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Sutural Pattern and Shell Stress in Baculites with Implications for Other Cephalopod Shell Morphologies Author(S): David K

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Sutural Pattern and Shell Stress in Baculites with Implications for Other Cephalopod Shell Morphologies Author(S): David K Paleontological Society Sutural Pattern and Shell Stress in Baculites with Implications for Other Cephalopod Shell Morphologies Author(s): David K. Jacobs Source: Paleobiology, Vol. 16, No. 3 (Summer, 1990), pp. 336-348 Published by: Paleontological Society Stable URL: http://www.jstor.org/stable/2400792 Accessed: 23/02/2010 16:21 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/action/showPublisher?publisherCode=paleo. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. Paleontological Society is collaborating with JSTOR to digitize, preserve and extend access to Paleobiology. http://www.jstor.org Paleobiology, 16(3), 1990, pp. 336-348 Sutural pattern and shell stress in Baculites with implications for other cephalopod shell morphologies David K. Jacobs Abstract.-In Baculites,a straight shelled ammonite, the constructional limits on shell shape resulting from the limited strength of nacre in tension are circumvented by a system of vaults in the phrag- mocone. Vaults bridge between regions of the phragmocone supported by the complex ammonite septal suture, and maintain the shell wall in compression when hydrostatic load induces bending moments. To determine how these vaults interact in the phragmocone to resist hydrostatic loading, measurements were made on a suite of Baculites specimens. In Baculites there is a statistically sig- nificant inverse relationship between circumferential curvature (radius of curvature) of the vaulted shell surface and the size of vaults spanning between sutural elements supporting the phragmocone. The inverse relationship between radius of curvature and the sizes of spans in this system of vaults results in the generation of comparable reactive forces at the ends of the vault spans where adjacent vaults interact. The equivalence of these reactive forces prevents the lateral displacement of the vault ends. Consequently, compressive stresses from adjacent vaults are superimposed on, and reduce, the tensional stress component of bending. Limiting tensile stress is of utmost importance in a lightweight shell composed of a brittle material such as nacre, which is strong in compression but weak in tension. Baculites is particularly appropriate for this study because its straighlt shell is curved only in the circumferential direction, thus simplifying the problem. However, sutural patterns in coiled am- monites appear to be similarly constrained to produce vaults in the phragmocone which vary inversely in curvature and span size. David K. Jacobs. Department of Geological Sciences, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061-0796. Current address: Museum of Paleontology, University of California, Berkeley, California94720 Accepted: March 21, 1990 Introduction in the structure of the shell itself. This un- The structural implications of sutural com- derstanding of the hydrostatic load borne on plexity in ammonites have long been a subject the shell led to the application of membrane of scientific interest. Buckland (1836) argued stress formulae for hollow thin-walled that the complex septal sutures of ammonites spheres and cylinders to the concave portions served to support the flattened flanks of am- of nautiloid septa and the tubular siphuncle monite phragmocone against hydrostatic (e.g., Westermann 1973, 1977, 1982). In these pressure.This idea was also advocated by Pfaff thin-walled structures, hydrostatic load pro- (1911), Spath (1919), and Westermann (1956). duces a purely tensional or compressional However, conclusive evidence of the pres- stress, termed a "membrane stress." Mem- sure difference across the shell wall of ceph- brane stresses are proportional to the radius alopods was not available to these authors of curvature and the pressure difference across (for a historical review of functional analyses the concave nautiloid septum and tubular si- of shelled cephalopods see Jacobs 1990). Fi- phuncle; they are inversely proportional to nally, Denton and Gilpin-Brown (1961, 1966) the septal or siphuncular thickness. and Denton et al. (1967) unequivocally dem- The distribution and magnitude of the onstrated that modern shelled cephalopods stresses in the ammonite phragmocone are contain gas at or below atmospheric pressure less easily assessed than the stresses in con- while submerged. Consequently, modern cave septa or tubular siphuncles. There are shelled cephalopods and, by analogy, fossil two reasons for this. First, ammonite phrag- shelled cephalopods support the entire hy- mocones do not conform to simple shells of drostatic load of the overlying water column revolution for which equations of membrane ? 1990 The Paleontological Society. All rights reserved. 0094-8373/90/ 1603-0006/$1.00 SUTURAL PATTERN AND SHELL WALL STRESS 337 stress are readily derived. The radius of cur- vature around the whorl in the ammonite RADIUS OF CURVATURE phragmocone is not constant; consequently, one would expect differential stress genera- tion in different regions of the phragmocone (Westermann 1971). Secondly, the phrag- Ri-Flank Radius mocone is supported at intervals by the septa. This support results in a flexural or bending R2-Dorsal Radius problem as the shell wall, bearing hydrostatic load, passes over and between the supports R3-Ventral Radius provided by the septal suture. Hewitt and Westermann (1986) attempted to model the bending stresses in spaces be- R2 tween sutural support in the relatively flat flanks of a Calliphyllocerasshell by analogy to Ri a flat plate. However, even the flanks of oxy- conic ammonites have some curvature; they are rarely, if ever, exactly flat. Due to their R3 curvature, portions of the phragmocone bridging between sutural elements form a se- ries of vaults rather than flat plates. In a tra- verse around the non-circular whorl section of a compressed ammonite morph, the radius of curvature necessarily changes (Fig. 1). In addition, spacing of sutural support of the shell wall is not uniform. The complexity of the suture and coiling geometry results in in the size of spans of shell wall variation FIGURE 1. The thick curve represents a cross-section between sutural elements in the sutural pat- through a Baculites shell. Three radii of curvature de- tern. This variation in sutural spacing appears scribe the major regions of curvature around the circum- ference of a Baculites shell. The radius of curvature of the to relate to the local curvature of the shell broad flanks of the shell, Rl, is many times greater than around the whorl. The larger radius of cur- that of the intermediate radius of curvature of the dorsal vature, "flatter," portions of the whorl have shell surface, R2, which is in turn substantially greater than the radius of curvature of the ventral R3. more closely spaced sutural support than the region, more tightly curved (smaller radius of cur- vature) portions of the shell (Buckland 1836; curvature and the spacing of support is ex- Spath 1919; Westermann 1956, 1971, 1975). amined to determine if it relates to the func- Due to the complex interdigitation of adja- tion of the ammonite shell as a series of vaults cent ammonoid sutures, septal support sur- supporting hydrostatic load. This will address rounds the vault spaces in the sutural pattern. the long standing question of the function of A greater proportion of the load on a doubly the ammonite suture and how the ammonite curved vault surface will be transferred in the suture may be functionally constrained. direction of the smaller radius of curvature. The Phragmocone Conceived of as a Series of The smaller radius of curvature necessarily Vaults.-Vaults combine the axial or mem- occurs around the whorl rather than around brane stresses, associated with thin-walled the coil of a planispiral shell. Consequently, pressurized spheres and cylinders, with the vaults in the phragmocone will bear more of bending stresses normally associated with the load around the whorl rather than around loaded beams or flat plates (Salvadori 1971). the coil, and it is this circumferential direc- Unlike plates, vaults produce outward thrust- tion around the whorl that is of interest. ing at their ends when loaded. This outward In this work, the relationship between shell thrusting is a consequence of bending mo- 338 DAVID K. JACOBS INTERACTIONOF THRUSTS IN A SERIES OF VAULTS c A -t B TA TB TA' TB' S S FIGURE2. In a series of uniformly loaded vaults which meet at supports, SA and SB, the outward thrusts of vault AB, TA and TB must be met by thrusts of similar magnitude, TA' and TB', generated by adjacent vaults if vault AB is to remain in compression. If TA' and TB' are not as large as TA and TB then the vault ends will displace outward and tensile stress will develop on the interior of the vault at C. ments in the vault. Unless this outward vented by equivalent reaction forces, then no thrusting is met by an opposing reaction force, dilation of the material on the interior of the bending moments in the vault will result in vault can occur. If there is no dilation then a large tensile stress component on the in- there must be no tensional stress.
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