SAREHATI UMAR · INTERACTIVE ENGINEERING LEARNING

Virtual Work Method

Civil Engineering Laboratory 2 · S1: Indeterminate Structures Using Virtual Work Method

Understand before you calculate

S1: Indeterminate Structures Using Virtual Work Method — explore the physical meaning of compatibility and the hypothetical unit force.

01 · The problem

Why can't equilibrium determine every reaction?

4Reaction components
3Equilibrium equations
1Redundant reaction

In a pin–pin portal frame, horizontal translation at B is prevented. We need one additional compatibility condition to determine the horizontal reaction.

02 · Explore the mechanics

Original pin–pin structure

W₁ABCD

Both supports are pinned

Support B cannot move horizontally in the original structure. Its horizontal reaction is unknown.

Physical restriction: δBx = 0

Deformations are deliberately exaggerated and schematic; they are not FEA results.

03 · Real versus virtual

What do M and m represent?

Real loading system — M

The actual loads and the unknown reaction H generate the real bending moment.

Column AC:
Virtual loading system — m

A hypothetical horizontal unit force at B generates the virtual bending moment. It is not added physically in the lab.

Column AC:
04 · Combine the systems

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.

05 · From theory to the laboratory

How the experiment demonstrates compatibility

01
ZeroSet dial gauge to zero
02
Apply loadUse specified loading point
03
ObserveCheck horizontal movement
04
BalanceRestore gauge to zero using horizontal load
05
CompareExperimental versus theoretical H
Key connection: The balancing force reproduces the restrained support condition used in compatibility analysis.

Portal Frame

Explore all three cases in the S1 lab sheet: vertical, horizontal and combined loading.

Structure & loading
W₁ = 6 NW₂ = 6 NABCDE L3L4L3L
Original pin–pin structure: support B is horizontally restrained.
Adjust applied load

Theoretical horizontal reaction
Theoretical H0.500 N

Results use the geometry and equal-EI assumptions in the laboratory manual. This is a conceptual deformation, not a calculated deflection.

THEORETICAL FOUNDATION

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.

Structure & loading
ABDCEWc = 4 NWe = 4 N Lh
Original pin–pin arch: support B is horizontally restrained.
Span, L1000 mm
Rise, h500 mm
Load position a₁ / a₂250 / 750 mm
Theoretical analysis inputs
Theoretical horizontal reaction
Theoretical H0.000 N

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.

H01Load position, a/L
Use this to discussshape and peak of H
Model basisParabolic theory only
THEORETICAL FOUNDATION

Derivation & Theoretical Basis — Two-Hinged Arch

Check Understanding

Five short questions · Instant ✓ / ✕ feedback with explanations

5 Questions