Tools › Structures › Thin-Walled Structures › Box Beam Shear Flow › Example
Bruhn's two-cell hexagonal torque box: cell shear flows, interior web flow and rate of twist (A6.10 Example 1)
| Tool | Box Beam Shear Flow |
| Source | Bruhn, E. F. (1973). Analysis and Design of Flight Vehicle Structures. Jacobs Publishing, Carmel, IN. Chapter A6, Articles A6.8 and A6.10, Example 1 (single-cell box and the same box with an interior web), as reproduced on the Mississippi State University study pages for the chapter. |
| Level | Undergraduate |
Problem
A thin-walled aluminum torque box (G = 4 × 10⁶ psi) is 8 in deep and 96 in long in cross-section: a 72 in rectangular middle with 12 in triangular noses at each end, skin 0.08 in thick on the left half and 0.06 in on the right, and a 0.05 in vertical web at mid-length dividing it into two cells of 336 in² each. Find the shear flow in each cell and in the web, the wall shear stresses and the rate of twist under a torque of 134,400 in-lb, and compare with the single-cell box without the web.
Inputs to Enter
- Nodes 1–8: (0, 0), (12, 4), (12, −4), (48, 4), (48, −4), (84, 4), (84, −4), (96, 0) in; no booms (the walls carry direct stress)
- Walls: 1-2, 1-3, 2-4, 3-5 t = 0.08 in; web 4-5 t = 0.05 in; 4-6, 5-7, 6-8, 7-8 t = 0.06 in; reference G = 4 Msi
- Torque T = 134,400 lb-in counter-clockwise, no shear load
Answers
- Equal-twist system: [1,376.2 −160 −672; −160 1,781.6 −672; 672 672 0] {q_I, q_II, G dθ/dz} = {0, 0, 134,400} → q_I = 111.66 lb/in, q_II = 88.34 lb/in (book 111.4 / 88.2)
- Interior web q = q_I − q_II = 23.3 lb/in (book 22.8); stresses 1,396 / 1,472 / 466 psi (book 1,392 / 1,477 / 456)
- J = 647.3 in⁴, rate of twist 5.19 × 10⁻⁵ rad/in (5.19 × 10⁻³ rad over 100 in); the single-cell box without the web has q = T/2A = 100 lb/in exactly, τ = 1,250 / 1,667 psi and 5.28 × 10⁻³ rad over 100 in (book 5.29 × 10⁻³)
- Shear centre of the two-cell box at x_S = 44.62 in on the axis of symmetry (not in the book)
Notes
The tool's default inputs are this box; press Submit. The book's flows differ from the exact solution of its own system by 0.2 % (rounding in the hand solution); the MSU page's twist for the two-cell case (3.31 × 10⁻³ rad) is inconsistent with its own flows and the tool reports 5.19 × 10⁻³. Every value is checked in test_box_beam_shear_flow.php together with Megson's Examples 20.4, 23.2 and 23.3, Problems P.23.3–P.23.5 and Kuhn's NACA TN 691 Examples 6–11, and against the numpy script References/Box-Beam/checks/boxbeam_numpy_check.py.