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

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