Structural Continuity

Transcription

1 University of Michigan Structures II Peter von Buelow Structural Continuity Q1. Why do beams that are continuous over multiple supports require a different method of analysis than single span simply supported beams? A1. They are statically indeterminate (simply supported beams are statically determinate) Q2. In multiple span continuous beams, will load in one span produce stress the other spans? A2. Yes Q3. What does the deflection method for indeterminate beams actually solve? A3. The center reaction Q4. What generally is the sign of the interior reaction moment found in a continuous beam? (assume gravity loads) A4. negative Q5. The beam shown to the right is: A5. Statically indeterminate Continuous over two spans Q6. Which of the loading patterns shown below will yield the largest NEGATIVE moment for the center of middle span of the 5-Span continuous beam? A6. B

2 University of Michigan Structures II page 2 Q7. If a continuous beam over two spans carries a distributed load that causes a positive moment within each span, what is the sign of the moment at the interior support? A7. Negative Q8. Why would a continuous beam over multiple supports require less material than a series of simply supported beams to support the same load? A8. The overall maximum moment is smaller Q9. In the Three Moment Theorem equation, where are the slope components located in the two spans? A9. They are located on the rignt side of the first span and on the left side of the second span. Q10. What makes continuous beams statically indeterminate? A10. Continuous beams having 3 or more supports will have 4 or more reactions which is more than can be solved with the 3 equations of static equilibrium. Q11. The deflection method to solve two continuous spans has what limitations in application? A11. It applies only to symmetric spans with symmetric loads Q12. What method of analysis can be used for continuous beams of two unequal spans with asymmetrical loading? A12. Either the slope method or the three-moment method Q13. What method of analysis can be used for a continuous beam of any number of spans? A13. Three-moment method

3 University of Michigan Structures II page 3 Q14. Which method of analysis should be used in order to determine all reacting forces for a continuous beam involving more than a two-span condition? A14. The Three-Moment Theorem Q15. Why is the analysis of a two-hinged frame different from that of a three hinged frame? A15. The removal of the third hinge makes the two-hinged frame statically indeterminate. Q16. Beside continuous beams, what is another example of a statically indeterminate structure? A16. Two hinge frame Q17. In a ridged frame system, will flexure in a beam have any effect on a column? A17. Yes Q18. How many continuous spans can be solved with the 3-moment equation? A18. Any number, but it requires an additional equation for every additional span Q19. In solving indeterminate beams, what does the slope method actually solve for? A19. The slope method solves for the moment at the middle support. Q20. In the deflection method does the solution vary depending on E or? A20. No Q21. Will a multiple span beam, with gravity loads, always contain both negative and positive moments? A21. Yes

4 University of Michigan Structures II page 4 Q22. What was the cause of the oscillation on the Millennia Bridge in London? A22. The synchronous movement of the pedestrians caused by the oscillation of the bridge Q23. In comparing the two frames with identical dimensions and loading, which would have the higher maximum moment: a 3-hinged arch or a ridged frame? A23. 3-hinged arch Q24. In the beam shown below, how many unknown moments need to be solved before finding the end reactions? A24. Two, at R2 and R3 Q25. In using the 3-moment equation to solve continuous span beams, how are the support reactions determined? A25. By constructing FBDs of each span Q26. In a continuous beam, what is the point of contraflexure? A26. A point on the beam between the upward and downward curvature Also a point of zero moment Q27. What is the value of the moment at the point of contraflexure? A27. Zero Q28. For a single span beam with both ends fixed, where is the moment the greatest? A28. At the support

5 University of Michigan Structures II page 5 Q29. Which of the following loading patterns for a continuous beam has the greatest positive moment in the middle span? A29. C Q30. Which of the following loading patterns for a continuous beam has the greatest negative moment at the interior reactions? A30. B