SM-1407 Deformation of Curved Beam

Experiments

  • Bending behaviour of a curved-axis beam.
    • circular beam
    • semi-circular beam
    • quadrant beam
    • curved davit beam
    • right angled beam
  • Application of the principle of virtual forces (the force method) to calculate deformation.
  • Second moment of area.
  • Comparison of calculated and measured  Deformations.

Specifications

  • Elastic deformation of curved-axis beams under load.
  • 5 different beams with the same cross-section: circular beam, semi-circular beam, quadrant beam, curved davit beam and right angled beam.
  • Bearing block to fix the beams.
  • Pillar with bearing to support the circular beam.
  • 1 set of weights to place the beam under load.
  • 3 dial gauges to record the horizontal and vertical deformation.
  • Box to house the components.

Description

This apparatus is design to demonstrate phenomena of deflection in a curved bar. In this apparatus dial gauge is attached to the frame to calculate the extent of deflection.

The study of how curved bars deflect is thus, important so as to estimate the total mechanical displacement of structures that incorporate curved sections. One of the more effective methods used to estimate deflections in curved bars come from Castiglione’s first theorem or from a unit-load method.

In construction engineering, a distinction is made between beams and arches. An arch is a statically indeterminate supported structure with a curved axis and two fixed support bearings or clamp fixings. The support bearings of an arch (such as a double-articulated arch) absorb forces vertically and horizontally. The ends of the arch in the bearings do not move. This produces the static arching effect of the system. In mechanical engineering, crane hooks and chain links are typical examples of a curved beam.

SM-1407 includes 5 different beams, borne on statically determinate supports: a circular beam, a semi-circular beam a quadrant beam, right angle beam and curved davit. The beam under test is loaded with a set of weights. Dial gauges record its horizontal and vertical deformations.

All 5 beams have the same cross-section and so the same 2nd moment of area. This enables test results to be directly compared. Simi-circular and circular beams are fixed to a bearing on the pillar. The quadrant beam is clamped into a bearing block.

The various elements of the experiment are clearly laid-out and housed securely in a box. The well-structured instructional material sets out the fundamentals and provides a step-by-step guide through the experiments.