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WP 130 Verification of stress hypotheses



  • Verification of the Rankine yield criterion and the Tresca yield criterion
  • Multi-axial loading of test specimens by pure bending, pure torsion or a combination of the two1
  • Statically determinate system by attachment of balance loads
  • Experiments with test specimens made of ductile metals


Technical Description

Stress hypotheses are applied in the science of the strength of materials when calculating comparative stresses where unequal stresses are combined.

The following stress hypotheses, taking into account material properties, have been tried and proven in practice: Rankine yield criterion (direct stress hypothesis), von Mises yield criterion (change of shape hypothesis) and Tresca yield criterion (shear stress hypothesis).

The experimental unit WP 130 is used to verify these comparative stress hypotheses on test specimens made of various metals. For the purpose, a multi-axial stress state is produced at a point on the specimen and the resulting deformation is measured.

The specimen is clamped on one end to the fixed frame. A loading plate is clamped to the specimen on the other end. A load is attached on the outer circumference of the plate. A balance load compensates for the dead-load of the plate and the load. As a result only direct and shearing stress occur at a point on the test specimen and shear forces are avoided.

The loading plate has a graduation grid enabling loads to be attached at 15° increments. This permits purely bending moment and tor as well as combined load moments to be achieved. Diametrically opposite the load, measurement points are provided on the loading plate to measure the deformation. This enables the deformation at the point of maximum deflection to be measured.

The various elements of the experiment are clearly laid-out and housed securely in a storage system.

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

Learning Objectives / Experiments

- generation of multi-axial loads on test samples made of ductile metals: 
  * steel, copper, brass, aluminium
- generation of various load moments
  * purely bending moment
  * pure torque
  * combined bending moment and torque
- determination of the yield point
- verification of the Rankine yield criterion 
- verification of the Tresca yield criterion 
- representation in Mohr’s Circle of stresses and strains


[1] experiments verifying comparative stress hypotheses from the science of the strength of materials
[2] 7 different load combinations of bending and torsion
[3] loading of the test specimen without shear force by compensation for the influence of dead-load
[4] test specimens made of steel, copper, brass, aluminium
[5] generation of load moments by means of load and lever arm
[6] measurement of the deformation at the point of maximum deflection
[7] storage system to house the components

Technical Data
- length: 49mm
- clamping length: 11,5mm 
- specimen diameter in measurement cross-section: d=4mm
Loads to place load on specimens
- 1x 2N (hanger), 1x 1N, 1x 2N, 1x 4N, 2x 8N
Loads to compensate for the load and the loading plate
- 1x1N, 2x2N, 1x4N, 2x8N
Lever arm: 100mm
- measuring range: 0...10mm 
- graduations: 0,01mm

Dimensions and Weight

LxWxH: 390x330x360mm
Weight: approx. 17kg
LxWxH: 720x480x178mm (storage system)
Weight: approx. 10kg (storage system)

Scope of Delivery
1 experimental unit
16 round test specimens 
(4x St, 4x Cu, 4x Al, 4x brass)
1 set of loads (loading)
1 set of loads (compensation)
1 hexagon socket wrench
1 storage system wth foam inlay
1 set of instructional material

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