Project Job Ref.
Section Sheet no./rev.
2
Calc. by Date Chk'd by Date App'd by Date
30-Nov-24
STEEL COLUMN DESIGN
In accordance with EN1993-1-1:2005 incorporating Corrigenda February 2006 and April 2009 and the UK national annex
Tedds calculation version 1.1.04
Design summary
Description Unit Provided Required Utilisation Result
Axial compression kN 539 150 0.278 PASS
Bending resistance (y-y) kNm 19 9 0.440 PASS
Bending resistance (z-z) kNm 19 9 0.440 PASS
Biaxial bending 0.248 PASS
Buckling in compression kN 357 150 0.420 PASS
Buckling in bending kNm 19 9 0.440 PASS
Combined buckling 0.984 PASS
Partial factors - Section 6.1
Resistance of cross-sections; M0 = 1
Resistance of members to instability; M1 = 1
Resistance of cross-sections in tension to fracture; M2 = 1.1
SHS 100x100x4.0 (Tata Steel Celsius)
Section depth, h, 100 mm
Section breadth, b, 100 mm
Mass of section, Mass, 11.9 kg/m
Section thickness, t, 4 mm
Area of section, A, 1519 mm2
Radius of gyration about y-axis, iy, 39.067 mm
Radius of gyration about z-axis, iz, 39.067 mm
Elastic section modulus about y-axis, Wel.y, 46363 mm3
100
Elastic section modulus about z-axis, Wel.z, 46363 mm3
Plastic section modulus about y-axis, Wpl.y, 54444 mm3
Plastic section modulus about z-axis, Wpl.z, 54444 mm3
4 Second moment of area about y-axis, Iy, 2318134 mm4
Second moment of area about z-axis, Iz, 2318134 mm4
100
Column details
Column section SHS 100x100x4.0
Steel grade S355
Yield strength fy = 355 N/mm2
Ultimate strength fu = 470 N/mm2
Modulus of elasticity E = 210 kN/mm2
Poisson’s ratio = 0.3
Shear modulus G = E / [2 (1 + )] = 80.8 kN/mm2
Column geometry
System length for buckling - Major axis Ly = 2700 mm
System length for buckling - Minor axis Lz = 2700 mm
The column is not part of a sway frame in the direction of the minor axis
The column is not part of a sway frame in the direction of the major axis
Project Job Ref.
Section Sheet no./rev.
3
Calc. by Date Chk'd by Date App'd by Date
30-Nov-24
Column loading
Axial load NEd = 150 kN (Compression)
Major axis moment at end 1 - Bottom My,Ed1 = 0.0 kNm
Major axis moment at end 2 - Top My,Ed2 = -8.5 kNm
Major axis bending is single curvature
Minor axis moment at end 1 - Bottom Mz,Ed1 = 8.5 kNm
Minor axis moment at end 2 - Top Mz,Ed2 = 0.0 kNm
Minor axis bending is single curvature
Major axis shear force Vy,Ed = 0 kN
Minor axis shear force Vz,Ed = 0 kN
Buckling length for flexural buckling - Major axis
End restraint factor; Ky = 1.000
Buckling length; Lcr_y = Ly Ky = 3000 mm
Buckling length for flexural buckling - Minor axis
End restraint factor; Kz = 1.000
Buckling length; Lcr_z = Lz Kz = 3000 mm
Web section classification (Table 5.2)
Coefficient depending on fy; = (235 N/mm2 / fy) = 0.814
Depth between fillets; cw = h - 3 t = 88.0 mm
Ratio of c/t; ratiow = cw / t = 22.00
Length of web taken by axial load; lw = min(NEd / (2 fy t), cw) =52.8 mm
For class 1 & 2 proportion in compression; = (cw/2 + lw/2) / cw = 0.800
Limit for class 1 web; Limit1w = (396 ) / (13 - 1) = ;34.27
The web is class 1
Flange section classification (Table 5.2)
Depth between fillets; cf = b - 3 t = 88.0 mm
Ratio of c/t; ratiof = cf / t = 22.00
Conservatively assume uniform compression in flange
Limit for class 1 flange; Limit1f = 33 = 26.85
Limit for class 2 flange; Limit2f = 38 = 30.92
Limit for class 3 flange; Limit3f = 42 = 34.17
The flange is class 1
Overall section classification
The section is class 1
Resistance of cross section (cl. 6.2)
Compression (cl. 6.2.4)
Design force; NEd = 150 kN
Design resistance; Nc,Rd = Npl,Rd = A fy / M0 = 539 kN
NEd / Nc,Rd = 0.278
PASS - The compression design resistance exceeds the design force
Bending - Major axis (cl. 6.2.5)
Design bending moment; My,Ed = max(abs(My,Ed1), abs(My,Ed2)) = 8.5 kNm
Project Job Ref.
Section Sheet no./rev.
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Calc. by Date Chk'd by Date App'd by Date
30-Nov-24
Section modulus; Wy = Wpl.y = ;54.4; cm3
Design resistance; Mc,y,Rd = Wy fy / M0 = 19.3 kNm
My,Ed / Mc,y,Rd = 0.44
PASS - The bending design resistance exceeds the design moment
Bending - Major axis(cl. 6.2.5)
Design bending moment; Mz,Ed = max(abs(Mz,Ed1), abs(Mz,Ed2)) = 8.5 kNm
Section modulus; Wz = Wpl.z = ;54.4; cm3
Design resistance; Mc,z,Rd = Wz fy / M0 = 19.3 kNm
Mz,Ed / Mc,z,Rd = 0.44
PASS - The bending design resistance exceeds the design moment
Combined bending and axial force (cl. 6.2.9)
Ratio design axial to design plastic resistance; n = abs(NEd) / Npl,Rd = 0.278
Ratio web area to gross area; aw = min(0.5, (A - 2 b t) / A) = 0.473
Ratio flange area to gross area; af = min(0.5, (A - 2 h t) / A) = 0.473
Bending - Major axis (cl. 6.2.9.1)
Design bending moment; My,Ed = max(abs(My,Ed1), abs(My,Ed2)) = 8.5 kNm
Plastic design resistance; Mpl,y,Rd = Wpl.y fy / M0 = 19.3 kNm
Modified design resistance; MN,y,Rd = Mpl,y,Rd min(1, (1 - n) / (1 - 0.5 aw)) = 18.3 kNm
My,Ed / MN,y,Rd = 0.465
PASS - Bending resistance in presence of axial load exceeds design moment
Bending - Minor axis (cl. 6.2.9.1)
Design bending moment; Mz,Ed = max(abs(Mz,Ed1), abs(Mz,Ed2)) = 8.5 kNm
Plastic design resistance; Mpl,z,Rd = Wpl.z fy / M0 = 19.3 kNm
Modified design resistance; MN,z,Rd = Mpl,z,Rd min(1, (1 - n) / (1 - 0.5 af)) = 18.3 kNm
Mz,Ed / MN,z,Rd = 0.465
PASS - Bending resistance in presence of axial load exceeds design moment
Biaxial bending
Exponent ; = min(6, 1.66 / (1 - 1.13 n2)) = ;1.82
Exponent ; = min(6, 1.66 / (1 - 1.13 n2)) = ;1.82
Section utilisation at end 1; URCS_1 = [abs(My,Ed1) / MN,y,Rd] + [abs(Mz,Ed1) / MN,z,Rd] = 0.248
Section utilisation at end 2; URCS_2 = [abs(My,Ed2) / MN,y,Rd] + [abs(Mz,Ed2) / MN,z,Rd] = 0.248
PASS - The cross-section resistance is adequate
Buckling resistance (cl. 6.3)
Yield strength for buckling resistance; fy = 355 N/mm2
Flexural buckling - Major axis
Elastic critical buckling force; Ncr,y = 2 E Iy / Lcr_y2 = 534 kN
Non-dimensional slenderness; y = (A fy / Ncr,y) = 1.005
Buckling curve (Table 6.2); a
Imperfection factor (Table 6.1); y = 0.21
Parameter ; y = 0.5 [1 + y (y - 0.2) +y2] = 1.090
Reduction factor; y = min(1.0, 1 / [y + (y2 -y2)]) = 0.662
Design buckling resistance; Nb,y,Rd = y A fy / M1 = 357.0 kN
Project Job Ref.
Section Sheet no./rev.
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Calc. by Date Chk'd by Date App'd by Date
30-Nov-24
NEd / Nb,y,Rd = 0.42
PASS - The flexural buckling resistance exceeds the design axial load
Flexural buckling - Minor axis
Elastic critical buckling force; Ncr,z = 2 E Iz / Lcr_z2 = 534 kN
Non-dimensional slenderness; z = (A fy / Ncr,z) = 1.005
Buckling curve (Table 6.2); a
Imperfection factor (Table 6.1); z = 0.21
Parameter ; z = 0.5 [1 + z (z - 0.2) +z2] = 1.090
Reduction factor; z = min(1.0, 1 / [z + (z2 -z2)]) = 0.662
Design buckling resistance; Nb,z,Rd = z A fy / M1 = 357.0 kN
NEd / Nb,z,Rd = 0.42
PASS - The flexural buckling resistance exceeds the design axial load
Minimum buckling resistance
Minimum buckling resistance; Nb,Rd = min(Nb,y,Rd, Nb,z,Rd) = 357.0 kN
NEd / Nb,Rd = 0.42
PASS - The axial load buckling resistance exceeds the design axial load
Buckling resistance moment (cl.6.3.2.1)
Square hollow section not subject to lateral torsional buckling therefore:-
Reduction factor; LT = 1.0
Design buckling resistance moment; Mb,Rd = LT Wy fy / M1 = 19.3 kNm
Design bending moment; My,Ed = max(abs(My,Ed1), abs(My,Ed2)) = 8.5 kNm
My,Ed / Mb,Rd = 0.44
PASS - The design buckling resistance moment exceeds the maximum design moment
Combined bending and axial compression (cl. 6.3.3)
Characteristic resistance to normal force; NRk = A fy = 539 kN
Characteristic moment resistance - Major axis; My,Rk = Wpl.y fy = ;19.3; kNm
Characteristic moment resistance - Minor axis; Mz,Rk = Wpl.z fy = ;19.3; kNm
y = if(abs(My,Ed1)<=abs(My,Ed2), My,Ed1 / if(My,Ed2>=0 kNm,max(My,Ed2,0.0001 kNm),My,Ed2), My,Ed2 / if(My,Ed1>=0
kNm,max(My,Ed1,0.0001 kNm),My,Ed1)) = 0.000
Moment distribution factor - Major axis; y = My,Ed1 / My,Ed2 = ;0.000
Moment factor - Major axis; Cmy = max(0.4, 0.6 + 0.4 y) = 0.600
Moment distribution factor - Minor axis; z = Mz,Ed2 / Mz,Ed1 = ;0.000
Moment factor - Minor axis; Cmz = max(0.4, 0.6 + 0.4 z) = 0.600
Moment distribution factor for LTB; LT = My,Ed1 / My,Ed2 = ;0.000
Moment factor for LTB; CmLT = max(0.4, 0.6 + 0.4 LT) = 0.600
Interaction factor kyy; kyy = Cmy [1 + min(0.8,y - 0.2) NEd / (y NRk / M1)] = 0.802
Interaction factor kzy; kzy = 0.6 kyy = 0.481
Interaction factor kzz; kzz = Cmz [1 + min(0.8,z - 0.2) NEd / (z NRk / M1)] = ;0.802
Interaction factor kyz; kyz = 0.6 kzz = 0.481
Section utilisation; URB_1 = NEd / (y NRk / M1) + kyy My,Ed / (LT My,Rk / M1) + kyz Mz,Ed / (Mz,Rk / M1)
URB_1 = 0.984
URB_2 = NEd / (z NRk / M1) + kzy My,Ed / (LT My,Rk / M1) + kzz Mz,Ed / (Mz,Rk / M1)
Project Job Ref.
Section Sheet no./rev.
6
Calc. by Date Chk'd by Date App'd by Date
30-Nov-24
STEEL BEAM ANALYSIS & DESIGN (EN1993-1-1:2005)
In accordance with EN1993-1-1:2005 incorporating Corrigenda February 2006 and April 2009 and the UK national annex
TEDDS calculation version 3.0.14
Load Envelope - Combination 1
2.290
0.0
mm 2659
A 1 B
Bending Moment Envelope
kNm
0.0
2.024
2.0
mm 2659
A 1 B
Shear Force Envelope
kN
3.0
3.045
0.0
-3.045
-3.0
mm 2659
A 1 B
Support conditions
Support A Vertically restrained
Rotationally free
Support B Vertically restrained
Rotationally free
Applied loading
Beam loads Permanent self weight of beam 1
Permanent full UDL 1.25 kN/m
Load combinations
Load combination 1 Support A Permanent 1.35
Variable 1.50
Permanent 1.35
Variable 1.50
Support B Permanent 1.35
Project Job Ref.
Section Sheet no./rev.
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Calc. by Date Chk'd by Date App'd by Date
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Variable 1.50
Analysis results
Maximum moment; Mmax = 2 kNm; Mmin = 0 kNm
Maximum moment span 1 segment 1; Ms1_seg1_max = 2 kNm; Ms1_seg1_min = 0 kNm
Maximum moment span 1 segment 2; Ms1_seg2_max = 0.5 kNm; Ms1_seg2_min = 0 kNm
Maximum moment span 1 segment 3; Ms1_seg3_max = 0 kNm; Ms1_seg3_min = 0 kNm
Maximum shear; Vmax = 3 kN; Vmin = -3 kN
Maximum shear span 1 segment 1; Vs1_seg1_max = 3 kN; Vs1_seg1_min = -2.7 kN
Maximum shear span 1 segment 2; Vs1_seg2_max = 0 kN; Vs1_seg2_min = -3 kN
Maximum shear span 1 segment 3; Vs1_seg3_max = 0 kN; Vs1_seg3_min = 0 kN
Deflection segment 4; max = 0 mm; min = 0 mm
Maximum reaction at support A; RA_max = 3 kN; RA_min = 3 kN
Unfactored permanent load reaction at support A; RA_Permanent = 2.3 kN
Maximum reaction at support B; RB_max = 3 kN; RB_min = 3 kN
Unfactored permanent load reaction at support B; RB_Permanent = 2.3 kN
Section details
Section type; PFC 300x100x46 (BS4-1)
Steel grade; S275
EN 10025-2:2004 - Hot rolled products of structural steels
Nominal thickness of element; t = max(tf, tw) = 16.5 mm
Nominal yield strength; fy = 265 N/mm2
Nominal ultimate tensile strength; fu = 410 N/mm2
Modulus of elasticity; E = 210000 N/mm2
16.5
300
9
16.5
100
Partial factors - Section 6.1
Resistance of cross-sections; M0 = 1.00
Resistance of members to instability; M1 = 1.00
Resistance of tensile members to fracture; M2 = 1.10
Lateral restraint
Span 1 has lateral restraint at supports plus 2500 mm and 5500 mm
Project Job Ref.
Section Sheet no./rev.
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Calc. by Date Chk'd by Date App'd by Date
30-Nov-24
Effective length factors
Effective length factor in major axis; Ky = 1.000
Effective length factor in minor axis; Kz = 1.000
Effective length factor for torsion; KLT.A = 1.000;
KLT.B = 1.000;
Classification of cross sections - Section 5.5
= [235 N/mm2 / fy] = 0.94
Internal compression parts subject to bending - Table 5.2 (sheet 1 of 3)
Width of section; c = d = 237 mm
c / tw = 28.0 <= 72 ; Class 1
Outstand flanges - Table 5.2 (sheet 2 of 3)
Width of section; c = b - tw - r1 = 76 mm
c / tf = 4.9 <= 9 ; Class 1
Section is class 1
Check shear - Section 6.2.6
Height of web; hw = h - 2 tf = 267 mm
Shear area factor; = 1.000
hw / tw < 72 /
Shear buckling resistance can be ignored
Design shear force; VEd = max(abs(Vmax), abs(Vmin)) = 3 kN
Shear area - cl 6.2.6(3); Av = A - 2 b tf + (tw + r1) tf = 2896 mm2
Design shear resistance - cl 6.2.6(2); Vc,Rd = Vpl,Rd = Av (fy / [3]) / M0 = 443 kN
PASS - Design shear resistance exceeds design shear force
Check bending moment at span 1 segment 1 major (y-y) axis - Section 6.2.5
Design bending moment; MEd = max(abs(Ms1_seg1_max), abs(Ms1_seg1_min)) = 2 kNm
Design bending resistance moment - eq 6.13; Mc,Rd = Mpl,Rd = Wpl.y fy / M0 = 169.8 kNm
Slenderness ratio for lateral torsional buckling
Correction factor - Table 6.6; kc = 0.945
C1 = 1 / kc2 = 1.12
Curvature factor; g = [1 - (Iz / Iy)] = 0.965
Poissons ratio; = 0.3
Shear modulus; G = E / [2 (1 + )] = 80769 N/mm2
Unrestrained length; L = 1.0 Ls1_seg1 = 2500 mm
Elastic critical buckling moment; Mcr = C1 2 E Iz / (L2 g) [Iw / Iz + L2 G It / (2 E Iz)] = 378.3
kNm
Slenderness ratio for lateral torsional buckling; LT = (Wpl.y fy / Mcr) = 0.67
Limiting slenderness ratio; LT,0 = 0.4
LT > LT,0 - Lateral torsional buckling cannot be ignored
Design resistance for buckling - Section 6.3.2.1
Buckling curve - Table 6.5; d
Imperfection factor - Table 6.3; LT = 0.76
Project Job Ref.
Section Sheet no./rev.
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Calc. by Date Chk'd by Date App'd by Date
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Correction factor for rolled sections; = 0.75
LTB reduction determination factor; LT = 0.5 [1 + LT (LT -LT,0) + LT2] = 0.771
LTB reduction factor - eq 6.57; LT = min(1 / [LT + (LT2 - LT2)], 1, 1 /LT2) = 0.782
Modification factor; f = min(1 - 0.5 (1 - kc) [1 - 2 (LT - 0.8)2], 1) = 0.973
Modified LTB reduction factor - eq 6.58; LT,mod = min(LT / f, 1) = 0.803
Design buckling resistance moment - eq 6.55; Mb,Rd = LT,mod Wpl.y fy / M1 = 136.4 kNm
PASS - Design buckling resistance moment exceeds design bending moment
Check vertical deflection - Section 7.2.1
Consider deflection due to variable loads
Limiting deflection;; lim = Ls1 / 360 = 7.4 mm
Maximum deflection span 1; = max(abs(max), abs(min)) = 0 mm
PASS - Maximum deflection does not exceed deflection limit
