Four-point beam bending

Figure 8.12 shows the principal types of test. In the Charpy test a beam of the polymer is held at each end and is struck at its centre by a hammer with one or two knife edges, giving a three- or four-point impulsive bending stress, respectively. Figure 8.13 shows a diagram of a standard Charpy impact tester. In the Izod test the specimen is held at one end and struck at the other. For either test a notch is cut in the sample at the point where it is to break and the sample is placed in the tester with the notch pointing away... 

With regard to American practice, fatigue test is performed according to ASTM D 7460 (2010) or AASHTO T 321 (2011). The standard specifies one procedure/test method, the four-point flexural bending test on prismatic (beam) specimens. 

Flexural strength is determined using beam-shaped specimens that are supported longways between two rollers. The load is then applied by either one or two rollers. These variants are called the three-point bend test and the four-point bend test, respectively. The stresses set up in the beam are complex and include compressive, shear and tensile forces. However, at the convex surface of the beam, where maximum tension exists, the material is in a state of pure tension (Berenbaum Brodie, 1959). The disadvantage of the method appears to be one of sensitivity to the condition of the surface, which is not surprising since the maximum tensile forces occur in the convex surface layer. 

Cui, W.C. and Wisnom, M.R. (1992). Contact finite element analysis of three- and four-point short beam bending of unidirectional composites. Composites Sci. Technol. 45, 323-334. 

For linear elastic materials, deflection at the load-point of a four-point bending beam is given by two different contributions, accounting for both bending and shear deformation. In the case of notched specimens, a third term accounting for crack length arises. The resulting analytical expression for the specimen compliance C is as follows ... 

In four-point bending, the stress for a rectangular beam and for a circular rod become respectively... 

Figure 8.19 Single edge-notched beam geometry. Loading is usually either three- (shown here) or four-point bending.

A notched beam of yttria-stabilized ZrOj containing a through-thickness surface crack is broken in four-point bending (mode I), beam depth 10 mm. The fracture stress was 100 MPa and the critical crack size (c) was 1 mm. The Young s modulus and Poisson s ratio of the ZrOj are 200 GPa and 0.30, respectively. 

Sketch a beam with a circular cross-section and show the region in which the normal stress is a maximum for four-point bending. Is this region a point, a line, a surface or a volume ... 

In another study, Martinola et al. (2002) evaluated the water permeability of cracked and uncracked HPFRCC by water absorption test. In their study, the amount of water taken up by capillary suction was determined on cubes cut out from the middle section of the beams, which were subjected to a four-point bending test. Maximum crack width in the cracked HPFRCC specimens was found to be about 0.10 mm. Both cracked and uncracked HPFRCC exhibited very low water absorption coefficient in their study. 

The flexural strength was obtained from four-point bending test on 38x38x305 mm plain PVB composite beams at a loading rate of 445 N/min, the corresponding stress increasing rate at the extreme fiber stress was 1.2 MPa/min. 

The applied load was calculated to impose a deflection that would normally limit the service load of such a slab in use in buildings. A deflection limit of 1/300 of the clear span was chosen that corresponds to a mid-span deflection of 11.9 mm. The corresponding experimental load was calculated according to Eq. (6.1) for four-point bending of a simply supported beam neglecting shear deformation ... 

From the measured deflections, the bending stiffness, El, of the beams was calculated using Eq. (7.1) for the four-point bending setup. Considering that shear stiffness was mainly given by the webs that were not subjected to obvious... 

These results can be compared to the same set of results obtained from the study on beam specimens (SLCOl and SLC02) in Section 8.2, which were subjected to four-point bending during 60 and 120 min fire exposure from the underside, see Table 8.6. In the former study, six-cell specimens were used in contrast to the four-cell specimens used here. The bending stiffnesses obtained from Section 8.2 were therefore corrected by a factor of 4/6 in order to make them comparable. At the end of fire exposure, the bending stiffness of the still-hot specimens (SLCOl/02) dropped to 46% and 43% of the initial value, which almost matched the values obtained for the column specimens. The post-fire stiffnesses (64% and 60%), however, were slightly lower than those of the column specimens (76% and 70%). 

Four-point bend tests were performed at room temperature and at 1400°C. All bending tests had an upper span of 10 mm and a lower span of 30 mm. An Instron-type universal tester was used for bending tests, with a constant cross head of 0.2 mm/min. Figure 5.36 shows the dimensions and coordinate system of the beam specimen with ground surface in a four-point bend test. 

One adhesive layer with elastic behaviour (027-3) and two adhesive layers with ductile behaviour (009-05 and 013.1) were selected for the large scale four-point bending tests. In addition to these bipartite beams with a single flexible adhesive layer, glulam beams of standard quality (GL24h) were tested as control. All the bipartite and control beams were manufactured with wood lamellas of the same quality SIO according to the German standard [12]. 

The bending is achieved by the movement of the centre load point(s) in vertical direction perpendicular to the longitudinal axis of the specimen. The two end points of the beam remain fixed (clamped). The applied periodical loading (force) is sinusoidal to obtain the required strain, e, amplitude of 50 3 microstrain. A schematic representation of the four-point bending test is given in Figure 7.6. 

The main part of a four-point bending apparatus together with the free translation and rotation principle of the beam is shown in Figure 7.7. 

This test method determines the asphalt s behaviour under repetitive fatigue loading in a four-point bending test equipment in which the inner and outer clamps are symmetrically placed and a slender rectangular-shaped specimen (prismatic beam) is used. The prismatic beam is subjected to four-point periodic sinusoidal bending with free rotation and translation at all load and reaction points. 

Bending is achieved by applying load to two points of the prismatic beam at L/3 and L/3 distance from the clamped ends of the specimen. The layout of the test device is similar to the one shown in Section 7.4.4 (Figure 7.6) for four-point bending. The periodic loading is sinusoidal and it can cause a constant moment and hence a constant strain between the inner clamps (in the middle of the specimen). 

Some beam specimens were fabricated whose flanges and webs were spliced at mid-span in a similar way to Fig. 8.13. The performance in four-point bending was encouraging, although yield in the aluminium alloy was rarely experienced. 

In order to overcome many of the difficulties associated with the indentation fracture toughness measurement as noted above, the single-edged notched beam (SENB) test - which often is used for metallic and polymeric materials - has been adapted to suit ceramics [24]. For this, a bar of ceramic, usually in the order of 3 x 4 mm cross-section and 25-45 mm length, has a notch introduced on one side. The bar is then loaded in four-point bending and the fiacture toughness determined from the failure load, Pm> as per ... 

Fig. 6.20. Overview of the four-point-bending ejqteriment (top), cross section of the reinforced concrete test beam (bottom left side) and side view of the experimental setup (bottom right side). Measure units given in [mm].

Ruzek B, Kvasnicka M (2001) Differential Evaluation Algorithm in the Earthquake Hypocenter Location. Pure and Applied Geophysics 158 667-693 Schechinger B, Vogel T (2006) Acoustic emission for monitoring a reinforced concrete beam subject to four-point-bending. Constraction and Building Materials, 21(3) 483-490... 

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