Editing Gateway Arch (section)

==Characteristics==

===Physical characteristics===
[[File:Gateway Arch windows.jpg|thumb|The windows of the observation deck are located around the apex of the arch.]]
Both the width and height of the arch are {{convert|630|ft|m|0}}.<ref name="facts"/><ref name="Bryant"/> The arch is the tallest memorial in the United States<ref name="nhlsum">{{cite web |url=http://tps.cr.nps.gov/nhl/detail.cfm?ResourceId=2017&ResourceType=Structure |title=National Historic Landmarks Program: Gateway Arch |publisher=National Historic Landmarks Program |access-date=December 14, 2010 |archive-url=https://web.archive.org/web/20090804114340/http://tps.cr.nps.gov/nhl/detail.cfm?ResourceId=2017&ResourceType=Structure |archive-date=August 4, 2009 |url-status=dead }}</ref> and the tallest stainless steel monument in the world.<ref name="Cobb">{{cite book |last=Cobb |first=Harold M. |title=The History of Stainless Steel |url=https://books.google.com/books?id=E30rCBeM8nkC&q=%22tallest+monument%22&pg=PA308 |year=2010 |publisher=[[ASM International (society)|ASM International]] |location=Materials Park, OH |isbn=978-1-61503-010-1 |pages=170–174, 308 }}</ref>

The cross-sections of the arch's legs are [[equilateral triangle]]s, narrowing from {{convert|54|ft|m}} per side at the bases to {{convert|17|ft|m}} per side at the top.<ref name="PopSci">{{cite journal |url=https://books.google.com/books?id=mi0DAAAAMBAJ&pg=PA91 |title=St. Louis' Two-Legged Tower: Tallest U.S. Monument |last=Remsberg |first=Charles |date=April 1964 |journal=[[Popular Science]] |volume=184 |issue=4 |pages=91–94 |issn=0161-7370 }}</ref> Each wall consists of a [[stainless steel]] skin covering a sandwich of two carbon-steel walls with [[reinforced concrete]] in the middle from ground level to {{convert|300|ft|m}}, with [[carbon steel]] to the peak.<ref name="Brinkman"/><ref name="Mogin">{{cite news |url=http://thetartan.org/2006/10/30/scitech/htw |title=How Things Work: The Gateway Arch |last=Mogin |first=Sarah |date=October 30, 2006 |newspaper=[[The Tartan (Carnegie Mellon University)|The Tartan]] |access-date=December 14, 2010 |archive-url=https://web.archive.org/web/20101231061036/http://thetartan.org/2006/10/30/scitech/htw |archive-date=December 31, 2010 |url-status=dead }}</ref> The arch is hollow to accommodate a unique tram system that takes visitors to an observation deck at the top.<ref name="csmonitor"/>

The [[structural load]] is supported by a [[Stressed skin|stressed-skin]] design.<ref name="Freeman">{{cite news |url=https://pqasb.pqarchiver.com/csmonitor_historic/access/219784512.html?dids=219784512:219784512&FMT=ABS&FMTS=ABS:AI |title=St. Louis Gateway Arch—a sweeping view |last=Freeman |first=Mary T. |date=November 4, 1967 |newspaper=[[The Christian Science Monitor]] |page=15 |access-date=December 17, 2010 |archive-url=https://www.webcitation.org/61hbjIgRp?url=http://hn.bigchalk.com/pqdocs/share4/pqimage/hnirs101v/201109141827/00611/32220/out.pdf |archive-date=September 14, 2011 |url-status=dead }}</ref> Each leg is embedded in {{convert|25980|ST|MT}} of concrete {{convert|44|ft|m}} thick<ref name="Bryant">{{cite news |url=https://www.chicagotribune.com/1985/10/28/gateway-arch-marks-20-years-over-st-louis/ |title=Gateway Arch Marks 20 Years Over St. Louis |last=Bryant |first=Tim |date=October 28, 1985 |newspaper=Chicago Tribune |agency=[[United Press International]] |page=12 |access-date=January 7, 2011 |issn=1085-6706 |archive-url=https://web.archive.org/web/20121007045359/http://articles.chicagotribune.com/1985-10-28/news/8503130852_1_eero-saarinen-jefferson-national-expansion-memorial-leg |archive-date=October 7, 2012 |url-status=live }}</ref> and {{convert|60|ft|m}} deep.<ref name="Sutton">{{cite news |url=https://pqasb.pqarchiver.com/chicagotribune/access/629600072.html?dids=629600072:629600072&FMT=ABS&FMTS=ABS:AI |title=Spectacle in Steel: St. Louis' Giant Gateway Arch |last=Sutton |first=Horace |date=December 5, 1965 |newspaper=Chicago Tribune |page=J21 |access-date=December 22, 2010 |archive-url=https://www.webcitation.org/61hc1jmrY?url=http://hn.bigchalk.com/pqdocs/share4/pqimage/hnirs101v/201109141831/32392/32213/out.pdf |archive-date=September 14, 2011 |url-status=dead }}</ref> {{convert|20|ft|m|spell=In}} of the foundation is in [[bedrock]].<ref name="Sutton"/> The arch is resistant to earthquakes<ref name="National Parks 1998">{{cite journal |url=https://books.google.com/books?id=KDq3pMiK03sC&pg=PA35 |title=On the Trail of Discovery |last=La Pierre |first=Yvette |journal=[[National Parks (magazine)|National Parks]] |date=July–August 1998 |volume=72 |issue=7–8 |publisher=[[National Parks Conservation Association]] |issn=0276-8186 }}</ref> and is designed to sway up to {{convert|18|in|cm}} in either direction,<ref>{{Cite web |url=http://www.gatewayarch.com/about/history/arch-faqs-facts.aspx |title=Plan Your Visit |access-date=April 17, 2016 |archive-date=April 18, 2016 |archive-url=https://web.archive.org/web/20160418032150/http://www.gatewayarch.com/about/history/arch-faqs-facts.aspx |url-status=dead }}</ref> while withstanding winds up to {{convert|150|mph|km/h}}.<ref name="Post-Dispatch"/> The structure weighs {{convert|42878|ST|MT}}, of which concrete composes {{convert|25980|ST|MT}}; structural steel interior, {{convert|2157|ST|MT}}; and the 6.3mm thick grade 304 stainless steel panels that cover the exterior of the arch, {{convert|886|ST|MT}}.<ref name="Offer"/><ref>{{cite web |url=https://www.doublestonesteel.com/blog/design/the-history-of-the-gateway-arch-st-louis-also-known-as-the-st-louis-arch-designed-by-eero-saarinen-and-completed-in-1965/#:~:text=The%20Gateway%20Arch%20is%20the%20largest%20stainless%20steel%20building%20in,how%20durable%20304%20can%20be. |title=The Gateway Arch, St Louis |date=July 6, 2015 }}</ref> This amount of stainless steel is the most used in any one project in history.<ref name="Cobb"/><ref name="Post-Dispatch"/>

===Mathematical elements===
[[File:St Louis Gateway Arch.jpg|thumb|left |The arch is a weighted catenary—its legs are wider than its upper section.]]
The geometric form of the structure was set by mathematical equations provided to Saarinen by the [[German-American]] engineer [[Hannskarl Bandel]]. Bruce Detmers and other architects expressed the geometric form in blueprints with this equation:<ref>{{cite web |url=https://www.nps.gov/jeff/planyourvisit/mathematical-equation.htm |title=Mathematical Equation |publisher=National Park Service |access-date=December 29, 2023 }}</ref>

<math>y = A \left( \cosh \frac {Cx}{L}-1 \right) \quad\Leftrightarrow\quad x = \frac {L}{C} \operatorname{arcosh} \left( 1 + \frac {y}{A} \right)</math>,

with the constants

<math>A = \frac {f_c} {Q_b/Q_t - 1} = 68.7672</math>

<math>C = \operatorname{arcosh} \frac {Q_b}{Q_t} = 3.0022</math>

where ''f<sub>c</sub>'' = {{cvt|625.0925|ft|m|4}} is the maximum height of centroid, ''Q<sub>b</sub>'' = {{cvt|1262.6651|sqft|m2|5}} is the maximum cross sectional area of arch at base, ''Q<sub>t</sub>'' = {{cvt|125.1406|sqft|m2|5}} is the minimum cross sectional area of arch at top, and ''L'' = {{cvt|299.2239|ft|m|5}} is the half width of centroid at the base. The triangular cross sectional area varies linearly with the vertical height of its centroid.

This [[hyperbolic function|hyperbolic cosine function]] describes the shape of a [[catenary]]. A chain that supports only its own weight forms a catenary; the chain is purely in tension.<ref name="KabaiTóth">{{cite web |url=http://demonstrations.wolfram.com/JeffersonNationalExpansionMemorial/ |title=Jefferson National Expansion Memorial |last1=Kabai |first1=Sándor |last2=Tóth |first2=János |publisher=[[Wolfram Demonstrations Project]] |access-date=December 14, 2010 }}</ref><ref>{{cite web |last=Weisstein |first=Eric |author-link=Eric W. Weisstein |url=http://mathworld.wolfram.com/Catenary.html |title=Catenary |work=[[MathWorld]] }}</ref> Likewise, an inverted catenary arch that supports only its own weight is purely in compression, with no shear. The catenary arch is the stablest of all arches since the thrust passes through the legs and is absorbed in the foundations, instead of forcing the legs apart.<ref name="Corrigan"/> The Gateway Arch itself is not a common catenary, but a more general curve of the form ''y''=''A''cosh (''Bx'').<ref>{{cite journal |last=Osserman |first=Robert |title=Mathematics of the Gateway Arch |url=https://www.ams.org/notices/201002/rtx100200220p.pdf |date=February 2010 |journal=[[Notices of the American Mathematical Society]] |issn=0002-9920 |volume=57 |issue=2 |pages=220–229 |archive-url=https://web.archive.org/web/20121023000925/http://www.ams.org/notices/201002/rtx100200220p.pdf |archive-date=October 23, 2012 |url-status=dead }}</ref> This makes it an ''inverted weighted catenary.''<ref name="The Rotarian">{{cite journal |url=https://books.google.com/books?id=DzcEAAAAMBAJ&q=weighted+catenary&pg=PA34 |title=Soaring Symbol for St. Louis |last=Hannon |first=Robert E. |pages=33–34 |journal=[[The Rotarian]] |date=June 1963 |volume=102 |issue=6 |issn=0035-838X }}</ref><ref>{{cite journal |url=https://books.google.com/books?id=BuMDAAAAMBAJ&q=weighted+catenary&pg=PA89 |title=The Incredible Gateway Arch: America's Mightiest National Monument |last=Hicks |first=Clifford B. |page=89 |journal=[[Popular Mechanics]] |date=December 1963 |volume=120 |issue=6 |issn=0032-4558 }}</ref> Saarinen chose a weighted catenary over a normal catenary curve because it looked less pointed and less steep. In 1959, he caused some confusion about the actual shape of the arch when he wrote, "This arch is not a true [[parabola]], as is often stated. Instead it is a catenary curve—the curve of a hanging chain—a curve in which the forces of thrust are continuously kept within the center of the legs of the arch." William V. Thayer, a professor of mathematics at [[St. Louis Community College]], later wrote to the ''[[St. Louis Post-Dispatch]]'' calling attention to the fact that the structure was a weighted catenary.<ref name="AIA 1983">{{cite journal |url=https://books.google.com/books?id=yQEyAQAAIAAJ |title=Is It a Catenary? |last=Crosbie |first=Michael J. |publisher=[[American Institute of Architects]] |date=June 1983 |volume=72 |issue=6 |journal=AIA Journal |pages=78–79 }}</ref>

===Lighting===
[[File:Gateway Arch Illuminated in Pink.jpg|thumb |left |The arch illuminated in pink in honor of [[Breast Cancer Awareness Month]]]]
[[File:Gateway Arch illuminated at night.jpg|thumb|right |upright |The arch's lighting system]]
The first proposal to illuminate the arch at night was announced on May 18, 1966, but the plan never came to fruition.<ref name="Arch timeline" /> In July 1998, funding for an arch lighting system was approved by St. Louis's Gateway Foundation,<ref name="Nevada Daily Mail"/> which agreed to take responsibility for the cost of the equipment, its installation, and its upkeep.<ref name="Duffy2">{{cite news |url=http://docs.newsbank.com/s/InfoWeb/aggdocs/AWNB/0EDCA514CED5FA3F/0DF73E411D70C6CA |title=Monument Soon Will Light Up The Night Sky; Arch Illumination Project Gets Green Light |last=Duffy |first=Robert W. |date=August 9, 2001 |work=[[St Louis Post-Dispatch]] |page=A1 |access-date=February 1, 2011 |issn=1930-9600 |archive-url=https://archive.today/20200108210212/https://www.webcitation.org/61hcFhrRb?url=http://iw.newsbank.com/iw-search/we/InfoWeb%3Fp_action=doc&p_theme=aggdocs&p_topdoc=1&p_docnum=1&p_sort=YMD_date:D&p_product=AWNB&p_docid=0EDCA514CED5FA3F&p_text_direct-0=document_id%3D(%200EDCA514CED5FA3F%20)&s_lang=en-US&p_nbid=G53N4EBEMTMxNjAzOTY5OC4yODI4N |archive-date=January 8, 2020 |url-status=dead }}</ref> In January 1999, [[MSNBC]] arranged a temporary lighting system for the arch so the monument could be used as the background for a visit by [[Pope John Paul II]].<ref name="Nevada Daily Mail">{{cite news |url=https://news.google.com/newspapers?id=OEArAAAAIBAJ&pg=1570,2526284 |title=St. Louis Gateway Arch will be illuminated at night |page=5A |work=[[The Nevada Daily Mail]] |agency=Associated Press |date=August 9, 2011 |access-date=January 29, 2011 }}</ref> Since November 2001, the arch has been bathed in white light between 10&nbsp;p.m. and 1&nbsp;a.m. via a system of floodlights.<ref>{{cite news |url=http://docs.newsbank.com/s/InfoWeb/aggdocs/AWNB/0EFF9946A5830D61/0D7C12F5A8A2A86A |title=Visitors Take A Shine To Illuminated Arch |date=November 23, 2001 |work=St. Louis Post-Dispatch |page=A1 |access-date=February 1, 2011 |issn=1930-9600 |archive-url=https://web.archive.org/web/20190707222431/http://infoweb.newsbank.com/iw-search/we/InfoWeb?p_action=doc&p_topdoc=1&p_docnum=1&p_sort=YMD_date%3AD&p_product=AWNB&p_text_direct-0=document_id%3D%28%200EFF9946A5830D61%20%29&p_docid=0EFF9946A5830D61&p_theme=aggdocs&p_queryname=0EFF9946A5830D61&f_openurl=yes&p |archive-date=July 7, 2019 |url-status=dead }}</ref> Designed by Randy Burkett, it comprises 44 lighting fixtures situated in four pits just below ground level.<ref name="Nevada Daily Mail"/><ref name="Duffy2"/>

On October 5, 2004, the [[United States Senate|U.S. Senate]], at the pressing of both of Missouri's US Senators, [[Jim Talent]] and [[Kit Bond]], approved a bill permitting the illumination in pink of the arch in honor of [[National Breast Cancer Awareness Month|breast cancer awareness month]].<ref>{{cite web |url=http://frwebgate.access.gpo.gov/cgi-bin/getdoc.cgi?dbname=108_cong_bills&docid=f:s2895cps.txt.pdf |title=Bill S. 2895 |publisher=[[United States Government Printing Office]] |access-date=February 1, 2011 |archive-url=https://web.archive.org/web/20121107231205/http://frwebgate.access.gpo.gov/cgi-bin/getdoc.cgi?dbname=108_cong_bills&docid=f:s2895cps.txt.pdf |archive-date=November 7, 2012 |url-status=dead }}</ref> Both [[Estée Lauder Companies|Estee Lauder]] and [[The May Department Stores Company|May Department Store Co.]] had championed the cause.<ref name="Jonsson"/> One employee said that the arch would be a "beacon&nbsp; ... for the importance of prevention and finding a cure."<ref>{{cite news |url=http://docs.newsbank.com/s/InfoWeb/aggdocs/AWNB/1059BDE80376C512/0DF73E411D70C6CA |title=Pink may light Arch in breast cancer fight |date=October 6, 2004 |newspaper=St. Louis Post-Dispatch |page=B1 |access-date=January 24, 2011 |issn=1930-9600 |archive-url=https://archive.today/20200108205644/https://www.webcitation.org/61hcN7eKt?url=http://iw.newsbank.com/iw-search/we/InfoWeb%3Fp_action=doc&p_theme=aggdocs&p_topdoc=1&p_docnum=1&p_sort=YMD_date:D&p_product=AWNB&p_docid=1059BDE80376C512&p_text_direct-0=document_id%3D(%201059BDE80376C512%20)&p_nbid=D59G54TKMTMxNjAzOTgwMy4xMDIzMzE6MTo3OnJhLT |archive-date=January 8, 2020 |url-status=dead }}</ref> While the National Park Service took issue with the plan due to the precedent it would set for prospective uses of the arch, it yielded due to a realization that it and Congress were "on the same team" and because the illumination was legally obligatory; on October 25, the plan was carried out.<ref>{{cite news |url=https://www.nytimes.com/2004/10/24/national/24arch.html |title=St. Louis Arch to Glow Pink for Anti-Cancer Cause |date=October 24, 2004 |work=The New York Times |agency=Associated Press |access-date=January 24, 2011 |archive-url=https://archive.today/20200108193100/https://www.webcitation.org/5w0oEBemX?url=http://www.nytimes.com/2004/10/24/national/24arch.html%3F_r=1 |archive-date=January 8, 2020 |url-status=dead }}</ref> The previous time the arch was illuminated for promotional purposes was on September 12, 1995,<ref>{{cite news |url=http://docs.newsbank.com/s/InfoWeb/aggdocs/AWNB/0EB0832E8A6B5A1B/0D7C12F5A8A2A86A |title='Oz On Ice' Promotion Will Light Up the Arch |last=Berger |first=Jerry |date=September 7, 1995 |work=St. Louis Post-Dispatch |page=1G |access-date=February 1, 2011 |archive-url=https://web.archive.org/web/20190707222949/http://infoweb.newsbank.com/iw-search/we/InfoWeb?p_action=doc&p_topdoc=1&p_docnum=1&p_sort=YMD_date%3AD&p_product=AWNB&p_text_direct-0=document_id%3D%28%200EB0832E8A6B5A1B%20%29&p_docid=0EB0832E8A6B5A1B&p_theme=aggdocs&p_queryname=0EB0832E8A6B5A1B&f_openurl=yes&p |archive-date=July 7, 2019 |url-status=dead }}</ref> under the management of local companies [[FleishmanHillard|Fleishman-Hillard]] and Technical Productions when a rainbow spectrum was shone on the arch to publicize the debut of [[Ringling Bros. and Barnum & Bailey Circus]]' ''[[The Wizard of Oz (1987 musical)#1990s productions|Wizard of Oz on Ice]]'' at the [[Scottrade Center|Kiel Center]].<ref name="Jonsson">{{cite news |url=http://docs.newsbank.com/s/InfoWeb/aggdocs/AWNB/105FAFC7B050569C/0D7C12F5A8A2A86A |title=Reflections of Hope |last=Jonsson |first=Greg |date=October 26, 2004 |work=St. Louis Post-Dispatch |page=A1 |access-date=February 1, 2011 |archive-url=https://web.archive.org/web/20190707223106/http://infoweb.newsbank.com/iw-search/we/InfoWeb?p_action=doc&p_topdoc=1&p_docnum=1&p_sort=YMD_date%3AD&p_product=AWNB&p_text_direct-0=document_id%3D%28%20105FAFC7B050569C%20%29&p_docid=105FAFC7B050569C&p_theme=aggdocs&p_queryname=105FAFC7B050569C&f_openurl=yes&p |archive-date=July 7, 2019 |url-status=dead }}</ref><ref>{{cite journal |title=Lighting Dimensions |url=https://books.google.com/books?id=GeZUAAAAMAAJ&q=%22Apparently_it%22 |page=20 |volume=20 |year=1996 |journal=Lighting Dimensions Associates }}</ref>