1 / 18

Chapter 5

Chapter 5. Deflection and Stiffness. A. Aziz Bazoune. Outline. Spring Rates Deflection in Tension, Compression & Torsion Deflection due to Bending Strain Energy Castigliano’s Theorem Statically Indeterminate Problems Compression Members Long Columns with Central Loading

nemo
Download Presentation

Chapter 5

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 5 Deflection and Stiffness A. Aziz Bazoune Chapter 5

  2. Outline • Spring Rates • Deflection in Tension, Compression & Torsion • Deflection due to Bending • Strain Energy • Castigliano’s Theorem • Statically Indeterminate Problems • Compression Members • Long Columns with Central Loading • Intermediate Length Columns with Central Loading Chapter 5

  3. Lec. 14 • Solved Problems Chapter 5

  4. Chapter 5

  5. Chapter 5

  6. Chapter 5

  7. Chapter 5

  8. Problem • A column is pinned at both ends has a length of 4.50 ft and a solid circular cross-section of 1.25 in diameter. If it is made of steel AISI 1020 CD what would be a safe column loading? • Material AISI 1020 CD Steel =  Sy = 57 ksi (Table A-20) • E = 30 Mpsi (Table A-5) • Ends: Pinned = Rounded-rounded case = C=1 (Table 5-2) • Eq. (5-48) • Calculate the slenderness ratio Solution Chapter 5

  9. Problem • Calculate the slenderness ratio • Since == Euler’s Column • Therefore Chapter 5

  10. Problem • Determine the critical load on a steel column having a rectangular cross-section, 12 mm X 18 mm and a length of 280 mm? It is proposed to use AISI 1040 HR Steel. The lower end of the column is inserted into a close-fitting socket and welded securely. The upper end is pinned. • Material AISI 1020 HR Steel  • Sy = 290 MPa (Table A-20) • E = 207 GPa (Table A-5) • Fixed-rounded end Condition  • C=1.2 (Table 5-2) • Radii of gyration Solution Chapter 5

  11. Problem • It is clear that and • On the other hand we have from Eq. 5-48 • Since • Apply the formula for Johnson’s column to find the critical load on the steel column. • kkg Chapter 5

  12. Chapter 5

  13. Problem • Therefore • kkg Chapter 5

  14. Problem • Design a rectangular section steel column having the following specifications: • Width of the column (w) is three times its thickness (t) • Maximum load that could be carried by the column is 100 kN • Material has a yield strength (Sy= 500 MPa) and a modulus of elasticity (E=207 GPa) • Assume end conditions constant C=1 in the weakest direction. • Column length l=150 mm and 400 mm) • Cross-section area is • or Solution Chapter 5

  15. Problem • Ixx • Iyy • or Solution Chapter 5

  16. Problem Chapter 5

  17. http://en.wikipedia.org/wiki/Leonhard_Euler Leonhard Paul Euler (pronounced Oiler; IPA [ˈɔʏlɐ]) (April 15, 1707 – September 18 [O.S. September 7] 1783) was a pioneering Swissmathematician and physicist, who spent most of his life in Russia and Germany. He published more papers than any other mathematician of his time.[2] Euler made important discoveries in fields as diverse as calculus and graph theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, s uch as the notion of a mathematical function.[3] He is also renowned for his work in mechanics, optics, and astronomy. Euler is considered to be the preeminent mathematician of the 18th century and one of the greatest of all time. He is also one of the most prolific; his collected works fill 60–80 quarto volumes.[4] A statement attributed to Pierre-Simon Laplace expresses Euler's influence on mathematics: "Read Euler, read Euler, he is the teacher (master) of us all".[5] Euler was featured on the sixth series of the Swiss 10-franc banknote[6] and on numerous Swiss, German, and Russian postage stamps. The asteroid2002 Euler was named in his honor. He is also commemorated by the Lutheran Church on their Calendar of Saints on May 24. Chapter 5

  18. QUESTIONS ? Thank U ! Chapter 5

More Related