Structural Analysis-I

1. Structural Analysis-I Dr. Ali Tayeh First Semester 2010-2011

2. Lecture 5 Trusses

3. Trusses هي عبارة عن منشاة متماسكة مستوي مكون من عدد من العناصر المتصلة يبعضها عند نهاياتها بمفصل أملس. تكون القوي الخارجية المؤثرة علية وردود الافعال كلها في مستوي واحد وتؤثر عند مفاصل الاتصال. تكون المفاصل مبرشمة أو ملتحمة بواسطة وصلات براشيم أو لحام .

4. فرضيات مبسطة للتحليل جميع اعضاء الجمالون Truss متصلة يبعضها البعض بواسطة مفاصل عديمة الاحتكاك بحيث تنقل القوة من عنصر لأخر وينعدم انتقال العزم. الاحمال الخارجية تحمل على الجمالون عند المفاصل. محور كل عضو من الاعضاء المتلاقية عند مفصل متقاطعة في نقطة.

5. Methods of Truss Analysis Method of Joints طريقة المفاصل. Method of Section طريقة القطع. Graphical Method طريقة الرسم.

6. Trusses in Building

7. Trusses Types for Building

10. Truss Bridge

11. Truss Bridge Types

13. Classification of coplanar Truss 1. Simple Truss

14. 2. Compound Truss عندما يتصل جمالون بسيط مع اخر بسيط بواسطة عنصر ربط link member

15. 3. Complex Truss لا تنطبق علية شروط الجمالون البسيط ولا المركب

16. Determinacy For plane truss If b+r = 2j statically determinate If b+r > 2j statically indeterminate Where b = number of bars r = number of external support reaction j = number of joints

17. Stability For plane truss If b+r < 2j unstable The truss can be statically determinate or indeterminate (b+r >=2j) but unstable in the following cases: External Stability: truss is externally unstable if all of its reactions are concurrent or parallel

18. Internal stability: Internally stable Internally unstable b + r = 2 j -------Statically determinateb + r > 2 j -------Statically Indeterminateb + r < 2 j -------Unstable Internally unstable

19. Classify each of the truss as stable , unstable, statically determinate or indeterminate. b + r = 2 j -------Statically determinateb + r > 2 j -------Statically Indeterminateb + r < 2 j -------Unstable b = 19 , r = 3 , j = 11 b = 15 , r = 4 , j = 9 b + r = 19 + 3 = 22 b + r = 15 +4 = 19 2 j = 2 (11) = 22 2 j = 2 (9) = 18 Statically determinate & Stable. Statically Indeterminate & Stable.

20. b + r = 2 j -------Statically determinateb + r > 2 j -------Statically Indeterminateb + r < 2 j -------Unstable b = 9 , r = 3 , j = 6 b = 12 , r = 3 , j = 8 b + r = 9 + 3 = 12 b + r = 12 + 3 = 15 2 j = 2 (6) = 12 2 j = 2 (8) = 16 Statically determinate & Stable. Unstable

21. The Method of Joints STEPS FOR ANALYSIS 1. If the support reactions are not given, draw a FBD of the entire truss and determine all the support reactions using the equations of equilibrium. 2. Draw the free-body diagramof a joint with one or two unknowns.Assume that all unknown member forces act in tension (pulling the pin) unless you can determine by inspection that the forces are compression loads. 3. Apply the scalar equations of equilibrium,  FX = 0 and FY = 0, to determine the unknown(s). If the answer is positive, then the assumed direction (tension)is correct, otherwise it is in the opposite direction (compression). 4. Repeat steps 2 and 3 at each joint in succession until all the required forces are determined.

22. The Method of Joints

23. Example 1 Solve the following truss

26. Group Work Determine the force in each member

27. Zero Force Member 1- If a joint has only two non-collinear members and there is no external load or support reaction at that joint, then those two members are zero-force members non-collinearغير واقعين على نفس الخط

28. Zero Force Member 2- If three members form a truss joint for which two of the members are collinear and there is no external load or reaction at that joint, then the third non-collinear member is a zero force member.

29. Example 2 Find Zero force member of the following truss