0.39 inch 10 mm l/300, deflection limitations under Design Serviceability Condition as per Topside Structural Design Basis ###
I-ET-3010.0H-1400-140-TF8-001, Cl. 9.2.1 ###
▲act > ▲all RE DESIGN ###
###
kN/m2
N/mm2
N/mm2 N/mm2
N/mm2 N/mm2
N/mm2
N/mm2
N/mm2 N/mm2
Pd =
▲act=
▲all =
B13
'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'.
G21
'fbx' is the actual X-axis bending stress and is calculated as follows: fbx = Mx*12/Sx
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.
G36
'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
L36
'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.
G37
'fbx' is the actual X-axis bending stress and is calculated as follows: fbx = Mx*12/Sx
L37
'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
G38
'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
L38
'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
G39
'Mrx' is the allowable resisting moment for X-axis bending, and is calculated as follows: Mrx = Fbx*Sx/12
L39
'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
G43
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)
L43
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.
I-RL-3010.0H-1428-140-SMN-001_A
SHEET 60 OF 64
11 ANNEX II.B – RAISED FLOOR COLUMN DESIGN
(As Per AISC 9th Edition ASD Manual)
Input Data:
Member Size: Member Properties: Y Select: HSS4x4x1/4 H = 4.000 in.
0.26 inch 6.67 mm l/180, deflection limitations under Design Serviceability Condition as per Topside Structural Design BasisI-ET-3010.0H-1400-140-TF8-001, Cl. 9.2.1
▲act < ▲all SAFE
kN/m2
N/mm2
N/mm2 N/mm2
N/mm2 N/mm2
N/mm2
N/mm2
N/mm2 N/mm2
Pd =
▲act=
▲all =
B13
'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'.
G21
'fbx' is the actual X-axis bending stress and is calculated as follows: fbx = Mx*12/Sx
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.
G36
'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
L36
'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.
G37
'fbx' is the actual X-axis bending stress and is calculated as follows: fbx = Mx*12/Sx
L37
'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
G38
'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
L38
'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
G39
'Mrx' is the allowable resisting moment for X-axis bending, and is calculated as follows: Mrx = Fbx*Sx/12
L39
'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
G43
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)
L43
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.
B51
'P' is the applied axial load on the member, which may be either a compression or tension load. Sign convention: + = compression, - = tension
0.39 inch 10 mm l/300, deflection limitations under Design Serviceability Condition as per Topside Structural Design Basis ###
I-ET-3010.0H-1400-140-TF8-001, Cl. 9.2.1 ###
▲act < ▲all SAFE ###
###
kN/m2
N/mm2
N/mm2 N/mm2
N/mm2 N/mm2
N/mm2
N/mm2
N/mm2 N/mm2
Pd =
▲act=
▲all =
B13
'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'.
G21
'fbx' is the actual X-axis bending stress and is calculated as follows: fbx = Mx*12/Sx
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.
G36
'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
L36
'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.
G37
'fbx' is the actual X-axis bending stress and is calculated as follows: fbx = Mx*12/Sx
L37
'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
G38
'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
L38
'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
G39
'Mrx' is the allowable resisting moment for X-axis bending, and is calculated as follows: Mrx = Fbx*Sx/12
L39
'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
G43
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)
L43
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.
