University of Michigan Structures II Peter von Buelow

Structural Continuity

Q1. Why do beams that are continuous over multiple supports require a differentmethod of analysis than single span simply supported beams?

A1. They are statically indeterminate

Q2. In multiple span continuous beams, will load in one span produce stress theother 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 by the 3-momentequation? (Gravity loads)

A4. Usually negative

Q5. The beam shown to the right is:

A5. Statically indeterminate

Q6. Which of the loading patterns shown below will yield the largest NEGATIVEmoment for the center of middle span of the 5-Span continuous beam?

A6. B

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Q7. If a continuous beam over two spans carries a distributed load that causes apositive moment within each span, what is the sign on the moment at the interiorsupport?

A7. Negative

Q8. Why would a continuous beam over multiple supports require less material thana series of simply supported beams to support the same load?

A8. The overall maximum moment is smaller

Q9. List one of the two qualifications for static indeterminacy?

A9. Cannot be solved by the three equations of statics alone, (or) internalforces and reactions are effected by movement or settlement of thesupports.

Q10. What makes continuous beams statically indeterminate?

A10. Continuous beams having 3 or more supports will have 4 or morereactions which is more than can be solved with the 3 equations of staticequilibrium.

Q11. Under what condition can the deflection method of analysis be used?

A11. 2 equal spans with symmetrical loading

Q12. What method of analysis can be used for continuous beams of 2 unequalspans with asymmetrical loading?

A12. Slope method

Q13. What is the method of analysis used for a continuous beam of any numberof spans?

A13. Three-moment method

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Q14. When selecting a section of a continuous beam to analyze as a free body,how many adjacent spans should be used?

A14. 2

Q15. Why is the analysis of a two-hinged frame different from that of a three hingedframe?

A15. The removal of the third hinge makes the two-hinged frame staticallyindeterminate.

Q16. In the Three Moment Theorem equation, where are the slope componentslocated in the two spans?

A16. They are located on the rignt side of the first span and the left side of thesecond span.

Q17. In a ridged frame system, will flexure in a beam have any effect on a column?

A17. Yes

Q18. Beside continuous beams, what is another example of a statically indeterminatestructure?

A18. Two hinge frame

Q19. For what does the deflection method solve?

A19. The center reaction

Q20. In the “deflection method” does the solution vary depending on E or I?

A20. No

Q21. For a multiple span beam, with gravity loads, will there always be both negativeand positive moments?

A21. Yes

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Q22. What was the cause of the oscillation on the Millennia Bridge in London?

A22. The synchronous movement of the pedestrians caused by the oscillationof the bridge

Q23. How many continuous spans can be solved with the 3-moment equation?

A23. Any number, but it requires an additional equation for every additionalspan

Q24. In the beam shown below, how many unknown moments need to be solvedbefore finding the end reactions?

A24. Two, at R2 and R3

Q25. In using the 3-moment equation to solve continuous span beams, how are thesupport 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

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?

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A28. At the support

Q29. In comparing the two frames with identical dimensions and loading, which wouldhave the higher maximum moment: a 3-hinged arch or a ridged frame?

A29. 3-hinged arch

Q30. In solving indeterminate beams, what does the slope method actually solve for?

A30. The slope method solves for the total moment at the middle support byadding the slope effect of the two sides.

Q31. Which of the following loading patterns for a continuous beam with three spanshas the greatest positive moment in the middle span if both dead load and liveload are consistent throughout all cases?

A31. Pattern C