Eurocode 3 Verification

Benchmarking against SCI P364, Designers' Guide to EN 1993-1-1, EUR 22898 EN, and Worked Examples in EC3 & EC4.

Benchmark Cases

126

Textbook Verified

Avg. Difference

0.43%

vs. Ref Sources

Check Coverage

Resistance Modes

Sections Supported

Shape Families

Verification Methodology

The Eurocode 3 engine implements the requirements of EN 1993-1-1: General rules and rules for buildings. Verification is performed using high-quality benchmarks from Designers' Guide to EN 1993-1-1 Eurocode 3 (Gardner & Nethercot), SCI P364 (Steel Building Design: Worked Examples for Open Sections), Worked Examples in EC3 & EC4, and EUR 22898 EN (Commentary and Worked Examples to EN 1993-1-5).

Cross-section Resistance: Verified for axial, bending, and shear according to Section 6.2 for all section classes.
Buckling Resistance: Flexural buckling (6.3.1) and Lateral-Torsional Buckling (6.3.2) verified against analytical solutions for all member types.
Combined stability: Implements Annex B (Method 2) for interaction factors k_yy, k_yz, k_zy, k_zz across diverse loading scenarios.

Benchmark Results

Description	Section	Expected	Result	Difference
406x178x54 UB flange class (pure bending)Designers' Guide to EN 1993-1-1, Ex 5.1	406x178x54 UB	Class 1	Class 1	0.00%
406x178x54 UB web class (pure bending)Designers' Guide to EN 1993-1-1, Ex 5.1	406x178x54 UB	Class 1	Class 1	0.00%
406x178x54 UB overall class (pure bending)Designers' Guide to EN 1993-1-1, Ex 5.1	406x178x54 UB	Class 1	Class 1	0.00%
406x178x54 UB flange class (N=300kN)Designers' Guide to EN 1993-1-1, Ex 5.1	406x178x54 UB	Class 1	Class 1	0.00%
406x178x54 UB web class (N=300kN)Designers' Guide to EN 1993-1-1, Ex 5.1	406x178x54 UB	Class 2	Class 2	0.00%
406x178x54 UB overall class (N=300kN)Designers' Guide to EN 1993-1-1, Ex 5.1	406x178x54 UB	Class 2	Class 2	0.00%
254x254x73 UC flange class (pure compression)Designers' Guide to EN 1993-1-1, Ex 6.2	254x254x73 UC	Class 2	Class 2	0.00%
254x254x73 UC overall classDesigners' Guide to EN 1993-1-1, Ex 6.2	254x254x73 UC	Class 2	Class 2	0.00%
229x89 Channel flange classDesigners' Guide to EN 1993-1-1, Ex 6.4	229x89 Channel	Class 1	Class 1	0.00%
229x89 Channel web classDesigners' Guide to EN 1993-1-1, Ex 6.4	229x89 Channel	Class 1	Class 1	0.00%
229x89 Channel overall classDesigners' Guide to EN 1993-1-1, Ex 6.4	229x89 Channel	Class 1	Class 1	0.00%
CHS 244.5x10 overall classDesigners' Guide to EN 1993-1-1, Ex 6.7	CHS 244.5x10	Class 1	Class 1	0.00%
RHS 200x100x16 flange classDesigners' Guide to EN 1993-1-1, Ex 6.9	RHS 200x100x16	Class 1	Class 1	0.00%
RHS 200x100x16 web classDesigners' Guide to EN 1993-1-1, Ex 6.9	RHS 200x100x16	Class 1	Class 1	0.00%
RHS 200x100x16 overall classDesigners' Guide to EN 1993-1-1, Ex 6.9	RHS 200x100x16	Class 1	Class 1	0.00%
229x89 Channel Vpl,RdDesigners' Guide to EN 1993-1-1, Ex 6.4	229x89 Channel	332 kN	332.1 kN	0.05%
UB 533x210x92 Mc,RdDesigners' Guide to EN 1993-1-1 / SCI P364	UB 533x210x92	649.0 kNm	649.0 kNm	0.00%
UB 406x178x74 rho factor (shear-bending)Designers' Guide to EN 1993-1-1, Ex 6.5	UB 406x178x74	0.27	0.274	1.50%
ⓘ Rounding of the ρ factor intermediate value — textbook rounds to 2 significant figures mid-calculation, engine retains full precision.
UB 406x178x74 My,V,Rd (Aw per Eq 6.30)Designers' Guide to EN 1993-1-1, Ex 6.5	UB 406x178x74	386.8 kNm	386.8 kNm	0.00%
H 305x305x240 Cl.6.2.9 biaxial interaction ratioDesigners' Guide to EN 1993-1-1, Ex 6.10	H 305x305x240	0.33	0.339	2.77%
ⓘ Textbook rounds reduced plastic moment MN,Rd and interaction terms to 2 significant figures. The engine retains full intermediate precision, leading to a slightly higher biaxial ratio.
UB 457x191x98 n ratio (N/Npl)Designers' Guide to EN 1993-1-1, Ex 6.6	UB 457x191x98	0.477	0.477	0.08%
UB 457x191x98 a parameterDesigners' Guide to EN 1993-1-1, Ex 6.6	UB 457x191x98	0.395	0.395	0.10%
UB 457x191x98 MN,y,RdDesigners' Guide to EN 1993-1-1, Ex 6.6	UB 457x191x98	342.2 kNm	342.2 kNm	0.01%
CHS 244.5x10 radius of gyration iDesigners' Guide to EN 1993-1-1, Ex 6.7	CHS 244.5x10	82.97 mm	82.97 mm	0.01%
CHS 244.5x10 λ_barDesigners' Guide to EN 1993-1-1, Ex 6.7	CHS 244.5x10	0.56	0.555	0.83%
CHS 244.5x10 χ (curve a)Designers' Guide to EN 1993-1-1, Ex 6.7	CHS 244.5x10	0.91	0.906	0.42%
CHS 244.5x10 Nb,RdDesigners' Guide to EN 1993-1-1, Ex 6.7	CHS 244.5x10	1836.5 kN	1836.5 kN	0.00%
CHS 244.5x10 buckling ratio (NEd=1630 kN)Designers' Guide to EN 1993-1-1, Ex 6.7	CHS 244.5x10	0.888	0.888	0.00%
H 305x305x240 iyDesigners' Guide to EN 1993-1-1, Ex 6.10	H 305x305x240	144.86 mm	144.85 mm	0.01%
H 305x305x240 λ_bar_yDesigners' Guide to EN 1993-1-1, Ex 6.10	H 305x305x240	0.23	0.234	1.65%
ⓘ Textbook rounds λ̄ to 2 decimal places. Engine retains full precision from section property calculations.
H 305x305x240 χ_y (curve b)Designers' Guide to EN 1993-1-1, Ex 6.10	H 305x305x240	0.99	0.988	0.20%
H 305x305x240 izDesigners' Guide to EN 1993-1-1, Ex 6.10	H 305x305x240	81.46 mm	81.47 mm	0.01%
H 305x305x240 λ_bar_zDesigners' Guide to EN 1993-1-1, Ex 6.10	H 305x305x240	0.59	0.594	0.65%
H 305x305x240 χ_z (curve c)Designers' Guide to EN 1993-1-1, Ex 6.10	H 305x305x240	0.79	0.789	0.12%
RHS 200x100x16 iyDesigners' Guide to EN 1993-1-1, Ex 6.9	RHS 200x100x16	66.56 mm	66.57 mm	0.01%
RHS 200x100x16 λ_bar_yDesigners' Guide to EN 1993-1-1, Ex 6.9	RHS 200x100x16	1.42	1.416	0.31%
RHS 200x100x16 χ_y (curve a)Designers' Guide to EN 1993-1-1, Ex 6.9	RHS 200x100x16	0.41	0.410	0.10%
RHS 200x100x16 izDesigners' Guide to EN 1993-1-1, Ex 6.9	RHS 200x100x16	37.17 mm	37.17 mm	0.01%
RHS 200x100x16 λ_bar_zDesigners' Guide to EN 1993-1-1, Ex 6.9	RHS 200x100x16	0.84	0.845	0.59%
RHS 200x100x16 χ_z (curve a)Designers' Guide to EN 1993-1-1, Ex 6.9	RHS 200x100x16	0.77	0.769	0.12%
UC 203x203x46 λ_bar_yWorked Examples in EC3 & EC4	UC 203x203x46	0.65	0.653	0.46%
UC 203x203x46 χ_y (curve b)Worked Examples in EC3 & EC4	UC 203x203x46	0.81	0.810	0.05%
UC 203x203x46 λ_bar_zWorked Examples in EC3 & EC4	UC 203x203x46	0.56	0.561	0.24%
UC 203x203x46 χ_z (curve c)Worked Examples in EC3 & EC4	UC 203x203x46	0.81	0.808	0.24%
UB 762x267x173 Mcr Segment CDDesigners' Guide to EN 1993-1-1	UB 762x267x173	4311 kNm	4311 kNm	0.01%
UB 762x267x173 λ_LT Segment CDDesigners' Guide to EN 1993-1-1	UB 762x267x173	0.63	0.629	0.13%
UB 762x267x173 χ_LT Segment CD (general)Designers' Guide to EN 1993-1-1	UB 762x267x173	0.82	0.822	0.26%
UB 762x267x173 λ_LT Segment BCDesigners' Guide to EN 1993-1-1	UB 762x267x173	0.55	0.547	0.54%
UB 762x267x173 χ_LT Segment BC (general)Designers' Guide to EN 1993-1-1	UB 762x267x173	0.86	0.863	0.32%
UB 762x267x173 Mb,Rd Segment BCDesigners' Guide to EN 1993-1-1	UB 762x267x173	1469 kNm	1471 kNm	0.10%
UB 457x191x82 λ_LTDesigners' Guide to EN 1993-1-1	UB 457x191x82	0.64	0.641	0.20%
UB 457x191x82 χ_LT (general)Designers' Guide to EN 1993-1-1	UB 457x191x82	0.82	0.816	0.51%
UB 457x191x82 Mb,RdDesigners' Guide to EN 1993-1-1	UB 457x191x82	411 kNm	411 kNm	0.06%
UC 203x203x46 Cl.6.3.3 ratio (Annex B)Worked Examples in EC3 & EC4	UC 203x203x46	0.51	0.503	1.37%
ⓘ Interaction factors kyy, kzy computed with full precision vs textbook's 2 d.p. rounding of intermediate χ and λ̄ values.
H 305x305x240 Cl.6.3.3 ratio (Annex B)Designers' Guide to EN 1993-1-1, Ex 6.10	H 305x305x240	0.97	0.967	0.34%
RHS 200x100x16 Cl.6.3.3 ratio (Annex B)Designers' Guide to EN 1993-1-1, Ex 6.9	RHS 200x100x16	0.94	0.947	0.73%
P364 Ex2: 533x210x92 AvSCI P364, Example 2	533x210x92 UKB	5723.6 mm²	5723.6 mm²	0.00%
P364 Ex2: 533x210x92 Vpl,RdSCI P364, Example 2	533x210x92 UKB	909 kN	909 kN	0.03%
P364 Ex2: 533x210x92 VEd/Vc,RdSCI P364, Example 2	533x210x92 UKB	0.297	0.297	0.03%
P364 Ex2: 533x210x92 MEd/Mc,RdSCI P364, Example 2	533x210x92 UKB	0.831	0.831	0.00%
P364 Ex3: 457x191x67 AvSCI P364, Example 3	457x191x67 UKB	4093.57 mm²	4093.57 mm²	0.00%
P364 Ex3: 457x191x67 Vpl,RdSCI P364, Example 3	457x191x67 UKB	650 kN	650 kN	0.01%
P364 Ex3: 457x191x67 Mc,RdSCI P364, Example 3	457x191x67 UKB	404.25 kNm	404.25 kNm	0.00%
P364 Ex3: 457x191x67 Mcr uniformSCI P364, Example 3	457x191x67 UKB	134.2 kNm	133.7 kNm	0.37%
P364 Ex3: 457x191x67 Mcr with C1=2.65SCI P364, Example 3	457x191x67 UKB	355.7 kNm	354.2 kNm	0.42%
P364 Ex3: 457x191x67 λ_LTSCI P364, Example 3	457x191x67 UKB	1.07	1.068	0.19%
P364 Ex3: 457x191x67 χ_LT baseSCI P364, Example 3	457x191x67 UKB	0.60	0.598	0.27%
P364 Ex3: 457x191x67 f factorSCI P364, Example 3	457x191x67 UKB	0.83	0.833	0.37%
P364 Ex3: 457x191x67 χ_LT,modSCI P364, Example 3	457x191x67 UKB	0.72	0.718	0.24%
P364 Ex3: 457x191x67 Mb,RdSCI P364, Example 3	457x191x67 UKB	291 kNm	290.4 kNm	0.22%
P364 Ex3: 457x191x67 MEd/Mb,RdSCI P364, Example 3	457x191x67 UKB	0.89	0.896	0.61%
P364 Ex5: 305x305x97 UKC flange classSCI P364, Example 5	305x305x97 UKC	Class 3	Class 3	0.00%
P364 Ex5: 305x305x97 UKC web classSCI P364, Example 5	305x305x97 UKC	Class 1	Class 1	0.00%
P364 Ex5: 305x305x97 UKC overall classSCI P364, Example 5	305x305x97 UKC	Class 3	Class 3	0.00%
P364 Ex5: 305x305x97 AvSCI P364, Example 5	305x305x97 UKC	3517.38 mm²	3517.38 mm²	0.00%
P364 Ex5: 305x305x97 Vpl,RdSCI P364, Example 5	305x305x97 UKC	721 kN	721 kN	0.01%
P364 Ex5: 305x305x97 Mc,Rd (elastic, Class 3)SCI P364, Example 5	305x305x97 UKC	514.75 kNm	514.75 kNm	0.00%
P364 Ex5: 305x305x97 MEd/Mc,RdSCI P364, Example 5	305x305x97 UKC	0.641	0.641	0.00%
P364 Ex5: 305x305x97 Mcr uniformSCI P364, Example 5	305x305x97 UKC	460.5 kNm	461.4 kNm	0.20%
P364 Ex5: 305x305x97 Mcr with C1=1.32SCI P364, Example 5	305x305x97 UKC	607.7 kNm	609.1 kNm	0.23%
P364 Ex5: 305x305x97 λ_LTSCI P364, Example 5	305x305x97 UKC	0.92	0.919	0.08%
P364 Ex5: 305x305x97 χ_LT baseSCI P364, Example 5	305x305x97 UKC	0.74	0.749	1.15%
ⓘ Engine uses continuous LTB curve formula; textbook rounds intermediate Φ_LT to 2 d.p.
P364 Ex5: 305x305x97 χ_LT,modSCI P364, Example 5	305x305x97 UKC	0.79	0.799	1.14%
ⓘ Cascading from EC3-91: textbook rounds Φ_LT to 2 d.p., propagating through to χ_LT,mod.
P364 Ex5: 305x305x97 Mb,RdSCI P364, Example 5	305x305x97 UKC	407 kNm	411 kNm	1.05%
ⓘ Cascading from χ_LT,mod precision difference (EC3-91/92). Engine gives a slightly higher Mb,Rd.
P364 Ex5: 305x305x97 MEd/Mb,RdSCI P364, Example 5	305x305x97 UKC	0.81	0.802	0.94%
P364 Ex9: 356x368x129 UKC flange classSCI P364, Example 9	356x368x129 UKC	Class 3	Class 3	0.00%
P364 Ex9: 356x368x129 UKC overall classSCI P364, Example 9	356x368x129 UKC	Class 3	Class 3	0.00%
P364 Ex9: 356x368x129 Nc,RdSCI P364, Example 9	356x368x129 UKC	5658 kN	5658 kN	0.00%
P364 Ex9: 356x368x129 NEd/Nc,RdSCI P364, Example 9	356x368x129 UKC	0.619	0.619	0.00%
P364 Ex9: 356x368x129 λ_bar_zSCI P364, Example 9	356x368x129 UKC	0.82	0.821	0.11%
P364 Ex9: 356x368x129 χ_zSCI P364, Example 9	356x368x129 UKC	0.65	0.649	0.15%
P364 Ex9: 356x368x129 Nb,RdSCI P364, Example 9	356x368x129 UKC	3678 kN	3672 kN	0.16%
P364 Ex9: 356x368x129 buckling ratioSCI P364, Example 9	356x368x129 UKC	0.952	0.953	0.16%
P364 Ex10: 305x305x97 λ_bar_ySCI P364, Example 10	305x305x97 UKC	0.516	0.516	0.05%
P364 Ex10: 305x305x97 χ_ySCI P364, Example 10	305x305x97 UKC	0.87	0.877	0.82%
P364 Ex10: 305x305x97 Nb,y,RdSCI P364, Example 10	305x305x97 UKC	2943 kN	2967 kN	0.82%
P364 Ex10: 305x305x97 λ_bar_zSCI P364, Example 10	305x305x97 UKC	0.449	0.449	0.05%
P364 Ex10: 305x305x97 χ_zSCI P364, Example 10	305x305x97 UKC	0.88	0.871	1.00%
ⓘ Engine uses continuous buckling curve c formula; textbook rounds intermediate Φ to 2 d.p.
P364 Ex4: 457x191x82 Vpl,RdSCI P364, Example 4	457x191x82 UKB	756 kN	756 kN	0.03%
P364 Ex4: 457x191x82 χ_LT,mod (6.3.2.3 rolled)SCI P364, Example 4	457x191x82 UKB	0.92	0.882	4.15%
ⓘ Engine uses the NCCI SN003 closed-form Mcr formula (standard analytical method). The textbook derives Mcr from LTBeam finite element software, which yields ~4% lower λ_LT for this section. The analytical result is conservative (safe side).
P364 Ex4: 457x191x82 Mb,RdSCI P364, Example 4	457x191x82 UKB	463 kNm	444 kNm	4.10%
ⓘ Cascading from Mcr method difference above. Engine uses NCCI SN003 analytical Mcr; textbook uses LTBeam FE software. Result is conservative (safe side).
P364 Ex11: 203x203x46 χ_ySCI P364, Example 11	203x203x46 UKC	0.80	0.810	1.20%
ⓘ Textbook rounds intermediate Φ to 2 d.p. in buckling curve b; engine retains full precision.
P364 Ex11: 203x203x46 χ_zSCI P364, Example 11	203x203x46 UKC	0.47	0.472	0.49%
P364 Ex11: 203x203x46 χ_LTSCI P364, Example 11	203x203x46 UKC	0.83	0.846	1.93%
ⓘ Engine’s SCI/NCCI C1 polynomial approximation overestimates C1 for this moment diagram, yielding a lower λ_LT (0.725 vs textbook 0.76 via LTBeam) and higher χ_LT. The structural interaction ratio remains within 1.6% of the textbook.
P364 Ex11: 203x203x46 Cl.6.3.3 combined ratioSCI P364, Example 11	203x203x46 UKC	0.98	0.996	1.59%
ⓘ Combined cascading effect from χ_y (EC3-111) and χ_LT (EC3-113) C1 approximation differences.
P364 Ex12: 457x191x67 χ_y (S355)SCI P364, Example 12	457x191x67 UKB	0.94	0.946	0.66%
P364 Ex12: 457x191x67 χ_z (S355)SCI P364, Example 12	457x191x67 UKB	0.62	0.627	1.14%
ⓘ Textbook rounds intermediate Φ to 2 d.p. in buckling curve b; engine retains full precision.
P364 Ex12: 457x191x67 χ_LT (S355, Class 3)SCI P364, Example 12	457x191x67 UKB	0.88	0.825	6.24%
ⓘ Engine uses NCCI SN003 analytical Mcr with fork support (free warping) at each 3m segment. The textbook uses LTBeam FE software which models warping continuity at the intermediate restraint, giving a higher Mcr. Lower χ_LT = lower capacity prediction = conservative (safe side).
P364 Ex12: 457x191x67 Cl.6.3.3 combined ratio (Class 3)SCI P364, Example 12	457x191x67 UKB	0.88	0.934	6.11%
ⓘ Cascading from χ_LT difference above. Engine’s analytical Mcr (fork support) vs textbook’s LTBeam (warping continuity) propagates into the 6.3.3 interaction factors. Result is conservative (safe side).
EUR 22898 §16: Panel I plate slenderness (450×12, S355)EUR 22898 EN, §16 (pp.182)	Plate panel 450×12	0.811	0.812	0.06%
EUR 22898 §16: Panel I reduction factor ρEUR 22898 EN, §16 (pp.182)	Plate panel 450×12	0.899	0.898	0.08%
EUR 22898 §16: Panel III plate slenderness (288×6, S355)EUR 22898 EN, §16 (pp.182)	Plate panel 288×6	1.038	1.039	0.06%
EUR 22898 §16: Panel III reduction factor ρEUR 22898 EN, §16 (pp.182)	Plate panel 288×6	0.759	0.759	0.02%
EUR 22898 §15: Bottom flange plate slenderness (700×26, S420)EUR 22898 EN, §15 (pp.174-178)	Plate panel 700×26	0.63	0.634	0.58%
EUR 22898 §15: Stiffener plate slenderness (350×8, S420)EUR 22898 EN, §15 (pp.174-178)	Plate panel 350×8	1.03	1.030	0.03%
EUR 22898 §15: Stiffener reduction factor ρEUR 22898 EN, §15 (pp.174-178)	Plate panel 350×8	0.763	0.764	0.09%
EUR 22898 §15: Inclined web plate slenderness (391×8, S420)EUR 22898 EN, §15 (pp.174-178)	Plate panel 391×8	1.15	1.150	0.03%
EUR 22898 §15: Inclined web reduction factor ρEUR 22898 EN, §15 (pp.174-178)	Plate panel 391×8	0.703	0.703	0.01%
EUR 22898 §15: kσ for web ψ=−1.30 (Table 4.1)EN 1993-1-5 Table 4.1 (kσ = 5.98(1−ψ)² for ψ < −1)	EN 1993-1-5 Table 4.1	31.63	31.63	0.00%
ⓘ EUR 22898 EN p.178 uses an approximate formula giving kσ=32.5; the correct Table 4.1 formula gives 31.63.
EUR 22898 §15: ρ web bending at λp=1.07, ψ=−1.30EUR 22898 EN, §15 (p.178)	Plate panel (bending)	0.853	0.853	0.01%
EUR 22898 Eq 4.1: ρ internal λp=2.0 ψ=1EUR 22898 EN, Eq 4.1 (pp.46-47)	EN 1993-1-5 Eq 4.1	0.445	0.445	0.00%
EUR 22898 Eq 4.2: ρ outstand λp=1.5EUR 22898 EN, Eq 4.2 (pp.46-47)	EN 1993-1-5 Eq 4.2	0.583	0.583	0.02%
EUR 22898 §15.2: Stiffener ρ at λp=0.857EUR 22898 EN, §15.2 (p.177)	Plate panel (stiffener)	0.868	0.867	0.08%
254x254x73 UC Compression Resistance Nc,Rd (S355)Designers' Guide to EN 1993-1-1, Ex 6.2	254x254x73 UC	3305 kN	3305.1 kN	0.00%
CHS 244.5x10 Section Compression Npl,Rd (S275)Designers' Guide to EN 1993-1-1, Ex 6.7	CHS 244.5x10	2026.75 kN	2025.9 kN	0.04%
RHS 200x100x16 Bending Resistance Mc,Rd (S355, Class 1)Designers' Guide to EN 1993-1-1, Ex 6.9	RHS 200x100x16	174.3 kNm	174.3 kNm	0.00%

Disclaimer: This verification page is provided for informative purposes only and does not constitute a guarantee of accuracy for all possible configurations. While we strive to ensure the correctness of our calculations through rigorous benchmarking, no software is entirely free of defects. Engineers must exercise independent professional judgement and verify results through their own checks before relying on any output for design or construction decisions. AutoCalcs accepts no liability for errors, omissions, or any consequences arising from the use of this software.

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