Design of a Concrete Terraced Structure

Vipsanius Incorporated

“Designs to stand the test of time”

Meet the Team

Project Manager: Josh Prines

Structural Team: Roberto Cintron, Kwaku Boampong, Nisarg Thakkar, Hal

Hamilton Jr.

Lower Hill Redevelopment Proposal

Architectural rendering courtesy of Bjarke Ingles Group

(BIG)

28-acre masterplan; 1,200 residential units, 1 million SF of retail

and commerce space

An attempt to combine a green network of walking and

bicycle paths with the urban street grid of downtown

Pittsburgh

Promote a sense of sustainability and community; reversing a

trend of vacating property in the area

Project Overview

Site Overview

Project Scope

Complete design of all above-grade structural members. The following items will be cast-in-place

on site:

Beams

Columns

Stairwell Shear Walls

Elevator Shear Walls

Floor Slabs

Construction Management

Complete Construction Schedule

Above-grade construction estimate

Return on Investment Analysis

Geotechnical will be subcontracted

Advantages of Using Concrete

Fire Resistance

Affordability

Material Availability

Durability

Floor Layouts

Structural Framing Layouts

Dead Loads

Risk Category: II (ASCE 7-

10, Table 1.5-1)

Slab:

7.5” thickness

Lightweight Concrete

(115 pcf)

Cast-in-place

Dead Loads (Cont.)

ASCE 7-10, Chapter C-3

Interior non-load bearing walls

6” thickness

Exterior load bearing wall

8” thickness – 87 psf

Mechanical Allowance – 5 psf

Elevator Enclosure Wall

8” thickness -100 psf

Minimum required 3” for fire resistance (2 hours)

Dead Loads

Live loads

Base values (ASCE 7-10, Table 4-1)

“Ordinary flat, pitched, and curved roofs”: 20 lb/ft²

“Private rooms and corridors serving them”: 40 lb/ft²

“Roofs used for roof gardens” (patios): 100 lb/ft²

Determined for each column and girder

Reduced according to sections 4.7.2 and 4.8.2 of ASCE 7-10

Tributary Areas

Main Wind Force Resisting System

Consists of the stairwell and elevator shafts

Moment frames were considered but

they’re not the MWFRS

Stairwell needed 5” thickness for fire

protection

Non-seismic region so shear walls were

sufficient

Wind loads

ASCE 7-10 Directional Procedure

(Chapter 27)

Complex building geometry

Conservative methodology to assign

appropriate wind pressures

Biggest Challenge: Torsion

Wind Load Cases (ASCE 7-10)

Four different load cases

Only considering the cases with torsion

(Case 2 and Case 4)

Case 2: Uses 75% of the design wind

pressure acting on the principal axis with the

torsional moment as shown.

Wind Load Cases (ASCE 7-10)

Case 4: 56% of the design wind pressure

acting on both faces of the building

simultaneously.

Underestimated eccentricity from this load

case

LATERAL LOAD ANALYSIS FOR BUILDINGS

WITH SETBACK By Victor W.-T. Cheung and

W. K. Tso, M. ASCE

Wind Design

Used tributary areas for each floor to

determine a resultant force per floor

Used the lever arm to determine the torsion

on the MWFRS

Torsion results

El. (ft) Torsion(kip-ft)

12 1262.59425

24 1145.19375

36 1046.440125

48 952.9305

60 880.228125

72 420.948

Total 5708.33475

Wind Load Design

We also used an article LATERAL LOAD ANALYSIS FOR BUILDINGS WITH

SETBACK By Victor W.-T. Cheung and W. K. Tso, M. ASCE

Used to properly calculate the eccentricities for both faces of the building

Also to apply shear per floor to analyze the shear walls

Snow Load Overview

Acts vertically on the structure

Supported by the columns

Each floor experiences a portion of the load due to stepped patios

Wind forces cause a drift on stepped side of building

Snow Load Analysis (ASCE 7-10;

Chapter 7)

Seismic Load Analysis (ASCE 7-10;

Chapters 11 & 12)

Seismic Load creates a gravity load and lateral load on structure

Torsion & Deflection

Seismic Design Category A

Determine base shear of structure using the equivalent lateral force

analysis

Load generated by the inertia of the mass of the structure

Redistributed to each level as a point load at the center of mass of the

structure

Broad Design

• Two-way and One-way slab (only corridor)

• Don’t need East-West horizontal members in corridor area

• Beam & Girder will be in same plane

• They will share tributary area

• Both will transfer load to column

• Lateral force resisting system

• Elevator shaft and shear walls

Slab Design

• Lightweight Concrete (115 pcf)

• Designed for Deflection (Service limit state)

• Check for Shear and Flexure

•Simple

•Useful where spans, loads, load distributions, and member sizes and proportions fall in usual range

Setting Upper

Limits to Span-Depth Ratio

• Complex

• Compared to predicted value imposed by codes

• Approximate

Calculate Deflection

Slab Design

One-Way

Short Direction

Flexural Reinforcement to resist entire load

Long Direction

Minimum steel for temperature and shrinkage effect

Two-Way

Flexural Reinforcement in

both direction

Slab Design

Effect of Edge beam on slab thickness

α-factor (Beam to slab stiffness ratio)

Slab thickness is uniform throughout irrespective of loading.

For Fire and Heat – 5”

One-way portion - 4.6”

Two-way portion - 7.5”

Minimum thickness required (International Building Code) - 3.5”

Selected thickness - 7.5”

Sufficient for seismic

One-Way Slab

Critical Section

Minimum thickness- l/28 = 4.3”

Correction factor when using

light weight concrete : 1.65 – 0.005w >= 1.09

Minimum thickness – 4.6”

One-Way Slab

Chosen thickness- 7.5”

Load Combination:

1.2 w(d) + 1.6 w(l) = 271.45 psf

Maximum moment based on moment coefficients and clear span

Mu As reinforcement

As is so small so Min As governs

Check for shear and crack control

Calculation for One-Way

One-Way Slab Cross Section

# 4 bar at spacing of 8” (spacing governed by crack control) (short direction)

# 4 bar at 15” o.c. (min reinforcement for temp. & shrinkage) (transverse direction)

Two-Way Slab

Critical Section

Biggest span

25’*25’

Minimum thickness (ACI):

ln/33 (interior) (without beams)

ln/30 (corner, exterior) (without beams)

When beams are present thickness reduces by 15%

Effect of edge beam (αf-factor) (Beam to slab stiffness ratio)

Light weight concrete correction factor

7.5”

Two-Way Slab

Chosen thickness- 7.5”

Direct-Design Method for

Moment distribution

Statical Moment (Mo)

Two-Way Slab Calculation

East-west Slab strip 5

A5 B5 C5

l1 25 20

ln23.3333333

318.3333

3

l2 25 25

A_inf 625 500

reduced live load (ksf) 0.034 0.034

Mo 279.6173.097

2

end mid end mid end

coeff -0.16 0.57 -0.7 -0.7 0.57 -0.16

neg & pos moment (kip-ft) -44.736 159.372 -195.72 -121.16898.6654

2 -27.6956

Sum of column moments (kip-ft) 44.736 70

27.69556

Two-Way Slab Cross Section

Moment Distribution to slab and beam

Mu As reinforcement

Column Strip – 5 #5 bars

Middle Strip – 10 #5 bars

Horizontal members: Design

Microsoft Excel spreadsheet

Base assumptions

4-k/in2 concrete

60-k/in2 steel

Equal reinforcement at top and bottom of beam

Includes formulas from ACI manual

Also includes references in ACI manual for easy corroboration

Optimized with Solver

Then manually rounded up to standard bar sizes

Some integrated integer constraints are included

Spreadsheet Workings

IF(input,output_if_true,output_if_false), OR(input_1,input_2,...)

Strength reduction factor φ=IF(εc>0.005,0.9,IF(εc<0.002,0.65,0.65+(εc-0.002)*250/3))

MAX(input_1,input_2,...), MIN(input_1,input_2,...)

Used in combination

Maximum transverse-reinforcement spacing smax=MIN(d/2,24,ph/8,12)*IF(VS>4*√(fc')*b*d,0.5,1)

Solver

Number minimized: Total materials, weighted by tensile strength

Adding 1 in3 of 60-k/in2 steel = adding 15 in3 of 4-k/in2 concrete

First, use “Ignore integer constraints” checkbox to reach optimal solution without encountering

errors

Integers: Base, height, 2 × transverse-reinforcement spacing

Then, reënable integer constraints to ensure constructability

Manually round bar sizes up to next standard size

Horizontal member cross-sections

Uniform Section Unique Sections

Horizontal member design

Column Design

Columns are vertical structural members designed to support axial

compressive loads, with or without moments

Design to support axial compressive load, with moments

Supported Loads:

Dead & Live Load from floors above

Live Roof Load

Snow Load

Critical load determined using ASCE 7-10, LRFD load combinations

Columns are extended into foundation

Column Design

Alternatives

Tied Columns

Rectangular

Typically used in low seismic regions

Economical

Spiral Columns

Circular

Improved ductility and strength

Expensive

Column Design Procedure

(Tied Columns)

Determine critical load on column, Pu

Select trial size and trial reinforcement ratio

based on material properties

Properties:

f’c = 4 ksi

fy = 60 ksi

Determine steel ratio using interaction

diagram (use critical load and moment for

diagram)

Select reinforcement using new steel ratio

Check the max load capacity, ΦPn > Pu

Select ties (ACI Code Section 7.10.5)

Column Design Summary

Shear Walls

(Overview)

One shear wall resisting in lateral force wall

each stairwell

Height of wall above ground = 72’

Length of wall = 20’

Wall extends into foundation

Designed to resist shear & flexure, axial load,

and moment/torsional effects

Steel reinforcement in front face and back face

In both vertical and horizontal directions

Shear Wall

(Design Procedure)

Determine shear force on each floor

Select trial rebar and reinforcement ratio based on material properties

Minimum percentage of reinforcement in ACI Code Section 11.9.9.4

Check factored moment strength

Maximum moment is at the base

Accounts for factored axial load (ACI Code Eq. 9-6)

Check factored shear strength

Maximum shear strength is at the base

Shear Wall Design Summary

Shear Wall Reinforcement

(Cross Section)

Elevator Shear Wall

ACI 318-11

Reinforced Concrete Mechanics and Design

6th edition

Results

Vertical Reinforcement

2 rows of #8 rebar @ 18” O.C. & 2 #8 bar @ 4” O.C for support at the corners

Horizontal Reinforcement

2 rows of #5 rebar @ 18” O.C

Market Analysis and Net Operating

Income

*Number shown above is the Hard Cost only Pittsburgh (2012) = $178.23

*Both Soft Costs and Land Costs are excluded Pittsburgh (2016) = $184.86

*Rental Statistics from 2014*

Expected Budget for Construction

High-Rent Luxury Apartments in

Pittsburgh, PA

Aria Cultural District Lofts (7th Street Across from North Shore)

$2.2/sqft (1BR/1BA) – 684-972 sqft

The Encore on 7th Apartments (7th Street Across from North Shore)

$2.3/sqft (1BR/1BR) – 800-1000 sqft

Flats on Fifth (5th Ave – Crawford Roberts Hill)

$2.5/sqft (1BR/1BA) – 661-814 sqft

$2.3/sqft (2BR/2BA) – 1054 sqft

Source: Apartments.com

Construction Budget

Quantity Take-off

&

Estimate

Quantity Take-off

Quantities only include above-grade quantities

Subgrade work subcontracted

Superstructure Concrete = 5048 cy

Structural Framing, Exterior Walls, Shear Walls

Reinforcing = 126 tons; 161,500 LF

#3, #4, #5, #8, #9, #11 bars

C.S.I. Divisions 1-16 (Excluding 2-Site Work)

Source: Design Cost Data Archives

Concrete Labor Costs

Source: Construction Estimating 3rd Edition (David Pratt)

Construction Estimate

Lower Hill Redevelopment Project 48,000 SF

Return on Investment: 7.4%

1. Fees, Permits, Field Supervision, Insurance, Temporary Utilities

2. Pilings, Earthwork, Utilities

3. Formwork, Cast-in-place, Reinforcement

4. -

5. Miscellaneous

6. Rough Carpentry

7. Insulation, Damp proofing, Caulking

8. Doors, Frames, Hardware, Aluminum Windows & Doors

9. Metal Studs, Plaster, Drywall, Carpet, Painting, Staining

10. Signage, Fire extinguishers, Mailboxes

11. Appliances

14. Elevators (1)

15. Basic Materials, Fire Protection, Plumbing, HVAC

16. Basic Materials, Wire Conduit, Panel Boards, Fixtures, Fire Alarms

(Labor Included in Values)

Construction Schedule

Start Date: 2/18/16 Project Completion: 3/17/17 282 Work Days; Approximately 13 months

Questions?