1. Project information
Calculation report
| Date | 31/10/2026 |
|---|
2. Overview of the structure
The structure with the numbers of the nodes (n), members (m) and supports (S), and the length of each member (mm).
| Sections and materials | Members |
|---|---|
| HEA180 · S235 | 1 |
2 nodes, 1 members · consequence class CC1, new build · design code Eurocode · Z is the vertical axis · units: kN, kNm, mm.
3. Summary of the results
| Quantity | Max. value | Combination | Where |
|---|---|---|---|
| Moment My (strong axis) | 31.8 kNm | ULS 6.10b (CC1 new) | member b, x = 2075 mm |
| Normal force N (− compression) | 0.0 kN | ULS 6.10a (CC1 new) | – |
| Shear force Vz (strong axis) | 30.7 kN | ULS 6.10b (CC1 new) | member b, x = 0 mm |
| Vertical reaction | 30.7 kN | ULS 6.10b (CC1 new) | node A |
| Displacement (max., incl. between nodes) | 8.38 mm | SLS char. | member b, x = 2075 mm |
| Deflection of a member (relative to chord) | 8.38 mm (L/495) | SLS char. | member b |
Moments, forces and reactions: the governing ULS combination. Displacement: the governing SLS combination (the ULS combinations if there is no SLS combination).
Highest unity check: UC 0.50 in member b (HEA180): deflection (SLS).
4. Nodes, members and supports
Nodes
| Node | x (mm) | y (mm) | z (mm) | Support |
|---|---|---|---|---|
| A | 0 | 0 | 0 | S1 |
| B | 4150 | 0 | 0 | S2 |
Members
| Member | Nodes | L (mm) | Section | Material | Remarks |
|---|---|---|---|---|---|
| b | A – B | 4150 | HEA180 | S235 |
Supports
| Support | Node | Restraint | Springs |
|---|---|---|---|
| S1 | A | pinned (translations fixed) | |
| S2 | B | pinned (translations fixed) |
5. Loads
Loads: Permanent (G)
| Type | On | Value |
|---|---|---|
| Line load | member b | X 0.00, Y 0.00, Z -2.08 kN/m |
Loads: Variable (Q)
| Type | On | Value |
|---|---|---|
| Line load | member b | X 0.00, Y 0.00, Z -9.00 kN/m |
The self weight of members, walls and slabs is automatic (case SW) and is not drawn. Loads are shown as in the model; combination factors are in the table at the end.
6. Load combinations
Consequence class CC1, new build.
| Combination | Kind | SW | G | Q |
|---|---|---|---|---|
| ULS 6.10a (CC1 new) | ULS | 1.22 | 1.22 | 0.54 |
| ULS 6.10b (CC1 new) | ULS | 1.08 | 1.08 | 1.35 |
| SLS char. | SLS | 1 | 1 | 1 |
| ULS 0.9·G favourable (CC1 new) | ULS | 0.9 | 0.9 | 0 |
| ULS 0.9·G + Variable (Q) (CC1 new) | ULS | 0.9 | 0.9 | 1.35 |
| ULS γG·G permanent only (CC1 new) | ULS | 1.22 | 1.22 | 0 |
| ULS 0.9·G + ψ0 variable (CC1 new) | ULS | 0.9 | 0.9 | 0.54 |
| SLS permanent (G) | SLS | 1 | 1 | 0 |
| SLS quasi-permanent (G + ψ2·Q) | SLS | 1 | 1 | 0.3 |
| SLS frequent (G + ψ1·Q) | SLS | 1 | 1 | 0.5 |
SW = Self weight; G = Permanent (G); Q = Variable (Q). SW = self weight.
7. Moments, normal forces and shear forces
Bending moment
Maximum 31.8 kNm in member b, x = 2075 mm. (ULS 6.10b (CC1 new))
Normal force
Maximum 0.0 kN (− compression) in member , x = 0 mm. (ULS 6.10a (CC1 new))
Shear force
Maximum 30.7 kN in member b, x = 0 mm. (ULS 6.10b (CC1 new))
Largest section forces per member — ULS 6.10b (CC1 new)
| Member | L (mm) | |M| max (kNm) | N at max |N| (kN) | |V| max (kN) |
|---|---|---|---|---|
| b | 4150 | 31.8 | 0.0 | 30.7 |
The 12 members with the largest moment. All members are in the calculation; open a member for the full values.
Support reactions
Largest vertical reaction 30.7 kN at node A. Total vertical reaction 61.3 kN. (ULS 6.10b (CC1 new))
Support reactions (envelope of the ULS combinations)
| Support | Node | x, y, z (mm) | FX (kN) | FY (kN) | FZ (kN) |
|---|---|---|---|---|---|
| S1 | A | 0, 0, 0 | 0.0 | 0.0 | 30.7 |
| S2 | B | 4150, 0, 0 | 0.0 | 0.0 | 30.7 |
For every component the value of the largest magnitude over all ULS combinations (sign as in the global axes, Z up), so the horizontal reactions are included. The largest vertical reaction (total 61.3 kN) occurs in ULS 6.10b (CC1 new). Forces in kN; there are no horizontal reactions or support moments.
Vertical support reactions: envelope of the ULS combinations (min / max)
| Support | Node | Min (kN) | Max (kN) |
|---|---|---|---|
| S1 | A | 4.55 | 30.67 |
| S2 | B | 4.55 | 30.67 |
Deformation
Maximum displacement 8.38 mm at node b. (SLS char.)
Deflection and sway check (SLS)
| Member | L (mm) | δ (mm) | Limit | Limit (mm) | δ / limit | |
|---|---|---|---|---|---|---|
| b | 4150 | 8.38 | L/250 | 16.60 | 0.50 | within the limit |
δ is the largest deflection relative to the chord between the member ends (columns: the horizontal sway of the top relative to the bottom, h = height; the bending of the column itself is not part of this check) in SLS char.. Standard limit L/250; set a stricter limit (e.g. L/500 with masonry or a brittle finish) per member. The values are project requirements: check the National Annex.
Results per combination
| Combination | M min (kNm) | M max (kNm) | V min (kN) | V max (kN) | N min (kN) | N max (kN) | Vertical reaction (kN): S1 / S2 | Max. displacement (mm) |
|---|---|---|---|---|---|---|---|---|
| ULS 6.10a (CC1 new) | 0.00 | 16.86 | -16.25 | 16.25 | 0.00 | 0.00 | 16.25 / 16.25 | 5.74 |
| ULS 6.10b (CC1 new) | 0.00 | 31.82 | -30.67 | 30.67 | 0.00 | 0.00 | 30.67 / 30.67 | 10.83 |
| SLS char. | 0.00 | 24.62 | -23.73 | 23.73 | 0.00 | 0.00 | 23.73 / 23.73 | 8.38 |
| ULS 0.9·G favourable (CC1 new) | 0.00 | 4.72 | -4.55 | 4.55 | 0.00 | 0.00 | 4.55 / 4.55 | 1.61 |
| ULS 0.9·G + Variable (Q) (CC1 new) | 0.00 | 30.88 | -29.76 | 29.76 | 0.00 | 0.00 | 29.76 / 29.76 | 10.50 |
| ULS γG·G permanent only (CC1 new) | 0.00 | 6.40 | -6.17 | 6.17 | 0.00 | 0.00 | 6.17 / 6.17 | 2.18 |
| ULS 0.9·G + ψ0 variable (CC1 new) | 0.00 | 15.18 | -14.63 | 14.63 | 0.00 | 0.00 | 14.63 / 14.63 | 5.16 |
| SLS permanent (G) | 0.00 | 5.24 | -5.05 | 5.05 | 0.00 | 0.00 | 5.05 / 5.05 | 1.78 |
| SLS quasi-permanent (G + ψ2·Q) | 0.00 | 11.06 | -10.66 | 10.66 | 0.00 | 0.00 | 10.66 / 10.66 | 3.76 |
| SLS frequent (G + ψ1·Q) | 0.00 | 14.93 | -14.39 | 14.39 | 0.00 | 0.00 | 14.39 / 14.39 | 5.08 |
Moment and shear force about the strong axis, section forces at 21 points per member; N − = compression. Displacement: the largest, including between the nodes.
8. Unity checks and calculations
Members coloured by their governing unity check: green up to UC 1.00, red above. The deflection check counts too.
| Member | Section | UC | Governing check |
|---|---|---|---|
| b | HEA180 | 0.50 | deflection (SLS) |
Member calculations
Detailed calculations of the members with a check (concrete EN 1992-1-1, steel EN 1993-1-1 / AISC 360).
Steel member b — HEA180, S235
EN 1993-1-1. Section properties are own calculations from nominal dimensions (see SOURCES.md).
1. Input
| Section | h × b × tw × tf (r) | 171.0 × 180.0 × 6.00 × 9.50 (15.0) mm |
| A, Iy, Iz | 45.27 cm², 2511.0 cm⁴, 924.6 cm⁴ | |
| Wel,y, Wpl,y | 293.7 cm³, 325.0 cm³ | |
| It, Iw | 15.10 cm⁴, 60290 cm⁶ | |
| Material | fy, E, G | 235 N/mm², 210000 N/mm², 81000 N/mm² |
| Length | 4150 mm | |
| Lateral restraint points | unrestrained lengths | none (ends only): 4150 mm |
| Load position, k, kw, ky, kz | top, 1, 1, 1, 1 |
2. Results per combination
| ULS 6.10a (CC1 new) | Lateral-torsional buckling (LTB), segment 1: x = 0–4150 mm, L = 4150 mm | 0.26 |
| ULS 6.10b (CC1 new) | Lateral-torsional buckling (LTB), segment 1: x = 0–4150 mm, L = 4150 mm | 0.49 |
| ULS 0.9·G favourable (CC1 new) | Lateral-torsional buckling (LTB), segment 1: x = 0–4150 mm, L = 4150 mm | 0.07 |
| ULS 0.9·G + Variable (Q) (CC1 new) | Lateral-torsional buckling (LTB), segment 1: x = 0–4150 mm, L = 4150 mm | 0.47 |
| ULS γG·G permanent only (CC1 new) | Lateral-torsional buckling (LTB), segment 1: x = 0–4150 mm, L = 4150 mm | 0.10 |
| ULS 0.9·G + ψ0 variable (CC1 new) | Lateral-torsional buckling (LTB), segment 1: x = 0–4150 mm, L = 4150 mm | 0.23 |
3. Calculation of every combination
ULS 6.10a (CC1 new) 0.26
0.22 Cross-section resistance x = 2075 mm
EN 1993-1-1 §5.5, 6.2
| ε [Table 5.2] | ε = √(235/fy) = √(235/235) | 1 |
| Flange outstand c/t [Table 5.2] | c = (b − tw − 2r)/2 = (180 − 6 − 2·15)/2 = 72; c/tf = 7.579 limits 9ε/10ε/14ε = 9/10/14 → class 1 | 7.5789 |
| Web c/t (bending) [Table 5.2] | c = h − 2tf − 2r = 171 − 2·9.5 − 2·15 = 122; c/tw = 20.333 limits 72ε/83ε/124ε = 72/83/124 → class 1 | 20.333 |
| Class (bending) [5.5] | class = max(flange, web) = max(1, 1) | 1 |
| ε [Table 5.2] | ε = √(235/fy) = √(235/235) | 1 |
| Flange outstand c/t [Table 5.2] | c = (b − tw − 2r)/2 = (180 − 6 − 2·15)/2 = 72; c/tf = 7.579 limits 9ε/10ε/14ε = 9/10/14 → class 1 | 7.5789 |
| Web c/t (compression) [Table 5.2] | c = h − 2tf − 2r = 171 − 2·9.5 − 2·15 = 122; c/tw = 20.333 limits 33ε/38ε/42ε = 33/38/42 → class 1 | 20.333 |
| Class (compression) [5.5] | class = max(flange, web) = max(1, 1) | 1 |
| Plastic axial resistance [6.2.4] | N_pl,Rd = A·fy/γM0 = 4526.624·235/1 | 1063.8 kN |
| Bending resistance y-y (plastic) [6.2.5] | M_c,y,Rd = Wpl,y·fy/γM0 = 324957.199·235/1 | 76.365 kNm |
| Bending resistance z-z (plastic) [6.2.5] | M_c,z,Rd = Wpl,z·fy/γM0 = 156507.081·235/1 | 36.779 kNm |
| Plastic shear resistance (z) [6.2.6] | V_pl,z,Rd = Avz·fy/(√3·γM0) = 1448.624·235/(√3·1) | 196.55 kN |
| Shear ratio [6.2.6] | V_Ed/V_pl,z,Rd = 0/196.545 | 0 |
| Axial ratio [6.2.4] | |N_Ed|/N_pl,Rd = 0/1063.757 | 0 |
| n = N_Ed/N_pl,Rd [6.2.9.1] | n = 0/1063.757 | 0 |
| a = (A − 2 b tf)/A ≤ 0,5 [6.2.9.1(5)] | a = (4526.624 − 2·180·9.5)/4526.624 | 0.24447 |
| Reduced M_N,y,Rd [6.2.9.1(5)] | M_pl,y,Rd(1−n)/(1−0,5a) ≤ M_pl,y,Rd = 76.365·(1−0)/(1−0.5·0.244) | 76.365 kNm |
| Reduced M_N,z,Rd [6.2.9.1(5)] | n ≤ a: M_pl,z,Rd; else M_pl,z,Rd[1 − ((n−a)/(1−a))²] = n = 0, a = 0.244 | 36.779 kNm |
| Interaction [6.2.9.1(6)] | [M_y,Ed/M_N,y,Rd]^α + [M_z,Ed/M_N,z,Rd]^β, α = 2, β = max(1; 5n) = [16.859/76.365]^2 + [0/36.779]^1 | 0.048738 |
| Bending ratio per axis [6.2.9.1(2), 6.2.5] | M_y,Ed/M_N,y,Rd and M_z,Ed/M_N,z,Rd (each ≤ 1,0) = 16.859/76.365 = 0.221; 0/36.779 = 0 | 0.22077 |
0.08 Cross-section resistance (maximum shear) x = 0 mm
EN 1993-1-1 §5.5, 6.2
| ε [Table 5.2] | ε = √(235/fy) = √(235/235) | 1 |
| Flange outstand c/t [Table 5.2] | c = (b − tw − 2r)/2 = (180 − 6 − 2·15)/2 = 72; c/tf = 7.579 limits 9ε/10ε/14ε = 9/10/14 → class 1 | 7.5789 |
| Web c/t (bending) [Table 5.2] | c = h − 2tf − 2r = 171 − 2·9.5 − 2·15 = 122; c/tw = 20.333 limits 72ε/83ε/124ε = 72/83/124 → class 1 | 20.333 |
| Class (bending) [5.5] | class = max(flange, web) = max(1, 1) | 1 |
| ε [Table 5.2] | ε = √(235/fy) = √(235/235) | 1 |
| Flange outstand c/t [Table 5.2] | c = (b − tw − 2r)/2 = (180 − 6 − 2·15)/2 = 72; c/tf = 7.579 limits 9ε/10ε/14ε = 9/10/14 → class 1 | 7.5789 |
| Web c/t (compression) [Table 5.2] | c = h − 2tf − 2r = 171 − 2·9.5 − 2·15 = 122; c/tw = 20.333 limits 33ε/38ε/42ε = 33/38/42 → class 1 | 20.333 |
| Class (compression) [5.5] | class = max(flange, web) = max(1, 1) | 1 |
| Plastic axial resistance [6.2.4] | N_pl,Rd = A·fy/γM0 = 4526.624·235/1 | 1063.8 kN |
| Bending resistance y-y (plastic) [6.2.5] | M_c,y,Rd = Wpl,y·fy/γM0 = 324957.199·235/1 | 76.365 kNm |
| Bending resistance z-z (plastic) [6.2.5] | M_c,z,Rd = Wpl,z·fy/γM0 = 156507.081·235/1 | 36.779 kNm |
| Plastic shear resistance (z) [6.2.6] | V_pl,z,Rd = Avz·fy/(√3·γM0) = 1448.624·235/(√3·1) | 196.55 kN |
| Shear ratio [6.2.6] | V_Ed/V_pl,z,Rd = 16.25/196.545 | 0.082676 |
| Axial ratio [6.2.4] | |N_Ed|/N_pl,Rd = 0/1063.757 | 0 |
| n = N_Ed/N_pl,Rd [6.2.9.1] | n = 0/1063.757 | 0 |
| a = (A − 2 b tf)/A ≤ 0,5 [6.2.9.1(5)] | a = (4526.624 − 2·180·9.5)/4526.624 | 0.24447 |
| Reduced M_N,y,Rd [6.2.9.1(5)] | M_pl,y,Rd(1−n)/(1−0,5a) ≤ M_pl,y,Rd = 76.365·(1−0)/(1−0.5·0.244) | 76.365 kNm |
| Reduced M_N,z,Rd [6.2.9.1(5)] | n ≤ a: M_pl,z,Rd; else M_pl,z,Rd[1 − ((n−a)/(1−a))²] = n = 0, a = 0.244 | 36.779 kNm |
| Interaction [6.2.9.1(6)] | [M_y,Ed/M_N,y,Rd]^α + [M_z,Ed/M_N,z,Rd]^β, α = 2, β = max(1; 5n) = [2.709e-16/76.365]^2 + [0/36.779]^1 | 1.258e-35 |
| Bending ratio per axis [6.2.9.1(2), 6.2.5] | M_y,Ed/M_N,y,Rd and M_z,Ed/M_N,z,Rd (each ≤ 1,0) = 2.709e-16/76.365 = 3.547e-18; 0/36.779 = 0 | 3.547e-18 |
0.26 Lateral-torsional buckling (LTB) segment 1: x = 0–4150 mm, L = 4150 mm
EN 1993-1-1 §6.3.2
| ε [Table 5.2] | ε = √(235/fy) = √(235/235) | 1 |
| Flange outstand c/t [Table 5.2] | c = (b − tw − 2r)/2 = (180 − 6 − 2·15)/2 = 72; c/tf = 7.579 limits 9ε/10ε/14ε = 9/10/14 → class 1 | 7.5789 |
| Web c/t (bending) [Table 5.2] | c = h − 2tf − 2r = 171 − 2·9.5 − 2·15 = 122; c/tw = 20.333 limits 72ε/83ε/124ε = 72/83/124 → class 1 | 20.333 |
| Class (bending) [5.5] | class = max(flange, web) = max(1, 1) | 1 |
| W_y (class 1) [6.3.2.2] | W_pl,y = 324957.199 mm³ | 324960 mm³ |
| π²·E·Iz/(k·L)² [NCCI SN003] | π²·E·Iz/(k·L)² = π²·210000·9.246e+6/(1·4150)² | 1112.7 kN (N·mm/mm) |
| C1 [NCCI SN003] | table value, uniform load (k = kw = 1,0) = C1 = 1.127, C2 = 0.454 | 1.127 |
| Load position z_g [NCCI SN003] | z_g = z_a − z_s (positive: load above the shear centre) = z_g = 85.5 mm | 85.5 mm |
| Square-root term [NCCI SN003] | (k/kw)²·Iw/Iz + (kL)²·G·It/(π²·E·Iz) + (C2·zg)² = (1/1)²·6.029e+10/9.246e+6 + (1·4150)²·81000·150965.805/(π²·210000·9.246e+6) + (0.454·85.5)² | 19017 |
| Elastic critical moment [NCCI SN003] | Mcr = C1·π²EIz/(kL)²·{√[...] − C2·zg} = 1.127·1112.719·(√19016.822 − 38.817) | 124.26 kNm |
| Check: numerical eigenvalue analysis | thin-walled beam FEM (Hermite elements) = M_cr,num = 124.442 kNm; deviation from the formula = 0.15 % information only | 124.44 kNm |
| Relative slenderness λ̄_LT [6.3.2.2(1)] | λ̄_LT = √(W_y·fy/Mcr) = √(324957.199·235/1.243e+8) | 0.78395 |
| LTB curve [Table 6.5] | Table 6.5: rolled I-section, h/b = 0.95 ≤ 2 = curve b, α_LT = 0.34 | 0.34 |
| Φ_LT [6.3.2.3(1)] | Φ_LT = 0,5[1 + α_LT(λ̄_LT − λ̄_LT,0) + β·λ̄_LT²], λ̄_LT,0 = 0,4, β = 0,75 = 0.5·[1 + 0.34·(0.784 − 0.4) + 0.75·0.784²] | 0.79574 |
| χ_LT [6.3.2.3(1)] | χ_LT = 1/(Φ_LT + √(Φ_LT² − β·λ̄_LT²)) ≤ 1,0 and ≤ 1/λ̄_LT² = 1/(0.796 + √(0.796² − 0.75·0.784²)) | 0.82591 |
| Correction factor k_c [Table 6.6] | Table 6.6 = k_c = 0.94 | 0.94 |
| f [6.3.2.3(2)] | f = 1 − 0,5(1 − k_c)[1 − 2(λ̄_LT − 0,8)²] ≤ 1,0 = 1 − 0.5·(1 − 0.94)·[1 − 2·(0.784 − 0.8)²] | 0.97002 |
| χ_LT,mod [6.3.2.3(2)] | χ_LT,mod = χ_LT/f ≤ 1,0 = 0.826/0.97 | 0.85144 |
| Buckling resistance moment [6.3.2.1(3)] | M_b,Rd = χ_LT·W_y·fy/γM1 = 0.851·324957.199·235/1 | 65.02 kNm |
| LTB ratio [6.3.2.1(1)] | M_Ed/M_b,Rd = 16.859/65.02 | 0.25929 |
ULS 6.10b (CC1 new) 0.49
0.42 Cross-section resistance x = 2075 mm
EN 1993-1-1 §5.5, 6.2
| ε [Table 5.2] | ε = √(235/fy) = √(235/235) | 1 |
| Flange outstand c/t [Table 5.2] | c = (b − tw − 2r)/2 = (180 − 6 − 2·15)/2 = 72; c/tf = 7.579 limits 9ε/10ε/14ε = 9/10/14 → class 1 | 7.5789 |
| Web c/t (bending) [Table 5.2] | c = h − 2tf − 2r = 171 − 2·9.5 − 2·15 = 122; c/tw = 20.333 limits 72ε/83ε/124ε = 72/83/124 → class 1 | 20.333 |
| Class (bending) [5.5] | class = max(flange, web) = max(1, 1) | 1 |
| ε [Table 5.2] | ε = √(235/fy) = √(235/235) | 1 |
| Flange outstand c/t [Table 5.2] | c = (b − tw − 2r)/2 = (180 − 6 − 2·15)/2 = 72; c/tf = 7.579 limits 9ε/10ε/14ε = 9/10/14 → class 1 | 7.5789 |
| Web c/t (compression) [Table 5.2] | c = h − 2tf − 2r = 171 − 2·9.5 − 2·15 = 122; c/tw = 20.333 limits 33ε/38ε/42ε = 33/38/42 → class 1 | 20.333 |
| Class (compression) [5.5] | class = max(flange, web) = max(1, 1) | 1 |
| Plastic axial resistance [6.2.4] | N_pl,Rd = A·fy/γM0 = 4526.624·235/1 | 1063.8 kN |
| Bending resistance y-y (plastic) [6.2.5] | M_c,y,Rd = Wpl,y·fy/γM0 = 324957.199·235/1 | 76.365 kNm |
| Bending resistance z-z (plastic) [6.2.5] | M_c,z,Rd = Wpl,z·fy/γM0 = 156507.081·235/1 | 36.779 kNm |
| Plastic shear resistance (z) [6.2.6] | V_pl,z,Rd = Avz·fy/(√3·γM0) = 1448.624·235/(√3·1) | 196.55 kN |
| Shear ratio [6.2.6] | V_Ed/V_pl,z,Rd = 0/196.545 | 0 |
| Axial ratio [6.2.4] | |N_Ed|/N_pl,Rd = 0/1063.757 | 0 |
| n = N_Ed/N_pl,Rd [6.2.9.1] | n = 0/1063.757 | 0 |
| a = (A − 2 b tf)/A ≤ 0,5 [6.2.9.1(5)] | a = (4526.624 − 2·180·9.5)/4526.624 | 0.24447 |
| Reduced M_N,y,Rd [6.2.9.1(5)] | M_pl,y,Rd(1−n)/(1−0,5a) ≤ M_pl,y,Rd = 76.365·(1−0)/(1−0.5·0.244) | 76.365 kNm |
| Reduced M_N,z,Rd [6.2.9.1(5)] | n ≤ a: M_pl,z,Rd; else M_pl,z,Rd[1 − ((n−a)/(1−a))²] = n = 0, a = 0.244 | 36.779 kNm |
| Interaction [6.2.9.1(6)] | [M_y,Ed/M_N,y,Rd]^α + [M_z,Ed/M_N,z,Rd]^β, α = 2, β = max(1; 5n) = [31.819/76.365]^2 + [0/36.779]^1 | 0.17361 |
| Bending ratio per axis [6.2.9.1(2), 6.2.5] | M_y,Ed/M_N,y,Rd and M_z,Ed/M_N,z,Rd (each ≤ 1,0) = 31.819/76.365 = 0.417; 0/36.779 = 0 | 0.41667 |
0.16 Cross-section resistance (maximum shear) x = 0 mm
EN 1993-1-1 §5.5, 6.2
| ε [Table 5.2] | ε = √(235/fy) = √(235/235) | 1 |
| Flange outstand c/t [Table 5.2] | c = (b − tw − 2r)/2 = (180 − 6 − 2·15)/2 = 72; c/tf = 7.579 limits 9ε/10ε/14ε = 9/10/14 → class 1 | 7.5789 |
| Web c/t (bending) [Table 5.2] | c = h − 2tf − 2r = 171 − 2·9.5 − 2·15 = 122; c/tw = 20.333 limits 72ε/83ε/124ε = 72/83/124 → class 1 | 20.333 |
| Class (bending) [5.5] | class = max(flange, web) = max(1, 1) | 1 |
| ε [Table 5.2] | ε = √(235/fy) = √(235/235) | 1 |
| Flange outstand c/t [Table 5.2] | c = (b − tw − 2r)/2 = (180 − 6 − 2·15)/2 = 72; c/tf = 7.579 limits 9ε/10ε/14ε = 9/10/14 → class 1 | 7.5789 |
| Web c/t (compression) [Table 5.2] | c = h − 2tf − 2r = 171 − 2·9.5 − 2·15 = 122; c/tw = 20.333 limits 33ε/38ε/42ε = 33/38/42 → class 1 | 20.333 |
| Class (compression) [5.5] | class = max(flange, web) = max(1, 1) | 1 |
| Plastic axial resistance [6.2.4] | N_pl,Rd = A·fy/γM0 = 4526.624·235/1 | 1063.8 kN |
| Bending resistance y-y (plastic) [6.2.5] | M_c,y,Rd = Wpl,y·fy/γM0 = 324957.199·235/1 | 76.365 kNm |
| Bending resistance z-z (plastic) [6.2.5] | M_c,z,Rd = Wpl,z·fy/γM0 = 156507.081·235/1 | 36.779 kNm |
| Plastic shear resistance (z) [6.2.6] | V_pl,z,Rd = Avz·fy/(√3·γM0) = 1448.624·235/(√3·1) | 196.55 kN |
| Shear ratio [6.2.6] | V_Ed/V_pl,z,Rd = 30.669/196.545 | 0.15604 |
| Axial ratio [6.2.4] | |N_Ed|/N_pl,Rd = 0/1063.757 | 0 |
| n = N_Ed/N_pl,Rd [6.2.9.1] | n = 0/1063.757 | 0 |
| a = (A − 2 b tf)/A ≤ 0,5 [6.2.9.1(5)] | a = (4526.624 − 2·180·9.5)/4526.624 | 0.24447 |
| Reduced M_N,y,Rd [6.2.9.1(5)] | M_pl,y,Rd(1−n)/(1−0,5a) ≤ M_pl,y,Rd = 76.365·(1−0)/(1−0.5·0.244) | 76.365 kNm |
| Reduced M_N,z,Rd [6.2.9.1(5)] | n ≤ a: M_pl,z,Rd; else M_pl,z,Rd[1 − ((n−a)/(1−a))²] = n = 0, a = 0.244 | 36.779 kNm |
| Interaction [6.2.9.1(6)] | [M_y,Ed/M_N,y,Rd]^α + [M_z,Ed/M_N,z,Rd]^β, α = 2, β = max(1; 5n) = [2.398e-16/76.365]^2 + [0/36.779]^1 | 9.861e-36 |
| Bending ratio per axis [6.2.9.1(2), 6.2.5] | M_y,Ed/M_N,y,Rd and M_z,Ed/M_N,z,Rd (each ≤ 1,0) = 2.398e-16/76.365 = 3.140e-18; 0/36.779 = 0 | 3.140e-18 |
0.49 Lateral-torsional buckling (LTB) segment 1: x = 0–4150 mm, L = 4150 mm
EN 1993-1-1 §6.3.2
| ε [Table 5.2] | ε = √(235/fy) = √(235/235) | 1 |
| Flange outstand c/t [Table 5.2] | c = (b − tw − 2r)/2 = (180 − 6 − 2·15)/2 = 72; c/tf = 7.579 limits 9ε/10ε/14ε = 9/10/14 → class 1 | 7.5789 |
| Web c/t (bending) [Table 5.2] | c = h − 2tf − 2r = 171 − 2·9.5 − 2·15 = 122; c/tw = 20.333 limits 72ε/83ε/124ε = 72/83/124 → class 1 | 20.333 |
| Class (bending) [5.5] | class = max(flange, web) = max(1, 1) | 1 |
| W_y (class 1) [6.3.2.2] | W_pl,y = 324957.199 mm³ | 324960 mm³ |
| π²·E·Iz/(k·L)² [NCCI SN003] | π²·E·Iz/(k·L)² = π²·210000·9.246e+6/(1·4150)² | 1112.7 kN (N·mm/mm) |
| C1 [NCCI SN003] | table value, uniform load (k = kw = 1,0) = C1 = 1.127, C2 = 0.454 | 1.127 |
| Load position z_g [NCCI SN003] | z_g = z_a − z_s (positive: load above the shear centre) = z_g = 85.5 mm | 85.5 mm |
| Square-root term [NCCI SN003] | (k/kw)²·Iw/Iz + (kL)²·G·It/(π²·E·Iz) + (C2·zg)² = (1/1)²·6.029e+10/9.246e+6 + (1·4150)²·81000·150965.805/(π²·210000·9.246e+6) + (0.454·85.5)² | 19017 |
| Elastic critical moment [NCCI SN003] | Mcr = C1·π²EIz/(kL)²·{√[...] − C2·zg} = 1.127·1112.719·(√19016.822 − 38.817) | 124.26 kNm |
| Check: numerical eigenvalue analysis | thin-walled beam FEM (Hermite elements) = M_cr,num = 124.442 kNm; deviation from the formula = 0.15 % information only | 124.44 kNm |
| Relative slenderness λ̄_LT [6.3.2.2(1)] | λ̄_LT = √(W_y·fy/Mcr) = √(324957.199·235/1.243e+8) | 0.78395 |
| LTB curve [Table 6.5] | Table 6.5: rolled I-section, h/b = 0.95 ≤ 2 = curve b, α_LT = 0.34 | 0.34 |
| Φ_LT [6.3.2.3(1)] | Φ_LT = 0,5[1 + α_LT(λ̄_LT − λ̄_LT,0) + β·λ̄_LT²], λ̄_LT,0 = 0,4, β = 0,75 = 0.5·[1 + 0.34·(0.784 − 0.4) + 0.75·0.784²] | 0.79574 |
| χ_LT [6.3.2.3(1)] | χ_LT = 1/(Φ_LT + √(Φ_LT² − β·λ̄_LT²)) ≤ 1,0 and ≤ 1/λ̄_LT² = 1/(0.796 + √(0.796² − 0.75·0.784²)) | 0.82591 |
| Correction factor k_c [Table 6.6] | Table 6.6 = k_c = 0.94 | 0.94 |
| f [6.3.2.3(2)] | f = 1 − 0,5(1 − k_c)[1 − 2(λ̄_LT − 0,8)²] ≤ 1,0 = 1 − 0.5·(1 − 0.94)·[1 − 2·(0.784 − 0.8)²] | 0.97002 |
| χ_LT,mod [6.3.2.3(2)] | χ_LT,mod = χ_LT/f ≤ 1,0 = 0.826/0.97 | 0.85144 |
| Buckling resistance moment [6.3.2.1(3)] | M_b,Rd = χ_LT·W_y·fy/γM1 = 0.851·324957.199·235/1 | 65.02 kNm |
| LTB ratio [6.3.2.1(1)] | M_Ed/M_b,Rd = 31.819/65.02 | 0.48937 |
ULS 0.9·G favourable (CC1 new) 0.07
0.06 Cross-section resistance x = 2075 mm
EN 1993-1-1 §5.5, 6.2
| ε [Table 5.2] | ε = √(235/fy) = √(235/235) | 1 |
| Flange outstand c/t [Table 5.2] | c = (b − tw − 2r)/2 = (180 − 6 − 2·15)/2 = 72; c/tf = 7.579 limits 9ε/10ε/14ε = 9/10/14 → class 1 | 7.5789 |
| Web c/t (bending) [Table 5.2] | c = h − 2tf − 2r = 171 − 2·9.5 − 2·15 = 122; c/tw = 20.333 limits 72ε/83ε/124ε = 72/83/124 → class 1 | 20.333 |
| Class (bending) [5.5] | class = max(flange, web) = max(1, 1) | 1 |
| ε [Table 5.2] | ε = √(235/fy) = √(235/235) | 1 |
| Flange outstand c/t [Table 5.2] | c = (b − tw − 2r)/2 = (180 − 6 − 2·15)/2 = 72; c/tf = 7.579 limits 9ε/10ε/14ε = 9/10/14 → class 1 | 7.5789 |
| Web c/t (compression) [Table 5.2] | c = h − 2tf − 2r = 171 − 2·9.5 − 2·15 = 122; c/tw = 20.333 limits 33ε/38ε/42ε = 33/38/42 → class 1 | 20.333 |
| Class (compression) [5.5] | class = max(flange, web) = max(1, 1) | 1 |
| Plastic axial resistance [6.2.4] | N_pl,Rd = A·fy/γM0 = 4526.624·235/1 | 1063.8 kN |
| Bending resistance y-y (plastic) [6.2.5] | M_c,y,Rd = Wpl,y·fy/γM0 = 324957.199·235/1 | 76.365 kNm |
| Bending resistance z-z (plastic) [6.2.5] | M_c,z,Rd = Wpl,z·fy/γM0 = 156507.081·235/1 | 36.779 kNm |
| Plastic shear resistance (z) [6.2.6] | V_pl,z,Rd = Avz·fy/(√3·γM0) = 1448.624·235/(√3·1) | 196.55 kN |
| Shear ratio [6.2.6] | V_Ed/V_pl,z,Rd = 0/196.545 | 0 |
| Axial ratio [6.2.4] | |N_Ed|/N_pl,Rd = 0/1063.757 | 0 |
| n = N_Ed/N_pl,Rd [6.2.9.1] | n = 0/1063.757 | 0 |
| a = (A − 2 b tf)/A ≤ 0,5 [6.2.9.1(5)] | a = (4526.624 − 2·180·9.5)/4526.624 | 0.24447 |
| Reduced M_N,y,Rd [6.2.9.1(5)] | M_pl,y,Rd(1−n)/(1−0,5a) ≤ M_pl,y,Rd = 76.365·(1−0)/(1−0.5·0.244) | 76.365 kNm |
| Reduced M_N,z,Rd [6.2.9.1(5)] | n ≤ a: M_pl,z,Rd; else M_pl,z,Rd[1 − ((n−a)/(1−a))²] = n = 0, a = 0.244 | 36.779 kNm |
| Interaction [6.2.9.1(6)] | [M_y,Ed/M_N,y,Rd]^α + [M_z,Ed/M_N,z,Rd]^β, α = 2, β = max(1; 5n) = [4.719/76.365]^2 + [0/36.779]^1 | 0.0038179 |
| Bending ratio per axis [6.2.9.1(2), 6.2.5] | M_y,Ed/M_N,y,Rd and M_z,Ed/M_N,z,Rd (each ≤ 1,0) = 4.719/76.365 = 0.062; 0/36.779 = 0 | 0.061789 |
0.02 Cross-section resistance (maximum shear) x = 0 mm
EN 1993-1-1 §5.5, 6.2
| ε [Table 5.2] | ε = √(235/fy) = √(235/235) | 1 |
| Flange outstand c/t [Table 5.2] | c = (b − tw − 2r)/2 = (180 − 6 − 2·15)/2 = 72; c/tf = 7.579 limits 9ε/10ε/14ε = 9/10/14 → class 1 | 7.5789 |
| Web c/t (bending) [Table 5.2] | c = h − 2tf − 2r = 171 − 2·9.5 − 2·15 = 122; c/tw = 20.333 limits 72ε/83ε/124ε = 72/83/124 → class 1 | 20.333 |
| Class (bending) [5.5] | class = max(flange, web) = max(1, 1) | 1 |
| ε [Table 5.2] | ε = √(235/fy) = √(235/235) | 1 |
| Flange outstand c/t [Table 5.2] | c = (b − tw − 2r)/2 = (180 − 6 − 2·15)/2 = 72; c/tf = 7.579 limits 9ε/10ε/14ε = 9/10/14 → class 1 | 7.5789 |
| Web c/t (compression) [Table 5.2] | c = h − 2tf − 2r = 171 − 2·9.5 − 2·15 = 122; c/tw = 20.333 limits 33ε/38ε/42ε = 33/38/42 → class 1 | 20.333 |
| Class (compression) [5.5] | class = max(flange, web) = max(1, 1) | 1 |
| Plastic axial resistance [6.2.4] | N_pl,Rd = A·fy/γM0 = 4526.624·235/1 | 1063.8 kN |
| Bending resistance y-y (plastic) [6.2.5] | M_c,y,Rd = Wpl,y·fy/γM0 = 324957.199·235/1 | 76.365 kNm |
| Bending resistance z-z (plastic) [6.2.5] | M_c,z,Rd = Wpl,z·fy/γM0 = 156507.081·235/1 | 36.779 kNm |
| Plastic shear resistance (z) [6.2.6] | V_pl,z,Rd = Avz·fy/(√3·γM0) = 1448.624·235/(√3·1) | 196.55 kN |
| Shear ratio [6.2.6] | V_Ed/V_pl,z,Rd = 4.548/196.545 | 0.02314 |
| Axial ratio [6.2.4] | |N_Ed|/N_pl,Rd = 0/1063.757 | 0 |
| n = N_Ed/N_pl,Rd [6.2.9.1] | n = 0/1063.757 | 0 |
| a = (A − 2 b tf)/A ≤ 0,5 [6.2.9.1(5)] | a = (4526.624 − 2·180·9.5)/4526.624 | 0.24447 |
| Reduced M_N,y,Rd [6.2.9.1(5)] | M_pl,y,Rd(1−n)/(1−0,5a) ≤ M_pl,y,Rd = 76.365·(1−0)/(1−0.5·0.244) | 76.365 kNm |
| Reduced M_N,z,Rd [6.2.9.1(5)] | n ≤ a: M_pl,z,Rd; else M_pl,z,Rd[1 − ((n−a)/(1−a))²] = n = 0, a = 0.244 | 36.779 kNm |
| Interaction [6.2.9.1(6)] | [M_y,Ed/M_N,y,Rd]^α + [M_z,Ed/M_N,z,Rd]^β, α = 2, β = max(1; 5n) = [1.998e-16/76.365]^2 + [0/36.779]^1 | 6.848e-36 |
| Bending ratio per axis [6.2.9.1(2), 6.2.5] | M_y,Ed/M_N,y,Rd and M_z,Ed/M_N,z,Rd (each ≤ 1,0) = 1.998e-16/76.365 = 2.617e-18; 0/36.779 = 0 | 2.617e-18 |
0.07 Lateral-torsional buckling (LTB) segment 1: x = 0–4150 mm, L = 4150 mm
EN 1993-1-1 §6.3.2
| ε [Table 5.2] | ε = √(235/fy) = √(235/235) | 1 |
| Flange outstand c/t [Table 5.2] | c = (b − tw − 2r)/2 = (180 − 6 − 2·15)/2 = 72; c/tf = 7.579 limits 9ε/10ε/14ε = 9/10/14 → class 1 | 7.5789 |
| Web c/t (bending) [Table 5.2] | c = h − 2tf − 2r = 171 − 2·9.5 − 2·15 = 122; c/tw = 20.333 limits 72ε/83ε/124ε = 72/83/124 → class 1 | 20.333 |
| Class (bending) [5.5] | class = max(flange, web) = max(1, 1) | 1 |
| W_y (class 1) [6.3.2.2] | W_pl,y = 324957.199 mm³ | 324960 mm³ |
| π²·E·Iz/(k·L)² [NCCI SN003] | π²·E·Iz/(k·L)² = π²·210000·9.246e+6/(1·4150)² | 1112.7 kN (N·mm/mm) |
| C1 [NCCI SN003] | table value, uniform load (k = kw = 1,0) = C1 = 1.127, C2 = 0.454 | 1.127 |
| Load position z_g [NCCI SN003] | z_g = z_a − z_s (positive: load above the shear centre) = z_g = 85.5 mm | 85.5 mm |
| Square-root term [NCCI SN003] | (k/kw)²·Iw/Iz + (kL)²·G·It/(π²·E·Iz) + (C2·zg)² = (1/1)²·6.029e+10/9.246e+6 + (1·4150)²·81000·150965.805/(π²·210000·9.246e+6) + (0.454·85.5)² | 19017 |
| Elastic critical moment [NCCI SN003] | Mcr = C1·π²EIz/(kL)²·{√[...] − C2·zg} = 1.127·1112.719·(√19016.822 − 38.817) | 124.26 kNm |
| Check: numerical eigenvalue analysis | thin-walled beam FEM (Hermite elements) = M_cr,num = 124.442 kNm; deviation from the formula = 0.15 % information only | 124.44 kNm |
| Relative slenderness λ̄_LT [6.3.2.2(1)] | λ̄_LT = √(W_y·fy/Mcr) = √(324957.199·235/1.243e+8) | 0.78395 |
| LTB curve [Table 6.5] | Table 6.5: rolled I-section, h/b = 0.95 ≤ 2 = curve b, α_LT = 0.34 | 0.34 |
| Φ_LT [6.3.2.3(1)] | Φ_LT = 0,5[1 + α_LT(λ̄_LT − λ̄_LT,0) + β·λ̄_LT²], λ̄_LT,0 = 0,4, β = 0,75 = 0.5·[1 + 0.34·(0.784 − 0.4) + 0.75·0.784²] | 0.79574 |
| χ_LT [6.3.2.3(1)] | χ_LT = 1/(Φ_LT + √(Φ_LT² − β·λ̄_LT²)) ≤ 1,0 and ≤ 1/λ̄_LT² = 1/(0.796 + √(0.796² − 0.75·0.784²)) | 0.82591 |
| Correction factor k_c [Table 6.6] | Table 6.6 = k_c = 0.94 | 0.94 |
| f [6.3.2.3(2)] | f = 1 − 0,5(1 − k_c)[1 − 2(λ̄_LT − 0,8)²] ≤ 1,0 = 1 − 0.5·(1 − 0.94)·[1 − 2·(0.784 − 0.8)²] | 0.97002 |
| χ_LT,mod [6.3.2.3(2)] | χ_LT,mod = χ_LT/f ≤ 1,0 = 0.826/0.97 | 0.85144 |
| Buckling resistance moment [6.3.2.1(3)] | M_b,Rd = χ_LT·W_y·fy/γM1 = 0.851·324957.199·235/1 | 65.02 kNm |
| LTB ratio [6.3.2.1(1)] | M_Ed/M_b,Rd = 4.719/65.02 | 0.072571 |
ULS 0.9·G + Variable (Q) (CC1 new) 0.47
0.40 Cross-section resistance x = 2075 mm
EN 1993-1-1 §5.5, 6.2
| ε [Table 5.2] | ε = √(235/fy) = √(235/235) | 1 |
| Flange outstand c/t [Table 5.2] | c = (b − tw − 2r)/2 = (180 − 6 − 2·15)/2 = 72; c/tf = 7.579 limits 9ε/10ε/14ε = 9/10/14 → class 1 | 7.5789 |
| Web c/t (bending) [Table 5.2] | c = h − 2tf − 2r = 171 − 2·9.5 − 2·15 = 122; c/tw = 20.333 limits 72ε/83ε/124ε = 72/83/124 → class 1 | 20.333 |
| Class (bending) [5.5] | class = max(flange, web) = max(1, 1) | 1 |
| ε [Table 5.2] | ε = √(235/fy) = √(235/235) | 1 |
| Flange outstand c/t [Table 5.2] | c = (b − tw − 2r)/2 = (180 − 6 − 2·15)/2 = 72; c/tf = 7.579 limits 9ε/10ε/14ε = 9/10/14 → class 1 | 7.5789 |
| Web c/t (compression) [Table 5.2] | c = h − 2tf − 2r = 171 − 2·9.5 − 2·15 = 122; c/tw = 20.333 limits 33ε/38ε/42ε = 33/38/42 → class 1 | 20.333 |
| Class (compression) [5.5] | class = max(flange, web) = max(1, 1) | 1 |
| Plastic axial resistance [6.2.4] | N_pl,Rd = A·fy/γM0 = 4526.624·235/1 | 1063.8 kN |
| Bending resistance y-y (plastic) [6.2.5] | M_c,y,Rd = Wpl,y·fy/γM0 = 324957.199·235/1 | 76.365 kNm |
| Bending resistance z-z (plastic) [6.2.5] | M_c,z,Rd = Wpl,z·fy/γM0 = 156507.081·235/1 | 36.779 kNm |
| Plastic shear resistance (z) [6.2.6] | V_pl,z,Rd = Avz·fy/(√3·γM0) = 1448.624·235/(√3·1) | 196.55 kN |
| Shear ratio [6.2.6] | V_Ed/V_pl,z,Rd = 0/196.545 | 0 |
| Axial ratio [6.2.4] | |N_Ed|/N_pl,Rd = 0/1063.757 | 0 |
| n = N_Ed/N_pl,Rd [6.2.9.1] | n = 0/1063.757 | 0 |
| a = (A − 2 b tf)/A ≤ 0,5 [6.2.9.1(5)] | a = (4526.624 − 2·180·9.5)/4526.624 | 0.24447 |
| Reduced M_N,y,Rd [6.2.9.1(5)] | M_pl,y,Rd(1−n)/(1−0,5a) ≤ M_pl,y,Rd = 76.365·(1−0)/(1−0.5·0.244) | 76.365 kNm |
| Reduced M_N,z,Rd [6.2.9.1(5)] | n ≤ a: M_pl,z,Rd; else M_pl,z,Rd[1 − ((n−a)/(1−a))²] = n = 0, a = 0.244 | 36.779 kNm |
| Interaction [6.2.9.1(6)] | [M_y,Ed/M_N,y,Rd]^α + [M_z,Ed/M_N,z,Rd]^β, α = 2, β = max(1; 5n) = [30.875/76.365]^2 + [0/36.779]^1 | 0.16347 |
| Bending ratio per axis [6.2.9.1(2), 6.2.5] | M_y,Ed/M_N,y,Rd and M_z,Ed/M_N,z,Rd (each ≤ 1,0) = 30.875/76.365 = 0.404; 0/36.779 = 0 | 0.40431 |
0.15 Cross-section resistance (maximum shear) x = 0 mm
EN 1993-1-1 §5.5, 6.2
| ε [Table 5.2] | ε = √(235/fy) = √(235/235) | 1 |
| Flange outstand c/t [Table 5.2] | c = (b − tw − 2r)/2 = (180 − 6 − 2·15)/2 = 72; c/tf = 7.579 limits 9ε/10ε/14ε = 9/10/14 → class 1 | 7.5789 |
| Web c/t (bending) [Table 5.2] | c = h − 2tf − 2r = 171 − 2·9.5 − 2·15 = 122; c/tw = 20.333 limits 72ε/83ε/124ε = 72/83/124 → class 1 | 20.333 |
| Class (bending) [5.5] | class = max(flange, web) = max(1, 1) | 1 |
| ε [Table 5.2] | ε = √(235/fy) = √(235/235) | 1 |
| Flange outstand c/t [Table 5.2] | c = (b − tw − 2r)/2 = (180 − 6 − 2·15)/2 = 72; c/tf = 7.579 limits 9ε/10ε/14ε = 9/10/14 → class 1 | 7.5789 |
| Web c/t (compression) [Table 5.2] | c = h − 2tf − 2r = 171 − 2·9.5 − 2·15 = 122; c/tw = 20.333 limits 33ε/38ε/42ε = 33/38/42 → class 1 | 20.333 |
| Class (compression) [5.5] | class = max(flange, web) = max(1, 1) | 1 |
| Plastic axial resistance [6.2.4] | N_pl,Rd = A·fy/γM0 = 4526.624·235/1 | 1063.8 kN |
| Bending resistance y-y (plastic) [6.2.5] | M_c,y,Rd = Wpl,y·fy/γM0 = 324957.199·235/1 | 76.365 kNm |
| Bending resistance z-z (plastic) [6.2.5] | M_c,z,Rd = Wpl,z·fy/γM0 = 156507.081·235/1 | 36.779 kNm |
| Plastic shear resistance (z) [6.2.6] | V_pl,z,Rd = Avz·fy/(√3·γM0) = 1448.624·235/(√3·1) | 196.55 kN |
| Shear ratio [6.2.6] | V_Ed/V_pl,z,Rd = 29.759/196.545 | 0.15141 |
| Axial ratio [6.2.4] | |N_Ed|/N_pl,Rd = 0/1063.757 | 0 |
| n = N_Ed/N_pl,Rd [6.2.9.1] | n = 0/1063.757 | 0 |
| a = (A − 2 b tf)/A ≤ 0,5 [6.2.9.1(5)] | a = (4526.624 − 2·180·9.5)/4526.624 | 0.24447 |
| Reduced M_N,y,Rd [6.2.9.1(5)] | M_pl,y,Rd(1−n)/(1−0,5a) ≤ M_pl,y,Rd = 76.365·(1−0)/(1−0.5·0.244) | 76.365 kNm |
| Reduced M_N,z,Rd [6.2.9.1(5)] | n ≤ a: M_pl,z,Rd; else M_pl,z,Rd[1 − ((n−a)/(1−a))²] = n = 0, a = 0.244 | 36.779 kNm |
| Interaction [6.2.9.1(6)] | [M_y,Ed/M_N,y,Rd]^α + [M_z,Ed/M_N,z,Rd]^β, α = 2, β = max(1; 5n) = [1.998e-16/76.365]^2 + [0/36.779]^1 | 6.848e-36 |
| Bending ratio per axis [6.2.9.1(2), 6.2.5] | M_y,Ed/M_N,y,Rd and M_z,Ed/M_N,z,Rd (each ≤ 1,0) = 1.998e-16/76.365 = 2.617e-18; 0/36.779 = 0 | 2.617e-18 |
0.47 Lateral-torsional buckling (LTB) segment 1: x = 0–4150 mm, L = 4150 mm
EN 1993-1-1 §6.3.2
| ε [Table 5.2] | ε = √(235/fy) = √(235/235) | 1 |
| Flange outstand c/t [Table 5.2] | c = (b − tw − 2r)/2 = (180 − 6 − 2·15)/2 = 72; c/tf = 7.579 limits 9ε/10ε/14ε = 9/10/14 → class 1 | 7.5789 |
| Web c/t (bending) [Table 5.2] | c = h − 2tf − 2r = 171 − 2·9.5 − 2·15 = 122; c/tw = 20.333 limits 72ε/83ε/124ε = 72/83/124 → class 1 | 20.333 |
| Class (bending) [5.5] | class = max(flange, web) = max(1, 1) | 1 |
| W_y (class 1) [6.3.2.2] | W_pl,y = 324957.199 mm³ | 324960 mm³ |
| π²·E·Iz/(k·L)² [NCCI SN003] | π²·E·Iz/(k·L)² = π²·210000·9.246e+6/(1·4150)² | 1112.7 kN (N·mm/mm) |
| C1 [NCCI SN003] | table value, uniform load (k = kw = 1,0) = C1 = 1.127, C2 = 0.454 | 1.127 |
| Load position z_g [NCCI SN003] | z_g = z_a − z_s (positive: load above the shear centre) = z_g = 85.5 mm | 85.5 mm |
| Square-root term [NCCI SN003] | (k/kw)²·Iw/Iz + (kL)²·G·It/(π²·E·Iz) + (C2·zg)² = (1/1)²·6.029e+10/9.246e+6 + (1·4150)²·81000·150965.805/(π²·210000·9.246e+6) + (0.454·85.5)² | 19017 |
| Elastic critical moment [NCCI SN003] | Mcr = C1·π²EIz/(kL)²·{√[...] − C2·zg} = 1.127·1112.719·(√19016.822 − 38.817) | 124.26 kNm |
| Check: numerical eigenvalue analysis | thin-walled beam FEM (Hermite elements) = M_cr,num = 124.442 kNm; deviation from the formula = 0.15 % information only | 124.44 kNm |
| Relative slenderness λ̄_LT [6.3.2.2(1)] | λ̄_LT = √(W_y·fy/Mcr) = √(324957.199·235/1.243e+8) | 0.78395 |
| LTB curve [Table 6.5] | Table 6.5: rolled I-section, h/b = 0.95 ≤ 2 = curve b, α_LT = 0.34 | 0.34 |
| Φ_LT [6.3.2.3(1)] | Φ_LT = 0,5[1 + α_LT(λ̄_LT − λ̄_LT,0) + β·λ̄_LT²], λ̄_LT,0 = 0,4, β = 0,75 = 0.5·[1 + 0.34·(0.784 − 0.4) + 0.75·0.784²] | 0.79574 |
| χ_LT [6.3.2.3(1)] | χ_LT = 1/(Φ_LT + √(Φ_LT² − β·λ̄_LT²)) ≤ 1,0 and ≤ 1/λ̄_LT² = 1/(0.796 + √(0.796² − 0.75·0.784²)) | 0.82591 |
| Correction factor k_c [Table 6.6] | Table 6.6 = k_c = 0.94 | 0.94 |
| f [6.3.2.3(2)] | f = 1 − 0,5(1 − k_c)[1 − 2(λ̄_LT − 0,8)²] ≤ 1,0 = 1 − 0.5·(1 − 0.94)·[1 − 2·(0.784 − 0.8)²] | 0.97002 |
| χ_LT,mod [6.3.2.3(2)] | χ_LT,mod = χ_LT/f ≤ 1,0 = 0.826/0.97 | 0.85144 |
| Buckling resistance moment [6.3.2.1(3)] | M_b,Rd = χ_LT·W_y·fy/γM1 = 0.851·324957.199·235/1 | 65.02 kNm |
| LTB ratio [6.3.2.1(1)] | M_Ed/M_b,Rd = 30.875/65.02 | 0.47486 |
ULS γG·G permanent only (CC1 new) 0.10
0.08 Cross-section resistance x = 2075 mm
EN 1993-1-1 §5.5, 6.2
| ε [Table 5.2] | ε = √(235/fy) = √(235/235) | 1 |
| Flange outstand c/t [Table 5.2] | c = (b − tw − 2r)/2 = (180 − 6 − 2·15)/2 = 72; c/tf = 7.579 limits 9ε/10ε/14ε = 9/10/14 → class 1 | 7.5789 |
| Web c/t (bending) [Table 5.2] | c = h − 2tf − 2r = 171 − 2·9.5 − 2·15 = 122; c/tw = 20.333 limits 72ε/83ε/124ε = 72/83/124 → class 1 | 20.333 |
| Class (bending) [5.5] | class = max(flange, web) = max(1, 1) | 1 |
| ε [Table 5.2] | ε = √(235/fy) = √(235/235) | 1 |
| Flange outstand c/t [Table 5.2] | c = (b − tw − 2r)/2 = (180 − 6 − 2·15)/2 = 72; c/tf = 7.579 limits 9ε/10ε/14ε = 9/10/14 → class 1 | 7.5789 |
| Web c/t (compression) [Table 5.2] | c = h − 2tf − 2r = 171 − 2·9.5 − 2·15 = 122; c/tw = 20.333 limits 33ε/38ε/42ε = 33/38/42 → class 1 | 20.333 |
| Class (compression) [5.5] | class = max(flange, web) = max(1, 1) | 1 |
| Plastic axial resistance [6.2.4] | N_pl,Rd = A·fy/γM0 = 4526.624·235/1 | 1063.8 kN |
| Bending resistance y-y (plastic) [6.2.5] | M_c,y,Rd = Wpl,y·fy/γM0 = 324957.199·235/1 | 76.365 kNm |
| Bending resistance z-z (plastic) [6.2.5] | M_c,z,Rd = Wpl,z·fy/γM0 = 156507.081·235/1 | 36.779 kNm |
| Plastic shear resistance (z) [6.2.6] | V_pl,z,Rd = Avz·fy/(√3·γM0) = 1448.624·235/(√3·1) | 196.55 kN |
| Shear ratio [6.2.6] | V_Ed/V_pl,z,Rd = 8.882e-16/196.545 | 4.519e-18 |
| Axial ratio [6.2.4] | |N_Ed|/N_pl,Rd = 0/1063.757 | 0 |
| n = N_Ed/N_pl,Rd [6.2.9.1] | n = 0/1063.757 | 0 |
| a = (A − 2 b tf)/A ≤ 0,5 [6.2.9.1(5)] | a = (4526.624 − 2·180·9.5)/4526.624 | 0.24447 |
| Reduced M_N,y,Rd [6.2.9.1(5)] | M_pl,y,Rd(1−n)/(1−0,5a) ≤ M_pl,y,Rd = 76.365·(1−0)/(1−0.5·0.244) | 76.365 kNm |
| Reduced M_N,z,Rd [6.2.9.1(5)] | n ≤ a: M_pl,z,Rd; else M_pl,z,Rd[1 − ((n−a)/(1−a))²] = n = 0, a = 0.244 | 36.779 kNm |
| Interaction [6.2.9.1(6)] | [M_y,Ed/M_N,y,Rd]^α + [M_z,Ed/M_N,z,Rd]^β, α = 2, β = max(1; 5n) = [6.396/76.365]^2 + [0/36.779]^1 | 0.0070156 |
| Bending ratio per axis [6.2.9.1(2), 6.2.5] | M_y,Ed/M_N,y,Rd and M_z,Ed/M_N,z,Rd (each ≤ 1,0) = 6.396/76.365 = 0.084; 0/36.779 = 0 | 0.083759 |
0.03 Cross-section resistance (maximum shear) x = 0 mm
EN 1993-1-1 §5.5, 6.2
| ε [Table 5.2] | ε = √(235/fy) = √(235/235) | 1 |
| Flange outstand c/t [Table 5.2] | c = (b − tw − 2r)/2 = (180 − 6 − 2·15)/2 = 72; c/tf = 7.579 limits 9ε/10ε/14ε = 9/10/14 → class 1 | 7.5789 |
| Web c/t (bending) [Table 5.2] | c = h − 2tf − 2r = 171 − 2·9.5 − 2·15 = 122; c/tw = 20.333 limits 72ε/83ε/124ε = 72/83/124 → class 1 | 20.333 |
| Class (bending) [5.5] | class = max(flange, web) = max(1, 1) | 1 |
| ε [Table 5.2] | ε = √(235/fy) = √(235/235) | 1 |
| Flange outstand c/t [Table 5.2] | c = (b − tw − 2r)/2 = (180 − 6 − 2·15)/2 = 72; c/tf = 7.579 limits 9ε/10ε/14ε = 9/10/14 → class 1 | 7.5789 |
| Web c/t (compression) [Table 5.2] | c = h − 2tf − 2r = 171 − 2·9.5 − 2·15 = 122; c/tw = 20.333 limits 33ε/38ε/42ε = 33/38/42 → class 1 | 20.333 |
| Class (compression) [5.5] | class = max(flange, web) = max(1, 1) | 1 |
| Plastic axial resistance [6.2.4] | N_pl,Rd = A·fy/γM0 = 4526.624·235/1 | 1063.8 kN |
| Bending resistance y-y (plastic) [6.2.5] | M_c,y,Rd = Wpl,y·fy/γM0 = 324957.199·235/1 | 76.365 kNm |
| Bending resistance z-z (plastic) [6.2.5] | M_c,z,Rd = Wpl,z·fy/γM0 = 156507.081·235/1 | 36.779 kNm |
| Plastic shear resistance (z) [6.2.6] | V_pl,z,Rd = Avz·fy/(√3·γM0) = 1448.624·235/(√3·1) | 196.55 kN |
| Shear ratio [6.2.6] | V_Ed/V_pl,z,Rd = 6.165/196.545 | 0.031367 |
| Axial ratio [6.2.4] | |N_Ed|/N_pl,Rd = 0/1063.757 | 0 |
| n = N_Ed/N_pl,Rd [6.2.9.1] | n = 0/1063.757 | 0 |
| a = (A − 2 b tf)/A ≤ 0,5 [6.2.9.1(5)] | a = (4526.624 − 2·180·9.5)/4526.624 | 0.24447 |
| Reduced M_N,y,Rd [6.2.9.1(5)] | M_pl,y,Rd(1−n)/(1−0,5a) ≤ M_pl,y,Rd = 76.365·(1−0)/(1−0.5·0.244) | 76.365 kNm |
| Reduced M_N,z,Rd [6.2.9.1(5)] | n ≤ a: M_pl,z,Rd; else M_pl,z,Rd[1 − ((n−a)/(1−a))²] = n = 0, a = 0.244 | 36.779 kNm |
| Interaction [6.2.9.1(6)] | [M_y,Ed/M_N,y,Rd]^α + [M_z,Ed/M_N,z,Rd]^β, α = 2, β = max(1; 5n) = [2.709e-16/76.365]^2 + [0/36.779]^1 | 1.258e-35 |
| Bending ratio per axis [6.2.9.1(2), 6.2.5] | M_y,Ed/M_N,y,Rd and M_z,Ed/M_N,z,Rd (each ≤ 1,0) = 2.709e-16/76.365 = 3.547e-18; 0/36.779 = 0 | 3.547e-18 |
0.10 Lateral-torsional buckling (LTB) segment 1: x = 0–4150 mm, L = 4150 mm
EN 1993-1-1 §6.3.2
| ε [Table 5.2] | ε = √(235/fy) = √(235/235) | 1 |
| Flange outstand c/t [Table 5.2] | c = (b − tw − 2r)/2 = (180 − 6 − 2·15)/2 = 72; c/tf = 7.579 limits 9ε/10ε/14ε = 9/10/14 → class 1 | 7.5789 |
| Web c/t (bending) [Table 5.2] | c = h − 2tf − 2r = 171 − 2·9.5 − 2·15 = 122; c/tw = 20.333 limits 72ε/83ε/124ε = 72/83/124 → class 1 | 20.333 |
| Class (bending) [5.5] | class = max(flange, web) = max(1, 1) | 1 |
| W_y (class 1) [6.3.2.2] | W_pl,y = 324957.199 mm³ | 324960 mm³ |
| π²·E·Iz/(k·L)² [NCCI SN003] | π²·E·Iz/(k·L)² = π²·210000·9.246e+6/(1·4150)² | 1112.7 kN (N·mm/mm) |
| C1 [NCCI SN003] | table value, uniform load (k = kw = 1,0) = C1 = 1.127, C2 = 0.454 | 1.127 |
| Load position z_g [NCCI SN003] | z_g = z_a − z_s (positive: load above the shear centre) = z_g = 85.5 mm | 85.5 mm |
| Square-root term [NCCI SN003] | (k/kw)²·Iw/Iz + (kL)²·G·It/(π²·E·Iz) + (C2·zg)² = (1/1)²·6.029e+10/9.246e+6 + (1·4150)²·81000·150965.805/(π²·210000·9.246e+6) + (0.454·85.5)² | 19017 |
| Elastic critical moment [NCCI SN003] | Mcr = C1·π²EIz/(kL)²·{√[...] − C2·zg} = 1.127·1112.719·(√19016.822 − 38.817) | 124.26 kNm |
| Check: numerical eigenvalue analysis | thin-walled beam FEM (Hermite elements) = M_cr,num = 124.442 kNm; deviation from the formula = 0.15 % information only | 124.44 kNm |
| Relative slenderness λ̄_LT [6.3.2.2(1)] | λ̄_LT = √(W_y·fy/Mcr) = √(324957.199·235/1.243e+8) | 0.78395 |
| LTB curve [Table 6.5] | Table 6.5: rolled I-section, h/b = 0.95 ≤ 2 = curve b, α_LT = 0.34 | 0.34 |
| Φ_LT [6.3.2.3(1)] | Φ_LT = 0,5[1 + α_LT(λ̄_LT − λ̄_LT,0) + β·λ̄_LT²], λ̄_LT,0 = 0,4, β = 0,75 = 0.5·[1 + 0.34·(0.784 − 0.4) + 0.75·0.784²] | 0.79574 |
| χ_LT [6.3.2.3(1)] | χ_LT = 1/(Φ_LT + √(Φ_LT² − β·λ̄_LT²)) ≤ 1,0 and ≤ 1/λ̄_LT² = 1/(0.796 + √(0.796² − 0.75·0.784²)) | 0.82591 |
| Correction factor k_c [Table 6.6] | Table 6.6 = k_c = 0.94 | 0.94 |
| f [6.3.2.3(2)] | f = 1 − 0,5(1 − k_c)[1 − 2(λ̄_LT − 0,8)²] ≤ 1,0 = 1 − 0.5·(1 − 0.94)·[1 − 2·(0.784 − 0.8)²] | 0.97002 |
| χ_LT,mod [6.3.2.3(2)] | χ_LT,mod = χ_LT/f ≤ 1,0 = 0.826/0.97 | 0.85144 |
| Buckling resistance moment [6.3.2.1(3)] | M_b,Rd = χ_LT·W_y·fy/γM1 = 0.851·324957.199·235/1 | 65.02 kNm |
| LTB ratio [6.3.2.1(1)] | M_Ed/M_b,Rd = 6.396/65.02 | 0.098374 |
ULS 0.9·G + ψ0 variable (CC1 new) 0.23
0.20 Cross-section resistance x = 2075 mm
EN 1993-1-1 §5.5, 6.2
| ε [Table 5.2] | ε = √(235/fy) = √(235/235) | 1 |
| Flange outstand c/t [Table 5.2] | c = (b − tw − 2r)/2 = (180 − 6 − 2·15)/2 = 72; c/tf = 7.579 limits 9ε/10ε/14ε = 9/10/14 → class 1 | 7.5789 |
| Web c/t (bending) [Table 5.2] | c = h − 2tf − 2r = 171 − 2·9.5 − 2·15 = 122; c/tw = 20.333 limits 72ε/83ε/124ε = 72/83/124 → class 1 | 20.333 |
| Class (bending) [5.5] | class = max(flange, web) = max(1, 1) | 1 |
| ε [Table 5.2] | ε = √(235/fy) = √(235/235) | 1 |
| Flange outstand c/t [Table 5.2] | c = (b − tw − 2r)/2 = (180 − 6 − 2·15)/2 = 72; c/tf = 7.579 limits 9ε/10ε/14ε = 9/10/14 → class 1 | 7.5789 |
| Web c/t (compression) [Table 5.2] | c = h − 2tf − 2r = 171 − 2·9.5 − 2·15 = 122; c/tw = 20.333 limits 33ε/38ε/42ε = 33/38/42 → class 1 | 20.333 |
| Class (compression) [5.5] | class = max(flange, web) = max(1, 1) | 1 |
| Plastic axial resistance [6.2.4] | N_pl,Rd = A·fy/γM0 = 4526.624·235/1 | 1063.8 kN |
| Bending resistance y-y (plastic) [6.2.5] | M_c,y,Rd = Wpl,y·fy/γM0 = 324957.199·235/1 | 76.365 kNm |
| Bending resistance z-z (plastic) [6.2.5] | M_c,z,Rd = Wpl,z·fy/γM0 = 156507.081·235/1 | 36.779 kNm |
| Plastic shear resistance (z) [6.2.6] | V_pl,z,Rd = Avz·fy/(√3·γM0) = 1448.624·235/(√3·1) | 196.55 kN |
| Shear ratio [6.2.6] | V_Ed/V_pl,z,Rd = 1.776e-15/196.545 | 9.038e-18 |
| Axial ratio [6.2.4] | |N_Ed|/N_pl,Rd = 0/1063.757 | 0 |
| n = N_Ed/N_pl,Rd [6.2.9.1] | n = 0/1063.757 | 0 |
| a = (A − 2 b tf)/A ≤ 0,5 [6.2.9.1(5)] | a = (4526.624 − 2·180·9.5)/4526.624 | 0.24447 |
| Reduced M_N,y,Rd [6.2.9.1(5)] | M_pl,y,Rd(1−n)/(1−0,5a) ≤ M_pl,y,Rd = 76.365·(1−0)/(1−0.5·0.244) | 76.365 kNm |
| Reduced M_N,z,Rd [6.2.9.1(5)] | n ≤ a: M_pl,z,Rd; else M_pl,z,Rd[1 − ((n−a)/(1−a))²] = n = 0, a = 0.244 | 36.779 kNm |
| Interaction [6.2.9.1(6)] | [M_y,Ed/M_N,y,Rd]^α + [M_z,Ed/M_N,z,Rd]^β, α = 2, β = max(1; 5n) = [15.181/76.365]^2 + [0/36.779]^1 | 0.039521 |
| Bending ratio per axis [6.2.9.1(2), 6.2.5] | M_y,Ed/M_N,y,Rd and M_z,Ed/M_N,z,Rd (each ≤ 1,0) = 15.181/76.365 = 0.199; 0/36.779 = 0 | 0.1988 |
0.07 Cross-section resistance (maximum shear) x = 4150 mm
EN 1993-1-1 §5.5, 6.2
| ε [Table 5.2] | ε = √(235/fy) = √(235/235) | 1 |
| Flange outstand c/t [Table 5.2] | c = (b − tw − 2r)/2 = (180 − 6 − 2·15)/2 = 72; c/tf = 7.579 limits 9ε/10ε/14ε = 9/10/14 → class 1 | 7.5789 |
| Web c/t (bending) [Table 5.2] | c = h − 2tf − 2r = 171 − 2·9.5 − 2·15 = 122; c/tw = 20.333 limits 72ε/83ε/124ε = 72/83/124 → class 1 | 20.333 |
| Class (bending) [5.5] | class = max(flange, web) = max(1, 1) | 1 |
| ε [Table 5.2] | ε = √(235/fy) = √(235/235) | 1 |
| Flange outstand c/t [Table 5.2] | c = (b − tw − 2r)/2 = (180 − 6 − 2·15)/2 = 72; c/tf = 7.579 limits 9ε/10ε/14ε = 9/10/14 → class 1 | 7.5789 |
| Web c/t (compression) [Table 5.2] | c = h − 2tf − 2r = 171 − 2·9.5 − 2·15 = 122; c/tw = 20.333 limits 33ε/38ε/42ε = 33/38/42 → class 1 | 20.333 |
| Class (compression) [5.5] | class = max(flange, web) = max(1, 1) | 1 |
| Plastic axial resistance [6.2.4] | N_pl,Rd = A·fy/γM0 = 4526.624·235/1 | 1063.8 kN |
| Bending resistance y-y (plastic) [6.2.5] | M_c,y,Rd = Wpl,y·fy/γM0 = 324957.199·235/1 | 76.365 kNm |
| Bending resistance z-z (plastic) [6.2.5] | M_c,z,Rd = Wpl,z·fy/γM0 = 156507.081·235/1 | 36.779 kNm |
| Plastic shear resistance (z) [6.2.6] | V_pl,z,Rd = Avz·fy/(√3·γM0) = 1448.624·235/(√3·1) | 196.55 kN |
| Shear ratio [6.2.6] | V_Ed/V_pl,z,Rd = 14.632/196.545 | 0.074448 |
| Axial ratio [6.2.4] | |N_Ed|/N_pl,Rd = 0/1063.757 | 0 |
| n = N_Ed/N_pl,Rd [6.2.9.1] | n = 0/1063.757 | 0 |
| a = (A − 2 b tf)/A ≤ 0,5 [6.2.9.1(5)] | a = (4526.624 − 2·180·9.5)/4526.624 | 0.24447 |
| Reduced M_N,y,Rd [6.2.9.1(5)] | M_pl,y,Rd(1−n)/(1−0,5a) ≤ M_pl,y,Rd = 76.365·(1−0)/(1−0.5·0.244) | 76.365 kNm |
| Reduced M_N,z,Rd [6.2.9.1(5)] | n ≤ a: M_pl,z,Rd; else M_pl,z,Rd[1 − ((n−a)/(1−a))²] = n = 0, a = 0.244 | 36.779 kNm |
| Interaction [6.2.9.1(6)] | [M_y,Ed/M_N,y,Rd]^α + [M_z,Ed/M_N,z,Rd]^β, α = 2, β = max(1; 5n) = [7.105e-15/76.365]^2 + [0/36.779]^1 | 8.657e-33 |
| Bending ratio per axis [6.2.9.1(2), 6.2.5] | M_y,Ed/M_N,y,Rd and M_z,Ed/M_N,z,Rd (each ≤ 1,0) = 7.105e-15/76.365 = 9.305e-17; 0/36.779 = 0 | 9.305e-17 |
0.23 Lateral-torsional buckling (LTB) segment 1: x = 0–4150 mm, L = 4150 mm
EN 1993-1-1 §6.3.2
| ε [Table 5.2] | ε = √(235/fy) = √(235/235) | 1 |
| Flange outstand c/t [Table 5.2] | c = (b − tw − 2r)/2 = (180 − 6 − 2·15)/2 = 72; c/tf = 7.579 limits 9ε/10ε/14ε = 9/10/14 → class 1 | 7.5789 |
| Web c/t (bending) [Table 5.2] | c = h − 2tf − 2r = 171 − 2·9.5 − 2·15 = 122; c/tw = 20.333 limits 72ε/83ε/124ε = 72/83/124 → class 1 | 20.333 |
| Class (bending) [5.5] | class = max(flange, web) = max(1, 1) | 1 |
| W_y (class 1) [6.3.2.2] | W_pl,y = 324957.199 mm³ | 324960 mm³ |
| π²·E·Iz/(k·L)² [NCCI SN003] | π²·E·Iz/(k·L)² = π²·210000·9.246e+6/(1·4150)² | 1112.7 kN (N·mm/mm) |
| C1 [NCCI SN003] | table value, uniform load (k = kw = 1,0) = C1 = 1.127, C2 = 0.454 | 1.127 |
| Load position z_g [NCCI SN003] | z_g = z_a − z_s (positive: load above the shear centre) = z_g = 85.5 mm | 85.5 mm |
| Square-root term [NCCI SN003] | (k/kw)²·Iw/Iz + (kL)²·G·It/(π²·E·Iz) + (C2·zg)² = (1/1)²·6.029e+10/9.246e+6 + (1·4150)²·81000·150965.805/(π²·210000·9.246e+6) + (0.454·85.5)² | 19017 |
| Elastic critical moment [NCCI SN003] | Mcr = C1·π²EIz/(kL)²·{√[...] − C2·zg} = 1.127·1112.719·(√19016.822 − 38.817) | 124.26 kNm |
| Check: numerical eigenvalue analysis | thin-walled beam FEM (Hermite elements) = M_cr,num = 124.442 kNm; deviation from the formula = 0.15 % information only | 124.44 kNm |
| Relative slenderness λ̄_LT [6.3.2.2(1)] | λ̄_LT = √(W_y·fy/Mcr) = √(324957.199·235/1.243e+8) | 0.78395 |
| LTB curve [Table 6.5] | Table 6.5: rolled I-section, h/b = 0.95 ≤ 2 = curve b, α_LT = 0.34 | 0.34 |
| Φ_LT [6.3.2.3(1)] | Φ_LT = 0,5[1 + α_LT(λ̄_LT − λ̄_LT,0) + β·λ̄_LT²], λ̄_LT,0 = 0,4, β = 0,75 = 0.5·[1 + 0.34·(0.784 − 0.4) + 0.75·0.784²] | 0.79574 |
| χ_LT [6.3.2.3(1)] | χ_LT = 1/(Φ_LT + √(Φ_LT² − β·λ̄_LT²)) ≤ 1,0 and ≤ 1/λ̄_LT² = 1/(0.796 + √(0.796² − 0.75·0.784²)) | 0.82591 |
| Correction factor k_c [Table 6.6] | Table 6.6 = k_c = 0.94 | 0.94 |
| f [6.3.2.3(2)] | f = 1 − 0,5(1 − k_c)[1 − 2(λ̄_LT − 0,8)²] ≤ 1,0 = 1 − 0.5·(1 − 0.94)·[1 − 2·(0.784 − 0.8)²] | 0.97002 |
| χ_LT,mod [6.3.2.3(2)] | χ_LT,mod = χ_LT/f ≤ 1,0 = 0.826/0.97 | 0.85144 |
| Buckling resistance moment [6.3.2.1(3)] | M_b,Rd = χ_LT·W_y·fy/γM1 = 0.851·324957.199·235/1 | 65.02 kNm |
| LTB ratio [6.3.2.1(1)] | M_Ed/M_b,Rd = 15.181/65.02 | 0.23349 |
Conclusion
Maximum unity check = 0.49 — ULS 6.10b (CC1 new): Lateral-torsional buckling (LTB), segment 1: x = 0–4150 mm, L = 4150 mm.
No lateral restraint points were given: LTB assumes restraint at the member ends only.
Calculation steps are in SI units (mm, N, kN, kNm, N/mm²).
For training, testing and educational use; not for the design of real structures.
For training, testing and educational use only. Not for design of real structures. Results are unverified. THE SOFTWARE IS PROVIDED 'AS IS', WITHOUT WARRANTY OF ANY KIND. Not a substitute for review by a licensed Professional Engineer (PE/SE) or equivalent.