER CASE: N/A PER THIS ANGLE LIST CASE 1: Equal or unequal-leg angles connected through the longer leg that are individual members or are web members of planar trusses with adjacent web members attached to the same side of the gusset plate or chord. CASE 2: Equal or unequal-leg angles connected through the longer leg that are web members of box or space trusses with adjacent web members attached to the same side of the gusset plate or chord. CASE 3: Single angle members w/ different end conditions from those described above, w/ leg ratios greater than 1.7, or w/ transverse loading. NOTE: The effects of eccentricity on single angle members can be neglected when the members are evaluated as axially loaded compression members using one of the effective slenderness ratios specified above, provided that: a.) members are loaded at the ends in compression through the same one leg. b.) members are attached by welding or by minimum two-bolt connections. c.) there are no intermediate transverse loads. per E5
B17
CASE 1: Angle bending members with lateral-torsional restraint along the length. CASE 2: Equal-leg angle w/ lateral-torsional restraint at maximum moment only. CASE 3: Equal-leg angle w/ no Lateral-torsional restraint. CASE 4: Unequal-leg angle w/ no Lateral-torsional restraint. per F10
B18
Per ASCE Load Combinations and AISC Specifications Sections B3.3 & B3.4: LRFD & ASD.
A36
For Pr/Pc > 0.2: Pr/Pc + (8/9)*(Mrx/Mcx+Mry/Mcy) < 1.0 For Pr/Pc < 0.2: Pr/(2Pc) + (Mrx/Mcx+Mry/Mcy) < 1.0 AISC Chapt. H [EQN H1-1A/B]
