Tools › Structures › Thin-Walled Structures

Thin-Walled Structures

10 tools in the Structures area.

Crippling Strength

Crippling (local post-buckling failure) stress and load of formed and extruded thin-walled compression members: angle, channel, zee, tee, I, cruciform, hat, lipped channel and zee, rectangular tube, or a typed list of flat elements. Three methods side by side: Gerard's generalized crippling formula from NACA TN 3784 and TN 3785 (angle-type, T-type and two-corner sections with the coefficients, exponents and cutoffs of the reports, g counted as flanges plus cuts), Needham's angle-element method as reproduced in Bruhn C7, and an element-by-element method in Needham's form, with the governing crippling stress, the crippling load, a margin of safety and a chart of the Gerard curve with the design point. The default is the extruded 2024-T4 tee LS 236 of NACA TN 3784 Table 9 (failing stress 31.0 ksi in the test; Gerard's T-type formula gives 31.2 ksi).

1 worked example reproduced, listed on the tool page.

Effective Sheet Width

Width of buckled sheet that keeps acting with a stringer in a compression panel: the sheet buckling stress for the stringer pitch and edge condition, then the effective width at the stringer stress by von Kármán's 1.9 t √(E/σ) rule, Marguerre's cube-root and square-root formulas (NACA TM 833), Koiter's and the Argyris–Dunne large-deflection results as given in Gerard's Handbook of Structural Stability Part IV (NACA TN 3784), Winter's 1947 formula and its AISI form, with an optional plasticity correction by Stowell's factor, the inter-rivet buckling limit of the rivet line (NACA TN 3785, Table 5 fixity coefficients), the effective area added to the stringer, a chart of effective-width ratio against stress ratio and a sketch of the stress across the sheet. Default: 0.040 in 2024-T3 sheet on stringers 4 in apart at a stringer stress of 35 ksi, checked against the closed forms.

1 worked example reproduced, listed on the tool page.

Stiffened Panel Compression

Compressive strength of a riveted sheet-stringer panel between frames: the stringer crippling stress by Gerard's generalized formulas (NACA TN 3784 and TN 3785), the von Kármán effective sheet width acting with the stringer, the stringer-plus-sheet column on the Johnson–Euler curve with the end-fixity coefficient, the inter-rivet buckling cutoff with the fastener end-fixity coefficients of NACA TN 3785 Table 5, and the wrinkling (forced crippling) analysis of NACA Report 1255 (Semonian and Peterson 1956) with its effective rivet offset chart, maximum-stress coefficient, plasticity factor, rivet-pitch and rivet-strength criteria, beside the monolithic panel crippling strength of TN 3785. The governing mode, the allowable running load and the margin of safety are reported with a chart of the column curve and the cutoffs. The default inputs are the numerical example of Report 1255 (2024-T3 Z-stiffened panel, 3/32-inch brazier-head rivets at 1 inch), whose printed values the page reproduces.

1 worked example reproduced, listed on the tool page.

Diagonal Tension Web

Strength analysis of a plane stiffened shear web working in incomplete diagonal tension by the engineering theory of Kuhn, Peterson and Levin (NACA TN 2661, 1952, Section 4), step by step and in the report's notation: the web buckling stress with the empirical edge-restraint coefficients and the plasticity correction, the loading ratio and the diagonal-tension factor k = tanh(0.5 log(τ/τcr)), the angle of the diagonal tension by the report's successive approximation, the average and maximum upright stresses, the maximum nominal web stress with the angle and flange-flexibility factors, the allowable web stress from the report's basic-allowable curves for 24S-T3 and Alclad 75S-T6, the upright checks for forced crippling and column failure (effective column length, riveted-column reduction), the secondary flange stresses and bending moment, the web-to-flange and upright rivet loads, a margin of safety for every check and the predicted failing load of each mode. The default case is the report's numerical example 1, NACA test beam I-40-4Da (24S-T3 web 0.039 in thick, 41.4 in deep, double angle uprights at 20 in, 30.3 kips of shear), whose printed values the page reproduces.

1 worked example reproduced, listed on the tool page.

Box Beam Shear Flow

Shear flow and rate of twist of single- and multi-cell thin-walled closed boxes under shear loads and torque, the Bredt–Batho theory of Megson's Aircraft Structures and Kuhn's NACA TN 691. The section is entered as numbered nodes (with optional boom areas for the idealized form) joined by walls of given thickness and shear modulus, straight or curved; the tool finds the cells itself. Pure torque gives the single-cell flow q = T/(2A), the twist rate and J = 4A²/∮ds/t, or for several cells the compatibility equations (equal twist in every cell) printed as a matrix and solved for the cell flows and J. Shear loads give the open-section flows after a cut in each cell, the closing flows from the zero-twist condition, the shear centre, the torque of the loads about it, the wall shear stresses with a margin against an entered allowable, and a figure of the section with every flow drawn as an arrow; the resultant of the flows is checked against the applied loads. The default is the two-cell hexagonal torque box of Bruhn's Analysis and Design of Flight Vehicle Structures (A6.10 Example 1): T = 134,400 lb-in gives q = 111.4 and 88.2 lb/in in the two cells and 22.8 lb/in in the interior web.

1 worked example reproduced, listed on the tool page.

Open Section Shear Flow

Shear flow distribution and shear centre of a thin-walled open section under transverse shear loads, by the thin-wall bending-shear equation of Megson and Bruhn: the section is a tree of straight walls (channel, lipped channel, zee, I, tee, angle, hat or circular arc from a few dimensions), or a boom-skin idealization typed as booms with areas joined by skins. The tool computes the thin-wall section properties about the centroid, walks the shear flow q(s) around every wall from the free edges (exact quadratic on each wall, with the jump at every boom), tabulates the flows and shear stresses at the nodes and at the maxima, locates the shear centre from the moment of the flows, compares it with the closed forms for the channel and the arc, checks that the flows balance the applied loads, and draws the flow distribution on the section. A load applied away from the shear centre adds a torque with the Saint-Venant twist rate and torsional shear stress. The default is Megson's Example 20.3, an idealized channel of four 300 mm² booms under 4.8 kN, whose printed flows of 6, 12 and 6 N/mm the page reproduces.

1 worked example reproduced, listed on the tool page.

Local Buckling Coefficients

Elastic and plastic local buckling of the flat plate elements of a thin-walled section by NACA TN 3781 (Gerard and Becker 1957, Handbook of Structural Stability Part I): the buckling coefficient k of a plate b × t under compression, shear or bending for any aspect ratio a/b, loaded edges simply supported or clamped, and unloaded edges simply supported, clamped, free or elastically restrained against rotation (restraint coefficient ε), from the exact Lévy solution for compression and converged energy solutions for shear, bending and clamped loaded edges; σ_cr = k π² E/(12(1 − ν²)) (t/b)²; Stowell's plasticity-reduction factors (NACA Report 898) with the Ramberg-Osgood stress-strain curve; the cladding reduction factor; the interaction of combined loads; and the local buckling of a whole section (I, channel, Z, tube, angle, tee, cruciform, hat, lipped channel or a typed element list) from the exact interaction of its elements, with the restraint-free lower bound and the equivalent edge restraint beside it. The report's long-plate coefficients (4.0, 6.98, 0.43, 1.28; 5.35, 8.98; 23.9, 41.8) and the moment-distribution values of NACA ARR 3K04 are printed beside the computed ones. The default is a 2024-T3 flange 1.5 in wide and 0.064 in thick with one edge free.

1 worked example reproduced, listed on the tool page.

Shear-Resistant Web

Design check of a stiffened plane shear web that must stay unbuckled at limit load (the shear-resistant beam of NACA TN 2661 Section 1 and Bruhn Chapter C10), the companion of the Diagonal Tension Web tool: the nominal web shear stress V/(h t), the elastic buckling stress of the panel between flanges and stiffeners by equation (32) of NACA TN 2661 with the simply-supported coefficient of Figure 12(a) and the empirical edge-restraint coefficients R_h and R_d of Figure 12(b), the simply-supported and clamped bounds of NACA TN 3781, the plasticity reduction E_sec/E on a Ramberg-Osgood curve, the margins against buckling at limit load and against the shear strength F_su at ultimate, the diagonal-tension factor k at ultimate when the web buckles between limit and ultimate load, the stiffener moment of inertia required by four criteria (Bruhn equation C10.8 from Wagner's general shear-buckling load, Bruhn Figure C10.9, Moore's NACA TN 862 test formula and the Stein-Fralich NACA TN 1851 theory of the transversely stiffened plate with Bleich's fit), the stiffener column check, the web-to-flange rivet load V Q/I with the diagonal-tension factor of equation (34), the upright-to-web rivet tension criteria, the weight per unit length and charts of the buckling stress and of the stiffener requirements against the spacing ratio d/h. The default case is a 10 in deep 2024-T3 web, 0.063 in thick, with single 0.75 by 0.75 by 0.063 in angle stiffeners at 6 in under a limit shear of 4,000 lb, checked against the report formulas and an independent numpy recomputation.

1 worked example reproduced, listed on the tool page.

Shear Lag in Box Beams

Shear lag in the stringer-sheet cover of a box beam under bending by Kuhn's substitute single-stringer method (NACA Report 739, Kuhn and Chiarito 1942): the cover's stringers are combined into one substitute stringer at their force centroid, the shear-lag parameter K = √(G t / (E b_S) (1/A_F + 1/A_L)) is formed bay by bay, the X-forces that correct the My/I stresses are solved from the recurrence formula, the substitute width is refined by successive approximations, and the stringer stresses across the cover follow the hyperbolic-cosine law with the finite-stringer correction. The page prints the flange stress increase and the centre-stringer deficiency at every station, the running shear in the cover sheet, the constant-section closed forms of NACA Report 608 for comparison, the cubic approximation of NACA ARR L-401, a drawing of the idealized cover and charts of the stresses along the span and across the cover. The default is the beam of Report 739 Figure 50 (Tables I to VII): 600 lb at the tip of a 48 in cantilever, 6 bays, G/E = 0.40.

1 worked example reproduced, listed on the tool page.

Beam-Column with Crippling

A thin-walled stringer or stiffener, with or without its effective sheet, carrying axial compression together with a lateral load or end moments: the exact pin-ended beam-column solutions of Timoshenko and Gere (uniform load, concentrated load and end couples superposed at the applied axial load), the magnification factor and C_m approximation printed beside them, the extreme-fibre stresses on the free flange and the sheet face, the crippling allowable of the section by Gerard's generalized formulas (NACA TN 3784 and TN 3785) or an entered value, the Johnson–Euler column allowable with the crippling cutoff, the interaction R_a + R_b = 1 with the amplified bending stress (the stringer check of Bruhn C7), the tension-flange check against F_tu, the proportional load factor at failure, and charts of the deflected shape, the moment diagram and the fibre stresses. The default is the 2024-T3 Z-stringer and sheet of the NACA Report 1255 numerical example (crippling stress 27.5 ksi from the report's tests) as a 19.6 in strut between frames under 9,000 lb of compression and 20 lb/in of lateral pressure load.

1 worked example reproduced, listed on the tool page.

Other Structures sections

Materials · Composites · Frames and Trusses · Beams · Loads and Dynamics · Joints · Stress and Strain · Stability · Plates and Shells · Contact · Stress Concentrations · Fatigue · Damage Tolerance