1. Important Laws in Structure VIP Revision

2. ∈=𝜎𝐸 𝛾=−∈𝑦∈𝑥 ∈𝑥=𝜎𝑥𝐸−𝛾𝜎𝑦𝐸+𝜎𝑧𝐸+𝛼𝑇 ∈𝑦=𝜎𝑦𝐸−𝛾𝜎𝑥𝐸+𝜎𝑧𝐸+𝛼𝑇 ∈𝑧=𝜎𝑧𝐸−𝛾𝜎𝑥𝐸+𝜎𝑦𝐸+𝛼𝑇

3. Bars 𝜎=𝑃𝐴 Average Stress ∈=𝑃𝐸𝐴 𝑑𝑢𝑑𝑥=∈ ∆𝑙=∈𝑙

4. shafts 𝜃=𝑇𝑙𝐺𝐽 𝐺=𝐸2(1+𝛾) 𝜏𝑚𝑎𝑥=𝑇𝑅𝐽 𝐽=𝜋2𝑅4 For Circular Sections. =𝑏𝑡33 For Thin Structure.

5. Deflection of Beams 𝜎=−𝑑2𝑉𝑑𝑥2𝐸 𝑦 =−𝑀𝑦𝐼 Special Case when 𝐸=𝑐𝑜𝑛𝑠𝑡. 𝑆=𝑑𝑀𝑑𝑥 𝑓=𝑑𝑆𝑑𝑥 𝐸𝐼𝑑2𝑉𝑑𝑥2=𝑀 𝑑2𝑑𝑥2𝐸𝐼𝑑2𝑉𝑑𝑥2=𝑀

6. Mohr circle 𝜏𝑚𝑎𝑥 C = 𝜎𝑥+𝜎𝑦2 R = (𝜏𝑥𝑦)2+(𝜎𝑦−𝜎𝑥2)2 𝜏𝑥𝑦 c 𝜎𝑚𝑎𝑥 𝜎𝑥 𝜎𝑚𝑖𝑛 𝜎𝑦

7. Thin walled Vessel 𝜎h=2𝜎𝑎=𝑃𝑟𝑡

8. References Lecture’s notes of Dr. Mohammad Tawfik: Cairo university Assistant Professor · February 2010 to present · Giza, Al Jizah, Egypt Aerospace Engineering Department Emirates Aviation College Assistant Professor · October 2008 to January 2010 · Dubai, United Arab Emirates Cairo university Adjunct Professor · November 2005 to January 2010 · Cairo, Egypt The British University in Egypt Assistant Professor · September 2007 to August 2008 German University in Cairo Assistant Professor · August 2003 to September 2007

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