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**CEE 4606 - Capstone II Structural Engineering**

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

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**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

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**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!!!

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**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

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**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

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**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!!!

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**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?

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**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!!!

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**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…

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**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…

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**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???

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**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

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

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

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

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

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**Framing Concepts Now we have a viable plan…**

Let’s think back through our load path now to identify our “heirarchy” of members Plan

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**Framing Concepts One-Way Slab (continuous) Beams Girders**

Interior (T-beams) Exterior (L-beams) Girders Plan

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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

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**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

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

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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

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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

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**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

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Two Load Path Options

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**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)

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**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

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**Connection / Analysis Issues**

Let’s first consider our continuous one-way slab (12” strip shown) framing into an exterior (spandrel) beam Plan

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**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)

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**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

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**Connection / Analysis Issues**

Now let’s consider our beam-girder joints Plan

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**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)

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**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

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**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)

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**Connection / Analysis Issues**

Finally, let’s look at beam-column and girder-column joints Three situations: Interior column Exterior column Corner column Plan

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**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

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**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

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**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

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**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)

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**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

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**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

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**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!

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**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)

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