SB10 · STATIC-TRUSS · Element Benchmarks

Asymmetric determinate two-bar truss (brace axial force)

Brace axial force, apex displacement & reactions — determinate bar absolute check

PASS 0.00% error tolerance 0% 10000 N vs 10000 N
§2

Technical features tested

  • element Truss — linear (small-displacement) bar
  • memberType brace, two-sided, no P-Delta
  • Orthonormal braces ⇒ K = (EA/L)·I
  • Statically determinate ⇒ exact closed form
  • Axial from elem_force.out localForce
§3

Problem description

Two prismatic braces span from a free apex N3 up to two fully fixed supports N1 and N2. A single apex point load with components along global −X and −Z puts both braces in tension. Because the two bar directions are mutually orthogonal, the assembled apex stiffness is diagonal, and the configuration is statically determinate — so the member axial forces, the apex displacement, and the two support reactions all follow from equilibrium and the EA/L bar law in closed form. A two-sided brace with P-Delta off is emitted as a linear Truss, which carries no geometric offset, so STRIX must reproduce every quantity to machine precision.

E1 (tension) E2 (tension) N1 N2 N3 (apex) Fz Fx Z X
Figure SB10. Asymmetric two-bar truss: fixed supports N1, N2 and loaded free apex N3 (both braces in tension).
§4

Geometry, properties & loading

Geometry

Braces
2 (E1, E2)
Length L
5000 mm
Area A
1000 mm²
Dir û1 (N3→N1)
(−0.6, 0, 0.8)
Dir û2 (N3→N2)
(0.8, 0, 0.6)

Material

Model
Elastic
E
200000 MPa
ν
0.3
Units
N · mm

Loading & BC

N1, N2
fixed 6-DOF
N3 load
Fx −10 kN, Fz −20 kN
N3 fixity
UY + rot fixed
Self-weight
off
Analysis
Linear static
§5

Reference solution

  1. Brace E1 axial NN1 = -(Fx*u1x + Fz*u1z)= 10000 N
  2. Brace E2 axial NN2 = -(Fx*u2x + Fz*u2z)= 20000 N
  3. Apex displacement u_zuz = Fz / (E*A/L)= −0.5 mm

Statically-determinate truss closed form — joint equilibrium (method of joints) gives the member axial forces and EA/L bar stiffness gives the apex displacement; a linear (small-displacement) bar carries no geometric offset, so every quantity is exact.

§6

Results comparison

Response quantityProbeSTRIXReferenceΔVerdict
Brace E1 axial N (N) E1.Ni 10000 10000 0.00% PASS
Brace E2 axial N (N) E2.Ni 20000 20000 0.00% PASS
Apex displacement u_x (mm) N3.ux −0.25 −0.25 0.00% PASS
Apex displacement u_z (mm) N3.uz −0.5 −0.5 0.00% PASS
Support N1 reaction R_x (N) N1.Fx −6000 −6000 0.00% PASS
Support N1 reaction R_z (N) N1.Fz 8000 8000 0.00% PASS
Support N2 reaction R_x (N) N2.Fx 16000 16000 0.00% PASS
Support N2 reaction R_z (N) N2.Fz 12000 12000 0.00% PASS
§7

Exactness

DiscretizationBrace E1 N (N)Δ
2 bars (exact)10000 0.00%

A statically-determinate truss needs no compatibility relations: the member forces follow from nodal equilibrium alone, and one linear Truss per member represents each bar exactly. There is nothing to refine — the response is discretization-exact, and every reference value is reproduced to machine precision (0 error against a 10⁻⁶% tolerance).

§8

Conclusion

PASS

STRIX reproduces the reference solution to 0.00% (tolerance 0%). The tested element and its formulation are verified against the reference.

§9

References & analysis files

  1. Hibbeler, R. C. — Structural Analysis. Method of joints for statically-determinate trusses; bar elongation δ = NL/EA.
  2. OpenSees — element Truss (linear, small-displacement bar).
  3. STRIX headless harness: generatePyForLoadCase → python.exe → parseAll.
Engine
v1.0.6 (opensees.pyd)
Run date
2026-08-31
Record
records/SB10.json
Evidence archive
verif-evidence-eng1.0.6-win-x64.zip · SB10/
sha256
(pending publish)