22-Mec-A4 Design and Manufacture of Machine Elements · December 2013

Question 2 of 8: Redesigning three joints for adhesive bonding

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

Paper format. National Examination, 07-Mec-A4 Design and Manufacture of Machine Elements, December 2013 — 3 hours, open book, any non-communicating calculator permitted. Eight questions on six pages, divided into Part A (manufacturing processes, Q1–Q4) and Part B (machine-element design, Q5–Q8). The rubric asks for three questions from Part A and two from Part B, five questions constituting a complete paper, all of equal value (20 % each). All eight questions are solved here.

Reference texts.

Kalpakjian & Schmid, Manufacturing Engineering and Technology, 7th ed. — sand casting and casting defects (Ch. 10–12), adhesive bonding and joint design (Ch. 32), fusion welding and weld defects (Ch. 30–31), sheet-metal shearing and blanking (Ch. 16).
Budynas & Nisbett, Shigley's Mechanical Engineering Design, 10th/11th ed. — eccentrically loaded shear joints (Ch. 8–9), combined stresses and stress transformation (Ch. 3), statically indeterminate shafts and deflection (Ch. 4), brakes and clutches (Ch. 16).
Hibbeler, Mechanics of Materials, 10th ed. — transverse shear (\(VQ/Ib\)), combined loading and Mohr's circle (Ch. 7–9).
Faires, Design of Machine Elements, 4th ed. — double-block (double-shoe) brakes, self-energizing geometry, equal-wear proportioning.
ASM Handbook Vol. 15 Casting and Vol. 6 Welding, Brazing and Soldering — hot-spot/shrinkage defects; hydrogen-induced cold cracking and preheat practice (see also CSA W59 and CSA W47.1 for Canadian fabrication practice).

Check: Part B is figure-driven. Every dimension used below was read from the printed figures. Two readings are stated explicitly in Given so a grader can substitute a different interpretation without redoing the method: (i) in Figure A the low rivet is taken as lying on the same vertical centreline as the third rivet of the top row (75 + 75 = 150 mm from the left-hand rivet); (ii) in Figure D the dimension \(a\) is the horizontal spacing, measured along the operating lever, between the pin taking the upper shoe link and the pin taking the lower shoe link, with the 10 in operating arm measured from the lower-link pin.

Question 2: Redesigning three joints for adhesive bonding (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

The governing principle. Structural adhesives are strong in shear and in compression, adequate in uniform tension, and very weak in peel and cleavage. The reason is not chemistry but stress distribution: a shear-loaded bondline distributes load over the whole overlap area, whereas peel and cleavage concentrate the entire load on a line at the edge of the bond, where the local stress is many times the average. Redesigning a joint for adhesive bonding therefore means doing three things at once: (i) convert the load path from tension/peel into shear, (ii) increase the bonded area so the average shear stress falls, and (iii) relieve the stress concentration at the ends of the bondline by tapering, filleting or using a compliant fillet of adhesive. A fourth, practical requirement is that the redesign must let the parts be assembled and clamped with a controlled bondline thickness (typically 0.1–0.25 mm), so self-locating features are worth adding.

Figure 2.1 — Each redesign converts a peel- or cleavage-loaded bondline into a large shear-loaded one, and removes the eccentricity that generates the peel in the first place.

Joint 1 — the T-joint. As drawn, the whole load is carried on the end face of the upright, a small area, and any transverse load on the upright applies a cleavage moment that peels the bond from one edge. The redesign lets the upright into a shallow machined slot (or a formed channel) in the base plate and adds bonded angle brackets or moulded fillets on both flanks. The bonded area is now the two flank faces plus the slot walls — several times the original — and a transverse load is reacted by shear down those flanks rather than by cleavage at a line. Radiusing the base of the upright and leaving a generous adhesive fillet spreads the remaining edge stress.

Joint 2 — the offset lap. A single lap is already a shear joint, so it is not hopeless, but the two load lines are offset by the thickness of the parts. That eccentricity produces a bending couple which rotates the joint and peels the adhesive at both ends of the overlap — the classic Goland–Reissner peel spike. The redesign makes the joint symmetric: a double-strap lap (or a joggled/recessed lap that brings the two load lines into one plane), with the strap ends tapered or scarfed so the adherend stiffness falls off gradually. An overlap length of roughly 5–10 times the adherend thickness is used; beyond that the extra length carries almost nothing because the shear is concentrated at the ends.

Joint 3 — the butt joint. A plain butt bond is the worst case: the bonded area equals the cross-section, the adhesive is loaded in direct tension with no redundancy, and any misalignment turns the tension into cleavage. Three acceptable redesigns are a scarf joint with a shallow slope (about 1:6 to 1:10, which multiplies the bond area by 6–10 and converts most of the load into shear while keeping the outside surfaces flush), a double-strap butt with tapered straps, or a tongue-and-groove / stepped-lap joint which additionally self-locates the parts and controls the bondline thickness during cure. Where the parts are tubular the same logic gives a sleeve or a stepped spigot.

Finally, three points apply to all three joints and are worth a mark each: the surfaces must be prepared (degreased, abraded or chemically etched, primed) because adhesive joints fail at the interface far more often than in the adhesive; the bondline thickness must be controlled (glass-bead spacers or the joint geometry itself); and the joint should be designed so that the adhesive is loaded in shear or compression under all service loads, including the accidental ones, since a joint that is only occasionally peeled will still fail by peeling.

Topic. Design of adhesively bonded joints — load-path conversion, bond area and peel/cleavage avoidance.

Key relations. Average bond shear stress \(\tau_{\text{avg}} = P/(b\,L)\) over overlap length \(L\) and width \(b\); the shear distribution is far from uniform, peaking at the overlap ends (Volkersen shear-lag, Goland–Reissner peel); useful overlap \(L \approx 5\!-\!10\,t\); scarf slope 1:6 to 1:10; typical structural-epoxy shear strength 20–40 MPa versus peel strengths one to two orders of magnitude lower.

Why this works. An adhesive layer is thin and compliant compared with the adherends, so load transfers between adherends only through shear in that layer, and the transfer is concentrated wherever the adherend strain changes fastest — the ends of the overlap. Anything that makes the adherends stiffer, more eccentric or shorter in overlap sharpens that concentration; anything that tapers the adherend, symmetrises the load path or lengthens the overlap flattens it. Peel is fatal because it turns a nominally area-carried load into a line-carried one, so the local stress no longer depends on how much area you bonded.

Common pitfall. "Fixing" a butt joint by simply making the bondline thicker or the adhesive stronger — neither changes the fact that the joint is in tension over a small area. Equally common is extending the overlap of a single lap indefinitely: past about ten adherend thicknesses the added length is nearly unloaded, and the eccentricity-driven peel at the ends is unchanged.

Source. Kalpakjian & Schmid, Manufacturing Engineering and Technology, 7th ed., Ch. 32 (adhesive bonding; joint design figures for lap, scarf, strap and tongue-and-groove joints); Shigley Ch. 9 (bonded and welded joint stress distributions).

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