##### Document Text Contents

Page 1

Project Job Ref.

Section Sheet no./rev.

1

Calc. by

A

Date

1/11/2011

Chk'd by Date App'd by Date

STEEL COLUMN DESIGN (EN 1993-1-1)

In accordance with recommended values

TEDDS calculation version 1.0.04

y y

z

z

200

6

20

0

Column and loading details

Column details

Column section; SHS 200x200x6.0

System length for buckling about y axis; Ly = ;3200; mm

System length for buckling about z axis; Lz = ;3200; mm;

Column loading

Axial load; NEd = 14 kN; (Compression)

Moment about y axis at end 1; My,Ed1 = -40.5 kNm

Moment about y axis at end 2; My,Ed2 = 0.0 kNm

Single curvature bending about y axis

Moment about z axis at end 1; Mz,Ed1 = 1.0 kNm

Moment about z axis at end 2; Mz,Ed2 = 0.0 kNm

Single curvature bending about z axis

Shear force parallel to z axis; Vz,Ed = 1 kN

Shear force parallel to y axis; Vy,Ed = 0 kN

Material details

Steel grade; S275

Yield strength; fy = 275 N/mm2

Ultimate strength; fu = 410 N/mm2

Modulus of elasticity; E = 210 kN/mm2

Poisson’s ratio; = 0.3

Shear modulus; G = E / [2 (1 + )] = 80.8 kN/mm2

Buckling length for flexural buckling about y axis

End restraint factor; Ky = 1.000

Buckling length; Lcr_y = Ly Ky = 3200 mm

Buckling length for flexural buckling about z axis

End restraint factor; Kz = 1.000

Buckling length; Lcr_z = Lz Kz = 3200 mm

Page 2

Project Job Ref.

Section Sheet no./rev.

2

Calc. by

A

Date

1/11/2011

Chk'd by Date App'd by Date

Section classification

Web section classification (Table 5.2)

Coefficient depending on fy; = (235 N/mm2 / fy) = 0.924

Depth between fillets; cw = h - 3 t = 182.0 mm

Ratio of c/t; ratiow = cw / t = 30.33

Length of web taken by axial load; lw = min(NEd / (2 fy t), cw) =4.1 mm

For class 1 & 2 proportion in compression; = (cw/2 + lw/2) / cw = 0.511

Limit for class 1 web; Limit1w = (396 ) / (13 - 1) = ;64.84

The web is class 1

Flange section classification (Table 5.2)

Depth between fillets; cf = b - 3 t = 182.0 mm

Ratio of c/t; ratiof = cf / t = 30.33

Conservatively assume uniform compression in flange

Limit for class 1 flange; Limit1f = 33 = 30.51

Limit for class 2 flange; Limit2f = 38 = 35.13

Limit for class 3 flange; Limit3f = 42 = 38.83

The flange is class 1

Overall section classification

The section is class 1

Resistance of cross section (cl. 6.2)

Shear parallel to z axis (cl. 6.2.6)

Design shear force; Vz,Ed = 1.0 kN

Shear area; Avz = A h / (b + h) = ;2309; mm2

Plastic shear resistance; Vpl,z,Rd = Avz (fy / (3)) / M0 = 366.6 kN

PASS - Shear resistance parallel to z axis exceeds the design shear force

Vz,Ed <= 0.5 Vpl,z,Rd - No reduction in f y required for bending/axial force

Compression (cl. 6.2.4)

Design force; NEd = 14 kN

Design resistance; Nc,Rd = Npl,Rd = A fy / M0 = 1270 kN

PASS - The compression design resistance exceeds the design force

Bending about y axis (cl. 6.2.5)

Design bending moment; My,Ed = max(abs(My,Ed1), abs(My,Ed2)) = 40.5 kNm

Section modulus about y axis; Wy = Wpl.y = ;334.9; cm3

Design resistance; Mc,y,Rd = Wy fy / M0 = 92.1 kNm

PASS - The bending design resistance about the y axis exceeds the design moment

Bending about z axis (cl. 6.2.5)

Design bending moment; Mz,Ed = max(abs(Mz,Ed1), abs(Mz,Ed2)) = 1.0 kNm

Section modulus about z axis; Wz = Wpl.z = ;334.9; cm3

Design resistance; Mc,z,Rd = Wz fy / M0 = 92.1 kNm

PASS - The bending design resistance about the z axis 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 = 0.011

Ratio web area to gross area; aw = min(0.5, (A - 2 b t) / A) = 0.480

Page 3

Project Job Ref.

Section Sheet no./rev.

3

Calc. by

A

Date

1/11/2011

Chk'd by Date App'd by Date

Ratio flange area to gross area; af = min(0.5, (A - 2 h t) / A) = 0.480

Bending about y axis (cl. 6.2.9.1)

Design bending moment; My,Ed = max(abs(My,Ed1), abs(My,Ed2)) = 40.5 kNm

Plastic design resistance; Mpl,y,Rd = Wpl.y fy / M0 = 92.1 kNm

Modified design resistance about y axis; MN,y,Rd = Mpl,y,Rd min(1, (1 - n) / (1 - 0.5 aw)) = 92.1 kNm

PASS - Bending resistance about y axis in presence of axial load exceeds design moment

Bending about z axis (cl. 6.2.9.1)

Design bending moment; Mz,Ed = max(abs(Mz,Ed1), abs(Mz,Ed2)) = 1.0 kNm

Plastic design resistance; Mpl,z,Rd = Wpl.z fy / M0 = 92.1 kNm

Modified design resistance about z axis; MN,z,Rd = Mpl,z,Rd min(1, (1 - n) / (1 - 0.5 af)) = 92.1 kNm

PASS - Bending resistance about z axis in presence of axial load exceeds design moment

Biaxial bending

Exponent ; = min(6, 1.66 / (1 - 1.13 n2)) = ;1.66

Exponent ; = min(6, 1.66 / (1 - 1.13 n2)) = ;1.66

Section utilisation at end 1; URCS_1 = [abs(My,Ed1) / MN,y,Rd] + [abs(Mz,Ed1) / MN,z,Rd] = 0.257

Section utilisation at end 2; URCS_2 = [abs(My,Ed2) / MN,y,Rd] + [abs(Mz,Ed2) / MN,z,Rd] = 0.000

PASS - The cross-section resistance is adequate

Buckling resistance (cl. 6.3)

Yield strength for buckling resistance; fy = 275 N/mm2

Flexural buckling about y axis

Elastic critical buckling force; Ncr,y = 2 E Iy / Lcr_y2 = 5836 kN

Non-dimensional slenderness; y = (A fy / Ncr,y) = 0.466

Buckling curve (Table 6.2); a

Imperfection factor (Table 6.1); y = 0.21

Parameter ; y = 0.5 [1 + y ( y - 0.2) + y2] = 0.637

Reduction factor; y = min(1.0, 1 / [ y + ( y2 - y2)]) = 0.934

Design buckling resistance; Nb,y,Rd = y A fy / M1 = 1186.4 kN

PASS - The flexural buckling resistance about the y axis exceeds the design axial load

Flexural buckling about z axis

Elastic critical buckling force; Ncr,z = 2 E Iz / Lcr_z2 = 5836 kN

Non-dimensional slenderness; z = (A fy / Ncr,z) = 0.466

Buckling curve (Table 6.2); a

Imperfection factor (Table 6.1); z = 0.21

Parameter ; z = 0.5 [1 + z ( z - 0.2) + z2] = 0.637

Reduction factor; z = min(1.0, 1 / [ z + ( z2 - z2)]) = 0.934

Design buckling resistance; Nb,z,Rd = z A fy / M1 = 1186.4 kN

PASS - The flexural buckling resistance about the z axis exceeds the design axial load

Minimum buckling resistance

Minimum buckling resistance; Nb,Rd = min(Nb,y,Rd, Nb,z,Rd) = 1186.4 kN

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 = 92.1 kNm

Project Job Ref.

Section Sheet no./rev.

1

Calc. by

A

Date

1/11/2011

Chk'd by Date App'd by Date

STEEL COLUMN DESIGN (EN 1993-1-1)

In accordance with recommended values

TEDDS calculation version 1.0.04

y y

z

z

200

6

20

0

Column and loading details

Column details

Column section; SHS 200x200x6.0

System length for buckling about y axis; Ly = ;3200; mm

System length for buckling about z axis; Lz = ;3200; mm;

Column loading

Axial load; NEd = 14 kN; (Compression)

Moment about y axis at end 1; My,Ed1 = -40.5 kNm

Moment about y axis at end 2; My,Ed2 = 0.0 kNm

Single curvature bending about y axis

Moment about z axis at end 1; Mz,Ed1 = 1.0 kNm

Moment about z axis at end 2; Mz,Ed2 = 0.0 kNm

Single curvature bending about z axis

Shear force parallel to z axis; Vz,Ed = 1 kN

Shear force parallel to y axis; Vy,Ed = 0 kN

Material details

Steel grade; S275

Yield strength; fy = 275 N/mm2

Ultimate strength; fu = 410 N/mm2

Modulus of elasticity; E = 210 kN/mm2

Poisson’s ratio; = 0.3

Shear modulus; G = E / [2 (1 + )] = 80.8 kN/mm2

Buckling length for flexural buckling about y axis

End restraint factor; Ky = 1.000

Buckling length; Lcr_y = Ly Ky = 3200 mm

Buckling length for flexural buckling about z axis

End restraint factor; Kz = 1.000

Buckling length; Lcr_z = Lz Kz = 3200 mm

Page 2

Project Job Ref.

Section Sheet no./rev.

2

Calc. by

A

Date

1/11/2011

Chk'd by Date App'd by Date

Section classification

Web section classification (Table 5.2)

Coefficient depending on fy; = (235 N/mm2 / fy) = 0.924

Depth between fillets; cw = h - 3 t = 182.0 mm

Ratio of c/t; ratiow = cw / t = 30.33

Length of web taken by axial load; lw = min(NEd / (2 fy t), cw) =4.1 mm

For class 1 & 2 proportion in compression; = (cw/2 + lw/2) / cw = 0.511

Limit for class 1 web; Limit1w = (396 ) / (13 - 1) = ;64.84

The web is class 1

Flange section classification (Table 5.2)

Depth between fillets; cf = b - 3 t = 182.0 mm

Ratio of c/t; ratiof = cf / t = 30.33

Conservatively assume uniform compression in flange

Limit for class 1 flange; Limit1f = 33 = 30.51

Limit for class 2 flange; Limit2f = 38 = 35.13

Limit for class 3 flange; Limit3f = 42 = 38.83

The flange is class 1

Overall section classification

The section is class 1

Resistance of cross section (cl. 6.2)

Shear parallel to z axis (cl. 6.2.6)

Design shear force; Vz,Ed = 1.0 kN

Shear area; Avz = A h / (b + h) = ;2309; mm2

Plastic shear resistance; Vpl,z,Rd = Avz (fy / (3)) / M0 = 366.6 kN

PASS - Shear resistance parallel to z axis exceeds the design shear force

Vz,Ed <= 0.5 Vpl,z,Rd - No reduction in f y required for bending/axial force

Compression (cl. 6.2.4)

Design force; NEd = 14 kN

Design resistance; Nc,Rd = Npl,Rd = A fy / M0 = 1270 kN

PASS - The compression design resistance exceeds the design force

Bending about y axis (cl. 6.2.5)

Design bending moment; My,Ed = max(abs(My,Ed1), abs(My,Ed2)) = 40.5 kNm

Section modulus about y axis; Wy = Wpl.y = ;334.9; cm3

Design resistance; Mc,y,Rd = Wy fy / M0 = 92.1 kNm

PASS - The bending design resistance about the y axis exceeds the design moment

Bending about z axis (cl. 6.2.5)

Design bending moment; Mz,Ed = max(abs(Mz,Ed1), abs(Mz,Ed2)) = 1.0 kNm

Section modulus about z axis; Wz = Wpl.z = ;334.9; cm3

Design resistance; Mc,z,Rd = Wz fy / M0 = 92.1 kNm

PASS - The bending design resistance about the z axis 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 = 0.011

Ratio web area to gross area; aw = min(0.5, (A - 2 b t) / A) = 0.480

Page 3

Project Job Ref.

Section Sheet no./rev.

3

Calc. by

A

Date

1/11/2011

Chk'd by Date App'd by Date

Ratio flange area to gross area; af = min(0.5, (A - 2 h t) / A) = 0.480

Bending about y axis (cl. 6.2.9.1)

Design bending moment; My,Ed = max(abs(My,Ed1), abs(My,Ed2)) = 40.5 kNm

Plastic design resistance; Mpl,y,Rd = Wpl.y fy / M0 = 92.1 kNm

Modified design resistance about y axis; MN,y,Rd = Mpl,y,Rd min(1, (1 - n) / (1 - 0.5 aw)) = 92.1 kNm

PASS - Bending resistance about y axis in presence of axial load exceeds design moment

Bending about z axis (cl. 6.2.9.1)

Design bending moment; Mz,Ed = max(abs(Mz,Ed1), abs(Mz,Ed2)) = 1.0 kNm

Plastic design resistance; Mpl,z,Rd = Wpl.z fy / M0 = 92.1 kNm

Modified design resistance about z axis; MN,z,Rd = Mpl,z,Rd min(1, (1 - n) / (1 - 0.5 af)) = 92.1 kNm

PASS - Bending resistance about z axis in presence of axial load exceeds design moment

Biaxial bending

Exponent ; = min(6, 1.66 / (1 - 1.13 n2)) = ;1.66

Exponent ; = min(6, 1.66 / (1 - 1.13 n2)) = ;1.66

Section utilisation at end 1; URCS_1 = [abs(My,Ed1) / MN,y,Rd] + [abs(Mz,Ed1) / MN,z,Rd] = 0.257

Section utilisation at end 2; URCS_2 = [abs(My,Ed2) / MN,y,Rd] + [abs(Mz,Ed2) / MN,z,Rd] = 0.000

PASS - The cross-section resistance is adequate

Buckling resistance (cl. 6.3)

Yield strength for buckling resistance; fy = 275 N/mm2

Flexural buckling about y axis

Elastic critical buckling force; Ncr,y = 2 E Iy / Lcr_y2 = 5836 kN

Non-dimensional slenderness; y = (A fy / Ncr,y) = 0.466

Buckling curve (Table 6.2); a

Imperfection factor (Table 6.1); y = 0.21

Parameter ; y = 0.5 [1 + y ( y - 0.2) + y2] = 0.637

Reduction factor; y = min(1.0, 1 / [ y + ( y2 - y2)]) = 0.934

Design buckling resistance; Nb,y,Rd = y A fy / M1 = 1186.4 kN

PASS - The flexural buckling resistance about the y axis exceeds the design axial load

Flexural buckling about z axis

Elastic critical buckling force; Ncr,z = 2 E Iz / Lcr_z2 = 5836 kN

Non-dimensional slenderness; z = (A fy / Ncr,z) = 0.466

Buckling curve (Table 6.2); a

Imperfection factor (Table 6.1); z = 0.21

Parameter ; z = 0.5 [1 + z ( z - 0.2) + z2] = 0.637

Reduction factor; z = min(1.0, 1 / [ z + ( z2 - z2)]) = 0.934

Design buckling resistance; Nb,z,Rd = z A fy / M1 = 1186.4 kN

PASS - The flexural buckling resistance about the z axis exceeds the design axial load

Minimum buckling resistance

Minimum buckling resistance; Nb,Rd = min(Nb,y,Rd, Nb,z,Rd) = 1186.4 kN

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 = 92.1 kNm