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  • 1. Important Laws in Structure
    VIP Revision
  • 2. ∈=𝜎𝐸
    𝛾=βˆ’βˆˆπ‘¦βˆˆπ‘₯
    ∈π‘₯=𝜎π‘₯πΈβˆ’π›ΎπœŽπ‘¦πΈ+πœŽπ‘§πΈ+𝛼𝑇
    βˆˆπ‘¦=πœŽπ‘¦πΈβˆ’π›ΎπœŽπ‘₯𝐸+πœŽπ‘§πΈ+𝛼𝑇
    βˆˆπ‘§=πœŽπ‘§πΈβˆ’π›ΎπœŽπ‘₯𝐸+πœŽπ‘¦πΈ+𝛼𝑇
    Β 
  • 3. Bars
    𝜎=𝑃𝐴 Average Stress
    ∈=𝑃𝐸𝐴
    𝑑𝑒𝑑π‘₯=∈
    βˆ†π‘™=βˆˆπ‘™
    Β 
  • 4. shafts
    πœƒ=𝑇𝑙𝐺𝐽
    𝐺=𝐸2(1+𝛾)
    πœπ‘šπ‘Žπ‘₯=𝑇𝑅𝐽
    𝐽=πœ‹2𝑅4 For Circular Sections.
    =𝑏𝑑33 For Thin Structure.
    Β 
  • 5. Deflection of Beams
    𝜎=βˆ’π‘‘2𝑉𝑑π‘₯2𝐸 𝑦
    =βˆ’π‘€π‘¦πΌ Special Case when 𝐸=π‘π‘œπ‘›π‘ π‘‘.
    𝑆=𝑑𝑀𝑑π‘₯
    𝑓=𝑑𝑆𝑑π‘₯
    𝐸𝐼𝑑2𝑉𝑑π‘₯2=𝑀
    𝑑2𝑑π‘₯2𝐸𝐼𝑑2𝑉𝑑π‘₯2=𝑀
    Β 
  • 6. Mohr circle
    πœπ‘šπ‘Žπ‘₯
    Β 
    C = 𝜎π‘₯+πœŽπ‘¦2
    R = (𝜏π‘₯𝑦)2+(πœŽπ‘¦βˆ’πœŽπ‘₯2)2
    Β 
    𝜏π‘₯𝑦
    Β 
    c
    πœŽπ‘šπ‘Žπ‘₯
    Β 
    𝜎π‘₯
    Β 
    πœŽπ‘šπ‘–π‘›
    Β 
    πœŽπ‘¦
    Β 
  • 7. Thin walled Vessel
    𝜎h=2πœŽπ‘Ž=π‘ƒπ‘Ÿπ‘‘
    Β 
  • 8. References
    Lecture’s notes of Dr. Mohammad Tawfik:
    Cairo university
    Assistant Professor Β· February 2010 to present Β· Giza, Al Jizah, Egypt
    Aerospace Engineering Department
    Emirates Aviation College
    Assistant Professor Β· October 2008 to January 2010 Β· Dubai, United Arab Emirates
    Cairo university
    Adjunct Professor Β· November 2005 to January 2010 Β· Cairo, Egypt
    The British University in Egypt
    Assistant Professor Β· September 2007 to August 2008
    German University in Cairo
    Assistant Professor Β· August 2003 to September 2007
  • 9. With our Best Wishes.
    Thank You.
    Made by NIXTY group.