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Effective Use of Timber in Architectural Applications

David Bowick, P.Eng. February 20, 2014

Taught the answer is usually Repetition, but is that true?

Efficiency – The great Myth

Repetition

Piece Count

Tonnage

More complex can be cheaper

What would Gary Williams Say?

Complexity Curve

Complexity

Slab Joists Trusses Opt. Joists Reciprocal

Quantity

Cost

Unit Cost

“But Dave, we want an example of efficient, complex construction!”

Reciprocal Framing - “A structure made up of mutually supporting beams in a closed circuit”

- Reciprocal Frame Architecture Olga Popovic Larsen, 2008

“He lifted himself by the seat of his pants and I'll never forget the grim look on his face

as he hoisted himself and took leave of this place “ - The Lorax Dr Suess, 1971

Reciprocal Frames

How it Works

How do you span 16’ joists 20’?

Example

Image from minktoast.net

Example

Fort York Armoury - Toronto Built in 1935

Example

NCFS Longhouse – Toronto, 2009 Levitt Goodman Architects Blackwell Engineers

Case Study Indian River Pavilion – PEI David Sisam Blackwell Engineers Construction Documents

Options 1 – Valley Framing Piece Count – 15 Total Volume – 5.8 m3 Largest Piece – 731 kg

Options 2 – Reciprocal Beam Piece Count – 37 Total Volume – 4.8 m3 Largest Piece – 268 kg

Options 3 – Reciprocal Joist Piece Count – 47 Total Volume – 5.6 m3 Largest Piece – 60 kg

Summary

Piece Count

Total Volume (m3)

Largest Piece (kg)

Valley Beam

Reciprocal Beam

Reciprocal Joist

15

5.8

731

37

4.8

268

47

5.6

60

Prestress is a method of strengthening or stiffening a structural element by introducing internal stresses. It can be applied during the manufacturing process or during the installation process.

What is Pre-Stress?

Tempered Glass Prestressed Concrete Tensile Structures

Prestressing can be used to couple a strong flexible element (steel tendon) with a weak stiff element (concrete) to create a strong stiff element (post tensioned concrete)

Why Pre-Stress?

Strength of Material

Stiffn

ess

of Sy

stem

*

* Strength of system held constant.

• Simple Span Roof

• L = 18m

• Structure at 2.0 m c/c

• d = 0.8 kPa

• l = 1.2 kPa

• w = 1.2 kPa (gross uplift)

Case Study

Sim

ple

Bea

m

Pin

ned

Ch

ord

Tru

ss

“But Dave… What about uplift?”

Pin

ned

Ch

ord

Tru

ss -

Up

lift

Co

nti

nu

ou

s C

ho

rd T

russ

We have a valid load path and it's strong, but to satisfy L/300 gross uplift deflection we need a section almost as big as the simple beam section. The cable utilization is negligible and the trussing is just “bling”.

The Dilemma

Co

nti

nu

ou

s C

ho

rd T

russ

w/

Pre

stre

ss

Simple Beam – 265x646

Pinned Chord Truss – 265x380 But it's irrelevant because it doesn't work for uplift. We could ballast for uplift, but increased load results in increased size. Cable oversized to achieve stiffness.

Continuous Chord Truss – 265x570 Governed by uplift stiffness.

Prestressed Truss – 265x342 40% Savings in glulam relative to non-prestressed truss. Remains rigid under load reversal.

Summary

An Aside About Uplift While we reasonably consider net uplift when designing for strength, we need to consider gross uplift when designing for stiffness.

An Aside About Deflection Criteria The “L-over” criteria for deflection is completely irrelevant for cantilevers.

A Possible Criteria

“So Dave… How do we design using prestress?”

Designing with Prestress Most non-linear versions of analysis programs such as ETABS and SAP can accommodate prestress directly.

L = LoT

where = coefficient of thermal expansion

L = TLo/AE

Therefore

LoT = TL

o/AE, and

T = T/AE or T = TAE/ *

Designing with Prestress Most simple analysis programs have the ability to accommodate stresses due to temperature changes. We can use this to apply prestress:

This is valid for a member restrained against perfectly rigid supports. Against elastic supports the force will be reduced by the movement of the supports and the temperature change will have to be adjusted.

“Dave… How do they erect this?”

Applying Prestress

Manufacture elements intentionally short by a specific amount. Force fit. This method is imprecise and probably appropriate for nominal prestress only.

DRIFTING

Elements can be pulled directly using a calibrated tension jack such as those used in prestressed concrete. This is probably most appropriate where prestress forces are large.

CONTROLLED STRETCH

The structure can be deformed intentionally using simple tools such as bottle jacks and come-alongs. The prestressing tendon can be attached under zero stress, then the jack or come-along relieved, transferring the load to the tendon. The measured impact of the prestressed element can be predicted fairly accurately so the deformation of the structure itself becomes the gauge.

SPRUNG STRUCTURE

“Dave, I'm still not comfortable. This is fine in principal, but I

have no feel for it?”

Think about Bow Saws Direct tensioning using lever

Think about Long Bows Tension by Springing Structure

Hydraulic Jacks

A Real Job

1. Install perimeter beams

and temporary jack at

mid-span

2. Install top chord, attaching

at one end and letting

bear on temporary jack

3. Pull down on other

end of beam to achieve

force noted

4. Attach cables and

connect to other beam,

then remove jack.

To Brace or Not to Brace

“Dave, I find tensile systems are complex. How do we apply these

methods to more complex systems?”

Load Case 1

100 kN Load Case 2

50 kN

Analyze the frame with cables as though the cables

were capable of resisting compression. Step 1:

Determine and apply prestrain to each cable that will

(hopefully) result in prestress to overcome the

compression.

T1 = T/EA

= (43,000N)/[(11.7x10-6)(135,000MPa)(283mm2)]

=96°C

T2 = T/EA

= (75,000N)/[(11.7x10-6)(135,000MPa)(283mm2)]

=167°C

Step 2: Or Misstep # 1

The prestress is not in internal

equilibrium. When we apply T

and analyze, the structure deforms

slightly to achieve equilibrium and

our forces change.

Make a note of the relationship between the

prestress forces.

P1/P2 = 40kN / 56kN

= 0.71

Analyze the system. Are the Forces what we expected?

When you apply prestress in a system, the forces will redistribute to achieve

equilibrium regardless of how you applied the prestrain.

Apply T to cable 1 only, and leave cable 2 alone.

Make a note of the relationship between the

prestress forces.

P1/P2 = 16.5 kN / 23.2 kN

= 0.71

Try This:

Apply T to cable 2 only, and leave cable 1 alone.

Again, make a note of the relationship between

the prestress forces.

P1/P2 = 19.1 kN / 26.8 kN

= 0.71

Now This:

Preq/P = 43.4/16.5

=2.63

Preq/P = 75/23.2

What Next: Determine the ratio of required prestress to the prestress resulting from an arbitrary application of prestrain for each cable.

Multiply your arbitrary T by the highest of these ratios. 3.23 in this case.

=3.23

But if we actually apply it this way, our frame drifts. The geometry

changes when the forces redistribute to generate equilibrium.

=23mm

This level of prestress is in equilibrium and adequate to

overcome the worst case cable compression. Apply T

Why isn’t the result exact?

T1=53300/[(11.7x10-6)(135000)(284)]

= 119 °C

T2=75000/[(11.7x10-6)(135000)(284)]

= 167 °C

Apply T to each element that will result in prestress that is distributed in proper proportion and is adequate to overcome the compression in the worst case.

Step 3:

The movement of the other elements under prestress all result in small changes

in force. In this case the top beam sags slightly relieving the prestress.

Load Case 1 + Prestress

=22.7 mm

Now, we are done!

Final Design Envelope Load Case 2 + Prestress

Load Case 1

100 kN

Load Case 2

50 kN

“Why go to all this trouble? Why wouldn’t I just use tension only

bracing, and let the compression side go slack? It looks like the final

design force is the same”

Load Case 1

100 kN

=37.4 mm

=>22.7 mm

With a conventional tension only system the “compression”

cable doesn’t contribute to stiffness, so if the system is

stiffness controlled, members have to be made larger to

compensate.

“Dave, you’ve convinced me. The technical arguments are compelling.

But how do I make it beautiful?”

Swage Eye and Fork

Cable Hardware

Open Spelter Socket

Cable Hardware

Take-up assembly, Open and Closed

Cable Hardware

Strut Hardware

Universal Pin Connectors

Architectural Swage Fitting

Rod Hardware

Forged Clevis

Rod Hardware

“Dave, what does this look like in real world projects?”

Milton Leisure Centre

Circa 1991

Circa 1999

Cawthra Community Centre

Completed 2004

Sir Sandford Fleming College

Rock community Church

Circa 2006

Lakefield College School

Circa 2006

Completed 2012

Local Church of the Saints

St. Catharines Aquatic Centre

Completed 2012

“Dave, those are all trusses. What about slabs and beams? And is it only useful

for pretty stuff?”

Stress Laminated Timber Bridge Decks

US Department of Transportation http://www.fhwa.dot.gov/publications/publicroads/97winter/p97wi32.cfm

Proposal for Two Way Prestressed Composite Wood/Concrete Bridge - Masters Thesis by Andrew Lehan, U of T

Prestressed Timber/FRP Bowstring Arch Bridge - Robert Widmann,

URS Meier, EMPA Swiss Federal Laboratories for Material Science and Technology, Structural Engineering Research Laboratory

“Dave, every client wants to work with CLT. How does this help?”

Using prestress we can join CLT panels together to span in their weak direction creating genuine two-way action. In this example a 7 ply assembly spans 6 m supporting 1.2 kPa Dead and 1.2 kPa snow.

In this example, we increased the bending capacity of a 215x380 beam by 22% using

prestress. Coincidentally this is almost exactly the increase achieved by increasing the beam

size by one ply. This is likely a useful technique only in applications where depth is

constrained. It could be the basis for full strength field splices of glulam beams, however.

“But wait, there’s MORE!”

Belleville (Spring) Washers

Some Things About Springs

Beam Reaction, R = 72 kN

Objective: Insert a stack of springs such that following shrinkage, the tension rod will retain nominal tension under load (to remain rigid). Say Tresidual = 15% R.

Maximum deformation of each spring to be 75% h0.

R = 72 kN Fresidual = R + Tresidual

= 72 kN + 15% * 72 kN = 82.8 kN

Consider nesting 3- DSC 112x57x6 Spring Washers

Now F75% = 43.8 kN Each Fresidual = 1/3 * 82.8 = 27.6 kN 25% = 0.63 mm @ F = 15.9 kN 50% = 1.25 mm @ F = 30.2 kN 75% = 1.88 mm @ F = 43.8 kN

By linear interpolation,

residual = (27.6-15.9)/(30.2-15.9)*1.25 + (30.2-27.6)/(30.2-15.9)*0.63 = 1.14mm

/stack = 75% - residual = 1.88 - 1.14 = 0.74 mm #stacks = residual / residual = 6.35/0.74 = 8.6

Say 9 Stacks

“Good judgment comes from experience. Experience comes from poor judgment”

-unknown

Thank You!

Bla

ckw

ell

This concludes The American Institute of Architects

Continuing Education Systems Course

Canadian Wood Council

Wood WORKS! Alberta

www.cwc.ca

www.wood-works.org