LESSON 4: DEGREE OF INDETERMINACY AND STABILITY

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1 God sells us all things at the price of labor. - Leonardo da Vinci LESSON 4: DEGREE OF INDETERMINACY AND STABILITY Labor Day, Monday, September 4, 2017 LESSON OBJECTIVES 1. Compute the degree of static indeterminacy (DOI) for 2D frames and beams using fundamental principles (Statics). 2. Compute the degree of static indeterminacy (DOI) for 2D frames and beams using the loop method 3. Compute the degree of static indeterminacy (DOI) for 2D frames and trusses. READING Excerpt from R.C. Hibbeler, on the webpage LABS THIS WEEK: In room 302 (computer lab) You MUST HAVE earbuds or headphones for the Video-Based Tutorials in SAP2000. You must still wear clothing that meets the lab safety rules (sorry), as the third hour will be conducted outside, as you will re-assemble parts of the disassembled Steel Sculpture. You do not need to have long hair tied back in a bun, however. HOMEWORK (Due Wednesday) - PRESENTATION DOES NOT COUNT. HAND IN THE ATTACHED PAGES

2 Name: HOMEWORK (Due Wednesday. Presentation does not count. Simply hand these pages in) 1. Determine the degree of indeterminacy (DOI) of the structure below: 2. Determine the degree-of-indeterminacy (DOI) of the structure below. B C A D 3. Apply a unit horizontal force to point B and show/explain why this structure is unstable, using Statics. Hint: all members are two-force members. B C A D 4. Determine the degree-of-indeterminacy (DOI) of the structure below.

3 5. The structure below is unstable. How many pin-ended diagonal (truss) members must be added to make this stable? 6. Determine the degree-of-indeterminacy (DOI) of the structure below. No. of Diagonal (truss) Members Req d = 7. Determine the degree-of-indeterminacy (DOI) of the structure below. 8. Determine the degree-of-indeterminacy (DOI) of the structure below. The X-braces cross but do not touch 9. Determine the degree-of-indeterminacy (DOI) of the structure below.

4 10. Determine the degree of indeterminacy (DOI) of the structure below: 11. Is this structure stable? All members are pin-ended Answer: Stable or Unstable 3 kips 12. All foundations are rigid except the rightmost foundation, which is a pinned support. All member-to-member connections are fixed (moment connections). 13. Arch with a pinned support on the left and a roller support on the right. 14. Arch with a pinned supports on the left and right. 15. Determine the degree of indeterminacy (DOI) of the structure below. The tie is a cable.

5 16. The truss is composed of pin-ended members, supported by a pinned support on the left and a roller support on the right. 17. Beam with pinned support at A, roller supports at B, E, and F. Study the connections at C and D carefully, recalling what you learned in lab last week. 18. Is this structure stable? At midspan, the connection consists of bolted plates, connecting the I-shaped beam webs. Answer: Stable or Unstable 19. Is this structure stable? At midspan, the connection consists of bolted web plates, and bolted flange plates, connecting the I-shaped beam webs and flanges. Answer: Stable or Unstable 20. Determine the degree of indeterminacy (DOI) of the structure below if it is a TRUE TRUSS: All Joints are pins (pin symbols omitted, for clarity).

6 21. Determine the degree of indeterminacy (DOI) of the structure below if connections are rigid (moment-resisting), unless noted by the pin symbol. Problems 22 through 24 refer to the building frame shown below. All supports are pinned. The diagonal brace is pin-ended. The beam to column connections: see the detail and recall what you learned from lab last week about connections. See Detail Detail: Shear Tab (plate) is welded to the column and connected to the web of the beam. The flanges (top and bottom plates) of the beam are not connected 22. DOI of the frame, as shown. 23. Determine the DOI if the brace is deleted. 24. For the frame as shown, determine the reaction components at support B. B y = kips B x = kips