ST151 · Methods for the Elastic Line

Experimental apparatus for comparing analytical and graphical methods to determine the elastic line of a beam

A single beam, loadable by a point force and — independently — by a pure bending moment, supported by any combination of clamp, articulated-with-force-gauge, and articulated-with-dial-gauge bearings. The apparatus is designed for one specific purpose: to let the student solve the same elastic-line problem by several different methods — the differential equation of the elastic line, the principle of virtual work, and Mohr's analogy (area-moment method) — and then verify each result against the measured deflection, slope and support reactions on a real beam.

Experiments

Determination of the elastic line of a beam by three different methods:
- analytical integration of the elastic-line equation
- principle of virtual work
- Mohr's analogy (area-moment method)
Elastic lines for statically determinate and statically indeterminate beams
Application of the principle of superposition
Load cases: point load and pure bending moment
Determination of the maximum deflection and the angle of inclination of the beam
Experimental determination of the clamping moments on fixed supports
Comparison of calculated and measured values

Beam

Length 1000 mm

Cross-section 20 × 4 mm

Material steel

Quantity 3 beams

Supports & loading

Clamp supports 2 × clamp fixing, each with dial gauge to read the angle of inclination — switchable to articulated use

Force-gauge support 1 × articulated with force gauge — reads the reaction directly for indeterminate cases

Moment generator device to apply a pure bending moment at an arbitrary point on the beam

Measurement

Support reaction force gauge, ±50 N, graduation 1 N

Deflection dial gauge, 0…20 mm, graduation 0.01 mm

Angle of inclination dial gauge integrated into the clamp supports and moment generator

Load set

Weights 7 × 1 N hangers · 28 × 1 N · 21 × 5 N

Delivery

3 beams (steel, 1000 × 20 × 4 mm)
2 clamp-fixing supports, 1 force-gauge support
Bending-moment generator device
3 deflection rollers with fixtures, 3 cables, 2 dial gauges
Calibrated weight set; storage case with foam inlay; instruction manual

42 kg