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Geometry

Nodes

ID	X (m)	Y (m)	Support
Node C0 ID	Node C0 X coordinate, metres	Node C0 Y coordinate, metres	Node C0 support type
Node C1 ID	Node C1 X coordinate, metres	Node C1 Y coordinate, metres	Node C1 support type
Node C2 ID	Node C2 X coordinate, metres	Node C2 Y coordinate, metres	Node C2 support type
Node C3 ID	Node C3 X coordinate, metres	Node C3 Y coordinate, metres	Node C3 support type

Members

ID	Start node	End node
Member M1 ID	Member M1 start node	Member M1 end node
Member M2 ID	Member M2 start node	Member M2 end node
Member M3 ID	Member M3 start node	Member M3 end node

Member section & material (applied to all members)

Family

Section

Steel grade

Member UDLs (kN/m, downward)

Member M1

M1 UDL

Member M2

M2 UDL

Member M3

M3 UDL

Node loads (kN, kN·m)

Node C0

C0 Fx

C0 Fy

C0 Mz

Node C1

C1 Fx

C1 Fy

C1 Mz

Node C2

C2 Fx

C2 Fy

C2 Mz

Node C3

C3 Fx

C3 Fy

C3 Mz

Frame Analysis

EN 1993-1-1 · HEA200 · S235

Governing checkMember M273.4%ALL CHECKS PASS

Checks

Check	Demand	Capacity	Util.	Status
M1 — bending	17.7 kN·m	100.9 kN·m	17.6%	PASS
M1 — shear	2.6 kN	245.3 kN	1.1%	PASS
M1 — axial	39.7 kN	1265.0 kN	3.1%	PASS
M1 — interaction	—	—	20.7%	PASS
M2 — bending	72.3 kN·m	100.9 kN·m	71.6%	PASS
M2 — shear	50.3 kN	245.3 kN	20.5%	PASS
M2 — axial	22.6 kN	1265.0 kN	1.8%	PASS
M2 — interactionGOVERNS	—	—	73.4%	PASS
M3 — bending	49.7 kN·m	100.9 kN·m	49.2%	PASS
M3 — shear	22.6 kN	245.3 kN	9.2%	PASS
M3 — axial	50.3 kN	1265.0 kN	4.0%	PASS
M3 — interaction	—	—	53.2%	PASS

First-order elastic analysis only — no P-Δ (second-order) effects.
No lateral-torsional buckling check on frame members.
EC3 combined axial+bending uses a disclosed conservative linear interaction (N/Nb,Rd + My/Mc,Rd ≤ 1), not the full §6.3.3 sway-buckling interaction.
A member’s own UDL is automatically resolved into along-member and perpendicular components regardless of the member’s angle.
A concentrated moment at a node transfers into every member framing into that node, since joints are modeled as fully rigid.
Geometry and results are in SI units (m, kN, kN·m) only.

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Stiffness-method solve▼

Beam-column assembly & solve

Kff · Uf = Pf (3 DOF/node: u, v, θ)

12 total DOF, 6 free

Solved — nodal displacements/rotations recovered

Global equilibrium check

ΣFx = ΣFy = 0 (applied + member self-loads + reactions)

ΣFx=0.000 kN, ΣFy=-0.000 kN

Satisfied

Member end forces & governing demand▼

Member M1 (HEA200)

Recovered via q = k·(T·u) + FEF

L=4.00 m

Mmax=17.7 kN·m, Vmax=2.6 kN, N=-39.7 kN

Member M2 (HEA200)

Recovered via q = k·(T·u) + FEF

L=6.00 m

Mmax=72.3 kN·m, Vmax=50.3 kN, N=-22.6 kN

Member M3 (HEA200)

Recovered via q = k·(T·u) + FEF

L=4.00 m

Mmax=49.7 kN·m, Vmax=22.6 kN, N=-50.3 kN

Support reactions▼

Reaction at C0

Rx=2.6 kN, Ry=39.7 kN, Mz=7.2 kN·m

Reaction at C3

Rx=-22.6 kN, Ry=50.3 kN, Mz=40.8 kN·m

Governing member M2▼

§6.2.5(2)Section modulus for Class 1

Class 1/2 → plastic modulus

Wpl,y = 429.5 × 10³ mm³

Wpl,y = 429500 mm³

§6.2.5(2)Design resistance for bending

Mc,Rd = Wpl,y · fy / γM0

Mc,Rd = 429500 × 235 / 1

Mc,Rd = 100.9 kN·m

§6.2.5(1)Cross-section bending check

MEd / Mc,Rd ≤ 1.0

72.3 / 100.9

Ratio = 0.716 → OK

§6.2.6(3)aShear area, rolled I-section

Av = A − 2b·tf + (tw + 2r)·tf ≥ η·hw·tw

Av = 5383 − 2×200×10 + (6.5 + 2×18)×10 = 1808; min 1326

Av = 1808 mm²

§6.2.6(2)Plastic shear resistance

Vpl,Rd = Av · (fy/√3) / γM0

Vpl,Rd = 1808 × (235/√3) / 1

Vpl,Rd = 245.3 kN

§6.2.6(6)Web shear buckling check

hw/tw ≤ 72ε/η, else EN 1993-1-5 §5 governs

26.2 vs 60.0

OK — no shear buckling check needed

§6.2.6(1)Shear check

VEd / Vpl,Rd ≤ 1.0

50.3 / 245.3

Ratio = 0.205 → OK

Table 5.2Material coefficient

ε = √(235 / fy)

ε = √(235 / 235)

ε = 1.000

Table 5.2Flange (outstand in compression)

c = (b − tw − 2r)/2; limits 9ε | 10ε | 14ε

c/tf = 78.8/10 = 7.88 vs 9.00 | 10.00 | 14.00

Flange: Class 1

Table 5.2Web (internal, in bending)

c = h − 2tf − 2r; limits 72ε | 83ε | 124ε

c/tw = 134.0/6.5 = 20.62 vs 72.0 | 83.0 | 124.0

Web: Class 1

§5.5.2(6)Section class = least favourable element class

max(flange, web)

max(1, 1)

Section: Class 1

EN 1993-1-1 Table 6.2Buckling curve selection (h/b=0.95, tf=10.0 mm)

curve y-y = b, curve z-z = c

EN 1993-1-1 §6.3.1.3Elastic critical buckling force, both axes

Ncr = π²·E·I/Lcr²

Lcr,y=6000 mm, Lcr,z=6000 mm

Ncr,y=2125.6 kN, Ncr,z=769.2 kN

EN 1993-1-1 (6.50)Non-dimensional slenderness

λ̄ = √(Npl,Rd/Ncr)

Npl,Rd=1265.0 kN

λ̄y=0.771, λ̄z=1.282

EN 1993-1-1 (6.49)Reduction factor χ (imperfection factor α from the curve)

χ = 1/(Φ+√(Φ²−λ̄²)) ≤ 1

αy=0.34, αz=0.49

χy=1.000 (λ̄≤0.2, buckling ignored per §6.3.1.2(4)), χz=1.000 (λ̄≤0.2, buckling ignored)

EN 1993-1-1 (6.47)Buckling resistance, both axes — governing axis controls

Nb,Rd = χ·A·fy/γM1

γM1=1

Nb,Rd,y=1265.0 kN, Nb,Rd,z=1265.0 kN → governs y-y

EN 1993-1-1 (disclosed simplification)Combined axial + bending — linear interaction

N/Nb,Rd + My/Mc,Rd ≤ 1.0

22.6/1265.0 + 72.3/100.9

Ratio = 0.734 → OK

Step values are shown in SI (m, kN, kN·m) regardless of the display-unit toggle.

Frame Analysis Calculator

Frame Analysis