CEE 4606 - Capstone II Structural Engineering

1. CEE 4606 - Capstone IIStructural Engineering Lecture 5 – Gravity Load Design (Part 1)

2. Outline • Review of Progress Report #1 Presentations • IBC Concrete Design Requirements • Beam & One Way Slab Design • Slab Thickness Considerations • Load Path and Framing Possibilities • Connection & Analysis Issues • Seismic Detailing Requirements • Work Tasks

3. Progress Report #1 Comments • Overall, a very good job • Comments on presentations: • Timing good • Don’t worry about the intro stuff next time • Know where our site is located – you have coordinates that are accurate to within 3 miles!!!

4. Progress Report #1 Comments • Range of values: • 100 to 150 mph design wind speed • Seismic Design Category D (unanimous) • 2000 to 2800 psi concrete strength • 49000 to 53400 psi steel yield strength

5. IBC Concrete Design Requirements • IBC Chapter 19 • Mimics ACI 318 Code • IBC 2000 version based on 1999 ACI 318 • IBC 2003 will use 2002 version of ACI 318 • First seven sections (1901 – 1907) correspond to ACI 318 Chapters 1 to 7

6. IBC Concrete Design Requirements • Section 1908 gives specific modifications to ACI 318 • Deals with “meat” of ACI Code • Sections 1909 – 1916 deal with specialized areas • Sec. 1910 – Seismic Design Requirements • Sec. 1912 – Anchorage to Concrete • Get to know this document!!!

7. Load Path / Framing Issues • Building Frame System • Frame for gravity load • Shear walls for lateral load • Consider support of the chapel gravity loads: • Where do the columns go? • What beams do I need? • How do I design my slab?

8. Beam & One Way Slab Design Review • We presumably know how to do the following from CEE 3422: • Design a rectangular beam of unknown cross-section size • Design a rectangular beam of known cross-section size • Design a simply supported one way slab

9. Beam & One Way Slab Design Review • We presumably know how to do the following from CEE 3422: • Design a T-beam for positive moment • Design a T-beam for negative moment • Design a doubly reinforced beam (beam with compression reinforcement) • Design a beam for shear

10. d M d M Design of Continuous Beams and Slabs Gap • You know how to design cross-sections for positive or negative moment • Reinforcement follows the moment diagram • Why continuous spans? • Moments • Deflections Two Simple Spans Continuous over Center Support

11. Design Moments (Uniform Dist. Loading) • Simple Spans • wL2/8 • Continuous Spans • Analysis far more complicated • What type of fixity do we actually have? • Must consider effects of patterned loading • Formation of plastic hinges allows for moment redistribution

12. Design Moments – Continuous Spans • We have four analysis options • Elastic Analysis (preferably STAAD) • Elastic Analysis w/ Moment Redistribution • Approximate Frame Analysis • ACI Approximate Moment Coefficients • See McCormac text Chapter 13

13. Slab Thickness Considerations • What governs the thickness of a slab? • Flexural Strength • Shear • Deflections • Usually, deflections will govern the thickness requirements for a one-way slab • Size slab based on deflection requirements • Check shear • Design reinforcement for flexure

14. Slab Thickness Considerations • Review McCormac text, Ch. 5 (serviceability) and Ch. 3 (one-way slabs) • Review notes from CEE 3422, lectures on one-way slab design and serviceability • ACI Sec. 9.5.2.1

15. Slab Thickness Considerations(such that we do not need to compute deflections) • For simply-supported beams, total beam depth ‘h’ must be at least L/16 • A 16 ft. long simply supported beam must be at least 12 in. deep. • For simply-supported one-way slabs, total slab thickness ‘h’ must be at least L/20 • A 10 ft. long simply supported one-way slab must be at least 6 in. deep. • You will have to look up other values!!!

16. Slab Thickness Considerations • Something to keep in mind…. • Your material properties! • These tables are based on normal strength concrete • You may wish to consider creative ways to adjust tables for your low concrete strength • Hint: Think about what the key concrete material property related to deflections is…

17. Load Path / Framing Possibilities • Now we can begin to develop a framing plan for our structure • Typical practice on site is a 5 in. thick slab • We have a methodology to determine how far a slab of a given thickness can span • Do our material properties have any effect? • Let’s look at a plan view of the two-story section…

18. Ln = 10.5 ft. Ln = 14.5 ft. Ln = 12.0 ft. Ln = 27.0 ft. Note: columns automatically placed at each wall end or corner Think we’ll need some additional framing members???

19. Framing Concepts • Let’s use a simple example for our discussion… • Column spacing • 30 ft. on center • Think about relating it to your design as we discuss… Plan

20. Framing Concepts • We can first assume that we’ll have major girders running in one direction in our one-way system Plan

21. Framing Concepts • If we span between girders with our slab, then we have a load path, but if the spans are too long… Plan

22. Framing Concepts • We will need to shorten up the span with additional beams Plan

23. Framing Concepts • But we need to support the load from these new beams, so we will need additional supporting members Plan

24. Framing Concepts • Now we have a viable plan… • Let’s think back through our load path now to identify our “heirarchy” of members Plan

25. Framing Concepts • One-Way Slab (continuous) • Beams • Interior (T-beams) • Exterior (L-beams) • Girders • Interior (T-beams) • Exterior (L-beams) Plan

26. Framing Concepts • Note that by running the one-way slab in this EW direction, we are actually making the EW running beams our major girders • The NS running beams simply transfer the load out to these girders (or directly to a column) Plan

27. Framing Concepts • Now let’s go back through with a slightly different load path Plan

28. Framing Concepts • We again assume that we’ll have major girders running in one direction in our one-way system Plan

29. Framing Concepts • This time, let’s think about shortening up the slab span by running beams into our girders. • Our one-way slab will transfer our load to the beams. Plan

30. Framing Concepts • With this approach, we have already established our “heirarchy” • The only difference is in the “direction” of our load path • 90 degree rotation Plan

31. Framing Concepts - Conclusions • Either load path will work • In this case, they are identical • With a rectangular bay (instead of a square) bay, there will be a difference • Tradeoff is usually in number of supporting members vs. span of supporting members

32. Two Load Path Options

33. Framing Concepts - Considerations • For your structure: • Look for a “natural” load path • Identify which column lines are best suited to having major framing members (i.e. girders) • Assume walls are not there for structural support, but consider that the may help you in construction (forming)

34. Connection / Analysis Issues • With continuous reinforced concrete framing systems, connections are a major issue with respect to: • Detailing of reinforcement at these congested areas • Assumptions regarding fixity of beams and slabs

35. Connection / Analysis Issues • Let’s first consider our continuous one-way slab (12” strip shown) framing into an exterior (spandrel) beam Plan

36. Slab-Exterior Beam Connection • Slab is a six span continuous system • Some fixity at end of slab due to torsional rigidity of exterior beam, but what happens when beam and slab crack? • Do we want to count on fixity? • Also, if we design slab for negative moment here, we must develop reinforcement (like a cantilever)

37. Slab-Exterior Beam Connection Typical assumptions: • Simple support at end • No moment in slab at end • Place some reinforcement at top of slab to control cracking • Design exterior beam for minimal torsion

38. Connection / Analysis Issues • Now let’s consider our beam-girder joints Plan

39. Beam-Girder Connection • Beam is a two span continuous system • Similar situation: some fixity at end of beam due to torsional rigidity of exterior girder, but what happens when beam and girder crack? • Do we want to count on fixity? • Also, if we design beam for negative moment here, we must develop reinforcement (like a cantilever)

40. Slab-Exterior Beam Connection Typical assumptions: • Simple support at end • No moment in beam at end • Place some reinforcement at top of beam to control cracking • Design exterior girder for minimal torsion

41. Analysis – One-Way Slab & T-Beams • For the simple elements just described, where supports are provided by beams and girders, • Supporting elements have some stiffness, but it is fairly small • Assumption of treating one-way slabs and T-beams as continuous beams is valid • A frame analysis is not needed since there are no columns involved • Simple analysis methods can be used if all assumptions are met (i.e. ACI moment coefficients)

42. Connection / Analysis Issues • Finally, let’s look at beam-column and girder-column joints • Three situations: • Interior column • Exterior column • Corner column Plan

43. Interior Column Connection • Girders framing in to a column: • Columns will provide some rigidity • Moments will depend upon distribution of stiffness • Frame analysis is warranted to determine these moments • Unbalanced loading (patterned live load) must be considered • Goal: Determine moments in girders (they will not necessarily be equal), as well as axial load & moment combinations for columns • Beam/girder reinforcement must be continuous through joint Plan Mcu M2 M1 Mcl

44. Exterior Column Connection • Same basic situation: • Columns will provide some rigidity • Moments will depend upon distribution of stiffness • Frame analysis is warranted to determine these moments • Unbalanced loading (patterned live load) must be considered • Goal: Determine moments in girders (they will not necessarily be equal), as well as axial load & moment combinations for columns • Beam/girder reinforcement must be developed for negative moment Plan Mcu M1 Mcl

45. Corner Column Connection • This is essentially the same situation as an exterior column • Note that where we have beams (not girders) framing into columns, the same principles apply • However, these moments are typically very small and will usually not control the design Plan Mcu M1 Mcl

46. Analysis – Girders & Beams Framing Into Columns • For these elements, support is provided by columns • Columns have substantial stiffness and will attract some moments • Assumption of treating these girders and beams as continuous beams is not valid • A frame analysis is needed to determine the appropriate distribution of moments • Elastic analysis is recommended (STAAD, PCABeam)

47. Seismic Detailing Requirements for Reinforced Concrete - Introduction • IBC Section 1910 • ACI 318-99 Chapter 21 • These two sections, together, identify specific detailing requirements related to seismic design of concrete structures • Level of detailing required is based on Seismic Design Category

48. Work Tasks • Determine final loads on the structure • Gravity loads (dead, live) • Lateral loads (seismic, wind) • Truss analysis on roof & design of roof members • Detailing of roof-to-structure connection • Develop a load path (framing plan) to support the gravity loads associated with the second story chapel

49. Work Tasks • Look into how the selection of Seismic Design Category D will affect concrete design detailing requirements for your beams, columns, and slab • Work on design of one-way slab, beams, and girders • We will discuss design for shear and torsion next time!

50. Assignment for Tuesday • Submit a detailed sketch showing your framing plan (load path for gravity loads) for the second story chapel • Identify all columns, beam, and girder locations, and specify a slab thickness • Summarize on one sheet how the selection of Seismic Design Category D will affect the detailing of your structure • Use a bullet item / list format to identify specific detailing requirements for your beams, columns, and slab • Don’t consider shear walls for now (they will be masonry)