Beams stresses

G39, Standard Practice for Preparation and Use of Bent-Beam Stress-corrosion Test Specimens, ASTM, West Conshohoken, PA, 1999. 

Three case studies are examined which illustrate the use of the bending beam stress experiment. The first is a comparison of two polymers for interlayer dielectrics. The second is of a neat epoxy resin commonly used for microelectronics encapsulation. The third is a polyimide coating used for protection of an integrated-circuit chip. 

The second ORNL microcantilever project, funded by the ATF and technically co-directed hy TSA, involves polymer-coated micro cantilevers. In this case, the explosive molecule would be adsorbed on the surface of the polymer, and the swelling or change in physical properties would be measured indicating the presence of an explosive. Several polymers are currently being developed to provide the necessary selectivity for the different types of explosives signatures. The sensitivity is similar to the non-coated cantilever estimated limit of detection of low parts-per-billion (with proper collection and preconcentration system, LOD should approach low parts-per-trillion). Figure 6 illustrates two modes of detection for the coated cantilevers beam stress response and beam resonant frequency response. 

Figure 6. Illustration of the two modes of detection for the coated cantilevers beam stress response and beam resonant frequency response...

Fig. 9.4 Bend beams specimen used in constant-deformation test [16]. Reprinted, with permission, from ASTM G 39-99 Standard Practice for Preparation and Use of Bent-Beam Stress-Corrosion Test Specimens copyright ASTM International, West Conshohocken, PA.

G. Haaijer, A.W. Loginow, Stress analysis of bent-beam stress corrosion specimen. Corrosion 21 (1965) 105-112. 

This ultimate moment of resistance is greater than the design moment of 378 kN m and the section is, therefore, satisfactory for this ultimate limit state. However, it has to be checked for the stresses in the serviceability limit state. As for the ultimate load method, the second moment of area of the composite section is 7.01 x 10 mm and the elastic modulus of the steel beam alone is 949 cm , and thus the stage 1 steel beam stress is... 

ASTM G 39, Practice for Preparation and Use of Bent-Beam Stress-Corrosion Test Specimens— This describes methods for design, preparation, and use of bent-beam stress-corrosion specimens. This standard covers apparatus for supporting specimens, basic design of a specimen, stress calculations, test conditions, exposure, and inspection techniques. 

As a result of these interlaboratory test programs, stancUud-ized test technique development has proceeded even slower than ever anticipated, realizing the difficulties encountered in defining acceptable levels of reproducibility and control of test variables. Since publication of the first edition of Manual 20, ASTM Standard G 168, Standard Practice for Making and Using Precracked Double Beam Stress Corrosion Specimens has been developed, a result of the interlaboratory program conducted on aluminum alloy 7075 [32]. 

Ibid., Vol. 03.02, G168., Standard Practice for Making and Using Double Beam Stress Corrosion Specimens."... 

Smooth specimens can be stressed by a constant load, by constant strain rate, or by constant deflection, which is the usual procedure. Typical specimens are (a) direct tension specimens, (b) C-ring specimens, (c) U-bend sp>ecimens, (d) bent beam specimens, and special techniques for weldments (see ASTM G 49, Practice for Preparation and Use of Direct Tension Stress-Corrosion Test Specimens ASTM G 38, Practices for Making and Using C-Ring Stress-Corrosion Test Specimen ASTM G 30, Practice for Making and Using U-Bend Stress-Corrosion Test Specimens ASTM G 39, Practice for Prep>aration and Use of Bent-Beam Stress-Corrosion Test Specimens and ASTM G 58, Practice for the Preparation of Stress-Corrosion Test Specimens for Weldments, respectively). 

The bending loads on a beam induce counteracting couples in the material of the beam and these represent the stresses in the beam. The beam stress for elastic materials has been explored extensively in texts such as Timoshenko and the relationships between the bending loads, the stress levels and the deformation of the beams and other members subject to bending stresses are well known. These relationships do not hold for materials that are not strictly elastic in behavior and are quite inaccurate in predicting the behavior of plastics materials which exhibit viscoelasticity and creep. 

Prismatic beams stressed by bending offer a simple means of testing sheet or plate material, typical arrangements being shown in Fig. 8.89a to e. Below the elastic limit the stresses may be calculatedor determined from the response of strain gauges attached to the surface at an appropriate position. 

Concrete has considerable strength in compression, but is very weak when loaded in tension. When used in beams stressed in bending, steel must be cast in the tensile side of the beam (as discussed in Ch. 4). 

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