Refer to Chapter 1 and References 1.7.1(a) and (b) for general information on stress analysis of beams.
Beams of solid, tubular, or similar cross sections can be assumed to fail through exceeding an allowable modulus of rupture in bending (Fb). In the absence of specific data, the ratio Fb/Ftu can be assumed to be 1.25 for solid sections.
4.4.1.1.1 Round Tubes — For round tubes, the value of Fb will depend on the D/t ratio as well as the compressive yield stress.
4.4.1.1.2 Unconventional Cross Sections — Sections other than solid or tubular should be tested to determine allowable bending stress.
Built-up beams will usually fail because of local failure of component parts.
The allowable stress for thin-web beams will depend on the nature of the failure and are determined from the allowable stress of the web in tension and of the flanges or stiffeners in compression.
The general formula for primary instability is given in Section 1.3.8. Formulas applicable to magnesium-alloy columns are given in Tables 4.4.2.1(a) and (b). See References 4.4.2(a) and (b).
| Alloy | K | n | m | Max. P/A |
|---|---|---|---|---|
| AZ31B, AZ61A | 2,900 | —* | 1.5 | Fcy |
| ZK60A-T5 | 3,300 | —* | 1.5 | 0.96 Fcy |
| General formula: P/A = K(Fcy)n / (L′/ρ)m (stress values in ksi). Formula is for members that do not fail by local buckling; see Figure 4.4.2.3(a). *The exponent n could not be reliably read from the scanned source (an unresolved OCR/print artifact in this cell) and is omitted here rather than approximated; consult MIL-HDBK-5J p. 4-53 directly for that value. | ||||
Table 4.4.2.1(b) gives the corresponding column formula for AZ31B-H24 magnesium-alloy sheet:
P/A = 1.05 Fcy − [1.05 Fcy2 (L′/ρ)2] / (4π2E), Max(P/A) = Fcy
See Figure 4.4.2.3(b).
MIL-HDBK-5J provides no additional narrative under this heading beyond the section title itself. See Section 4.4.2.1 for the applicable column formulas and Section 4.4.2.3 for the associated column-property figures.
Curves of the allowable column stresses for various magnesium-alloy columns are given in Figures 4.4.2.3(a) and (b). The allowable stress is plotted against the effective slenderness ratio defined by Equation 3.10.2.3.
Figure 4.4.2.3(a). Allowable column stresses for magnesium-alloy columns.
Figure 4.4.2.3(b). Allowable column stresses for AZ31B-H24 magnesium-alloy sheet.
The general statements relating to aluminum-alloy tubing in Section 3.10.3 are applicable to magnesium tubing.
An empirical curve of the allowable torsional modulus of rupture for AZ61A-F magnesium-alloy round tubing (specification WW-T-825) is given in Figure 4.4.3.2.
Figure 4.4.3.2. Torsional modulus of rupture for AZ61A-F magnesium-alloy round tubing.