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Two Stage Analysis Procedure: Podium Design

Part 2: Rigid Lower Portion

Philip Miller, S.E.

Topic Outline

• Types of Podium Construction

• Example Buildings

• PT Basics

• PT Analysis

• Modeling Tips

• Load Balancing Example

• ACI 318-14 Requirements

• Layout guidelines

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TYPES OF PODIUM CONSTRUCTION

Types of Podium Construction

• Post-tensioned Concrete deck on concrete walls and columns

• Reinforced Concrete deck on concrete walls and column

• Concrete over metal deck on combination of steel beams, columns, and Masonry walls (less common)

• Locally, the post-tensioned slab is the most common type of podium, often due to parking below

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EXAMPLE BUILDINGS

Example Buildings

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Example Buildings

Example Buildings

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Example Buildings

Example Buildings

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POST TENSIONED BASICS

Post Tensioned Basics

• Post Tensioned (PT) Concrete uses stranded steel cables with end anchors to create compression in the slab via tensioning the cable. Post-tensioning occurs after the concrete is poured, vs. pre-tensioning where tensioning occurs before concrete placement (more common in precast industry with factory conditions).

• PT cables can be bonded to the surrounding concrete, or unbonded by isolating the cable with a plastic sheathing. Most common type locally is unbonded PT.

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Post Tensioned Basics

• Typical cables are ½”Ø or 0.6”Ø, constructed of 7 wires (1 core wire and 6 perimeter wires, wound into a helix around the core). This is a STRAND.

• 1 or more STRANDS are known as a TENDON. Single-strand tendons are common in unbonded PT construction for economics and ease of placement. Multi-strand tendons are common in bonded construction.

• PT can be external or internal to the slab. Internal PT is most common, though external tendons are useful in retrofits.

Unbonded PT Graphic PTI Technical NotesIssue 5, Sept. 1994

POST TENSIONED ANALYSIS

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Post Tensioned Analysis

• PT cables provide compression to the concrete, enhancing its shear strength and reducing flexural tension

• PT cables are also draped over the supports in a parabolic profile, similar to a suspension bridge. A high profile at the supports and a low profile near the midspan provides lift at the midspan when the cables are stressed. It also produces reactions (up or down) at the supports.

Post Tensioned Analysis

Note drape of tendons, banded tendons and uniform tendons

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Post Tensioned Analysis

• Ideally, the lift offsets most of the dead load. This is known as load balancing.

• In most podium slabs, loading, spans, supports and geometry vary greatly. Use software for analysis.

MODELING TIPS

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Modeling Tips

• Generally loading on a podium is complex, and you’ll want to use software that can capture two-way bending action

• Adapt Floor Pro

• Bentley RAM Concept

• CSI SAFE

• Dlubal RFEM

• Risa Floor ES

• Others

• Most software relies on FEM meshing and ACI Equivalent Frame method (full width slab) for PT member design

Modeling Tips

• Input Area load, Line loads and point loads directly or build a superstructure model to track loads

• ACI specifies skip loading for live loads on adjacent and doubly-adjacent – check your software!

• Loading can get complex, but some simplifying assumptions can be made:

• Extending line loads across small openings instead of modeling point loads

• Enveloping similar wall loads into groups for easier tracking

• Point loads from overturning (shear walls) often don’t govern the design slab strip due to reduction in live load moments in IBC seismic load combinations. If so they may be omitted.

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LOAD BALANCING EXAMPLELet’s look at a simplified example from PTI DC20.7 “Design, Construction and Maintenance

of Cast-In-Place Post-Tensioned Concrete Parking Structures”, 2001.

Load Balancing Example

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Load Balancing Example

(b) Loads tendons impose on beam. Tendons primarily cause uplift, and downward reactions on the supports. In indeterminate structures, the uplift also causes secondary reactions due to support restraint, which in turn create secondary moments, which need to be designed for.

(c) Balanced Moment caused by 1klf uplift (wl²/8 and .07wL²)

Load Balancing Example

• Secondary moments can be calculated by either the direct method or indirect method. Both methods yield similar results. The direct method uses secondary reactions to calculate secondary moments, while the indirect method calculates secondary moments by considering the difference in balanced moments and the PT profile at every point along a span.

Direct Method: (steps a,b,c,d,f)

Indirect Method:(steps a,b,d,e,f)

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Load Balancing Example

(d) “Secondary” or hyperstatic reactions: Add Va, Vb and Vc to reactions produced by 1klf uplift.e.g. Vb=2*17.77=35.54 downRup@B=10/8wL=37.5 upSo Rbal@B = 1.96 down.This step not needed for indirect method.

Direct Method: (steps a,b,c,d,f)

In the direct method, we calculate the secondary reactions as follows to obtain secondary moments.

Load Balancing ExampleIn the indirect method, the secondary moment is found by the following:Secondary Moment = Balanced Moment –Primary Moment

(f) Secondary moments from secondary reactions in (d)

(e) Primary moments = F*e at any point along the spane.g. 100k*9”/12 = 75kft100k*10”/12 = 83.33kft. This step not needed for direct method.

Indirect Method:(steps a,b,d,e,f)

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Load Balancing ExampleBACKGROUND FOR EXAMPLE

Load Balancing ExampleBACKGROUND FOR EXAMPLE

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Load Balancing Example

Stress = P/A +/- M/S

BACKGROUND FOR EXAMPLE

Load Balancing ExampleBACKGROUND FOR EXAMPLE

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Load Balancing Example

• Summary:

• Secondary moments must be accounted for in member design, with a load factor of 1.0.

• Since loading is complex, hand calculations are not very practical.

• It is helpful to understand the process for validating computer models.

ACI 318-14 REQUIREMENTS

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ACI 318-14 Requirements

• To be considered prestressed, effective stress in the slab must be at least 125psi (8.2.3). Commonly 200psi is targeted in initial design. Effective stress must account for all losses from anchor seating, creep, temperature, friction, etc. One ½”Ø unbonded tendon is worth about 26.75kips after losses.

• Minimum concrete cover for prestressed concrete is ¾” to 1” (increase for fire rating if needed).

ACI 318-14 Requirements

• Typical required fire ratings from IBC are 2 to 3 hours, depending on construction types/separation

• Commonly parking below wood residential requires a 3-hour rating, which means 2” of cover to post tensioning in the end bays (unrestrained, prescriptive method of table 721 for siliceous aggregate). The calculated method table 722 requires even more at 2 3/8” cover.

• You may also want additional cover for post-installed attachments above or below the slab

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ACI 318-14 RequirementsConcrete Cover requirements for Fire Rating (IBC 2015)

ACI 318-14 Requirements

• To crack or not to crack? That is the question…

• 2-way PT slabs must be class U with ft<6√f’c

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ACI 318-14 Requirements

ACI 318-14 Requirements

• Deflection requirements: Note total deflection must include cracked sections (if applicable) and long term effects (creep)

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ACI 318-14 Requirements

• Minimum rebar requirements: Depends on tension in the span and section considered. Note that a well-balanced slab can eliminate much of the bottom steel for gravity loads (you may want some for diaphragm shear from lateral loads).

LAYOUT GUIDELINES

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Layout Guidelines

• Typical column spacing is about 30’ each way. Typical columns are 16”x24” or larger.

• In general , the span/depth ratio of PT slabs should be between 40 and 45. Transfer slabs are often thicker, say 12” to 16”, depending on the load.

• Slab precompression usually ranges from 150-250psi. More than 350psi is rare. One ½”Ø tendon imparts about 26.7kips effective force after losses are considered.

• Tendons are grouped over the columns in one direction (banded) and distributed in the other direction (uniform)

Layout Guidelines

Note drape of tendons, banded tendons and uniform tendons

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Layout Guidelines

• Restraint to Shrinkage cracking can be minimized with favorable shear wall layouts. ¾” to 1” per 100’ is common.

Fig 2.8-2 PTI DC20.7

Usually just using the stair cores will not work!

Layout Guidelines

• Closure strips/expansion joint guidelines from PTI DC20.7

• If slab length is

• Less than 250 feet = no closure strip

• Greater than 250 feet, but less than 325 feet = one centrally located closure strip

• Greater than 325 feet = one centrally located expansion joint

• These guidelines assume a favorable shear wall layout. Adjust as necessary

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Layout Guidelines

• Closure strips should remain open as long as practicable to allow for shrinkage, though thick transfer slabs may take longer to shrink than owners have patience.

• v/s = volume to surface ratio = half the slab thickness

Table 2.8-2 PTI DC20.7

v/s = 6.0 11% 20% 29%v/s = 8.0 6% 11% 16%

Layout Guidelines

• Where would you place shear walls, closure strips and/or expansion joints on the following plan views?

10

0’

60

’

220’60’ 60’ 80’80’

12

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12

0’

12

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240’

48

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120’

120’

60’

60

’6

0’

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Layout GuidelinesClosure strip

Expansion joint

Shear wall (coordinate length &location with architect)

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60

’220’60’ 60’ 80’80’

12

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12

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12

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240’

48

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120’

120’

60’

60

’6

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Layout Guidelines

• Summary

• With proper initial shear wall layout you can avoid a lot of problems

• It’s not always possible to satisfy client needs and building configuration. Use your judgment.

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Just for fun