Lecture 4: Curvature - MIT OpenCourseWare
CurvaturePosition Tangency Curvature - Continuity1
In Defense of the CurveA Story of the Organic2
Hugo HÄringvsL u d w i g M i e s va n d e r R o h e3
In a conversation between Mies van der Roheand Hugo Häring, Mies inquires, “our steelbeams, they have been born straight haven’tthey?” he then argues, “It takes a great deal ofeffort to bend them”.M i e s va n d e r R o h e “ M i e s S p e a k s : I D o N o t D e s i g n B u i l d i n g s . ”A r c h i t e c t u r a l R e v i e w, N o . 8 6 2 , D e c e m b e r 1 9 6 8 : 4 5 2 .4
Edition Axel Menges GmbH (Michael Robinson). All rights reserved.This content is excluded from our Creative Commons license.For more information, see http://ocw.mit.edu/fairuse.Hugo Häring, Friedrichstrasse Office Building, 1922, Competition Entry (left) The Museum of Modern Art (MoMA). All rights reserved.This content is excluded from our Creative Commons license.For more information, see http://ocw.mit.edu/fairuse.Ludwig Mies van der Rohe, Friedrichstrasse Office Building, 1922, Competition Entry (right)5
The Museum of Modern Art (MoMA). All rights reserved.This content is excluded from our Creative Commons license.For more information, see http://ocw.mit.edu/fairuse.Hugo Häring, Country House, 1923/24, Elevation and Plans (left)Ludwig Mies van der Rohe, Brick Country House, 1923, Plan (above) Edition Axel Menges GmbH (Michael Robinson). All rights reserved.This content is excluded from our Creative Commons license.For more information, see http://ocw.mit.edu/fairuse.6
Courtesy of Vicente del Amo Hernández. Used with permission.Eladio Dieste, Church of Christ the Worker, 1958-60 (left)Photograph courtesy of Charles MacEachen on Flickr.Ludwig Mies van der Rohe, S. R. Crown Hall, 1956 (right)7
These images are in the public domain.Source: Federal Housing Administration. Planning Profitable Neighborhoods, Technical Bulletin No. 7. Washington, D.C., Government Printing Office, 1938.8
Photograph of Thonet bending forms incorporating a metal stripremoved due to copyright restrictions.Source: Von Vegesack, Alexander. Thonet: Classic Furniture inBent Wood and Tubular Steel. Rizzoli, 1997.See page 11 of "In Defense of the Curve: Provoked by Reason" for a reference image.Gerrit Rietveld, Red-Blue Chair, 1917–19.Photograph courtesy of defining Design on Flickr.Drawing of Gerrit Rietveld, Detail Connection, Red-Blue Chair, 1917-19removed due to copyright restrictions.Source: Kuper, M., and I. Van Zijl. Gerrit Rietveld 1888–1964: TheComplete Works. Princeton Architectural Press, 1993.See page 10 of "In Defense of the Curve: Provoked by Reason" for a reference image.Photograph of Adolf Loos, Café Museum Chair, 1908removed due to copyright restrictions.See page 12 of "In Defense of the Curve: Provoked by Reason"for a reference image.Drawing of Mies van der Rohe, Plug weld procedure: connection prepared,beam placed, plug weld, connection finished.Image by MIT OpenCourseWare.Michael Thonet, No. 14 Chair, 1859–60.Photograph courtesy of Holger.Ellgaard on Wikimedia Commons.9
Photographs of Charles and Ray Eames, Leg Splint, 1941 (left);Charles and Ray Eames, Body Splint, 1941 (upper right);Leg Splint Demonstration, 1941 (lower right)removed due to copyright restrictions.Source: Neuhart, John, and Marilyn Neuhart. Eames Design. 1st ed. Abrams, 1989.See page 13 of "In Defense of the Curve: Provoked by Reason" for a reference image.10
Photographs of Charles Eames casting fiberglass (left);Charles and Ray Eames, LCW Chair, 1945, Plywood Process (upper right);Charles and Ray Eames, Plastic Armchair, 1950–53, Fiberglass Process (lower right)removed due to copyright restrictions.Source: Neuhart, John, and Marilyn Neuhart. Eames Design. 1st ed. Abrams, 1989.See page 14 of "In Defense of the Curve: Provoked by Reason" for a reference image.11
Ludwig Mies van der Rohe, Drafting exercise for first-year students at the Armour Institute, 1938. Source unknown. All rights re
Gerrit Rietveld, Red-Blue Chair, 1917–19. Photograph courtesy of defining Design on Flickr. Photograph of Adolf Loos, Café Museum Chair, 1908 removed due to copyright restrictions. See page 12 of "In Defense of the Curve: Provoked by Reason" for a reference image. Drawing of Gerrit Rietveld, Detail Connection, Red-Blue Chair, 1917-19
Introduction of Chemical Reaction Engineering Introduction about Chemical Engineering 0:31:15 0:31:09. Lecture 14 Lecture 15 Lecture 16 Lecture 17 Lecture 18 Lecture 19 Lecture 20 Lecture 21 Lecture 22 Lecture 23 Lecture 24 Lecture 25 Lecture 26 Lecture 27 Lecture 28 Lecture
dius of curvature R c 2.5 cm, exerts on a straight stent inserted into a curved vessel. A measure of curvature of a bent stent was calculated as a reciprocal of the radius of curvature for a middle curve of each stent (a small radius of curvature means a large curvature). Interpreting the Models In the relevant figures, blue/cyan denotes .
develop the kinematics. These approaches support constant or variable curvature functions. A comparative study of v e kinematic modeling methods - lumped system dynamic model [22], constant curvature [18], two-step modied con-stant curvature [23], variable curvature kinematics [24] with Cosserat rod and beam theory [25], and series solution
Riemannian Geometry Dr Emma Carberry Semester 2, 2015 Lecture 15 [Riemannian Geometry - Lecture 15]Riemannian Geometry - Lecture 15 Riemann Curvature Tensor Dr. Emma Carberry September 14, 2015 Sectional curvature Recall that as a (1;3)-tensor, the Riemann curvature endomorphism of the Levi-Civita connection ris R(X;Y)Z r X(r YZ) r Y(r XZ .
Lecture 1: A Beginner's Guide Lecture 2: Introduction to Programming Lecture 3: Introduction to C, structure of C programming Lecture 4: Elements of C Lecture 5: Variables, Statements, Expressions Lecture 6: Input-Output in C Lecture 7: Formatted Input-Output Lecture 8: Operators Lecture 9: Operators continued
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Also, the radius of curvature Rx, Fig. 6.2.2, is the reciprocal of the curvature, Rx 1/ x. Fig. 6.2.2: Angle and arc-length used in the definition of curvature As with the beam, when the slope is small, one can take tan w/ x and d /ds / x and Eqn. 6.2.2 reduces to (and similarly for the curvature in the y direction) 2 2 2
for pure bending or bending moment and axial load is consid-ered the same [3]. The curvature for state II, bending moment and axial load, can be relat-ed to the curvature in pure bending, by 5 . L 5 . , E 5 . ¿. The curvature 5 . ¿ is caused by the bending moment due to the axial force N acting at the centre of gravity of the total section
