Differences between single-beam and double-beam structures in paper stiffness testers

There are two types of paper stiffness testers: single-beam and double-beam structures. The single-beam type operates on the cantilever principle, offering simple operation and fast speed. It is suitable for testing uniform materials such as thin paper, but it may be affected by local variations in the sample. The double-beam type uses symmetrical loading, providing a more uniform bending force and more stable results. It is suitable for thick cardboard or anisotropic materials, though its operation is slightly more complex. The choice between the two should be based on testing standards, sample thickness, and precision requirements.

Overview

Paper stiffness is a key physical indicator to measure the bending resistance of paper, and its measurement is usually done with the help of a dedicated stiffness tester. In instrument design, the structural form of the loading beam directly affects the measurement principle, accuracy and scope of application. At present, the mainstream design is divided into single beam structure and double beam structure, and there are significant differences between the two in mechanical structure, mechanical model and applicable scenarios. Understanding these differences helps users choose the appropriate instrument configuration based on their actual testing needs.

Single girder structure

Single-girder structures usually use the cantilever beam principle. The specimen is fixed at one end and the other in a free state, and a vertical force is applied at the free end through a single loading beam to bend the specimen to a specific angle while measuring the applied force or moment. Its mechanical model is relatively simple, and the calculation of the bending moment M can be simplified as:

M = F × L

where F is the applied force and L is the length of the force arm (usually the length of the specimen outstretched). The structure is straightforward, easy to maintain and calibrate, and the clamping requirements for specimens are relatively relaxed. However, due to the application of force only from one side, the overall stiffness characteristics may not be fully reflected for paper with uneven or obvious anisotropy.

Double girder structure

Double girder structures usually use the principle of two-point or four-point bending. The specimen is supported horizontally on two support beams and is subjected to downward symmetrical force through the two loading beams located above. This symmetrical loading method creates a uniform bending moment field in the specimen test area. The calculation of its bending moment M is more complex in four-point bending and can be expressed as:

M = (F × d) / 2

where F is the total loading force, and d is the distance between the internal loading point and the outer support point. The double-beam structure can effectively reduce the effect of shear forces and allow the specimen to be tested in a pure bending state, and the results are more representative of the flexural stiffness of the material itself, especially for the accurate evaluation of thick cardboard or anisotropic materials.

Comparison of differences

Contrast dimensions	Single girder structure
Loading method	Single-point cantilever loading
Mechanical state	Bending and shear compounding
Applicable samples	Ordinary tissue paper, isotropic materials
Measure efficiency	Easy to operate and fast to test
Data consistency	It is more sensitive to local defects in the sample

Contrast dimensions	Double girder structure
Loading method	Symmetrical two- or four-point loading
Mechanical state	Approximate pure bending
Applicable samples	Cardboard, cardboard, anisotropic materials
Measure efficiency	The operation is slightly more complicated and the preparation time is longer
Data consistency	The result is more stable and represents overall performance

Structure selection

The choice of single or double girder structure should be based on specific test criteria and sample characteristics. Many international standards (e.g., ISO 2493, GB/T 22364) clearly define test methods. For conventional printing writing paper, toilet paper and other thin page materials, single-beam instruments are widely used due to their high efficiency. For thicker or complex materials such as corrugated cardboard and coated cardboard, the double-beam structure can provide testing conditions that are more in line with the mechanical nature of the material, reducing errors caused by clamping or stress concentration. In addition, if the laboratory needs to conduct in-depth research, such as analyzing the elastic modulus of the material, the pure bending data provided by the double-beam structure is more reliable.

Summary

Single beam and double beam structure are the two core designs of paper stiffness testers, each with its own physical basis and applicable fields. The single-beam structure is based on the cantilever beam principle, which is suitable for rapid screening and routine tissue paper testing; The double-beam structure is based on the principle of symmetrical bending, which is suitable for the most demanding thick paper and cardboard tests, and provides purer bending mechanical data. Users should make reasonable choices based on the standards to be followed, the thickness and uniformity of the sample to be tested, and the purpose of application of the required data to ensure the accuracy and representativeness of the stiffness measurement results.

References

ISO 2493: Determination of stiffness on paper and cardboard (static bending method)

GB/T 22364-2018: Determination of bending stiffness on paper and cardboard

Bristow, J.A., Paper Performance Test Handbook. Paper Industry Press.

Mark, R.E., Paper Mechanics. Materials Science Series.