Understand before you calculate
S1: Indeterminate Structures Using Virtual Work Method — explore the physical meaning of compatibility and the hypothetical unit force.
Why can't equilibrium determine every reaction?
In a pin–pin portal frame, horizontal translation at B is prevented. We need one additional compatibility condition to determine the horizontal reaction.
Original pin–pin structure
Both supports are pinned
Support B cannot move horizontally in the original structure. Its horizontal reaction is unknown.
Deformations are deliberately exaggerated and schematic; they are not FEA results.
What do M and m represent?
The actual loads and the unknown reaction H generate the real bending moment.
A hypothetical horizontal unit force at B generates the virtual bending moment. It is not added physically in the lab.
Virtual work + compatibility
For the bending-only formulation used in the manual, the virtual-work displacement at B must equal zero because B is horizontally restrained in the original structure.
The zero refers to horizontal translation at support B — the entire structure can still deform.
How the experiment demonstrates compatibility
Portal Frame
Explore all three cases in the S1 lab sheet: vertical, horizontal and combined loading.
Results use the geometry and equal-EI assumptions in the laboratory manual. This is a conceptual deformation, not a calculated deflection.
Derivation & Theoretical Basis — Portal Frame
Two-Hinged Arch
Explore load at C, load at E, and combined loading. The specimen view stays close to the laboratory model, while the equation and influence line use the parabolic theoretical model from the manual.
| Span, L | 1000 mm |
| Rise, h | 500 mm |
| Load position a₁ / a₂ | 250 / 750 mm |
The theoretical equation uses the manual's parabolic arch model and specified stiffness assumption. The laboratory specimen is approximately semicircular; discuss this difference when comparing theory and experiment.
Influence lineHow does a moving unit load change H?Click to explore the moving 1 N load
Compact view of the parabolic-model influence line. Move a 1 N load from A to B.
| Use this to discuss | shape and peak of H |
| Model basis | Parabolic theory only |
Derivation & Theoretical Basis — Two-Hinged Arch
Check Understanding
Five short questions · Instant ✓ / ✕ feedback with explanations