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Geometry

Nodes

ID	X (m)	Y (m)	Support
Node B0 ID	Node B0 X coordinate, metres	Node B0 Y coordinate, metres	Node B0 support type
Node B1 ID	Node B1 X coordinate, metres	Node B1 Y coordinate, metres	Node B1 support type
Node B2 ID	Node B2 X coordinate, metres	Node B2 Y coordinate, metres	Node B2 support type
Node B3 ID	Node B3 X coordinate, metres	Node B3 Y coordinate, metres	Node B3 support type
Node B4 ID	Node B4 X coordinate, metres	Node B4 Y coordinate, metres	Node B4 support type
Node T1 ID	Node T1 X coordinate, metres	Node T1 Y coordinate, metres	Node T1 support type
Node T2 ID	Node T2 X coordinate, metres	Node T2 Y coordinate, metres	Node T2 support type
Node T3 ID	Node T3 X coordinate, metres	Node T3 Y coordinate, metres	Node T3 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 M4 ID	Member M4 start node	Member M4 end node
Member M5 ID	Member M5 start node	Member M5 end node
Member M6 ID	Member M6 start node	Member M6 end node
Member M7 ID	Member M7 start node	Member M7 end node
Member M8 ID	Member M8 start node	Member M8 end node
Member M9 ID	Member M9 start node	Member M9 end node
Member M10 ID	Member M10 start node	Member M10 end node
Member M11 ID	Member M11 start node	Member M11 end node
Member M12 ID	Member M12 start node	Member M12 end node
Member M13 ID	Member M13 start node	Member M13 end node

Member section & material (applied to all members)

Family

Section

Steel grade

Node loads (kN)

Node B0

B0 Fx

B0 Fy

Node B1

B1 Fx

B1 Fy

Node B2

B2 Fx

B2 Fy

Node B3

B3 Fx

B3 Fy

Node B4

B4 Fx

B4 Fy

Node T1

T1 Fx

T1 Fy

Node T2

T2 Fx

T2 Fy

Node T3

T3 Fx

T3 Fy

Truss Analysis

EN 1993-1-1 · HEA160 · S235

Governing checkMember M1173.3%ALL CHECKS PASS

Checks

Check	Demand	Capacity	Util.	Status
M1	200.0 kN (tension)	911.1 kN	22.0%	PASS
M2	200.0 kN (tension)	911.1 kN	22.0%	PASS
M3	200.0 kN (tension)	911.1 kN	22.0%	PASS
M4	200.0 kN (tension)	911.1 kN	22.0%	PASS
M5	266.7 kN (compression)	456.7 kN	58.4%	PASS
M6	266.7 kN (compression)	456.7 kN	58.4%	PASS
M7	100.0 kN (tension)	911.1 kN	11.0%	PASS
M8	0.0 kN (zero)	911.1 kN	0.0%	PASS
M9	100.0 kN (tension)	911.1 kN	11.0%	PASS
M10	250.0 kN (compression)	340.8 kN	73.3%	PASS
M11GOVERNS	250.0 kN (compression)	340.8 kN	73.3%	PASS
M12	83.3 kN (tension)	911.1 kN	9.1%	PASS
M13	83.3 kN (tension)	911.1 kN	9.1%	PASS

Models an idealized pin-jointed truss — every member carries pure axial force only, and loads can only be applied at nodes, not along a member’s length.
Stiffness-method solve with 2-DOF/joint bar elements — mathematically equivalent to the method of joints for a statically determinate truss; a linear-elastic, small-deflection (first-order) analysis only.
Net-section rupture at connections is not checked — verify separately at any bolted/welded joint.
A distributed load must be approximated as statically-equivalent point loads at the nearest joints.
Geometry and results are in SI units (m, kN, kN·m) only.
If the structure actually has rigid, moment-resisting joints, use Frame Analysis instead.

Related calculators

⌐Frame Analysis

Arbitrary-geometry 2D rigid frame analysis — graphical or accessible table geometry input, direct stiffness method with member self-loads, and combined bending/shear/axial checks per EC3 and AISC 360.

⋈Connection Design

Bolted shear (single/double angle, shear tab), bolted moment (flush/extended end-plate) and welded steel connections — bolt shear, bearing, block shear, prying action and fillet weld group capacity per EN 1993-1-8 and AISC 360.

◫Section Properties

Area, centroid, moment of inertia, section modulus, radius of gyration, plastic modulus and torsion constant — pick a standard steel section or enter a custom rectangle, I/W, channel, angle, T, circular or hollow shape.

Truss Analysis v1.0Validated against 16 benchmark cases →Learn: What does "statically determinate" actually mean? →Learn: Buckling: why slender steel members fail differently than stocky ones →Learn: Moment frames vs braced frames vs shear walls: how lateral systems actually differ →

Geometry & determinacy▼

Model summary

8 joints, 13 members, 3 reaction components

8 joints, 13 members, 3 reactions

StaticsDeterminacy count (necessary, not sufficient — the stiffness solve below is the rigorous check)

m + r = 2j ?

13 + 3 vs 2×8 = 16

m+r=16 → statically determinate

Stiffness-method solve▼

Bar-element assembly & solve

Kff · Uf = Pf (2 DOF/joint, axial-only elements)

16 total DOF, 13 free

Solved — joint displacements recovered

Global equilibrium check

ΣFx = ΣFy = 0 (applied loads + reactions)

ΣFx=-0.000 kN, ΣFy=0.000 kN

Satisfied

Member axial forces▼

Member M1 (HEA160)

N = (EA/L)·Δ, tension +ve

L=4.00 m

N = 200.0 kN (tension)

Member M2 (HEA160)

N = (EA/L)·Δ, tension +ve

L=4.00 m

N = 200.0 kN (tension)

Member M3 (HEA160)

N = (EA/L)·Δ, tension +ve

L=4.00 m

N = 200.0 kN (tension)

Member M4 (HEA160)

N = (EA/L)·Δ, tension +ve

L=4.00 m

N = 200.0 kN (tension)

Member M5 (HEA160)

N = (EA/L)·Δ, tension +ve

L=4.00 m

N = -266.7 kN (compression)

Member M6 (HEA160)

N = (EA/L)·Δ, tension +ve

L=4.00 m

N = -266.7 kN (compression)

Member M7 (HEA160)

N = (EA/L)·Δ, tension +ve

L=3.00 m

N = 100.0 kN (tension)

Member M8 (HEA160)

N = (EA/L)·Δ, tension +ve

L=3.00 m

N = 0.0 kN (zero)

Member M9 (HEA160)

N = (EA/L)·Δ, tension +ve

L=3.00 m

N = 100.0 kN (tension)

Member M10 (HEA160)

N = (EA/L)·Δ, tension +ve

L=5.00 m

N = -250.0 kN (compression)

Member M11 (HEA160)

N = (EA/L)·Δ, tension +ve

L=5.00 m

N = -250.0 kN (compression)

Member M12 (HEA160)

N = (EA/L)·Δ, tension +ve

L=5.00 m

N = 83.3 kN (tension)

Member M13 (HEA160)

N = (EA/L)·Δ, tension +ve

L=5.00 m

N = 83.3 kN (tension)

Support reactions▼

Reaction at B0

Rx = -0.0 kN, Ry = 150.0 kN

Reaction at B4

Rx = 0.0 kN, Ry = 150.0 kN

Governing member M11 — compression▼

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 = 62.0/9 = 6.89 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 = 104.0/6 = 17.33 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=9.0 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=5000 mm, Lcr,z=5000 mm

Ncr,y=1387.0 kN, Ncr,z=510.7 kN

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

λ̄ = √(Npl,Rd/Ncr)

Npl,Rd=911.1 kN

λ̄y=0.810, λ̄z=1.336

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=0.718, χz=0.374

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

Nb,Rd = χ·A·fy/γM1

γM1=1

Nb,Rd,y=654.1 kN, Nb,Rd,z=340.8 kN → governs z-z

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

Truss Analysis Calculator

Truss Analysis