Beams neutral axis

The portal frame was reasonably comprehensively instrumented. Back-to-back rosette strain gauges were bonded to the beam neutral axis at midspan and a further 24 uniaxial strain gauges were bonded to the frame at the locations shown in Figure 1(a). Nine dial gauges, and four LVDTs... 

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. 

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... 

Plastic flow can also set up residual stresses. The beam shown in Fig. I6-2(a) is supported at two points and loaded by two equal forces Fapplied near each end. At any point between the two supports the stress in the outside fibers is constant, tensile on the top of the beam and compressive on the bottom. These stresses are a maximum on the outside surfaces and decrease to zero at the neutral axis, as indicated by the stress diagram at the right of (a). This diagram shows how the longitudinal stress varies across the section AA, when all parts of the beam are... 

The effect was first observed after uniaxial deformation, but such deformation is not restricted to pure tension and compression. Plastic bending, for example, causes true macrostress (Fig. 16-2), but the deformation mode is predominantly a tension or compression of layers parallel to the neutral axis of the beam. The longitudinal residual stress indicated by x-rays is therefore the sum of true macrostress and pseudo-macrostress, and the x-ray result will be numerically larger at either surface than the result obtained by dissection. 

When a beam is bent, a continuous gradation of stress occurs from a maximum tensile stress on one surface through a neutral axis to a maximum compressive stress on the other surface. It is the maximum tensile stress and strain that are calculated. Because of the geometry differences and the fact that in bending tests the surface stress rather than a homogeneous stress is considered, values for strength and modulus cannot be simply equated with those from normal tensile tests, although in theory they are equal. 

Nb = number of bolts used in tail beam or flange lug N = width of flange of tail beam with a web stiffener (N = 1.0 without web stiffener) nL = number of head or side lugs P =pick end load, lb Pe = equivalent load, lb Pl = longitudinal load per lug, lb Pr = radial load, lb Pt = transverse load per lug, lb Rb = radius of base ring to neutral axis, in. 

An example of the foregoing is an RP beam [Figure 8.17 (c)] made up of five layers having three different moduli of elasticity, and three different strengths. The neutral axis, found by applying the neutral axis X equation, is 0.415 in fi-om the bottom of the cross-section. Distances from the neutral axis to the centers of the individual layers are computed, and the stiffness factor El calculated. This is found to be ... 

To determine the effective bending stiffness, the position of the neutral axis of the post-fire specimens after different fire exposure durations was first determined by beam theory, based on the post-fire elastic modulus distribution shown in Figure 8.19. The resulting distances from the previous hot face were 114.5 mm for P-WCl,... 

Fig. 4.2 illustrates the geometric definitions of a cantilevered IPMC beam. The beam is clamped at one end (2 = 0), and is subject to an actuation voltage producing the tip displacement w t) at the other end z = L). The neutral axis of the beam is denoted by x = 0, and the upper and lower surfaces are denoted hy x = h and x = —h, respectively. We are interested in obtaining the relationships between the applied voltage and both the resulting current (impedance model) and the tip displacement (actuation model). 

Studies with the hybrid pultrusion of glass and carbon at the University of Mississippi have shown that the flexural stiffness of a glass/epoxy composite could be significantly improved by the addition of carbon fiber, symmetrically distributed at the outer surfaces of the composite beams, but perhaps this is not surprising, since the glass occupies the neutral axis. 

Bending moment n. The resultant moment about the neutral axis of a beam or column, at any point along its span, of the system of forces that produce bending. 

Neutral axis n. In a beam or column subject to bending moments, the surface near the center of the beam and perpendicular to the applied loads upon which neither tensile nor compressive stress is acting. In homogeneous beams with depth-symmetrical cross-sections, the neutral axis is exactly at the center. 

---