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SE 110.47 Methods to determine the elastic line



  • Comparison of different methods to determine the elastic line: virtual work, Mohr’s Analogy
  • Statically determinate and indeterminate systems
  • Various load cases: point load or bending momen


Technical Description

Beams are key structural elements in mechanical engineering and in construction which are subject to deformation under load. In the case of a simple beam this deformation can be predicted by various methods, such as the principle of virtual work.

The beam under investigation in SE 110.47 can be supported by different bearing methods. Two supports with clamp fixings and an articulated supports with a force measurement dial gauge are provided to realise statically determinate or indeterminate systems. The two supports with clamp fixings are provided with dial gauges and can also be used as articulated supports. These dial gauges enable the angle of inclination of the beam to be determined at the support. A third dial gauge records the deflection of the beam at a random point. A device is additionally provided to generate a bending moment at a random point on the beam. A fourth dial gauge records the angle of inclination of the device.

The beam is placed under load by loads (point load and coupled forces to generate the bending moment). The clamping moment on the supports can be determined by means of loads.

The various elements of the experiment are clearly laid-out and housed securely in a storage system. The complete experimental setup is arranged in the frame SE 112.

The well-structured instructional material sets out the fundamentals and provides a step-by-step guide through the experiments.

Learning Objectives / Experiments

- elastic lines for statically determinate or  indeterminate beams under load 
- determination of the elastic line of a beam by 
  * the principle of virtual work (calculation)
  * Mohr’s Analogy (area moment method devised by
     Mohr; graphical representation)
- application of the principle of superposition
- determination of the
  * maximum deflection of the beam
  * angle of inclination of the beam
- comparison between calculated and measured 
  values for angle of inclination and deflection 


[1] comparison of different methods to determine the elastic line
[2] statically determinate or indeterminate beam
[3] 2 supports with clamp fixing, optionally as articulated support with measurement of angle of inclination or clamp fixing
[4] articulated support with force measurement dial gauge
[5] device to generate a bending moment
[6] dial gauge with generation of moment to measure the angle of inclination
[7] dial gauge to record the deformations of the beam
[8] loads to subject the beam to point loads or moment
[9] loads to determine the clamping moments on the supports with clamp fixings
[10] storage system to house the components
[11] experimental setup in frame SE 112

Technical Data
- length: 1000mm
- cross-section: 20x4mm
- material: steel
Measuring ranges
- force: -50...+50N, graduations: 1N
- travel: 0...0,20mm, graduations: 0,01mm
- 7x 1N (hanger)
- 28x 1N
- 21x 5N

Dimensions and Weight
LxWxH: 1170x480x178mm (storage system)
Weight: approx. 42kg (total)

Scope of Delivery
3 beams 
2 supports with clamp fixings
1 support with force gauge
1 device to generate the moment
1 set of loads 
3 deflection rollers with fixture
3 cables
2 dial gauges with bracket
1 movable hook 
1 storage system with foam inlay 
1 set of instructional material

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