"BEAMCOL9" --- STEEL BEAM AND COLUMN ANALYSIS / CODE CHECK Program Description: "BEAMCOL9" is a spreadsheet program written in MS-Excel for the purpose of analysis and code steel beams and columns. Specifically, beams and columns are analyzed / code checked per th Edition Allowable Stress Design (ASD) Manual. Both actual and allowable stresses are comput final result being a computed "stress ratio" of actual stress/allowable stress. Also, a lis members which satisfy the code check is displayed for convenience. This program is a workbook consisting of six (6) worksheets, described as follows: Worksheet Name Description Doc This documentation sheet Analysis / Code Check for W, S, M, and HP Shapes BeamCol(Built-Up) Analysis / Code Check for Non-Database and Built-Up Shape BeamCol(C) Analysis / Code Check for Channel Shapes BeamCol(Tube) Analysis / Code Check for Rectangular HSS (Tube) Shapes BeamCol(Pipe) Analysis / Code Check for Round HSS and Pipe Shapes Program Assumptions and Limitations: 1. This program follows the procedures and guidelines of the AISC 9th Edition Allowable St (1989). 2. This program uses the database of member dimensions and section properties from the "AI Database", Version 3.0 (2001) as well as the AISC 9th Edition (ASD) Manual (1989). 3. The "BeamCol(Built-Up)" worksheet is valid for AISC W, S, M, and HP shapes NOT containe Edition Manual, as well as for non-hybird and doubly-symmetrical ("I" shaped) built-up their flanges continuously welded to the web and which DO NOT quailify as plate girder (Note: the AISC Code limiting value on the web for built-up beams not to qualify as pl (d-2*tf)/tw <= 760/SQRT(0.60*Fy) 4. This program is NOT valid for tees (WT shapes) and angles. 5. In this program for members subjected to known loadings consisting of axial load (compr and/or uniaxial or biaxial bending, both the actual and allowable stress are computed, being a computed "stress ratio" of actual stress/allowable stress. 6. The "BeamCol(Built-Up)" worksheet will require the input for the total depth, web thick flange thickness. Then, all the remaining section properties are automatically calcul non-sloping flanges. 7. This program utilizes an "Allowable Stress Increase Factor" (ASIF) which is a multiplier calculated allowable stresses Fa, Fbx, and Fby and also the Euler column buckling stre It is used and appears ONLY in the stress ratio calculation. Typically a value of 1.0 value of 1.333 may be used for load combinations which include wind or seismic loads. 8. If an axially loaded compression member has a value of the maximum slenderness ratio K*L then a message will appear. However, this program DOES NOT consider or deem a particu "inadequate" based on the slenderness ratio of 200 being exceeded. 9. For the case of combined axial compression with bending, if the calculated value of fa > allowed) then a warning (error!) message will appear. 10. When the values of either 'Lx', 'Ly', or 'Lb' are input = 0' (or actually <= 1.0'), this 11. When a stiffened element (web) of a member subjected to axial compression is classified element (exceeding non-compact limits) based on local buckling criteria, then the prog AISC Appendix B. BeamCol(I)
'P' is the applied axial load on the member, which may be either a compression or tension load. Sign convention: + = compression, - = tension
B14
'Mx' is the applied flexural bending moment about the X-axis (major axis) of the member. Note: the value input MUST BE positive (+).
B15
'My' is the applied flexural bending moment about the Y-axis (minor axis) of the member. Note: the value input MUST BE positive (+).
A19
Note: See section of this worksheet (to the right) for input data which may be used to determine the 'Kx' to be used for input here.
B19
'Kx' is the effective length factor about the X-axis (major axis) for an axially loaded compression member. Typical values are as follows: Column End Conditions "Kx" Value (bottom-top) (Recommended) Fixed-Fixed 0.65 Fixed-Pinned 0.80 Fixed-Slider 1.2 Pinned-Pinned 1.0 Fixed-Free 2.1 Pinned-Slider 2.0 where: Fixed end denotes rotation fixed and translation fixed. Pinned end denotes rotation free and translation fixed. Slider end denotes rotation fixed and translation free. Free end denotes rotation free and translation free.
A20
Note: See section of this worksheet (to the right) for input data which may be used to determine the 'Ky' to be used for input here.
B20
'Ky' is the effective length factor about the Y-axis (minor axis) for an axially loaded compression member. Typical values are as follows: Column End Conditions "Ky" Value (bottom-top) (Recommended) Fixed-Fixed 0.65 Fixed-Pinned 0.80 Fixed-Slider 1.2 Pinned-Pinned 1.0 Fixed-Free 2.1 Pinned-Slider 2.0 where: Fixed end denotes rotation fixed and translation fixed. Pinned end denotes rotation free and translation fixed. Slider end denotes rotation fixed and translation free. Free end denotes rotation free and translation free.
B21
'Lx' is the actual unbraced length of member for column-type (axial compression) buckling about X-axis (major axis). Note: for input values of Lx <=1.0', this program will use a value =1.0'.
B22
'Ly' is the actual unbraced length of member for column-type (axial compression) buckling about Y-axis (minor axis). Note: for input values of Ly <=1.0', this program will use a value =1.0'.
H22
'Qs' is the allowable stress reduction factor for an unstiffened compression element (flange) of member determined from AISC Appendix B and is calculated as follows: when 95/SQRT(Fy/kc) < bf/(2*tf) < 195/SQRT(Fy/kc) Qs = 1.293-0.00309*bf/(2*tf)*SQRT(Fy/kc) Eqn. A-B5-3 when bf/(2*tf) > 195/SQRT(Fy/kc) Qs = 26,200*kc/(Fy*bf/(2*tf)) Eqn. A-B5-4 Note: Qs = 1.0 for all W, S, and M shapes for Fy = 36 or 50 ksi. However, Qs < 1.0 for HP14X73, HP13X60, and HP12X53
B23
'Lb' is the actual unbraced length of the compression flange of the member for X-axis (major axis) bending. The "unbraced length" can be more specifically defined as the distance between cross sections braced against twist or lateral displacement of the compression flange. Notes: 1. For most cases, 'Lb' is equal to 'Ly'. 2. For cantilevers braced against twist only at the support, 'Lb' may conservatively be taken as the actual length. 3. For input values of Lb <=1.0', this program will use a value =1.0'.
H23
'Qa' is the ratio of effective profile area of an axially loaded compression member to its total (gross) profile area from AISC Appendix B and is calculated as follows: when h/tw > 253/SQRT(Fy) be = 253*tw/SQRT(f)*(1-44.3/((h/tw)*SQRT(f)) <= h Eqn. A-B5-8 Ae = A-(h-be)*tw Qa = (A-(h-be)*tw)/A where: be = effective length of web of member h = d-2*tf f = computed compressive stress based on effecive area Ae = effective area of member
A24
Note: See section of this worksheet (to the right) for input data which may be used to determine the 'Cb' to be used for input here.
B24
'Cb' is the allowable stress bending coefficient dependent on the moment gradient, for bending about the X-axis (major axis). 'Cb' is determined as follows: Cb = 1.75+1.05*(Mx1/Mx2)+0.3*(Mx1/Mx2)^2 <= 2.3 where: Mx1 = smaller X-axis (major axis) bending moment at either of the ends of the unbraced length Mx2 = larger X-axis (major axis) bending moment at either of the ends of the unbraced length Mx1/Mx2 = positive for reverse curvature bending (both have same signs) = negative for single curvature bending (both have opposite signs) Notes: 1. When the bending moment at any point within an unbraced length is larger than that at both ends of this length, then use 'Cb' = 1.0. 2. 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. 3. For cantilever beams, 'Cb' may be conservatively assumed = 1.0.
H24
'Sx(eff)' is the effective X-axis (major axis) section modulus of an axially loaded compression member, based on a reduced effective width of web, 'be', and is calculated as follows for W, S, M, and HP shapes: Sx(eff) = Sx-tw*(d-2*tf-be)^3/(6*d)
A25
Note: See section of this worksheet (to the right) for input data which may be used to determine the 'Cmx' to be used for input here.
B25
'Cmx' is the coefficient applied to the X-axis (major axis) bending term in the interaction equation (H1-1) and is dependent upon column curvature caused by applied moments. The 'Cmx' coefficient value is determined as follows: Category A: For compression members in frames subject to joint translation (sidesway), Cmx = 0.85. Category B: For rotationally restrained compression members in frames braced against joint translation (no sidesway) and not subject to transverse loading between their supports in the plane of bending, Cmx =0.6-0.4*(Mx1/Mx2) where: Mx1 = smaller X-axis (major axis) bending moment at either of the ends of the unbraced length Mx2 = larger X-axis (major axis) bending moment at either of the ends of the unbraced length Mx1/Mx2 = positive for reverse curvature bending (both have same signs) = negative for single curvature bending (both have opposite signs) Category C: For rotationally restrained compression members in frames braced against joint translation (no sidesway) and subject to transverse loading between their supports in the plane of bending, the following values of 'Cmx' are permitted : 1. For members whose ends are restrained against rotation in the plane of bending, Cmx = 0.85. 2. For members whose ends are unrestrained against rotation in the plane of bending, Cmx = 1.0.
H25
'Sy(eff)' is the effective Y-axis (minor axis) section modulus of an axially loaded compression member, based on a reduced effective width of web, 'be', and is calculated as follows for W, S, M, and HP shapes: Sy(eff) = Sy-(d-2*tf-be)*tw^3/(6*bf)
A26
Note: See section of this worksheet (to the right) for input data which may be used to determine the 'Cmy' to be used for input here.
B26
'Cmy' is the coefficient applied to the Y-axis (minor axis) bending term in the interaction equation (H1-1) and is dependent upon column curvature caused by applied moments. The 'Cmy' coefficient value is determined as follows: Category A: For compression members in frames subject to joint translation (sidesway), Cmy = 0.85. Category B: For rotationally restrained compression members in frames braced against joint translation (no sidesway) and not subject to transverse loading between their supports in the plane of bending, Cmy =0.6-0.4*(My1/My2) where: My1 = smaller Y-axis (minor axis) bending moment at either of the ends of the unbraced length My2 = larger Y-axis (minor axis) bending moment at either of the ends of the unbraced length My1/My2 = positive for reverse curvature bending (both have same signs) = negative for single curvature bending (both have opposite signs) Category C: For rotationally restrained compression members in frames braced against joint translation (no sidesway) and subject to transverse loading between their supports in the plane of bending, the following values of 'Cmy' are permitted : 1. For members whose ends are restrained against rotation in the plane of bending, Cmy = 0.85. 2. For members whose ends are unrestrained against rotation in the plane of bending, Cmy = 1.0.
B27
'ASIF' is the Allowable Stress Increase Factor which is applied to all the allowable stresses and the Euler column buckling stresses used in the stress ratio calculation. Note: for example, a value of 1.333 can be used for the 'ASIF' for load combinations which include wind or seismic. Otherwise, use 1.0.
B32
The expression 'Kx*Lx/rx' is the effective slenderness ratio for members subjected to axial compression load. Note: 'Lx' is converted from feet to inches in the evaluation of the expression.
E32
'Lc' is the maximum unbraced length of the compression flange at which the allowable X-axis (major axis) bending stress maybe taken at 0.66*Fy, or from AISC Code Eqn. F1-3 when applicable. Lc = smaller of: 76*bf/SQRT(Fy) or 20000/((d/Af)*Fy)
H32
'fby' is the actual Y-axis (minor axis) bending stress and is calculated as follows: fby = My*12/Sy
B33
The expression 'Ky*Ly/ry' is the effective slenderness ratio for members subjected to axial compression load. Note: 'Ly' is converted from feet to inches in the evaluation of the expression.
E33
'Lu' is the maximum unbraced length of the compression flange at which the allowable X-axis (major axis) bending stress maybe taken at 0.60*Fy when Cb = 1.
H33
'Fby' is the allowable Y-axis (minor axis) bending stress and is calculated as follows: For either compression or tension due to bending, when bf/(2*tf) <= 65/SQRT(Fy): Fby = 0.75*Fy (Eqn. F2-1) when 65/SQRT(Fy) < bf/(2*tf) <= 95/SQRT(Fy): Fby = Fy*(1.075-0.005*bf/(2*tf)*SQRT(Fy)) (Eqn. F2-2) when bf/(2*tf) > 95/SQRT(Fy): Fby = 0.60*Fy (Eqn. F2-3)
B34
'Cc' is the column (compression) slenderness ratio separating elastic and inelastic buckling, and is calculated as follows: Cc = SQRT(2*p^2*E/Fy) where: E = modulus of elasticity for steel = 29,000 ksi
E34
Note: In the expression 'Lb/rt', the value of 'Lb' is converted from feet to inches in the evaluation.
H34
'Mry' is the allowable resisting moment for Y-axis (minor axis) bending, and is calculated as follows: Mry = Fby*Sy/12
B35
'fa' is the actual compression stress for an axially loaded compression member and is calculated as follows: fa = P/A 'ft' is the allowable tension stress for an axially loaded tension member and is calculated as follows: ft = P/A
E35
'fbx' is the actual X-axis (major axis) bending stress and is calculated as follows: fbx = Mx*12/Sx
B36
'Fa' is the allowable compression stress for an axially loaded compression member and is calculated as follows: For: K*L*12/r <= Cc = SQRT(2*p^2*E/Fy) use Eqn. E2-1: Fa = (1-(K*L*12/r)^2/(2*Cc)^2)*Fy/(5/3+3*(K*L*12/r)/(8*Cc)-(K*L*12/r)^3/(8*Cc^3)) For: K*L*12/r > Cc = SQRT(2*p^2*E/Fy) use Eqn. E2-2: Fa = 12*p^2*E/(23*(K*L*12/r)^2) Note: the larger value of either Kx*Lx*12/rx or Ky*Ly*12/ry is to be used in the equations above to determine 'Fa'. 'Ft' is the allowable tension stress for an axially loaded tension member and is calculated as follows: Ft = 0.60*Fy
E36
'Fbx' is the allowable X-axis (major axis) bending stress and is calculated as follows: For either compression or tension due to bending, when bf/(2*tf) <= 65/SQRT(Fy), and d/tw compact criteria are met, and Lb <= Lc: Fbx = 0.66*Fy (Eqn. F1-1) when 65/SQRT(Fy) < bf/(2*tf) <= 95/SQRT(Fy) and Lb <= Lc: Fbx = Fy*(0.79-0.002*bf/(2*tf)*SQRT(Fy)) (Eqn. F1-3) when bf/(2*tf) > 95/SQRT(Fy) and Lb <= Lc: Fbx = 0.60*Fy (Eqn. F1-5) For tension due to bending, when the compact criteria are not met, Fbx = 0.60*Fy For compression due to bending, and member is either compact or non- compact and Lb > Lc: when SQRT(102000*Cb/Fy) <= Lb*12/rt <= SQRT(510000*Cb/Fy): Fbx = (2/3-Fy*(Lb*12/rt)^2/(1530000*Cb))*Fy <= 0.60*Fy (Eqn. F1-6) when Lb*12/rt >= SQRT(510000*Cb/Fy): Fbx = 170000*Cb/((Lb*12/rt)^2) <= 0.60*Fy (Eqn. F1-7) and for ANY value of Lb*12/rt: Fbx = 12000*Cb/(Lb*12*d/Af) <= 0.60*Fy (Eqn. F1-8) Note: for 'Fbx' use larger value of either Eqn. F1-6 and Eqn. F1-8, or Eqn. F1-7 and F1-8, depending on the value of 'Lb*12/rt' as noted above. Also, note that Eqn. F1-8 is applicable only to sections with a compression flange that is solid and approximately rectangular.
B37
'Pa' is the allowable axial load for compression (or tension if applicable), and is calculated as follows: Pa = Fa*A
E37
'Mrx' is the allowable resisting moment for X-axis (major axis) bending, and is calculated as follows: Mrx = Fbx*Sx/12
E41
F'ex is the Euler compressive buckling stress divided by factor of safety for the X-axis (major axis), and is calculated as follows: F'ex = 12*p^2*E/(23*(Kx*Lx*12/rx)^2)
H41
F'ey is the Euler compressive buckling stress divided by factor of safety for the Y-axis (minor axis), and is calculated as follows: F'ey = 12*p^2*E/(23*(Ky*Ly*12/ry)^2)
B44
"S.R." is the Stress Ratio for the member which is calculated as follows: For members with combined axial compression and bending when fa/Fa > 0.15 per Eqn. H1-1: S.R. = fa/(ASIF*Fa) + Cmx*fbx/((1-fa/(ASIF*F'ex))*(ASIF*Fbx)) + Cmy*fby/((1-fa/(ASIF*F'ey))*(ASIF*Fby)) <= 1.0 and per Eqn. H1-2: S.R. = fa/(ASIF*0.60*Fy) + fbx/(ASIF*Fbx) + fby/(ASIF*Fby) <= 1.0 Note: program will display the results of the larger value obtained from either Eqn. H1-1 or Eqn. H1-2 For members with combined axial compression and bending when fa/Fa <= 0.15 per Eqn. H1-3: S.R. = fa/(ASIF*Fa) + fbx/(ASIF*Fbx) + fby/(ASIF*Fby) <= 1.0 For members with combined axial tension and bending: S.R. = ft/(ASIF*Ft) + fbx/(ASIF*Fbx) + fby/(ASIF*Fby) <= 1.0 Note: in this case the Stress Ratio computed from just the compressive bending stress(s) must also be checked.
"BEAMCOL9.xls" ProgramVersion 3.4
4 of 10 04/07/2023 23:16:02
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"BEAMCOL9.xls" ProgramVersion 3.4
5 of 10 04/07/2023 23:16:02
STEEL BEAM AND COLUMN ANALYSIS / CODE CHECKStress Code Check Per AISC 9th Edition Manual (ASD)
For Shapes Not in Database or Built-Up Shapes Not Classified as Plate Girders Job Name: Subject: ###
Job Number: Originator: Checker: ######
Input Data: SingleReverse
Member Data: Member Properties: Y Bracedd = 12.375 in. A = 11.91 in.^2 Unbraced
tw = 0.250 in. d = 12.375 in. tf = 0.375bf = 12.000 in. tw = 0.250 in. P(be) =tf = 0.375 in. bf = 12.000 in. be =
tf = 0.375 in. Qa =Member Loadings: rt = 3.292 in. d = 12.375 X h = 11.625
For a section to NOT be classified as a plate girder, the following depth to web thickness criteria must be met: h/tw <= 760/SQRT(Fbx) where: h = d-2*tf Fbx = allowable X-axis (major axis) bending stress
B16
'P' is the applied axial load on the member, which may be either a compression or tension load. Sign convention: + = compression, - = tension
B17
'Mx' is the applied flexural bending moment about the X-axis (major axis) of the member. Note: the value input MUST BE positive (+).
B18
'My' is the applied flexural bending moment about the Y-axis (minor axis) of the member. Note: the value input MUST BE positive (+).
A22
Note: See section of this worksheet (to the right) for input data which may be used to determine the 'Kx' to be used for input here.
B22
'Kx' is the effective length factor about the X-axis (major axis) for an axially loaded compression member. Typical values are as follows: Column End Conditions "Kx" Value (bottom-top) (Recommended) Fixed-Fixed 0.65 Fixed-Pinned 0.80 Fixed-Slider 1.2 Pinned-Pinned 1.0 Fixed-Free 2.1 Pinned-Slider 2.0 where: Fixed end denotes rotation fixed and translation fixed. Pinned end denotes rotation free and translation fixed. Slider end denotes rotation fixed and translation free. Free end denotes rotation free and translation free.
H22
'Qs' is the allowable stress reduction factor for an unstiffened compression element (flange) of member determined from AISC Appendix B and is calculated as follows: when 95/SQRT(Fy/kc) < bf/(2*tf) < 195/SQRT(Fy/kc) Qs = 1.293-0.00309*bf/(2*tf)*SQRT(Fy/kc) Eqn. A-B5-3 when bf/(2*tf) > 195/SQRT(Fy/kc) Qs = 26,200*kc/(Fy*bf/(2*tf)) Eqn. A-B5-4 where: if h/tw > 70, kc = 4.05/((h/tw)^0.46), else kc = 1.0 (Note: h = d-2*tf)
A23
Note: See section of this worksheet (to the right) for input data which may be used to determine the 'Ky' to be used for input here.
B23
'Ky' is the effective length factor about the Y-axis (minor axis) for an axially loaded compression member. Typical values are as follows: Column End Conditions "Ky" Value (bottom-top) (Recommended) Fixed-Fixed 0.65 Fixed-Pinned 0.80 Fixed-Slider 1.2 Pinned-Pinned 1.0 Fixed-Free 2.1 Pinned-Slider 2.0 where: Fixed end denotes rotation fixed and translation fixed. Pinned end denotes rotation free and translation fixed. Slider end denotes rotation fixed and translation free. Free end denotes rotation free and translation free.
H23
'Qa' is the ratio of effective profile area of an axially loaded compression member to its total (gross) profile area from AISC Appendix B and is calculated as follows: when h/tw > 253/SQRT(Fy) be = 253*tw/SQRT(f)*(1-44.3/((h/tw)*SQRT(f)) <= h Eqn. A-B5-8 Ae = A-(h-be)*tw Qa = (A-(h-be)*tw)/A where: be = effective length of web of member h = d-2*tf f = computed compressive stress based on effecive area Ae = effective area of member
B24
'Lx' is the actual unbraced length of member for column-type (axial compression) buckling about X-axis (major axis). Note: for input values of Lx <=1.0', this program will use a value =1.0'.
H24
'Sx(eff)' is the effective X-axis (major axis) section modulus of an axially loaded compression member, based on a reduced effective width of web, 'be', and is calculated as follows for 'I' type shapes: Sx(eff) = Sx-tw*(d-2*tf-be)^3/(6*d)
B25
'Ly' is the actual unbraced length of member for column-type (axial compression) buckling about Y-axis (minor axis). Note: for input values of Ly <=1.0', this program will use a value =1.0'.
H25
'Sy(eff)' is the effective Y-axis (minor axis) section modulus of an axially loaded compression member, based on a reduced effective width of web, 'be', and is calculated as follows for 'I' type shapes: Sy(eff) = Sy-(d-2*tf-be)*tw^3/(6*bf)
B26
'Lb' is the actual unbraced length of the compression flange of the member for X-axis (major axis) bending. The "unbraced length" can be more specifically defined as the distance between cross sections braced against twist or lateral displacement of the compression flange. Notes: 1. For most cases, 'Lb' is equal to 'Ly'. 2. For cantilevers braced against twist only at the support, 'Lb' may conservatively be taken as the actual length. 3. For input values of Lb <=1.0', this program will use a value =1.0'.
A27
Note: See section of this worksheet (to the right) for input data which may be used to determine the 'Cb' to be used for input here.
B27
'Cb' is the allowable stress bending coefficient dependent on the moment gradient, for bending about the X-axis (major axis). 'Cb' is determined as follows: Cb = 1.75+1.05*(Mx1/Mx2)+0.3*(Mx1/Mx2)^2 <= 2.3 where: Mx1 = smaller X-axis (major axis) bending moment at either of the ends of the unbraced length Mx2 = larger X-axis (major axis) bending moment at either of the ends of the unbraced length Mx1/Mx2 = positive for reverse curvature bending (both have same signs) = negative for single curvature bending (both have opposite signs) Notes: 1. When the bending moment at any point within an unbraced length is larger than that at both ends of this length, then use 'Cb' = 1.0. 2. 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. 3. For cantilever beams, 'Cb' may be conservatively assumed = 1.0.
A28
Note: See section of this worksheet (to the right) for input data which may be used to determine the 'Cmx' to be used for input here.
B28
'Cmx' is the coefficient applied to the X-axis (major axis) bending term in the interaction equation (H1-1) and is dependent upon column curvature caused by applied moments. The 'Cmx' coefficient value is determined as follows: Category A: For compression members in frames subject to joint translation (sidesway), Cmx = 0.85. Category B: For rotationally restrained compression members in frames braced against joint translation (no sidesway) and not subject to transverse loading between their supports in the plane of bending, Cmx =0.6-0.4*(Mx1/Mx2) where: Mx1 = smaller X-axis (major axis) bending moment at either of the ends of the unbraced length Mx2 = larger X-axis (major axis) bending moment at either of the ends of the unbraced length Mx1/Mx2 = positive for reverse curvature bending (both have same signs) = negative for single curvature bending (both have opposite signs) Category C: For rotationally restrained compression members in frames braced against joint translation (no sidesway) and subject to transverse loading between their supports in the plane of bending, the following values of 'Cmx' are permitted : 1. For members whose ends are restrained against rotation in the plane of bending, Cmx = 0.85. 2. For members whose ends are unrestrained against rotation in the plane of bending, Cmx = 1.0.
A29
Note: See section of this worksheet (to the right) for input data which may be used to determine the 'Cmy' to be used for input here.
B29
'Cmy' is the coefficient applied to the Y-axis (minor axis) bending term in the interaction equation (H1-1) and is dependent upon column curvature caused by applied moments. The 'Cmy' coefficient value is determined as follows: Category A: For compression members in frames subject to joint translation (sidesway), Cmy = 0.85. Category B: For rotationally restrained compression members in frames braced against joint translation (no sidesway) and not subject to transverse loading between their supports in the plane of bending, Cmy =0.6-0.4*(My1/My2) where: My1 = smaller Y-axis (minor axis) bending moment at either of the ends of the unbraced length My2 = larger Y-axis (minor axis) bending moment at either of the ends of the unbraced length My1/My2 = positive for reverse curvature bending (both have same signs) = negative for single curvature bending (both have opposite signs) Category C: For rotationally restrained compression members in frames braced against joint translation (no sidesway) and subject to transverse loading between their supports in the plane of bending, the following values of 'Cmy' are permitted : 1. For members whose ends are restrained against rotation in the plane of bending, Cmy = 0.85. 2. For members whose ends are unrestrained against rotation in the plane of bending, Cmy = 1.0.
B30
'ASIF' is the Allowable Stress Increase Factor which is applied to all the allowable stresses and the Euler column buckling stresses used in the stress ratio calculation. Note: for example, a value of 1.333 can be used for the 'ASIF' for load combinations which include wind or seismic. Otherwise, use 1.0.
B35
The expression 'Kx*Lx/rx' is the effective slenderness ratio for members subjected to axial compression load. Note: 'Lx' is converted from feet to inches in the evaluation of the expression.
E35
'Lc' is the maximum unbraced length of the compression flange at which the allowable X-axis (major axis) bending stress maybe taken at 0.66*Fy, or from AISC Code Eqn. F1-3 when applicable. Lc = smaller of: 76*bf/SQRT(Fy) or 20000/((d/Af)*Fy)
H35
'fby' is the actual Y-axis (minor axis) bending stress and is calculated as follows: fby = My*12/Sy
B36
The expression 'Ky*Ly/ry' is the effective slenderness ratio for members subjected to axial compression load. Note: 'Ly' is converted from feet to inches in the evaluation of the expression.
E36
'Lu' is the maximum unbraced length of the compression flange at which the allowable X-axis (major axis) bending stress maybe taken at 0.60*Fy when Cb = 1.
H36
'Fby' is the allowable Y-axis (minor axis) bending stress and is calculated as follows: For either compression or tension due to bending, when bf/(2*tf) <= 65/SQRT(Fy): Fby = 0.75*Fy (Eqn. F2-1) when 65/SQRT(Fy) < bf/(2*tf) <= 95/SQRT(Fy): Fby = Fy*(1.075-0.005*bf/(2*tf)*SQRT(Fy)) (Eqn. F2-2) when bf/(2*tf) > 95/SQRT(Fy): Fby = 0.60*Fy (Eqn. F2-3)
B37
'Cc' is the column (compression) slenderness ratio separating elastic and inelastic buckling, and is calculated as follows: Cc = SQRT(2*p^2*E/Fy) where: E = modulus of elasticity for steel = 29,000 ksi
E37
Note: In the expression 'Lb/rt', the value of 'Lb' is converted from feet to inches in the evaluation.
H37
'Mry' is the allowable resisting moment for Y-axis (minor axis) bending, and is calculated as follows: Mry = Fby*Sy/12
B38
'fa' is the actual compression stress for an axially loaded compression member and is calculated as follows: fa = P/A 'ft' is the allowable tension stress for an axially loaded tension member and is calculated as follows: ft = P/A
E38
'fbx' is the actual X-axis (major axis) bending stress and is calculated as follows: fbx = Mx*12/Sx
B39
'Fa' is the allowable compression stress for an axially loaded compression member and is calculated as follows: For: K*L*12/r <= Cc = SQRT(2*p^2*E/Fy) use Eqn. E2-1: Fa = (1-(K*L*12/r)^2/(2*Cc)^2)*Fy/(5/3+3*(K*L*12/r)/(8*Cc)-(K*L*12/r)^3/(8*Cc^3)) For: K*L*12/r > Cc = SQRT(2*p^2*E/Fy) use Eqn. E2-2: Fa = 12*p^2*E/(23*(K*L*12/r)^2) Note: the larger value of either Kx*Lx*12/rx or Ky*Ly*12/ry is to be used in the equations above to determine 'Fa'. 'Ft' is the allowable tension stress for an axially loaded tension member and is calculated as follows: Ft = 0.60*Fy
E39
'Fbx' is the allowable X-axis (major axis) bending stress and is calculated as follows: For either compression or tension due to bending, when bf/(2*tf) <= 65/SQRT(Fy), and d/tw compact criteria are met, and Lb <= Lc: Fbx = 0.66*Fy (Eqn. F1-1) when 65/SQRT(Fy) < bf/(2*tf) <= 95/SQRT(Fy) and Lb <= Lc: Fbx = Fy*(0.79-0.002*bf/(2*tf)*SQRT(Fy)) (Eqn. F1-3) when bf/(2*tf) > 95/SQRT(Fy) and Lb <= Lc: Fbx = 0.60*Fy (Eqn. F1-5) For tension due to bending, when the compact criteria are not met, Fbx = 0.60*Fy For compression due to bending, and member is either compact or non- compact and Lb > Lc: when SQRT(102000*Cb/Fy) <= Lb*12/rt <= SQRT(510000*Cb/Fy): Fbx = (2/3-Fy*(Lb*12/rt)^2/(1530000*Cb))*Fy <= 0.60*Fy (Eqn. F1-6) when Lb*12/rt >= SQRT(510000*Cb/Fy): Fbx = 170000*Cb/((Lb*12/rt)^2) <= 0.60*Fy (Eqn. F1-7) and for ANY value of Lb*12/rt: Fbx = 12000*Cb/(Lb*12*d/Af) <= 0.60*Fy (Eqn. F1-8) Note: for 'Fbx' use larger value of either Eqn. F1-6 and Eqn. F1-8, or Eqn. F1-7 and F1-8, depending on the value of 'Lb*12/rt' as noted above. Also, note that Eqn. F1-8 is applicable only to sections with a compression flange that is solid and approximately rectangular.
E40
'Mrx' is the allowable resisting moment for X-axis (major axis) bending, and is calculated as follows: Mrx = Fbx*Sx/12
E43
F'ex is the Euler compressive buckling stress divided by factor of safety for the X-axis (major axis), and is calculated as follows: F'ex = 12*p^2*E/(23*(Kx*Lx*12/rx)^2)
H43
F'ey is the Euler compressive buckling stress divided by factor of safety for the Y-axis (minor axis), and is calculated as follows: F'ey = 12*p^2*E/(23*(Ky*Ly*12/ry)^2)
B46
"S.R." is the Stress Ratio for the member which is calculated as follows: For members with combined axial compression and bending when fa/Fa > 0.15 per Eqn. H1-1: S.R. = fa/(ASIF*Fa) + Cmx*fbx/((1-fa/(ASIF*F'ex))*(ASIF*Fbx)) + Cmy*fby/((1-fa/(ASIF*F'ey))*(ASIF*Fby)) <= 1.0 and per Eqn. H1-2: S.R. = fa/(ASIF*0.60*Fy) + fbx/(ASIF*Fbx) + fby/(ASIF*Fby) <= 1.0 Note: program will display the results of the larger value obtained from either Eqn. H1-1 or Eqn. H1-2 For members with combined axial compression and bending when fa/Fa <= 0.15 per Eqn. H1-3: S.R. = fa/(ASIF*Fa) + fbx/(ASIF*Fbx) + fby/(ASIF*Fby) <= 1.0 For members with combined axial tension and bending: S.R. = ft/(ASIF*Ft) + fbx/(ASIF*Fbx) + fby/(ASIF*Fby) <= 1.0 Note: in this case the Stress Ratio computed from just the compressive bending stress(s) must also be checked.
"BEAMCOL9.xls" ProgramVersion 3.4
6 of 10 04/07/2023 23:16:02
Fby =
"BEAMCOL9.xls" ProgramVersion 3.4
7 of 10 04/07/2023 23:16:02
STEEL BEAM AND COLUMN ANALYSIS / CODE CHECKStress Code Check Per AISC 9th Edition Manual (ASD)
For C and MC ShapesJob Name: Subject: ###
Job Number: Originator: Checker: ###Single
Input Data: ReverseBraced
Member Size: Member Properties: Y UnbracedSelect: C10x20 A = 5.87 in.^2 tf=0.436
d = 10.000 in. be =Member Loadings: tw = 0.379 in. Qa =
P = 0.00 kips bf = 2.740 in. xbar=0.606Mx = 10.00 ft-kips tf = 0.436 in. d=10 XMy = 0.00 ft-kips 0.606 in. ###
'P' is the applied axial load on the member, which may be either a compression or tension load. Sign convention: + = compression, - = tension
B14
'Mx' is the applied flexural bending moment about the X-axis (major axis) of the member. Note: the value input MUST BE positive (+).
B15
'My' is the applied flexural bending moment about the Y-axis (minor axis) of the member. Note: the value input MUST BE positive (+).
A19
Note: See section of this worksheet (to the right) for input data which may be used to determine the 'Kx' to be used for input here.
B19
'Kx' is the effective length factor about the X-axis (major axis) for an axially loaded compression member. Typical values are as follows: Column End Conditions "Kx" Value (bottom-top) (Recommended) Fixed-Fixed 0.65 Fixed-Pinned 0.80 Fixed-Slider 1.2 Pinned-Pinned 1.0 Fixed-Free 2.1 Pinned-Slider 2.0 where: Fixed end denotes rotation fixed and translation fixed. Pinned end denotes rotation free and translation fixed. Slider end denotes rotation fixed and translation free. Free end denotes rotation free and translation free.
A20
Note: See section of this worksheet (to the right) for input data which may be used to determine the 'Ky' to be used for input here.
B20
'Ky' is the effective length factor about the Y-axis (minor axis) for an axially loaded compression member. Typical values are as follows: Column End Conditions "Ky" Value (bottom-top) (Recommended) Fixed-Fixed 0.65 Fixed-Pinned 0.80 Fixed-Slider 1.2 Pinned-Pinned 1.0 Fixed-Free 2.1 Pinned-Slider 2.0 where: Fixed end denotes rotation fixed and translation fixed. Pinned end denotes rotation free and translation fixed. Slider end denotes rotation fixed and translation free. Free end denotes rotation free and translation free.
B21
'Lx' is the actual unbraced length of member for column-type (axial compression) buckling about X-axis (major axis). Note: for input values of Lx <=1.0', this program will use a value =1.0'.
H21
'Qs' is the allowable stress reduction factor for an unstiffened compression element (flange) of member determined from AISC Appendix B and is calculated as follows: when 95/SQRT(Fy/kc) < bf/(2*tf) < 195/SQRT(Fy/kc) Qs = 1.293-0.00309*bf/tf*SQRT(Fy/kc) Eqn. A-B5-3 when bf/(2*tf) > 195/SQRT(Fy/kc) Qs = 26,200*kc/(Fy*(bf/tf)^2) Eqn. A-B5-4 Note: Qs = 1.0 for all C shapes for Fy = 36 or 50 ksi.
B22
'Ly' is the actual unbraced length of member for column-type (axial compression) buckling about Y-axis (minor axis). Note: for input values of Ly <=1.0', this program will use a value =1.0'.
H22
'Qa' is the ratio of effective profile area of an axially loaded compression member to its total (gross) profile area from AISC Appendix B and is calculated as follows: when h/tw > 253/SQRT(Fy) be = 253*tw/SQRT(f)*(1-44.3/((h/tw)*SQRT(f)) <= h Eqn. A-B5-8 Ae = A-(h-be)*tw Qa = (A-(h-be)*tw)/A where: be = effective length of web of member h = d-2*tf f = computed compressive stress based on effecive area Ae = effective area of member
B23
'Lb' is the actual unbraced length of the compression flange of the member for X-axis (major axis) bending. The "unbraced length" can be more specifically defined as the distance between cross sections braced against twist or lateral displacement of the compression flange. Notes: 1. For most cases, 'Lb' is equal to 'Ly'. 2. For cantilevers braced against twist only at the support, 'Lb' may conservatively be taken as the actual length. 3. For input values of Lb <=1.0', this program will use a value =1.0'.
H23
'Sx(eff)' is the effective X-axis (major axis) section modulus of an axially loaded compression member, based on a reduced effective width of web, 'be', and is calculated as follows for C sections: Sx(eff) = Sx-tw*(d-2*tf-be)^3/(6*d)
A24
Note: See section of this worksheet (to the right) for input data which may be used to determine the 'Cb' to be used for input here.
B24
'Cb' is the allowable stress bending coefficient dependent on the moment gradient, for bending about the X-axis (major axis). 'Cb' is determined as follows: Cb = 1.75+1.05*(Mx1/Mx2)+0.3*(Mx1/Mx2)^2 <= 2.3 where: Mx1 = smaller X-axis (major axis) bending moment at either of the ends of the unbraced length Mx2 = larger X-axis (major axis) bending moment at either of the ends of the unbraced length Mx1/Mx2 = positive for reverse curvature bending (both have same signs) = negative for single curvature bending (both have opposite signs) Notes: 1. When the bending moment at any point within an unbraced length is larger than that at both ends of this length, then use 'Cb' = 1.0. 2. 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. 3. For cantilever beams, 'Cb' may be conservatively assumed = 1.0.
H24
'Sy(eff)' is the effective Y-axis (minor axis) section modulus of an axially loaded compression member, based on a reduced effective width of web, 'be', and is calculated as follows for C sections: Sy(eff) = Sy-((d-2*tf-be)*tw^3/12+(d-2*tf-be)*tw*(xbar-tw/2)^2)/(bf-xbar)
A25
Note: See section of this worksheet (to the right) for input data which may be used to determine the 'Cmx' to be used for input here.
B25
'Cmx' is the coefficient applied to the X-axis (major axis) bending term in the interaction equation (H1-1) and is dependent upon column curvature caused by applied moments. The 'Cmx' coefficient value is determined as follows: Category A: For compression members in frames subject to joint translation (sidesway), Cmx = 0.85. Category B: For rotationally restrained compression members in frames braced against joint translation (no sidesway) and not subject to transverse loading between their supports in the plane of bending, Cmx =0.6-0.4*(Mx1/Mx2) where: Mx1 = smaller X-axis (major axis) bending moment at either of the ends of the unbraced length Mx2 = larger X-axis (major axis) bending moment at either of the ends of the unbraced length Mx1/Mx2 = positive for reverse curvature bending (both have same signs) = negative for single curvature bending (both have opposite signs) Category C: For rotationally restrained compression members in frames braced against joint translation (no sidesway) and subject to transverse loading between their supports in the plane of bending, the following values of 'Cmx' are permitted : 1. For members whose ends are restrained against rotation in the plane of bending, Cmx = 0.85. 2. For members whose ends are unrestrained against rotation in the plane of bending, Cmx = 1.0.
A26
Note: See section of this worksheet (to the right) for input data which may be used to determine the 'Cmy' to be used for input here.
B26
'Cmy' is the coefficient applied to the Y-axis (minor axis) bending term in the interaction equation (H1-1) and is dependent upon column curvature caused by applied moments. The 'Cmy' coefficient value is determined as follows: Category A: For compression members in frames subject to joint translation (sidesway), Cmy = 0.85. Category B: For rotationally restrained compression members in frames braced against joint translation (no sidesway) and not subject to transverse loading between their supports in the plane of bending, Cmy =0.6-0.4*(My1/My2) where: My1 = smaller Y-axis (minor axis) bending moment at either of the ends of the unbraced length My2 = larger Y-axis (minor axis) bending moment at either of the ends of the unbraced length My1/My2 = positive for reverse curvature bending (both have same signs) = negative for single curvature bending (both have opposite signs) Category C: For rotationally restrained compression members in frames braced against joint translation (no sidesway) and subject to transverse loading between their supports in the plane of bending, the following values of 'Cmy' are permitted : 1. For members whose ends are restrained against rotation in the plane of bending, Cmy = 0.85. 2. For members whose ends are unrestrained against rotation in the plane of bending, Cmy = 1.0.
B27
'ASIF' is the Allowable Stress Increase Factor which is applied to all the allowable stresses and the Euler Column Buckling stresses used in the stress ratio calculation. Note: for example, a value of 1.333 can be used for the 'ASIF' for load combinations which include wind or seismic. Otherwise, use 1.0.
B32
The expression 'Kx*Lx/rx' is the effective slenderness ratio for members subjected to axial compression load. Note: 'Lx' is converted from feet to inches in the evaluation of the expression.
E32
'Lu' is the maximum unbraced length of the compression flange at which the allowable X-axis (major axis) bending stress maybe taken at 0.60*Fy when Cb = 1.
H32
'fby' is the actual Y-axis (minor axis) bending stress and is calculated as follows: fby = My*12/Sy
B33
The expression 'Ky*Ly/ry' is the effective slenderness ratio for members subjected to axial compression load. Note: 'Ly' is converted from feet to inches in the evaluation of the expression.
E33
'fbx' is the actual X-axis (major axis) bending stress and is calculated as follows: fbx = Mx*12/Sx
H33
'Fby' is the allowable Y-axis (minor axis) bending stress and is calculated as follows: For either compression or tension due to bending, when bf/tf <= 65/SQRT(Fy): Fby = 0.75*Fy (Eqn. F2-1) when 65/SQRT(Fy) < bf/tf <= 95/SQRT(Fy): Fby = Fy*(1.075-0.005*bf/tf*SQRT(Fy)) (Eqn. F2-2) when bf/tf > 95/SQRT(Fy): Fby = 0.60*Fy (Eqn. F2-3)
B34
'Cc' is the column (compression) slenderness ratio separating elastic and inelastic buckling, and is calculated as follows: Cc = SQRT(2*p^2*E/Fy) where: E = modulus of elasticity for steel = 29,000 ksi
E34
'Fbx' is the allowable X-axis (major axis) bending stress and is calculated as follows: For compression due to bending, bf/tf <= 95/SQRT(Fy) and Lb > Lc: Fbx = 12000*Cb/(Lb*12*d/Af) <= 0.60*Fy (Eqn. F1-8) For tension due to bending: Fbx = 0.60*Fy
H34
'Mry' is the allowable resisting moment for Y-axis (minor axis) bending, and is calculated as follows: Mry = Fby*Sy/12
B35
'fa' is the actual compression stress for an axially loaded compression member and is calculated as follows: fa = P/A 'ft' is the allowable tension stress for an axially loaded tension member and is calculated as follows: ft = P/A
E35
'Mrx' is the allowable resisting moment for X-axis (major axis) bending, and is calculated as follows: Mrx = Fbx*Sx/12
B36
'Fa' is the allowable compression stress for an axially loaded compression member and is calculated as follows: For: K*L*12/r <= Cc = SQRT(2*p^2*E/Fy) use Eqn. E2-1: Fa = (1-(K*L*12/r)^2/(2*Cc)^2)*Fy/(5/3+3*(K*L*12/r)/(8*Cc)-(K*L*12/r)^3/(8*Cc^3)) For: K*L*12/r > Cc = SQRT(2*p^2*E/Fy) use Eqn. E2-2: Fa = 12*p^2*E/(23*(K*L*12/r)^2) Note: the larger value of either Kx*Lx*12/rx or Ky*Ly*12/ry is to be used in the equations above to determine 'Fa'. 'Ft' is the allowable tension stress for an axially loaded tension member and is calculated as follows: Ft = 0.60*Fy
B37
'Pa' is the allowable axial load for compression (or tension if applicable), and is calculated as follows: Pa = Fa*A
E41
F'ex is the Euler compressive buckling stress divided by factor of safety for the X-axis (major axis), and is calculated as follows: F'ex = 12*p^2*E/(23*(Kx*Lx*12/rx)^2)
H41
F'ey is the Euler compressive buckling stress divided by factor of safety for the Y-axis (minor axis), and is calculated as follows: F'ey = 12*p^2*E/(23*(Ky*Ly*12/ry)^2)
B44
"S.R." is the Stress Ratio for the member which is calculated as follows: For members with combined axial compression and bending when fa/Fa > 0.15 per Eqn. H1-1: S.R. = fa/(ASIF*Fa) + Cmx*fbx/((1-fa/(ASIF*F'ex))*(ASIF*Fbx)) + Cmy*fby/((1-fa/(ASIF*F'ey))*(ASIF*Fby)) <= 1.0 and per Eqn. H1-2: S.R. = fa/(ASIF*0.60*Fy) + fbx/(ASIF*Fbx) + fby/(ASIF*Fby) <= 1.0 Note: program will display the results of the larger value obtained from either Eqn. H1-1 or Eqn. H1-2 For members with combined axial compression and bending when fa/Fa <= 0.15 per Eqn. H1-3: S.R. = fa/(ASIF*Fa) + fbx/(ASIF*Fbx) + fby/(ASIF*Fby) <= 1.0 For members with combined axial tension and bending: S.R. = ft/(ASIF*Ft) + fbx/(ASIF*Fbx) + fby/(ASIF*Fby) <= 1.0 Note: in this case the Stress Ratio computed from just the compressive bending stress(s) must also be checked.
'P' is the applied axial load on the member, which may be either a compression or tension load. Sign convention: + = compression, - = tension
B14
'Mx(max)' is the maximum applied design flexural bending moment about the X-axis of the member. Note: the value input MUST BE positive (+).
B15
'Mx1' is the smaller X-axis bending moment at either of the ends of the unbraced length. Note: 'Mx1' should be input with a positive (+) value for single curvature and a negative (-) value for single curvature in the unbraced length (Lbx) being considered. 'Mx1' is used in AISC Eqn. F3-2 to determine the the critical unbraced length value, 'Lcx'
B16
'Mx2' is the larger X-axis bending moment at either of the ends of the unbraced length. Note: 'Mx2' is often = 'Mx(max)'. 'Mx2' is used in AISC Eqn. F3-2 to determine the the critical unbraced length value, 'Lcx'.
B17
'My(max)' is the maximum applied design flexural bending moment about the Y-axis of the member. Note: the value input MUST BE positive (+).
B18
'My1' is the smaller Y-axis bending moment at either of the ends of the unbraced length. Note: 'My1' should be input with a positive (+) value for single curvature and a negative (-) value for single curvature in the unbraced length (Lby) being considered. 'My1' is used in AISC Eqn. F3-2 to determine the the critical unbraced length value, 'Lcy'
B19
'My2' is the larger Y-axis bending moment at either of the ends of the unbraced length. Note: 'My2' is often = 'My(max)'. 'My2' is used in AISC Eqn. F3-2 to determine the the critical unbraced length value, 'Lcy'.
A23
Note: See section of this worksheet (to the right) for input data which may be used to determine the 'Kx' to be used for input here.
B23
'Kx' is the effective length factor about the X-axis for an axially loaded compression member. Typical values are as follows: Column End Conditions "Kx" Value (bottom-top) (Recommended) Fixed-Fixed 0.65 Fixed-Pinned 0.80 Fixed-Slider 1.2 Pinned-Pinned 1.0 Fixed-Free 2.1 Pinned-Slider 2.0 where: Fixed end denotes rotation fixed and translation fixed. Pinned end denotes rotation free and translation fixed. Slider end denotes rotation fixed and translation free. Free end denotes rotation free and translation free.
A24
Note: See section of this worksheet (to the right) for input data which may be used to determine the 'Ky' to be used for input here.
B24
'Ky' is the effective length factor about the Y-axis for an axially loaded compression member. Typical values are as follows: Column End Conditions "Ky" Value (bottom-top) (Recommended) Fixed-Fixed 0.65 Fixed-Pinned 0.80 Fixed-Slider 1.2 Pinned-Pinned 1.0 Fixed-Free 2.1 Pinned-Slider 2.0 where: Fixed end denotes rotation fixed and translation fixed. Pinned end denotes rotation free and translation fixed. Slider end denotes rotation fixed and translation free. Free end denotes rotation free and translation free.
B25
'Lx' is the actual unbraced length of member for column-type (axial compression) buckling about X-axis. Note: for input values of Lx <=1.0', this program will use a value =1.0'.
B26
'Ly' is the actual unbraced length of member for column-type (axial compression) buckling about Y-axis. Note: for input values of Ly <=1.0', this program will use a value =1.0'.
B27
'Lbx' is the actual unbraced length of the member for X-axis bending. Notes: 1. For most cases, 'Lbx' is equal to 'Ly'. 2. For cantilevers braced against twist only at the support, 'Lbx' may conservatively be taken as the actual length. 3. For input values of Lbx <=1.0', this program will use a value =1.0'.
B28
'Lby' is the actual unbraced length of the member for Y-axis bending. Notes: 1. For most cases, 'Lby' is equal to 'Lx'. 2. For cantilevers braced against twist only at the support, 'Lby' may conservatively be taken as the actual length. 3. For input values of Lby <=1.0', this program will use a value =1.0'.
A29
Note: See section of this worksheet (to the right) for input data which may be used to determine the 'Cmx' to be used for input here.
B29
'Cmx' is the coefficient applied to the X-axis bending term in the interaction equation (H1-1) and is dependent upon column curvature caused by applied moments. The 'Cmx' coefficient value is determined as follows: Category A: For compression members in frames subject to joint translation (sidesway), Cmx = 0.85. Category B: For rotationally restrained compression members in frames braced against joint translation (no sidesway) and not subject to transverse loading between their supports in the plane of bending, Cmx =0.6-0.4*(Mx1/Mx2) where: Mx1 = smaller X-axis bending moment at either of the ends of the unbraced length Mx2 = larger X-axis bending moment at either of the ends of the unbraced length Mx1/Mx2 = positive for reverse curvature bending (both have same signs) = negative for single curvature bending (both have opposite signs) Category C: For rotationally restrained compression members in frames braced against joint translation (no sidesway) and subject to transverse loading between their supports in the plane of bending, the following values of 'Cmx' are permitted : 1. For members whose ends are restrained against rotation in the plane of bending, Cmx = 0.85. 2. For members whose ends are unrestrained against rotation in the plane of bending, Cmx = 1.0.
A30
Note: See section of this worksheet (to the right) for input data which may be used to determine the 'Cmy' to be used for input here.
B30
'Cmy' is the coefficient applied to the Y-axis bending term in the interaction equation (H1-1) and is dependent upon column curvature caused by applied moments. The 'Cmy' coefficient value is determined as follows: Category A: For compression members in frames subject to joint translation (sidesway), Cmy = 0.85. Category B: For rotationally restrained compression members in frames braced against joint translation (no sidesway) and not subject to transverse loading between their supports in the plane of bending, Cmy =0.6-0.4*(My1/My2) where: My1 = smaller Y-axis bending moment at either of the ends of the unbraced length My2 = larger Y-axis bending moment at either of the ends of the unbraced length My1/My2 = positive for reverse curvature bending (both have same signs) = negative for single curvature bending (both have opposite signs) Category C: For rotationally restrained compression members in frames braced against joint translation (no sidesway) and subject to transverse loading between their supports in the plane of bending, the following values of 'Cmy' are permitted : 1. For members whose ends are restrained against rotation in the plane of bending, Cmy = 0.85. 2. For members whose ends are unrestrained against rotation in the plane of bending, Cmy = 1.0.
B31
'ASIF' is the Allowable Stress Increase Factor which is applied to all the allowable stresses and the Euler column buckling stresses used in the stress ratio calculation. Note: for example, a value of 1.333 can be used for the 'ASIF' for load combinations which include wind or seismic. Otherwise, use 1.0.
B36
The expression 'Kx*Lx/rx' is the effective slenderness ratio for members subjected to axial compression load. Note: 'Lx' is converted from feet to inches in the evaluation of the expression.
E36
'Lcx' is the maximum unbraced length of the member at which the allowable X-axis bending stress maybe taken at 0.66*Fy. Lcx = (1950+1200*Mx1/Mx2)*b/Fy ( Eqn. F3-2) Note: for HSS sections, b = B-3*t
H36
'Lcy' is the maximum unbraced length of the member at which the allowable X-axis bending stress maybe taken at 0.66*Fy. Lcy = (1950+1200*My1/My2)*b/Fy ( Eqn. F3-2) Note: for HSS sections, b = H-3*t
B37
The expression 'Ky*Ly/ry' is the effective slenderness ratio for members subjected to axial compression load. Note: 'Ly' is converted from feet to inches in the evaluation of the expression.
E37
'fbx' is the actual X-axis bending stress and is calculated as follows: fbx = Mx*12/Sx
H37
'fby' is the actual Y-axis bending stress and is calculated as follows: fby = My*12/Sy
B38
'Cc' is the column (compression) slenderness ratio separating elastic and inelastic buckling, and is calculated as follows: Cc = SQRT(2*p^2*E/Fy) where: E = modulus of elasticity for steel = 29,000 ksi
E38
'Fbx' is the allowable X-axis bending stress and is calculated as follows: For either compression or tension due to bending, when b/t <= 190/SQRT(Fy), H/B <= 6, and Lbx <= Lcx: Fbx = 0.66*Fy (Eqn. F3-1) when either 190/SQRT(Fy) < b/t <= 238/SQRT(Fy) or Lbx > Lcx: Fbx = 0.60*Fy (Eqn. F3-3) Note: for HSS sections and X-axis bending, b = B-3*t
H38
'Fby' is the allowable Y-axis bending stress and is calculated as follows: For either compression or tension due to bending, when b/t <= 190/SQRT(Fy), B/H <= 6, and Lby <= Lcy: Fby = 0.66*Fy (Eqn. F3-1) when either 190/SQRT(Fy) < b/t <= 238/SQRT(Fy) or Lby > Lcy: Fby = 0.60*Fy (Eqn. F3-3) Note: for HSS sections and Y-axis bending, b = H-3*t
B39
'fa' is the actual compression stress for an axially loaded compression member and is calculated as follows: fa = P/A 'ft' is the allowable tension stress for an axially loaded tension member and is calculated as follows: ft = P/A
E39
'Mrx' is the allowable resisting moment for X-axis bending, and is calculated as follows: Mrx = Fbx*Sx/12
H39
'Mry' is the allowable resisting moment for Y-axis bending, and is calculated as follows: Mry = Fby*Sy/12
B40
'Fa' is the allowable compression stress for an axially loaded compression member and is calculated as follows: For: K*L*12/r <= Cc = SQRT(2*p^2*E/Fy) use Eqn. E2-1: Fa = (1-(K*L*12/r)^2/(2*Cc)^2)*Fy/(5/3+3*(K*L*12/r)/(8*Cc)-(K*L*12/r)^3/(8*Cc^3)) For: K*L*12/r > Cc = SQRT(2*p^2*E/Fy) use Eqn. E2-2: Fa = 12*p^2*E/(23*(K*L*12/r)^2) Note: the larger value of either Kx*Lx*12/rx or Ky*Ly*12/ry is to be used in the equations above to determine 'Fa'. 'Ft' is the allowable tension stress for an axially loaded tension member and is calculated as follows: Ft = 0.60*Fy
B41
'Pa' is the allowable axial load for compression (or tension if applicable), and is calculated as follows: Pa = Fa*A
E43
F'ex is the Euler compressive buckling stress divided by factor of safety for the X-axis, and is calculated as follows: F'ex = 12*p^2*E/(23*(Kx*Lx*12/rx)^2)
H43
F'ey is the Euler compressive buckling stress divided by factor of safety for the Y-axis, and is calculated as follows: F'ey = 12*p^2*E/(23*(Ky*Ly*12/ry)^2)
B46
"S.R." is the Stress Ratio for the member which is calculated as follows: For members with combined axial compression and bending when fa/Fa > 0.15 per Eqn. H1-1: S.R. = fa/(ASIF*Fa) + Cmx*fbx/((1-fa/(ASIF*F'ex))*(ASIF*Fbx)) + Cmy*fby/((1-fa/(ASIF*F'ey))*(ASIF*Fby)) <= 1.0 and per Eqn. H1-2: S.R. = fa/(ASIF*0.60*Fy) + fbx/(ASIF*Fbx) + fby/(ASIF*Fby) <= 1.0 Note: program will display the results of the larger value obtained from either Eqn. H1-1 or Eqn. H1-2 For members with combined axial compression and bending when fa/Fa <= 0.15 per Eqn. H1-3: S.R. = fa/(ASIF*Fa) + fbx/(ASIF*Fbx) + fby/(ASIF*Fby) <= 1.0 For members with combined axial tension and bending: S.R. = ft/(ASIF*Ft) + fbx/(ASIF*Fbx) + fby/(ASIF*Fby) <= 1.0 Note: in this case the Stress Ratio computed from just the compressive bending stress(s) must also be checked.
"BEAMCOL9.xls" ProgramVersion 3.4
10 of 10 04/07/2023 23:16:02
STEEL BEAM AND COLUMN ANALYSIS / CODE CHECKPer AISC 9th Edition Manual (ASD)For Round HSS and Pipe Shapes
'P' is the applied axial load on the member, which may be either a compression or tension load. Sign convention: + = compression, - = tension
B14
'Mx(max)' is the maximum applied design flexural bending moment about the X-axis of the member. Note: the value input MUST BE positive (+).
B15
'Mx1' is the smaller X-axis bending moment at either of the ends of the unbraced length. Note: 'Mx1' should be input with a positive (+) value for single curvature and a negative (-) value for single curvature in the unbraced length (Lbx) being considered. 'Mx1' is used in AISC Eqn. F3-2 to determine the the critical unbraced length value, 'Lcx'
B16
'Mx2' is the larger X-axis bending moment at either of the ends of the unbraced length. Note: 'Mx2' is often = 'Mx(max)'. 'Mx2' is used in AISC Eqn. F3-2 to determine the the critical unbraced length value, 'Lcx'.
B17
'My(max)' is the maximum applied design flexural bending moment about the Y-axis of the member. Note: the value input MUST BE positive (+).
B18
'My1' is the smaller Y-axis bending moment at either of the ends of the unbraced length. Note: 'My1' should be input with a positive (+) value for single curvature and a negative (-) value for single curvature in the unbraced length (Lby) being considered. 'My1' is used in AISC Eqn. F3-2 to determine the the critical unbraced length value, 'Lcy'
B19
'My2' is the larger Y-axis bending moment at either of the ends of the unbraced length. Note: 'My2' is often = 'My(max)'. 'My2' is used in AISC Eqn. F3-2 to determine the the critical unbraced length value, 'Lcy'.
A23
Note: See section of this worksheet (to the right) for input data which may be used to determine the 'Kx' to be used for input here.
B23
'Kx' is the effective length factor about the X-axis for an axially loaded compression member. Typical values are as follows: Column End Conditions "Kx" Value (bottom-top) (Recommended) Fixed-Fixed 0.65 Fixed-Pinned 0.80 Fixed-Slider 1.2 Pinned-Pinned 1.0 Fixed-Free 2.1 Pinned-Slider 2.0 where: Fixed end denotes rotation fixed and translation fixed. Pinned end denotes rotation free and translation fixed. Slider end denotes rotation fixed and translation free. Free end denotes rotation free and translation free.
A24
Note: See section of this worksheet (to the right) for input data which may be used to determine the 'Ky' to be used for input here.
B24
'Ky' is the effective length factor about the Y-axis for an axially loaded compression member. Typical values are as follows: Column End Conditions "Ky" Value (bottom-top) (Recommended) Fixed-Fixed 0.65 Fixed-Pinned 0.80 Fixed-Slider 1.2 Pinned-Pinned 1.0 Fixed-Free 2.1 Pinned-Slider 2.0 where: Fixed end denotes rotation fixed and translation fixed. Pinned end denotes rotation free and translation fixed. Slider end denotes rotation fixed and translation free. Free end denotes rotation free and translation free.
B25
'Lx' is the actual unbraced length of member for column-type (axial compression) buckling about X-axis. Note: for input values of Lx <=1.0', this program will use a value =1.0'.
B26
'Ly' is the actual unbraced length of member for column-type (axial compression) buckling about Y-axis. Note: for input values of Ly <=1.0', this program will use a value =1.0'.
B27
'Lbx' is the actual unbraced length of the member for X-axis bending. Notes: 1. For most cases, 'Lbx' is equal to 'Ly'. 2. For cantilevers braced against twist only at the support, 'Lbx' may conservatively be taken as the actual length. 3. For input values of Lbx <=1.0', this program will use a value =1.0'.
B28
'Lby' is the actual unbraced length of the member for Y-axis bending. Notes: 1. For most cases, 'Lby' is equal to 'Lx'. 2. For cantilevers braced against twist only at the support, 'Lby' may conservatively be taken as the actual length. 3. For input values of Lby <=1.0', this program will use a value =1.0'.
A29
Note: See section of this worksheet (to the right) for input data which may be used to determine the 'Cmx' to be used for input here.
B29
'Cmx' is the coefficient applied to the X-axis bending term in the interaction equation (H1-1) and is dependent upon column curvature caused by applied moments. The 'Cmx' coefficient value is determined as follows: Category A: For compression members in frames subject to joint translation (sidesway), Cmx = 0.85. Category B: For rotationally restrained compression members in frames braced against joint translation (no sidesway) and not subject to transverse loading between their supports in the plane of bending, Cmx =0.6-0.4*(Mx1/Mx2) where: Mx1 = smaller X-axis bending moment at either of the ends of the unbraced length Mx2 = larger X-axis bending moment at either of the ends of the unbraced length Mx1/Mx2 = positive for reverse curvature bending (both have same signs) = negative for single curvature bending (both have opposite signs) Category C: For rotationally restrained compression members in frames braced against joint translation (no sidesway) and subject to transverse loading between their supports in the plane of bending, the following values of 'Cmx' are permitted : 1. For members whose ends are restrained against rotation in the plane of bending, Cmx = 0.85. 2. For members whose ends are unrestrained against rotation in the plane of bending, Cmx = 1.0.
A30
Note: See section of this worksheet (to the right) for input data which may be used to determine the 'Cmy' to be used for input here.
B30
'Cmy' is the coefficient applied to the Y-axis bending term in the interaction equation (H1-1) and is dependent upon column curvature caused by applied moments. The 'Cmy' coefficient value is determined as follows: Category A: For compression members in frames subject to joint translation (sidesway), Cmy = 0.85. Category B: For rotationally restrained compression members in frames braced against joint translation (no sidesway) and not subject to transverse loading between their supports in the plane of bending, Cmy =0.6-0.4*(My1/My2) where: My1 = smaller Y-axis bending moment at either of the ends of the unbraced length My2 = larger Y-axis bending moment at either of the ends of the unbraced length My1/My2 = positive for reverse curvature bending (both have same signs) = negative for single curvature bending (both have opposite signs) Category C: For rotationally restrained compression members in frames braced against joint translation (no sidesway) and subject to transverse loading between their supports in the plane of bending, the following values of 'Cmy' are permitted : 1. For members whose ends are restrained against rotation in the plane of bending, Cmy = 0.85. 2. For members whose ends are unrestrained against rotation in the plane of bending, Cmy = 1.0.
B31
'ASIF' is the Allowable Stress Increase Factor which is applied to all the allowable stresses and the Euler column buckling stresses used in the stress ratio calculation. Note: for example, a value of 1.333 can be used for the 'ASIF' for load combinations which include wind or seismic. Otherwise, use 1.0.
B36
The expression 'Kx*Lx/rx' is the effective slenderness ratio for members subjected to axial compression load. Note: 'Lx' is converted from feet to inches in the evaluation of the expression.
E36
'Lcx' is the maximum unbraced length of the member at which the allowable X-axis bending stress maybe taken at 0.66*Fy. Lcx = (1950+1200*Mx1/Mx2)*b/Fy ( Eqn. F3-2) Note: for Round HSS (pipe) sections, b = D
H36
'Lcy' is the maximum unbraced length of the member at which the allowable Y-axis bending stress maybe taken at 0.66*Fy. Lcy = (1950+1200*My1/My2)*b/Fy ( Eqn. F3-2) Note: for Round HSS (pipe) sections, b = D
B37
The expression 'Ky*Ly/ry' is the effective slenderness ratio for members subjected to axial compression load. Note: 'Ly' is converted from feet to inches in the evaluation of the expression.
E37
'fbx' is the actual X-axis bending stress and is calculated as follows: fbx = Mx*12/Sx
H37
'fby' is the actual Y-axis bending stress and is calculated as follows: fby = My*12/Sy
B38
'Cc' is the column (compression) slenderness ratio separating elastic and inelastic buckling, and is calculated as follows: Cc = SQRT(2*p^2*E/Fy) where: E = modulus of elasticity for steel = 29,000 ksi
E38
'Fbx' is the allowable X-axis bending stress and is calculated as follows: For either compression or tension due to bending, when D/t <= 3300/Fy and Lbx <= Lcx: Fbx = 0.66*Fy (Eqn. F3-1) when either 3300/Fy < D/t or Lbx > Lcx: Fbx = 0.60*Fy (Eqn. F3-3)
H38
'Fby' is the allowable Y-axis bending stress and is calculated as follows: For either compression or tension due to bending, when D/t <= 3300/Fy and Lby <= Lcy: Fby = 0.66*Fy (Eqn. F3-1) when either 3300/Fy < D/t or Lby > Lcy: Fby = 0.60*Fy (Eqn. F3-3)
B39
'fa' is the actual compression stress for an axially loaded compression member and is calculated as follows: fa = P/A 'ft' is the allowable tension stress for an axially loaded tension member and is calculated as follows: ft = P/A
E39
'Mrx' is the allowable resisting moment for X-axis bending, and is calculated as follows: Mrx = Fbx*Sx/12
H39
'Mry' is the allowable resisting moment for Y-axis bending, and is calculated as follows: Mry = Fby*Sy/12
B40
'Fa' is the allowable compression stress for an axially loaded compression member and is calculated as follows: For: K*L*12/r <= Cc = SQRT(2*p^2*E/Fy) use Eqn. E2-1: Fa = (1-(K*L*12/r)^2/(2*Cc)^2)*Fy/(5/3+3*(K*L*12/r)/(8*Cc)-(K*L*12/r)^3/(8*Cc^3)) For: K*L*12/r > Cc = SQRT(2*p^2*E/Fy) use Eqn. E2-2: Fa = 12*p^2*E/(23*(K*L*12/r)^2) Note: the larger value of either Kx*Lx*12/rx or Ky*Ly*12/ry is to be used in the equations above to determine 'Fa'. 'Ft' is the allowable tension stress for an axially loaded tension member and is calculated as follows: Ft = 0.60*Fy
B41
'Pa' is the allowable axial load for compression (or tension if applicable), and is calculated as follows: Pa = Fa*A
E43
F'ex is the Euler compressive buckling stress divided by factor of safety for the X-axis, and is calculated as follows: F'ex = 12*p^2*E/(23*(Kx*Lx*12/rx)^2)
H43
F'ey is the Euler compressive buckling stress divided by factor of safety for the Y-axis, and is calculated as follows: F'ey = 12*p^2*E/(23*(Ky*Ly*12/ry)^2)
B46
"S.R." is the Stress Ratio for the member which is calculated as follows: For members with combined axial compression and bending when fa/Fa > 0.15 per Eqn. H1-1: S.R. = fa/(ASIF*Fa) + Cmx*fbx/((1-fa/(ASIF*F'ex))*(ASIF*Fbx)) + Cmy*fby/((1-fa/(ASIF*F'ey))*(ASIF*Fby)) <= 1.0 and per Eqn. H1-2: S.R. = fa/(ASIF*0.60*Fy) + fbx/(ASIF*Fbx) + fby/(ASIF*Fby) <= 1.0 Note: program will display the results of the larger value obtained from either Eqn. H1-1 or Eqn. H1-2 For members with combined axial compression and bending when fa/Fa <= 0.15 per Eqn. H1-3: S.R. = fa/(ASIF*Fa) + fbx/(ASIF*Fbx) + fby/(ASIF*Fby) <= 1.0 For members with combined axial tension and bending: S.R. = ft/(ASIF*Ft) + fbx/(ASIF*Fbx) + fby/(ASIF*Fby) <= 1.0 Note: in this case the Stress Ratio computed from just the compressive bending stress(s) must also be checked.
