Combined Stress - Open Michigan

Combined Stress - Open Michigan

Unless otherwise noted, the content of this course material is licensed under a Creative Commons Attribution 3.0 License. http://creativecommons.org/licenses/by/3.0/ 2009, Peter Von Buelow You assume all responsibility for use and potential liability associated with any use of the material. Material contains copyrighted content, used in accordance with U.S. law. Copyright holders of content included in this material should contact [email protected] with any questions, corrections, or clarifications regarding the use of content. The Regents of the University of Michigan do not license the use of third party content posted to this site unless such a license is specifically granted in connection with particular content. Users of content are responsible for their compliance with applicable law. Mention of specific products in this material solely represents the opinion of the speaker and does not represent an endorsement by the University of Michigan. For more information about how to cite these materials visit https://open.umich.edu/education/about/terms-of-use. Any medical information in this material is intended to inform and educate and is not a tool for self-diagnosis or a replacement for medical evaluation, advice, diagnosis or treatment by a healthcare professional. You should speak to your physician or make an appointment to be seen if you have questions or concerns about this information or your medical condition. Viewer discretion is advised: Material may contain medical images that may be disturbing to some viewers. Architecture 324 Structures II

Combined Stress Axial vs. Eccentric Load Combined Stress Interaction Formulas Source: Caspar David Friedrich from Man und Frau den Mond betrachtend 1830-35 Alte Nationalgalerie, Berlin University of Michigan, TCAUP Structures II Slide 2/9 Axial Stress Loads pass through the centroid of the section

Member is straight Load less than buckling load f = P/A Source: University of Michigan, Department of Architecture University of Michigan, TCAUP Structures II Slide 3/9 Eccentric Loads Load offset from centroid

M=Pe Total load = P + M Interaction formula P Mc f A I fa fb 1.0 Fa Fb University of Michigan, TCAUP

Source: University of Michigan, Department of Architecture Structures II Slide 4/9 Combined Stress Stresses combine by superposition Values add or subtract by sign Source: University of Michigan, Department of Architecture University of Michigan, TCAUP

Structures II Slide 5/9 Example Source: University of Michigan, Department of Architecture Determine external reactions University of Michigan, TCAUP Structures II Slide 6/9 Example

Determine internal member forces: Axial and Flexural Determine axial and flexural stresses Use interaction formula to determine combined stresses at key locations (e.g. extreme fibers) University of Michigan, TCAUP Structures II Slide 7/9 Rafters

Flexure + Axial P Mc f A I P = 22.5 # A = 5.25 in2 fc = 22.5 / 5.25 = 4.28 psi M = PL/4 = 39# x 96 /4 = 936 - # c = 1.5 /2 = 0.75 Iy = 3.5(1.53)/12 = 0.984 in4 fb = 963 (0.75)/0.984 = 713.14 30 f = fc + fb = 717.4 psi

45#(sin60) = 39# Or 90 M = PL/4 = 45# x 83.14 /4 = 936 - # fb = 963 (0.75)/0.984 = 713.14 45# 45#(cos60) = 22.5# 60 University of Michigan, TCAUP Structures II

Slide 8/9 Other Examples University of Michigan, TCAUP Structures II Slide 9/9 Second Order Stress P Delta Effect P 1. Eccentric load causes bending moment 2. Bending moment causes deflection,

3. P x causes additional moment 4. The additional P moment causes additional deflection, 1 University of Michigan, TCAUP Structures II Slide 10/9 Treehouse Form Exploration University of Michigan, TCAUP

Structures II Slide 11/19 Treehouse Details Pinned at ends Radius bent at joints Continuous sections Welded seams

University of Michigan, TCAUP 12/19 Structures II Slide Treehouse Details Pinned at ends

Radius bent at joints Continuous sections Welded seams University of Michigan, TCAUP /19 Structures II Slide 13 Treehouse Erection

3 sections Trucked to site Erected with mobile crane One day process University of Michigan, TCAUP 19 Structures II Slide 14/ Treehouse Erection

3 sections Trucked to site Erected with mobile crane One day process University of Michigan, TCAUP 19 Structures II Slide 15/ Treehouse

Finished University of Michigan, TCAUP 19 Structures II Slide 16/ Treehouse Finished University of Michigan, TCAUP 19

Structures II Slide 17/ Treehouse Finished University of Michigan, TCAUP 19 Structures II Slide 18/ Treehouse

Finished University of Michigan, TCAUP 19 Structures II Slide 19/

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