See Chapter 1 and Reference 1.7.1 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.
Round Tubes — For round tubes, the value of Fb will depend on the D/t ratio as well as the ultimate tensile stress. The bending moduli of rupture of round tubes of various aluminum alloys are given in Figure 3.10.1.1.1. It should be noted that these values apply only when the tubes are restrained against local buckling at the loading points.
Figure 3.10.1.1.1. Bending modulus of rupture for aluminum alloy round tubing.
Unconventional Cross Section — Sections other than solid or tubular should be tested to determine the allowable bending stress.
Built-up beams will usually fail because of local failures of the component parts. In aluminum-alloy construction, the strength of fittings and joints is an important feature (see Reference 3.10.1.2).
The allowable stress for thin-web beams will depend on the nature of the failure and is determined from the allowable stresses 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.
The local stability of aluminum alloy column sections may be determined using the methods outlined in References 3.10.2.2(a) through (e).
Curves of the allowable column stresses for round and streamline tubing are given in Figure 3.10.2.3. The allowable stress is plotted against the effective slenderness ratio, as defined by Equation 3.10.2.3.
Figure 3.10.2.3(1 of 4). Allowable column stress (Fc) versus L′/ρ for 2024-T3 and 6061-T6 aluminum alloy tubing. Dashed lines are D/t cutoff construction lines linking the column curve to the crushing-stress chart at right.
Figure 3.10.2.3(2 of 4). Crushing stress (Fcc) versus D/t for 2024-T3 and 6061-T6 aluminum alloy tubing.
Figure 3.10.2.3(3 of 4). Allowable column stress (Fc) versus L′/ρ, general curve keyed to D/t = 10 through 50 (D = basic round tube diameter).
Figure 3.10.2.3(4 of 4). Crushing stress (Fcc) versus D/t, general curve corresponding to the chart above.
The torsional failure of aluminum-alloy tubes may be due to plastic failure of metal, elastic instability of the walls, or an intermediate condition. Pure shear failure will not usually occur within the range of wall thicknesses commonly used for aircraft tubing.
The curves of Figures 3.10.3.2(a) through (g) are derived from the method outlined in Reference 2.8.1.1 and take into account the parameter L/D. The theoretical results set forth in Reference 2.8.3.2 have been found to be in good agreement with the experimental results.
Figure 3.10.3.2(a). Torsional modulus of rupture—2014-T6 aluminum alloy rolled rod.
Figure 3.10.3.2(b). Torsional modulus of rupture—2014-T6 aluminum alloy forging.
Figure 3.10.3.2(c). Torsional modulus of rupture—2024-T3 aluminum alloy tubing.
Figure 3.10.3.2(d). Torsional modulus of rupture—2024-T4 aluminum alloy tubing.
Figure 3.10.3.2(e). Torsional modulus of rupture—6061-T6 aluminum alloy tubing.
Figure 3.10.3.2(f). Torsional modulus of rupture—7075-T6 aluminum alloy rolled rod.
Figure 3.10.3.2(g). Torsional modulus of rupture—7075-T6 aluminum alloy forging.