Neutral axis

Torsion bars and leaf springs are less efficient than axial springs because some of the material is not fully loaded the material at the neutral axis, for instance, is not loaded at all. Consider - since we will need the equations in a moment - the case of a leaf spring. 

Figure 12.2 shows that the stress in the beam is zero along the neutral axis at its centre, and is a maximum at the surface, at the mid-point of the beam (because the bending moment is biggest there). The maximum surface stress is given by... 

Shear Stress. For a rectangular cross-section, the maximum value of Q occurs at the neutral axis, and, because the width b of the beam is a constant 3 in., the maximum value of the shear stress occurs at the neutral axis. 

Significantly, a flexural specimen is not in a state of uniform stress. When a simply supported specimen is loaded, the side of the material opposite the loading undergoes the greatest tensile loading. The side of the material being loaded experiences compressive stress (Fig. 2-16). These stresses decrease linearly toward the center of the sample. Theoretically the center is a plane, called the neutral axis, experiences no stress. 

Real differences between the tensile and the compressive yield stresses of a material may cause the stress distribution within the test specimen to become very asymmetric at high strain levels. This cause the neutral axis to move from the center of the specimen toward the surface which is in compression. This effect, along with specimen anisotropy due to processing, may cause the shape of the stress-strain curve obtained in flexure to dif-... 

Fig. 3-1 Properties of some common cross-sections based on mechanical engineering analysis (na = neutral axis).

Bending moments caused by eccentricity of the centre of the working pressure relative to the neutral axis of the vessel. 

The polycarbonate glazing is modeled as a simply supported plate subjected to nonlinear center deflections up to 15 times the pane thickness. Using the finite element solution of Moore (Reference 4), the resistance function is generated for each pane under consideration. Typically, the resistance is concave up, as illustrated for typical pane sizes in Figure 1. This occurs because membrane stresses induced by the stretching of the neutral axis of the pane become more pronounced as the ratio of the center pane deflection to the pane... 

Sandorf, 1980 Whitney, 1985 Whitney and Browning, 1985). According to the classical beam theory, the shear stress distribution along the thickness of the specimen is a parabolic function that is symmetrical about the neutral axis where it is at its maximum and decreases toward zero at the compressive and tensile faces. In reality, however, the stress field is dominated by the stress concentration near the loading nose, which completely destroys the parabolic shear distribution used to calculate the apparent ILSS, as illustrated in Fig 3.18. The stress concentration is even more pronounced with a smaller radius of the loading nose (Cui and Wisnom, 1992) and for non-linear materials displaying substantial plastic deformation, such as Kevlar fiber-epoxy matrix composites (Davidovitz et al., 1984 Fisher et al., 1986), which require an elasto-plastic analysis (Fisher and Marom, 1984) to interpret the experimental results properly. 

Because the birefringence measurement is an integrated effect along the path of the beam in the sample, it is important that the flow be two-dimensional with the neutral axis parallel to the axis of that beam. For that reason, the width of the flow channel (which defines the length of the beam in the sample) must be relatively large relative to its height. A rule of thumb that is often used is a factor of 10, and the value used in this work was... 

Generally, when testing materials with a nonlinear stress-strain behavior, the tests should be conducted under uniform stress fields, such that the associated damage evolution is also uniform over the gauge section where the material s response is measured. Because the stress field varies with distance from the neutral axis in bending tests, uniaxial tension or compression tests are preferred when characterizing the strength and failure behavior of fiber-reinforced composites. 

The intrinsic strength of boron can be estimated in a flexure test. Assuming that in a flexure test the core and interface are near the neutral axis, critical tensile stresses would not develop at the core or interface Flexure tests on boron fibers lightly etched to remove any surface defects yield a strength of 14 GPa (DiCarlo, 1985). Without etching, the strength is about half this value... 

It is assumed that the bending moment applied to the root section of the tube is the plastic limit moment. Let the neutral axis be defined by the angle... 

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