Flexural modulus, calculation

Another resonant frequency instmment is the TA Instmments dynamic mechanical analy2er (DMA). A bar-like specimen is clamped between two pivoted arms and sinusoidally oscillated at its resonant frequency with an ampHtude selected by the operator. An amount of energy equal to that dissipated by the specimen is added on each cycle to maintain a constant ampHtude. The flexural modulus, E is calculated from the resonant frequency, and the makeup energy represents a damping function, which can be related to the loss modulus, E". A newer version of this instmment, the TA Instmments 983 DMA, can also make measurements at fixed frequencies as weU as creep and stress—relaxation measurements. 

The flexural modulus is the ratio, within the elastic limit, of stress to corresponding strain. It is calculated by drawing a tangent to the steepest initial straight-line portion of the load-deflection curve and using an appropriate formula. 

Figure 6.8 plots the reinforcement ratios for short glass fibre reinforced polyamide (PA-GF) versus neat polyamide for six important characteristics calculated versus density and material cost. These characteristics are tensile strength, tensile and flexural modulus, impact strength, HDT A and B. 

The temperature dependence of the material properties of the molding compound should be considered to calculate the stress accurately. The average TEC and average Flexural Modulus were calculated using Equation (2). These values are considered to be adequate for the comparison of the local stress of the molding compound (Table I). 

Fig. 6. Values of back-calculated modulus for the joints as a function of measured crack length. (Note that the known value of the flexural modulus, E, of the substrate was 126GPa)...

Absorbed energy was calculated from the area under the load-deflection curves. Flexural modulus of elasticity was calculated from the load-deflection relation between 0 and the maximum load. Average properties of all composites are shown in Table 6. 

However, not aU composite deck boards would satisfy even this low support span requirement. Trex deck board, for example, has flexural modulus equal to 175,000 psi (hsted on Trex technical data sheet). Using Eq. (7.45), one can calculate that at L = 12 in., I = bhVl2 = 0.895 (b = 5-1/2", h = 1-1/4"), load at the deflection of L/180 =... 

Calculations show that for a stair tread with a 24-in. span (allowed deflection 0.133"), a composite board should have aEX I value of 548,016 lb X in.. This would be applicable to a hollow GeoDeck Heavy Duty composite deck board (8.1" X 1.55,1 = 1.858 in., E = 374,000 psi, and EX I = 694,892 lb X in. ). For a solid board of a standard dimension (5.5" X 1.25", I = 0.895 in. ), flexural modulus should be at least 776,416 psi, and composite deck boards of such stiffness are not available as yet on the current market (see Table 7.34), except those made of wood. For thin solid board, such as 5.5" X 15/16" (/ = 0.378 in. ), flexural modulus applicable for stair tread with 24" span should be at least 2,054,000 psi, which is much higher than that for typical wood (Table 7.34). 

Deflection of the loaded board can be predicted provided that the load and its location on the board is known, as well as the span, the moment of inertia, and the flexural modulus of the board, and assnming that the load and the deflection are within the linear relationship between each other. If the load is outside of this relationship (higher), a deflection wonld be higher than calculated using formulas... 

In reality, the immediate deflection was of 0.095 in., that is, 26% lower than predicted, not higher. This can be explained by an inaccurate value of the flexural modulus reported by the manufacturer. Indeed, flex modulus for this particular Trex product, calculated from the above experiment, was 221,000 psi, not 175,000 psi. Other figures for Trex board flexural modulus were of 193,000 + 19,000 psi (Table 7.30), 214,000 + 8,000 psi and 224,800 psi (Table 7.34, footnote). 

The modified board had 11% lower mass (calculated). Mathematical modeling (see Fig. 7.18) showed that the modified board had about the same flexural strength and 9% higher flexural modulus compared to the conventional board (the upper profile in Fig. 7.17). 

Density and flexural modulus, 205 Density, 53, 54, 57, 59, 63, 69-71, 73,105, 124, 134, 137, 146, 147, 154, 202-223, 258, 384, 414, 500, 567, 569, 571 Buckling, effect on, 209 calculations, 217 commercial deck boards, 215 cross-sectional, 212, 213 distribution, 212, 213 hollow board, 212, 213 flexural modulus, correlation with, 205 microbial contamination, effect on, 210 microbial degradation, effect on, 210 moisture content, effect of, 209 panels of hollow boards, 212, 213 ribs of hollow boards, 212, 213... 

With the geometrical details of the specimens, including the initial crack length a, the physical crack length augmented to account for crack tip plastic deformation (the fracture mirror length) aBs> the dynamic yield stress o-y and the dynamic flexural modulus E, the fracture mechanics parameters Ki, Ju and can be calculated [OlGre]. 

To assess flexural modulus of the hardened adhesive a specimen 200 X 25 X 12 mm deep tested in four point bending may be used. The sample under test is loaded transversely at the third points at a erosshead speed of 1 mm/minute and the eentral deflection recorded (Fig. 2.16). From the load-deflection curve, the secant modulus at 0.2% strain may be calculated. A lower limit on flexural modulus may be specified to prevent problems due to creep of the adhesive under sustained loads, whereas the upper limit will be to reduee stress concentrations arising from strain incompatibilities, for example at ehanges in section. 

Flexural modulus (flex modulus) n. The ratio, within the elastic limit, of the applied stress in the outermost fibers of a test specimen in three-point, static flexure, to the calculated strain in those outermost fibers, according to ASTM test D 790 or D 790M. For a given material and similar specimen dimensions and manufacture, the modulus values obtained will usually be a little higher than those found in a tensile test such as D 638, and may differ, too, from the moduli found in the cantilever-beam test, D 747. 

Three-point bending on an X-aerogel beam specimen allows measurements of flexural modulus and strength. The ASTM standard D790 (Standard Test Methods for Flexural Properties of Unreinforced and Reinforced Plastics and Electrical Insulating Materials) specifies a length/width ratio of 16. The stress [Pg.509]

Flexural strength is the force per unit area required to break a material in bending. Rexural modulus is the ratio of the elastic limit of stress to corresponding strain and relates to the stiffness of a material under load. Load-deformation measurements are obtained by applying a force to the centre of a sample in the form of a beam or bar which is supported at both ends as illustrated in Fig. 9.8. The flexural modulus (FM) is calculated from the slope m of the steepest initial portion of the... 

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