0000012907 00000 n For example, even if a wall stud shrinks or expands in the middle of a wall, it's not likely to make a measurable change in overall building width - it simply expands and contracts inside its adjoining joist bays. Holz Roh- Werkst. 5. 0000009167 00000 n The following simple formula for the coefficient of thermal linear expansion in a building material is written to measure the percentage change in length per degree of temperature change: = (Change in Length / Original Length) / Change in Temperature. It sounds as if something is hitting it. We can help you find the most appropriate wood solution. I feel I should have been advised of this BEFORE construction. Bookshelf On 2020-03-18 by (mod) - coefficient of expansion for marble. 0000006308 00000 n Textbook of woodtechnology. Accessibility Principles of wood science and technologysolid wood. Learner, Research in Conservation, 2004 ISBN 0-89236-779-2 [Chemistry of modern paints, overview of analytical methods, pyrolysis-gas chromatography signatures of basic modern paints and their constituents, Fourier transform infrared spectroscopy for paint analysis, direct temperature-resolved mass spectrometry, and analysis in practice - technical reference useful for forensic paint science, focused on art works -DF], Building Pathology, Deterioration, Diagnostics, and Intervention, Samuel Y. Harris, P.E., AIA, Esq., ISBN 0-471-33172-4, John Wiley & Sons, 2001 [General building science-DF - ** Particularly useful text **, Understanding Ventilation, John Bower, The Healthy House Institute, ISBN 0-9637156-5-8, 1995 [General building science-DF - ** Particularly useful text.
Sketch at page top and accompanying text are reprinted/adapted/excerpted with permission from Solar Age Magazine - editor Steven Bliss. 3. 2022 WoodWorks All Rights Reserved. MeSH 0000015089 00000 n But I'm reluctant to pretend to diagnose and repair sounds without any more information; Of course there is something to be done, and in many cases the repair is economically reasonable. How do building materials change in dimension in response to temperature changes, sun, shade, ice, snow?How do the dimensions of different building materials vary with temperature, heat, cold?Table of Coefficient of Expansion of Building Materials. ASTM. The coefficient of linear expansion of Aluminium is about 22x(10^-6) m/mC. Vol. The linear expansion of a heated solid (or liquid) is measured by. 0.0000123 - 0.0000129 or 0.000029 (other sources), (ppm) = 29 (0600 C) 2009 Apr 8;131(13):4866-71. doi: 10.1021/ja809631r. Woodcanexperience dimensional movement with temperature changes.
by (Mod)- engineer tunes-up table of coefficients of expansion of materials. Prod. Zaved. HermanYou ask an interesting question but we need to be rather clear, and perhaps more narrow in our question and answer since even a traditional wood frame house has plenty of other materials involved in its construction besides wood. Estimate the wood carbon footprint of your project. As the Wood Handbook notes: Even in the longitudinal (grain) direction, where dimensional change caused by moisture change is very small, such changes will still predominate over corresponding dimensional changes as a result of thermal expansion unless the wood is very dry initially. Environ Pollut. J. - Anonymoys by private email 2020/10/17. Our Comment Box is provided by Countable Web Productions countable.ca, Click to Show or Hide Citations & References, CLTE Coefficient of Linear Thermal Expansion for Common Building Materials, Linear Thermal Expansion Coefficients of Metals and Alloys, METAL ROOFING: 'FIXING' for THERMAL MOVEMENT, THE COEFFICIENTS OF THERMAL EXPANSION OF WOOD AND WOOD PRODUCTS, WOOD HANDBOOK, PHYSICAL PROPERTIES of WOOD - Chapter 3 Physical Properties & Moisture RElations of Wood, VINYL SIDING COEFFICIENT of LINEAR EXPANSION, Best Practices Guide to Residential Construction, HOME INSPECTION EDUCATION COURESES (Canada), HOME INSPECTION EDUCATION: HOME STUDY COURSES, 0.00000447 (molding & extruding compound). (U8(EnR:WWufg\i]F*Tdc7w :~2^Vk&RR-sKfcTJ@{PaW`b}t? Skaar, C. 1988. 0000019725 00000 n Stay up-to-date on industry news, innovative projects, and more. McGraw-Hill, New York.nKollmann, F. P. 1968. The conceptual explanation is that different materials expand and contract at different rates - as illustrated in the article above on this page on coefficients of thermal expansion. 2008 Jul 30;130(30):9660-1. doi: 10.1021/ja803623u. Neue Versuche ber die Ausdehnung von Krpern durch die Wrme. At temperatures above 0 C during heating, water migrated out of fiber-saturated cell walls; the resulting shrinkage reduced the expansion significantly and between 20 and 70 C even led to contraction. 0000011635 00000 n
The site is secure. Would you like email updates of new search results? Review of disposal technologies for chromated copper arsenate (CCA) treated wood waste, with detailed analyses of thermochemical conversion processes. Relative humidities for Douglas-fir wood between 10 and 70 F. Wood Sci. The coefficient of thermal expansion is defined such that measures the percentage change in the length of the material per degree of temperature change. 4.33 mm, for you inch-people, is 0.17 inches across just 12 ft. of length. It's extremely aggravating.Thank you and I hope to hear from you soon. I am trying to figure out HOW I can capture these sounds as evidence of what is happening here daily! Because panel products start at a low moisture content (~8-12% MC) and are directly exposed to the elements during construction (in many cases increasing to >19% MC), the expansion of these products is likely to be more pronounced. Longitudinal dimensional change due to moisture change is negligible, meaning the length of a stud or floor joist will essentially remain unchanged. I suspect that other materials such as siding expand and contract more than the frame - considerably more - which is why installation instructions call for appropriate gaps. I have been dealing with this problem for over a year. Sorption isotherms of twelve woods at sub-freezing temperatures. Mr. Bower has retired from the field but his book continues to be important], Dampness in buildings, Diagnosis, Treatment, Instruments, T.A. Please enable it to take advantage of the complete set of features! Granite = 0.0000044 (also Limestone, Marble) Standard methods for testing small clears pecimens of timber. Thermal expansion of wood.
At freezing temperatures during cooling, moisture diffused out of the saturated cell walls and condensed as ice crystals in the cell cavities; the resulting shrinkage supplemented true thermal contraction and caused large coefficients of thermal expansion in a broad sense. All proprietary rights other than copyright, such as patent rights. New York: McGrawHill. Wood Sci. Input the volume of structural wood in a building, and our Carbon Calculator will estimate how much carbon is stored in the wood.
Suggestion to take out "percentage".Also, the table should list all numbers in the same format (i.e., you have "0.00000234", "16.9 ppm", "4.5 x 10(-5)", and also show (sometimes) the units in the table, even including C for a table that everything else is in F. The units are already given in the column header, so suggestion to take out units, convert those that are in C to F, and format all numbers to be in a single format. POPPING SNAPPING NOISE DIAGNOSIS is the topic home page where we organize all of our diagnostic and repair articles on this. Girods P, Dufour A, Rogaume Y, Rogaume C, Zoulalian A. J Hazard Mater. Or re-stating, aluminum siding will expand along its length from 21 to about 24 micrometers (about 22 um) per meter of length for each 1C increase in its temperature. Thermal expansion. Rep. R 1487 U.S. For. 
2(2):125-128A.nHendershot, O. P. 1924. Obviously he can fix what isn't present. I'd suggest replacing with: "Definition of CLTE: The coefficient of linear thermal expansion (CLTE) of any material is the change of a material's dimension per unit change in temperature."2. What thermal expansion of composite marble dimensions 20ft by 30 ft at 40degree centigrade? The WoodWorks paper,Accommodating Shrinkage in Multi-Story Wood-Frame Structures, discusses this, as does technical note U425Temporary Expansion Joints for Large Buildingsfrom APA. 0000008884 00000 n
Forsatth, C. C. 1946. Epub 2008 Feb 12. @~ Rc$Mx.w&-5N^"nH&-R2'$cfV|c!`(4L7(pF_"87ZI^e9=(E!pCf!pGl\"BFd)58 (US7
JoTI.*v0pk!*+MW"8,PqTs The shrinkage due to reduced MC is more significant than the expansion due to increased temperature; therefore, the net result is shrinkage. 0000004788 00000 n
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As wood experiences an increase in temperature, it may experience some thermal expansion, but there is also a loss of MC. ASTM D143. It is NOT any sort of animal. In larger buildings (over 80 in length), it is recommended to increase the gap between panels and take additional construction sequencing precautions to avoid panel buckling. However, the authors reserve the following as set forth in the Copyright Law: 1. 5(3): 198-204.nNikolov, S., and A. Rajev. #
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bhm@.0,,P7BMr:. Those noises can appear as banging, knocking, or clicks, squeaks, or tapping sounds as metal or other components of your Florida patio move against one another during temperature changes, also affected by wind and changes in humidity, even barometric pressure. For. Use your browser's on-page search function such as Ctrl-F to search the page above for "marble" to find more details. trailer
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My problem is that I am hearing intermittent banging and knocking noises coming from the pillars and the areas of roof. 0000012929 00000 n
Or use the SEARCH BOX found below to Ask a Question or Search InspectApedia. Thermal expansion and contraction, is probably the culprit, anon. "The CoTE does not indicate percentage change, it indicates change per unit dimension of material. The coefficient of linear thermal expansion (CLTE) of any material is the change of a material's dimension per unit change in temperature. Page 76 in L. E. Wise, Wood chemistry, 1st ed. However, the Society may grant rights with respect to Journal issues as a whole. 1967.
The right to use all or part of this article in future works of their own, such as lectures, press releases, reviews, text books, or reprint books. 0000006285 00000 n
Where we get into trouble fixing thermal expansion/contraction noises are where large, expensive materials have been "permanently" installed such as in some metal roof systems, as we discuss. So you'd look only at framing members whose position is such that their thickness determines the overall wall width or length. Bethesda, MD 20894, Web Policies That's probably pretty-few: corner posts, intermediate posts not abutting an open joist bay. 2005 Mar;134(2):301-14. doi: 10.1016/j.envpol.2004.07.025. J. Zemizdat, Sofia, p. 79-87.nOgarkova, T. V. 1961. CoTE or Coefficient of Thermal Expansion gives change per unit dimension of material in response to change (increase or decrease) in the material's temperature . In the case of whole articles, such third parties must obtain Society of Wood Science and Technology written permission as well. 
Schwinden und Quellen des Holzes durch Klte. Prod. government site. Holz Roh- Werkst. This transfer grants the Society of Wood Science and Technology permission to republish all or any part of the article in any form, e.g., reprints for sale, microfiche, proceedings, etc.
"The coefficient of thermal expansion is defined such that measures the percentage change in the length of the material per degree of temperature change. I never would have agreed to this. As the piece is 3.6m long, for a temperature increase of 55C, the elongation will be: 22 x 3.6 x 55 x (10^-6) = 4356 x10^-6 m = 4.35 mm. That's enough to make a popping or banging noise if the aluminum siding is installed too-tightly or is constrained between vertical abutting trim. Browse through the WoodWorks award gallery to see the future of wood designed buildings. 0000011658 00000 n What I do find interesting is that I do seem to hear it more frequently when there are slightly breezy conditions but I still hear it whether it's breezy or not. L-*;apEr_&R`F)@/8P!"s HE%6n3U)]B +0c0 #IHAlS(D:&U/"1hEdEK@]Wf3. Try the search box just below, or if you prefer, post a question or comment in the Comments box below and we will respond promptly. The thermal expansion of wood. 0000010396 00000 n Ann. J Am Chem Soc. Holz Roh- Werkst. West Conshohocken,PA: American Society for Testing and Materials. ; Ct, W.A., Jr. 1968. Untersuchungen ber die kltebedingten Lngennderungen kleiner Holzproben. So there's nothing that can be done? 0000002287 00000 n Be careful in comparing the coefficient of expansion of different materials from different reference sources for thermal expansion coefficients as various references quote in degrees C, others in degrees F. Usually people use the term CLTE or Coefficient of Linear Thermal Expansion as expansion along the long dimension of a material is most likely to be greater and thus of greater concern in construction. Suggestions from a licensed professional engineer:1. FV5 }Tk$c'!\49N qhb1LQeG.t #`4#h@)#h98l|si'$'lXZ-P ]W-~/cd.lbq`mhvhvpshfv6-mJMFiVS*'Zke#mQIN={"S1fzj0 9Q\*lQ>nZk7*+\-i"mZ6ZJ|#n Or see THERMAL EXPANSION of MATERIALS FAQs - questions & answers posted originally at this page. Section 4.4 the American Wood Councils National Design Specification (NDS) for Wood ConstructionManualalso provides commentary on this subject, and includes coefficients of thermal expansion for a number of wood species. = coefficient of linear expansion (C1), 0.0000080 (Concrete structure = 0.0000055), SS 301SS 303, 304, 305 & SS 308SS 309SS 316 & SS 317 SS 321 & SS 347SS 403SS 420 & 430FSS 446SS 501 & SS 502, 0.0000063 - 0.0000073 (also Iron, forged), 0.0000028 or in other sources 0.4 to 0.5 x 10-5 parallel to the grain, and 3.4 to 5.8 x 10 -5 at right angles to the fiber direction or grain. New York, Inc. Steven Bliss served as editorial director and co-publisher of, Our recommended books about building & mechanical systems design, inspection, problem diagnosis, and repair, and about indoor environment and IAQ testing, diagnosis, and cleanup are at the, Analysis of Modern Paints, Thomas J.S. 133(3): 400-429.nWangaard, F. F. 1957. 1927 and 1928. Role of moisture in hygro-thermal recovery of wood. 0000007775 00000 n Careers. If I were doing this I'd first look outside at the components that are getting the most heat from sun exposure. 0000013988 00000 n Thermal expansion was largest tangentially and smallest in the longitudinal direction. This could be expected on the basis of the low stiffness of moist wood. Chem. Fortschritte der Physik in den Jahren 1850 und 1851 6:48-52.nVillari, E. 1868. Accommodating thermal movement isnt generally considered necessary, but designers of wood-frame buildings should account for expansion during construction due to increased moisture exposure. Thermal removal of nitrogen species from wood waste containing urea formaldehyde and melamine formaldehyde resins. 0000016282 00000 n The https:// ensures that you are connecting to the 1997. 1, 4th ed. 17(12): 43-48.nHedlin, C. P. 1969. Can you help me figure this out? This site needs JavaScript to work properly. An official website of the United States government. Ann. While concrete and steel buildings are typically designed with expansion joints to account for thermal movement due to environmental temperature fluctuations, wood has a significantly lower coefficient of thermal expansion. Shika Rikogaku Zasshi. FOIA 1946. Unless the wood is very dry initially (perhaps 3% or 4% moisture content or less), shrinkage caused by moisture loss on heating will be greater than thermal expansion, so the net dimensional change on heating will be negative. Before Vissh Lesotekhnicheski Institut, Nauchni Trudove 14, Seria Mehanichna Tekhnologija Na D'rvesinata. Lesnoj Zhurnal 4(4): 106-110.nPerkitny, T., and L. Heliska-Raczkowska. 20(9):364-368.nKubler, H. 1973. No. Oxley & E.G. As we discuss at CRACKS in FIBERGLASS SHINGLES, we have not found a source defining the coefficient of thermal expansion of asphalt roof shingles- CONTACT Us if you can provide that information. As noted in Chapter 4 of the USDA Forest Products LabsWood Handbook, The thermal expansion coefficients of completely dry wood are positive in all directions; that is, wood expands on heating and contracts on cooling. However, moisture fluctuations impact dimensional movement of the wood at the same time. At SKYLIGHT LEAK DIAGNOSIS & REPAIR we include an example of failure of roof flashing cement that has lost its ability to tolerate thermal expansion and contraction on the building. I contacted the builder and told him about it. Kollman, F.F.P. For wood at usual moisture levels, net dimensional changes will generally be negative after prolonged heating.. 0000001699 00000 n But because so many building material failures and leaks derive from cracks or openings due to thermal expansion of materials in length, that is our focus here. He came out about 4-5 months ago to inspect it. If I had a traditional wood frame house, say 25' x 35' how many inches would it shrink and grow from -10F to 100 F? We include a discussion of the definition of thermal coefficient of expansion, how thermal expansion causes trouble in building materials, and how to use the data in the thermal expansion table to calculate changes in material size as temperatures change. -*IB@/%"@B""4^FFC01&3j4"Ch4P3.CjI",g2prw@M u@7E1{bYh4Qhb2;@5Z)H`8Q"{Dd2r806UZ-VG/B^{-5X-)cw;b8C zZV}!IpX bxsGc:O5lnY.V5-j1')|!:@)zllh`pJzJ8*@dZn/l'1t/B B!$K"6$ H;[A? .pPw@9#674@0$R$Hol+P3A@7#:C(@)`Au7HZ(1%)2'ScX 1966. The copyright of an article published in Wood and Fiber Science is transferred to the Society of Wood Science and Technology (for U. S. Government employees: to the extent transferable), effective if and when the article is accepted for publication.
Clipboard, Search History, and several other advanced features are temporarily unavailable. >] Vjr2H$TB endstream endobj 149 0 obj 1128 endobj 150 0 obj << /Type /Font /Subtype /Type1 /Name /F10 /FirstChar 32 /LastChar 255 /Widths [ 278 333 474 556 556 889 722 238 333 333 389 584 278 333 278 278 556 556 556 556 556 556 556 556 556 556 333 333 584 584 584 611 975 722 722 722 722 667 611 778 722 278 556 722 611 833 722 778 667 778 722 667 611 722 667 944 667 667 611 333 278 333 584 556 333 556 611 556 611 556 333 611 611 278 278 556 278 889 611 611 611 611 389 556 333 611 556 778 556 556 500 389 280 389 584 278 722 722 722 667 722 778 722 556 556 556 556 556 556 556 556 556 556 556 278 278 278 278 611 611 611 611 611 611 611 611 611 611 556 400 556 556 556 350 556 611 737 737 1000 333 333 549 1000 778 713 549 549 549 556 576 494 713 823 549 274 370 365 768 889 611 611 333 584 549 556 549 612 556 556 1000 278 722 722 778 1000 944 556 1000 500 500 278 278 549 494 556 667 167 556 333 333 611 611 556 278 278 500 1000 722 667 722 667 667 278 278 278 278 778 778 0 778 722 722 722 278 333 333 333 333 333 333 333 333 333 333 ] /Encoding /MacRomanEncoding /BaseFont /DCMMBA+Arial-BoldMT /FontDescriptor 151 0 R >> endobj 151 0 obj << /Type /FontDescriptor /Ascent 1466 /CapHeight 1466 /Descent -431 /Flags 32 /FontBBox [ -167 -210 1000 913 ] /FontName /DCMMBA+Arial-BoldMT /ItalicAngle 0 /StemV 0 /FontFile 164 0 R /CharSet (/i/T/n/A/s/r/c/C/x/u/space/p/t/e/G/d/o/a) /XHeight 1062 >> endobj 152 0 obj << /Filter /LZWDecode /Length 149 0 R >> stream The Michigan Statewide Carpenters and Millwrights Joint Apprentice and Training From 1 story to 18, were here to support the success of your commercial and multi-family wood building projects with one-on-one project assistance.
; deZeeuw, C. 1980. Lab., Madison.nYates, B. 2:469 and 4:21. One can write similar formulas to calculate the coefficient of thermal expansion of a material in area (applicable, for example in thermal splitting of asphalt roof shingles ) or to calculate the coefficient of thermal expansion of volume. 2008 Nov 30;159(2-3):210-21. doi: 10.1016/j.jhazmat.2008.02.003. J.
7(11):410-416.nWeatherwax, R. C., and A. J. Stamm. 0000000991 00000 n Unable to load your collection due to an error, Unable to load your delegates due to an error. [Click to enlarge any image]. Thermal expansions of beech wood (in Bulgarian). 12. J Am Chem Soc. CLTE may be expressed as a fraction or as a power of ten as you'll see in the table below. This interactive resource includes up-to-date information on topics from mass timber products and design best practices to taller wood construction and sustainability. Coefficient of Expansion in inches of expansion per inch of material per degree F. 12(1):43-45.n. sharing sensitive information, make sure youre on a federal 0000015112 00000 n So they move differently and so move against one another to produce sound. 1962. official website and that any information you provide is encrypted 0000006421 00000 n We also provide an ARTICLE INDEX for this topic, or you can try the page top or bottom SEARCH BOX as a quick way to find information you need. Ask your roofer to be prepared to come by quickly the next time there's a prolonged session of noises from your patio, and also see if you can yourself by careful observation, perhaps aided by a mechanic's stethoscope, pinpoint the location of at least one connection that's noisy. Holz Roh-Werkst. Impact of metallophilicity on "colossal" positive and negative thermal expansion in a series of isostructural dicyanometallate coordination polymers. Let's convert that to inches: 0.11 ft x 12 (inches per foot) = 0.132 inches. The .gov means its official. 24(10):481-486.nSchirp, M., and H. Kbler. 0000001677 00000 n Lngennderungen bei der Wrmebehandlung frischen Holzes. Tangential coefficients of thermal expansion at 12% moisture content and room temperature averaged 53 X 10-1 mm/(mm C) for redwood, 70 X 10-6 mm/(mm C) for northern red oak, 38 X 10-6 mm/(mm C) for Douglas-fir and yellow birch. Login to access subscriber-only resources. Experimental-Untersuchungen ber einige Eigenschaften des mit seinen Fasern parallel oder transversal durchschnit-tenen Holzes. Continue readingat THERMAL EXPANSION of HOT WATER or select a topic from the closely-related articles below, or see the complete ARTICLE INDEX.
Coefficients in the longitudinal direction and for plywood were below 10 X 10-6 mm/(mm C) on the average. Learn about wood products and make a new contact to facilitate material fulfillment for your next project. In that case we still have the option of insulating under the roof to reduce noise transmission into the building interior. After endlessly searching online I happened across your site. I have inspected for everything including birds, insects, lizards, squirrels etc. (If we've got this right). Ucheb. The coefficients of thermal expansion of wood and wood products. ber die Ausdehnung des Eises. Phys. George, a retired EE, wrote. 17(3):77-86.nKbler, H. 1962. THERMAL EXPANSION of MATERIALS at InspectApedia.com - online encyclopedia of building & environmental inspection, testing, diagnosis, repair, & problem prevention advice. We have no relationship with advertisers, products, or services discussed at this website. This enclosure cost me $13,000 and I can't even enjoy it! Principles ofwood science and technology Isolid wood. Wood is hygroscopic, meaning it has the ability to absorb and release moisture. While an accurate answer would include the effect of the siding color on thermal gain from direct exposure to sunlight along with the angle of sunlight hitting the siding and the duration of sun exposure, what follows is a "ballpark" calculation ignoring those niceties. I am desperate to fix this issue as these knocking sounds interfere with my peace and enjoyment. Apologies for the delay. 0000010373 00000 n Gobert, ISBN 0-408-01463-6, Butterworths, 1983-1987 [General building science-DF], Certainteed Weatherboard fiber cement siding and trim products - see certainteed.com/ or see certainteed.com/resources/sidingandtrimspecsheet.pdf, "Moisture Control in buildings: Putting Building Science in Green Building," Alex Wilson, Environmental Building News, Vol. Springer-Verlag, BerlinHeidelbergNew York.nKbler, H. 1959. the increase in length in the siding segment will be, 22 x 20ft x 25C x (10-6) = 0.011ft of expansion. HHS Vulnerability Disclosure, Help Discover mass timber projects across the US and connect with their teams. The following section from Chapter 4 of the Wood Handbook explains this: Wood that contains moisture reacts differently to varying temperature than does nearly oven-dry wood. This clearly isn't a voice. 1978 Oct;19(48):239-53. Note: appearance of your Comment below may be delayed: if your comment contains an image, web link, or text that looks to the software as if it might be a web link, your posting will appear after it has been approved by a moderator. .h/P4f(2Cj Linear thermal expansion of wood, as measured with sealed cylindrical specimens at constant moisture content, generally increased with the amount of bound water. Vyssh. Pages 193-194 in F. P. Kollmann and W. A. Ct, Jr., eds. Prod. 0000002002 00000 n Disclaimer, National Library of Medicine [Good tutorial, "Moisture 101" outlining the physics of moisture movement in buildings and a good but incomplete list of general suggestions for moisture control - inadequate attention given to exterior conditions such as roof and surface drainage defects which are among the most-common sources of building moisture and water entry.--DJF]. Panel buckling, which occurs when there is no room for panel expansion, is prevented with a standard 1/8-inch space between all sheathing panel edges and end joints as recommended by APA in Technical Note D481NMinimizing Buckling of Wood Structural Panels. The coefficient of expansion for pine is 0.0000028 inches per inch of material per degree F. You could add up the widths of all of the framing members whose width or narrow dimension is along the same axis as a house exterior wall - but not all of those would change the building width. You'll also have to make some assumptions about moisture levels and perhaps tightness of framing and framing connectors. 2. The right to grant or refuse permission to third parties to republish all or part of the article or translations thereof.