SM-1404 Deflection of Beam Apparatus

Experiments

  • Investigation of the deflection for statically determinate and statically indeterminate straight beams
    • cantilever beam
    • inter mediate beam, single-span beam, dual- or triple-span beam
    • formulation of the differential equation for the elastic line
  • Deflection on a cantilever beam
    • measurement of deflection at the force application point
  • Deflection of a dual-span beam on three supports
    • measurement of the support reactions
    • measurement of the deformations
  • Influence of the material (modulus of elasticity) and the beam cross-section (geometry) on the elastic line.
  • Maxwell-Betti coefficients and law application of the principle of virtual work on statically determinate and indeterminate beams.
  • Determination of lines of influence
    • arithmetically
    • qualitatively by way of force method (Müller-Breslau)

 

Specifications

  • Elastic lines of statically determinate and indeterminate beams under various clamping conditions.
  • 3 steel beams with different cross-sections.
  • 3 brass beams with different cross-sections.
  • 3 aluminum beams with different cross-sections.
  • 3 MS beams with different cross-sections.
  • 1 coper beam.
  • 3 articulated, height-adjustable supports with force gauge range 100N; least count 0.5N.
  • 2 support with clamp fixing.
  • Force gauges can be zeroed, peck and tracking function is avaliable in force gauge.
  • 3 dial gauges to record deformations with three dial gauge supports, dial gauge 0-20mm, least count 0.01mm.
  • 4 sets of weights with adjustable riders.
  • Anodised aluminium section frame housing the experiment.
  • Storage system to house the components.

Description

Beam is a structural member used to withstand load primarily by resisting bending. Internally beam experiences compressive, shear and tensile stresses.

The equipment is used for measurement of deflections and slopes of a beam under bending and compare with values calculated by differential equation and Area Moment Method. The beam has two adjustable height end supports with an interchangeable knife edges and a cantilever end clamp. Load hangers are used for point loads and a number of weights are used for uniform load. Deflections and slopes are measured by dial gauges.

Beams are key structural elements in mechanical engineering and in construction. A beam is a bar-shaped component in which the dimensions of the cross-section are much smaller than the length and which is subjected to load along and perpendicular to its longitudinal axis. The load perpendicular to the longitudinal axis causes a deformation of the beam – that is, bending. Based on its size, the beam is viewed as a one-dimensional model.

The science of the strength of materials deals with stress and strain resulting from the application of load to a component. Many fundamental principles of the strength of materials can be illustrated well by a straight beam.

The beam under investigation in SM-1404 can be supported in different ways. This produces statically determinate and indeterminate systems which are placed under load by up to four sets of weights. The load application points are movable. Three dial gauges record the resulting deformation. Three articulated supports with integral force gauges indicate the support reactions directly. The articulated supports are height-adjustable, so as to compensate for the influence of the deadweight of the beam under investigation.

Many beams of different thicknesses and made of different materials demonstrate the influence of the geometry and of the modulus of elasticity on the deformation of the beam under load.

The various elements of the experiment are clearly laid-out and housed securely in a storage system. The complete experimental set-up is arranged in the frame. The well-structured instructional material sets out the fundamentals and provides a step-by-step guide through the experiments.