1. CEE 4606 - Capstone II Structural Engineering
CEE 7402 Forensic Engineering
CEE Capstone II Structural Engineering
Lecture 5 – Gravity Load Design (Part 1)

2. CEE 7402 Forensic Engineering
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 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 – Seismic Design Requirements
Sec – 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. 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 d M
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

15. For simply-supported beams, total beam depth ‘h’ must be at least L/16
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. CEE 7402 Forensic Engineering
Note: columns automatically placed at each wall end or corner
Ln = 27.0 ft.
Ln = 10.5 ft.
Ln = 14.5 ft.
Ln = 12.0 ft.
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 Girders
Interior (T-beams)
Exterior (L-beams)
Girders
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. Now let’s go back through with a slightly different load path
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
M cu M2 M1
M cl

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
M cu M1
M cl

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
M cu M1
M cl

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 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. CEE 7402 Forensic Engineering
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. CEE 7402 Forensic Engineering
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
CEE 7402 Forensic Engineering
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)