Structural Connections in Plywood Friction-Fit Construction
by
MASSACHUSETTS IN6TT"UTE
OF TECHNOLOGY
Mali E. Wagner
JUL 0 12014
Submitted to the
Department of Architecture
in Partial Fulfillment of the Requirements for the Degree of
LIBRARIES
Bachelor of Science in Architecture
at the
Massachusetts Institute of Technology
June 2014
2014 Mali E. Wagner
All Rights Reserved
The author hereby grants to MIT permission to reproduce and to
distribute publicly paper and electronic copies of this thesis document in whole or in part
in any medium now known or hereafter created.
Signature redacted
Signature of Author ..........................
..........
artent of Architecture
~May 23, 2X9
Signature redacted
Certified By .........................................................
.
John A. Ougndorf
Professor of Architecture and Civil and Environmental Engineering
Thesis Supervisor
Signature redacted
Accepted By ..............................................................
J0 Meejin Yoon
Associate ofessor of Architecture
Director of the Undergraduate Architecture Program
Structural Connections in Plywood Friction-Fit Construction
by
Mali E. Wagner
Thesis Committee
John A. Ochsendorf
Professor of Architecture and Civil and Environmental Engineering
Thesis Supervisor
Caitlin Mueller
PhD, Building Technology
Thesis Reader
Structural Connections in Plywood Friction-Fit Construction
by
Mali E. Wagner
Submitted to the Department of Architecture
on May 23, 2014 in Partial Fulfillment of the
Requirements for the Degree Bachelor of Science in Architecture
ABSTRACT
CNC mills allow precise fabrication of planar parts with embedded joinery which can be
assembled into complex 3D geometries without the use of foreign mechanical fasteners. This
thesis studies the behavior of the friction-fit attachment geometries which serve as the sole
means of structural connections. The thesis begins by describing the process of converting digital
files into physical objects. Next is presented precedents for the use of this system to create both
functional and abstract forms, including kits of parts for residential buildings. A review is given
of the ongoing research into attachment design optimization and open-source customization,
revealing the unanswered question of how the attachments can meet load demands. yourHouse, a
full-scale home composed of %"plywood friction-fit parts, is selected as a case study through
which the structural performance of the integrated attachments can be analyzed.
A series of load tests are performed on the structural connections identified in the house. The
function of these connections permits the internal structure and sheathing elements to perform as
composite beams for carrying bending. The methodology and expected behavior of the parts are
presented, followed by the test results. Next, a discussion and analysis of the data and
observations are given to provide first approximations of the system's wind load and gravity load
capacity. Finally, recommendations regarding component design, span tables, and the
construction method are given with justifications based on the empirical data.
Thesis Supervisor: John A. Ochsendorf
Title: Professor of Architecture and Civil and Environmental Engineering
ACKNOWLEDGEMENTS
I would like to express my immense appreciation for the support I received from the following
people who were instrumental in the completion of this thesis:
Professor John A. Ochsendorf, for introducing me to structural analysis methods. He is, without
a doubt, the catalyst for my ever-increasing fascination with structurally expressive, efficient,
and elegant design. More than just an effective teacher and brilliant engineer, he is kind,
encouraging, and understanding. He has been instrumental in my success at MIT by setting a
high standard for academic work and being a compassionate mentor. Thank You.
Professor Lawrence Sass, for giving me the opportunity to conduct research as part of his team in
Summer 2013 and sharing his personal documents with me so that I could study the structural
performance of integral attachments. I am grateful for the skills I have learned while working
with him and appreciate every bit of advice. Thank You.
Caitlin Mueller, PhD/BT, for her commitment to my success and for sharing her extensive
knowledge of structures with me. The chance to discuss my analysis with her every step of the
way throughout the past five months has been priceless. Her encouragement and dedication to
meaningful, accurate analysis kept me on my toes even when my feet were tired. I cannot thank
you enough for your time and mentorship.
Instructor Christopher Dewart, for his assistance in the fabrication of the testing models and for
sharing his knowledge of the mechanics of plywood.
Instructor Stephen Rudolph, for his assistance in running the load tests and collecting data, as
well as for the valuable discussions we had on observations during the tests.
Table of Contents
Chapter 1. Introduction....................................................................................13
1.1 M otivation .......................................................................................
1.2 Problem Statement ............................................................................
1.3 Scope of Research ..........................................................................
1.4 Research Objectives ........................................................................
Chapter 2. Literature Review ...............................................................................
2.1 Digital Fabrication Technology: CNC Milling..........................................15
2.2 Rapidly Prototyped Furniture and Housing .............................................
2.3 yourHouse: Case for Study ...............................................................
2.4 Ongoing and Open Research .............................................................
2.5 Chapter Summary..............................................................................29
13
13
14
14
15
18
22
26
Chapter 3. Structural Analysis of Sheathing Ties: Methodology ..................................
3.1 Theoretical Calculations ......................................................................
3.2 Alternate Designs ...............................................................................
3.3 Testing Procedure ...........................................................................
3.4 Chapter Summary ..........................................................................
31
31
32
35
37
Chapter 4. Structural Analysis of Sheathing Ties: Results .........................................
4.1 Test Results ...................................................................................
4.1.1 Standard Jack ........................................................................
4.1.2 Biscuit ................................................................................
4.1.3 Curved Jack ......................................................................
4.1.4 Small Jack ........................................................................
4.1.5 Skinny Jack ......................................................................
4.2 Discussion of Results ......................................................................
4.3 Test Summary................................................................................50
39
39
39
40
41
42
43
44
Chapter 5.
5.1
5.2
5.3
Structural Analysis of Assembled System: Methodology .............................
Model Configuration.......................................................................51
Theoretical Calculations ..................................................................
Chapter Summary ..............................................................................
51
Chapter 6. Structural Analysis of Assembled System: Results ....................................
6.1 Test Results .....................................................................................
6.1.1 Continuous Stud and Panel ....................................................
6.1.2 Non-Continuous Stud ......................................
61
61
61
63
54
59
65
6.1.3 Non-Continuous Sheathing ........................................................
...... 66
6.2 Discussion of Results .......................................................
..72
.....
6.3 Test Summary ....................................................
Chapter 7. Design Recommendations .................................................................
7.1 Jack Design and Use ........................................................................
7.2 Designing with Distributed Loads ........................................................
7.2.1 Finding a Relationship ..........................................................
7.2.2 Given Span .....................................................................
7.2.3 Given Design Load .............................................................
7.3 Constructability ..............................................................................
7.4 Chapter Summary ..........................................................................
73
73
75
75
77
79
81
83
...... 85
Chapter 8. Conclusions ...............................................................
85
8.1 Summary of Contributions .................................................................
8.2 Future Research...............................................................................87
8.3 Closing Remarks....................................................................88
References............................................................
-.... ..---
Appendix A. Simpson Strong Tie Test and Results ....................................................
89
91
Appendix B. Sheathing Tie Test Results................................................................103
Appendix C. Assembled System Test Results ..........................................................
113
Appendix D. Span Tables and Charts................................................................119
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Chapter 1. Introduction
1.1 Motivation
Digital fabrication technology has enabled the construction of complex 3D geometries
from interlocking planar parts. These planar structures are able to be held together purely
through friction between integral attachments. One advantage of this fairly new manufacturing
and construction system is the capacity for flat packing and shipping parts to consumers who can
assemble the object with no special tools or fasteners. Objects such as chairs, toys, and even
houses have been fabricated of planar parts. While computational tools have been developed to
automate and optimize the attachment design, there is a gap in the knowledgebase regarding the
structural performance of the embedded joinery. There remains the need to assess the material
properties and behavior of the attachment geometry of planar structures which can be integrated
into the early design phase.
1.2 Problem Statement
Traditional wood-frame construction has been studied and tested extensively, resulting in
comprehensive building codes used by designers and contractors to select materials, set spans
and heights, and appropriately space metal fasteners. The expansive knowledge and sometimes
complex calculations are provided for the ensured safety of occupants. Prescriptive measures for
supporting extreme load conditions, such as hurricanes and seismic activity, are even available
for designers and engineers (ASCE, 2010). Though beyond the scope of most building codes and
engineering aides, studies have been conducted which recommend the installation of metal ties
as a means of reinforcing wood-frame buildings against the enormous loads from tornadoes
(Prevatt, 2013; BPAT, 1999). Load tests to analyze the metal strap's effectiveness in preventing
uplift from tornado winds were also performed by the author (results of this test can be found in
Appendix A). Because so much effort has gone into evaluating the performance of conventional
wood construction, the lack of information on the performance of friction-fit construction will
prevent its implementation as an alternative for creating habitable, long-term structures.
The research presented in this thesis is conducted in order to set a precedent for
systematic analysis of the friction-fit attachments proposed as structural connections for CNCmilled homes. As the friction-fit system is applied at the scale of full residential construction, the
load demand on the integral attachments increases dramatically from that of a single person
13
chair. These attachments must be studied under applied loads to characterize their local behavior
and determine their capacity for transmitting forces. This will allow for an estimate of the
system's capacity for meeting wind load and gravity load demands based on empirical data. It is
the intention of the author to contribute first approximations of the system's load capacity and
possible design alterations to future, broader studies of the friction-fit system.
1.3 Scope of Research
This thesis aims to contribute data and analysis to the necessary investigation into the
structural performance of plywood friction-fit homes. The first step is identifying the intended
behavior of the assembled system. Next, the structural connections undergo load tests to
determine their effectiveness in transmitting forces between parts. Finally, recommendations are
made for the implementation of the friction-fit system and preliminary span tables are generated.
It is important that the tests performed as part of this research are reproducible for future
iterations of the friction-fit home design. Furthermore, the test specimens were fabricated in the
same manner intended for final home production, reducing possible performance anomalies.
However, due to the size limitations of the load machines, global composite behavior of the
friction-fit assembly is not included in the research. Another important consideration is that the
analytic model accurately represents the test data when extrapolated to a range of depths and
spans. Therefore, straightforward and universally accepted equilibrium equations are used. The
test data's relationship to theoretically calculated expectations is used to identify the most
accurate analytic approach.
1.4 Research Objectives
This thesis attempts to complete the following tasks for a specific example of friction-fit
residential construction:
-
Characterize the local behavior of the structural connections
Identify the governing failure mechanism and its associated load capacity
-
Provide recommendations for component design and configuration to improve structural
performance where needed
Generate aides for designing with wind and gravity loads
-
14
Chapter 2. Literature Review
This chapter provides background information on how digital fabrication technology has
come to be used in home construction. First, the chapter describes the process of design and
fabrication of 3D forms in terms of the advantages of and restrictions set by the fabrication
technology, specifically laser cutting and CNC milling. The second part of the chapter presents
furniture making and a survey of companies which produce homes designed of CNC milled parts
as two examples of how digital fabrication has presented itself as a potential replacement for
traditional carpentry. Next, the chapter examines a specific house model of friction-fit plywood
parts and provides information on the mechanical characteristics of plywood. The final section of
the chapter compiles a summary of the ongoing research topics in rapidly prototyped planar
structures and concludes that the query into the structural behavior has not been systematically
studied.
2.1 Digital Fabrication Technology: CNC Milling
Architectural design has experienced a massive shift towards digital models and
renderings, and the move toward digital fabrication technology is already underway. Solid
objects can be 3D printed at a small scale in the exact form seen on the computer screen. Parts
for a model can be precisely cut using a laser cutter, eliminating the need for knives and
imprecise cuts. The use of laser cutters and CNC routers, and digital fabrication technology in
general, requires the use of 3D and/or 2D digital drafting software, such as AutoCAD and
Rhinoceros. Therefore, the design process is a combination of sketches and 3D modeling, with
an emphasis on the digital drafting. While the software may provide new possibilities for shapes
and forms, it also limits the designer to his or her own specific knowledge of the software.
Because all designs must end up in digital form before any parts can be fabricated, the design is
restricted by the designer's drafting skills. Otherwise, time must be spent learning and mastering
new commands in the software, though this may not be the goal of the designer. Larsen and
Schindler (2008) of the Norwegian University of Science and Technology present a case study
from a class on CNC fabricated timber structures, and note that while the goal was not to teach a
specific computer program to the class, it was necessary for the final export of the designs to the
production machinery. The particular software used by the designer must be able to export a file
type compatible with the machine code generator software. For planar structures, which are
15
buildings comprised of all "flat" parts like the friction-fit system, the 3D model requires many
time consuming steps before it is even sent to the CAM/CNC software.
The conversion from 3D geometry to polylines to be cut by the laser cutter or CNC router
begins with dividing the sheathing panels and studs into parts which fit on the material sheet
stock. From there, interface connections are integrated into the individual parts. For instance, the
house under consideration in this research adds tabs along the wall and floor studs which mate
with slots in the interior and exterior sheathing panels. After the interface connections are
modeled, each component of the house must be converted to a 2D polyline and labeled. The parts
are then arranged inside of a bounding box of the same dimensions as the sheet stock being cut
(Fig. 2.1).
1
2
2
3
4
5
(stage 3)
(stage 2)
(stage i)
initial solid
shape
6
7
8
10
9
M-- T7
6
6
7
9r
Figure 2.1 Conversion of 3D model to 2D polylines for laser cutting and CNC milling (Sass, 2007)
16
11
For small models of few parts, this process can be fairly quick. Yet, for a house of many
parts, this process is incredibly time consuming and requires a systematic progression so as not
to miss or repeat parts. For laser cutters, the 2D lines must be color coded so that small cuts
within parts are processed first and larger, bounding cuts are processed last. This prevents
possible shifting of the material before small cuts are made. When the material has been
purchased and the laser cutter is available, the cut file of 2D lines can be plotted. The plot dialog
requires the user to test power, speed, and frequency settings on the material for clean cuts which
do not burn the material and the line colors must be assigned an order.
The process described above is useful for producing scaled models of planar structure
designs, as the laser cutter bed can only accept rather small sheet stock material. Furthermore, a
120 Watt laser cutter is only able to cut materials as thick as 1/8th inch, which is not practical for
full scale construction. However, Lawrence Sass (2007), a professor in the Computation stream
of MIT's Department of Architecture, has conducted research that demonstrates the
compatibility of the 3D and 2D file with the CNC mill at full scale production. This means that
the file can be scaled to match the increase in material thickness. For instance, the file cut in 1/16
inch material on the laser cutter can be scaled up by a factor of six to be CNC milled in % inch
material (Fig. 2.2). This allows all joinery to remain it its relative location on the building
components as well as preserving the precise fit of all parts so that friction can occur.
Figure 2.2 Full Scale Instant House in Y" plywood (A) fabricated from same file used to create test model in
1/16" cardboard (B) (Sass, 2007)
17
Though the desk model can be instantly scaled and used for the full production model,
the 2D file must be exported to CAM software where the CNC router tool paths are assigned and
the CNC code is generated. This requires that the user learn new software and ensure that all cuts
will be accurate. While the entire process of converting a design to a digitally manufactured
product can be time consuming and tedious, the end product is a kit of parts which are precisely
cut, high quality, and ready to assemble. The same file and laser cutter settings or CNC code can
be re-run again and again, producing exactly the same parts. This is desirable for rapid housing
where the need is urgent, such as in post-disaster areas. Moreover, because the parts are held
together by friction between perfectly mated joinery, there is no need for additional fasteners or
special machinery to assemble the parts. Rather than professional carpenters, any person with a
rubber mallet can fit the pieces together and produce a full building. The ease of construction
makes the building ideal for locations and situations where time and money are just not
available.
2.2 Rapidly Prototyped Furnitureand Housing
Furniture making and wood construction are two fields which are quickly being
infiltrated by digital fabrication technology. In particular, furniture makers are using CNC mills
to carve intricate patterns into stone, polymers, and wood parts, saving the time and cost of
carving by hand (Postell, 2012). CNC mills have also been used to create chairs and other
furniture which are assembled through integral attachments. Noel Davis (2006), a graduate of
MIT"s Department of Architecture, presented a series of ergonomic chairs whose parts were cut
with a single CNC tool and are held together through friction between joints. These chairs were
designed to be ergonomic and to be cost effective. While no structural calculations were
performed, the design of the parts was also a product of structural intuition and considered how
each piece should be sculpted to carry specific load conditions. Material was conserved where
forces were low and material was added at high stress areas. The joints were also precisely cut to
create a strong friction hold between parts. Figure 2.3 depicts the final chair design and
highlights the embedded joinery.
18
Figure 2.3 Ergonomic chair of CNC milled parts with embedded joinery; details shown on right (Davis, 2006)
Furniture made of CNC cut parts is now commercially available through open-source
hardware manufacturers. Designs can be either submitted or selected from a manufacturer who
will cut the parts and ship them in a flat pack which is "ready to assemble" (France, 2014; Saul,
2011). Much of the furniture relies on integral attachments which are friction-fit. Some are also
designed to allow for disassembly for transportation purposes. Other items, such as shelves of
interlocking panels, allow the buyer to assemble the piece in many different configurations. Not
only has CNC milling allowed for intricate carving of furniture pieces, it also produces simple
interlocking pieces which the consumer can disassemble and rearrange as desired.
Similarly, several companies have been founded in recent years which take the same idea
of integral attachments and apply it to a much larger scale. WikiHouse, Eentileen Arkitektur, and
Facit Homes are just three examples of architecture firms who are using digital technology to
produce homes (Fig. 2.4, 2.5, and 2.6). Each takes a distinct approach. WikiHouse allows the
consumer to select a home design and download a parts file for CNC milling. Eentileen and Facit
Homes mill parts and assemble blocks which are then compiled on-site. Each entitity includes
conservation of material and ease of assembly as part of their driving motivations for creating
digitally fabricated homes. However, only Facit Homes provides images of the assembled blocks
19
under a load test (Fig. 2.7), though no actual data is provided on the structural performance of the
building connections. Furthermore, while all of these houses use some form of embedded
joinery, none of them rely on friction fit parts alone. Mechanical fasteners are used throughout
the houses, and can thus reference existing codes for fasteners in wood construction when
determining load capacity. The next section will present a house which uses no external
fasteners.
Figure 2.4 WikiHouse: Cut files sent to consumer for production and assembly (WikiHouse website)
W
,
Figure 2.5 Eentileen: Assembled blocks compiled on site (Premium byg, Eentileen website)
20
.fIO.
Figure 2.6 Facit Homes: Insulated blocks compiled on site (Facit Homes Website)
V7r
Figure 2.7 Facit Homes: Insulated blocks compiled on site (Facit Homes Website)
21
2.3 Friction-Fit House: Case for Study
This section presents the friction-fit house proposed by Professor Lawrence Sass of
MIT's Department of Architecture. Unlike the other homes currently on the market, Professor
Sass's Instant Shelter (Fig. 2.8) and yourHouse (Fig 2.9) are composed solely of CNC milled
parts which use friction between integral attachments as the only form of structural connections
(Digital Design and Fabrication Group). Concrete footings with embedded metal bolts are the
only instance in which foreign materials are used, providing a sturdy foundation for the building
to be built upon. Professor Sass (2007) demonstrates of a fabrication process which uses a single
digital model to produce the same building across scales, from a prototype table model to full
scale, inhabitable construction. His research intention is to develop a shortened product
development which relates the final product to the preliminary design phase, which includes
physical prototypes that establish workflow and allow for design evaluation. In addition to the
condensed design and manufacturing process, the use of embedded joinery and a simple
assembly method enables the house to be flat-packed and shipped as a kit of part as an option for
low-cost, rapidly deployable housing (Fig 2.10).
Figure 2.9 yourHouse at MoMA, Manhattan (Sass
Figure 2.8 Instant House (Sass 2007, 308)
2010)
22
2N-E MArE JAL
P'RO O1TYPE HOUSE
Figure 2.10 CNC parts flat-packed, shipped, and assembled on-site (Digital Design and Fabrication Group, n.d.)
The full scale yourHouse was fabricated for the Museum of Modem Art in 2008 for the
exhibition "Home Delivery: Fabricating the Modem Dwelling" (Sass, 2010). This specific model
is used in this thesis to identify the structural connections in the friction-fit construction system.
Documents obtained directly from Professor Sass are consulted for accurate information on the
dimensions of the components and to compile an understanding of the building's assembly. The
first document is a schematic of the building structure which illustrates the parts of the building
and describes the layout. This document provides information on spans and supports, as well as
diagrams which clarify the function and development of the embedded joinery and sheathing
ties. Figure 2.11, taken from this document, shows the development of integral attachments on
the various stud conditions. Figure 2.12 shows the breakdown of the solid wall geometry into
sheathing panels with slots to mate with tabs on the studs and the sheathing tie which reassemble the panels into a single plane. Figures 2.13 and 2.14 depict the assembly of the interior
structure of contours and the layout of the sheathing panels, respectively.
23
0 AftWhrient
0s
Dart
@
ti dIgN
Aft
0
s
r/
LH
[L] attachment geometries
S]straight section rib
it
V®
-4
,--~
KV
(5)
LT ] tee section rib
[ L ] corner rib
4
f
:
[ T ] tee section rib
[ L ] corner rib
Figure 2.11 Conversion of various stud/contour conditions into CNC-ready parts with embedded joinery (Sass, 2008.
Available upon request)
dan
Jack
[;D
-i
4 Prong
3 Prong
m
1 Prong
Figure 2.12 "Wall Schema" and "Attachment Geometries" (Sass, 2008. Available upon request)
24
3" dart
throughout
eyes
3.14" BC Grade
plywood (paintod)
K1S
-
6" slab section
Figure 2.13 Assembled stud/contours (Sass, 2008. Available upon request)
-
'
'plywood
3/4" BC Grade
(paInted)
Figure 2.14 Layout of sheathing panels with slots for tab Insertion and sheathing ties between panels (Sass, 2008.
Available upon request)
25
All of the contours have slots which allow them to interface with overlapping,
perpendicular contours. This type ofjoint enables the bi-lateral configuration of the internal
structure. The tabs along the stud edges attach the sheathing panels to the grid of contours. The
sheathing ties, which are called Jacks, unite the sheathing panels into a single plane (Fig. 2.12).
Tabs and jacks are the primary means of providing a structural connection to allow the assembly
to achieve a composite system for carrying gravity and wind loads. The following section will
delineate the ongoing research into integral attachments such as these for digitally fabricated
geometries, showing that their analysis as a viable structural connection is still open research.
2.4 Ongoing and Open Research
This section presents papers which explore the computation and fabrication of
interlocking pieces which can be used to construct both functional and non-functional objects.
Like Davis's chair and Professor Sass'syourHouse, the digital designs are converted into 2D cut
files which are then exported to CNC mill type machines. The objects, like tables, chairs, and
toys, derive their stability through integral attachments rather than mechanical fasteners such as
screws and nails.
The research papers presented here use this principal to create many complex forms which
require intricate placement and sizing of the interlocking slots. This presents the challenge taken
on by the research of developing a parametric approach to optimizing the attachment design.
Schwartzburg and Pauly (2011, 2013) create a design tool which imposes constraints on the
movement of the parts in a model during design of the 3D shape. As the model is altered and
planar parts are added or subtracted, the computation updates the attachment design in an
iterative process (Fig. 2.15 and 2.16). Similarly, Hildebrand et al. (2012) creates a design
algorithm which evaluates the construction feasibility of designs. The tool allows complex 3D
shape abstractions to be built of slotted planar parts with a guarantee of constructability (Fig.
2.17 and 2.18). Both of these studies create tools which deal with the attachment design for
complex geometry to ensure constructability and rigidity. However neither of these tools is
equipped to evaluate material properties and stress requirements as part of the design process.
26
optimization
separable
locked
Figure 2.15 Optimization of planar surface orientation and attachment design
(Schwartzburg, 2013)
A'l
assembli order
Figure 2.16 Complex geometry of planar surfaces with optimized attachment design
(Schwartzburg, 2013)
n4~
Irnsenion
Input mesh
Plane datastructure
Preprocessing
Export
Figure 2.17 Construction process begins with 3D mesh input and results in planar pieces which are
guaranteed to construct the desired shape (Hildebrand, 2012)
Figure 2.18 Planar pieces with optimized attachment design for constructing familiar shape abstractions
(Hildebrand, 2012)
27
The field of planar structures, in which flat packs of parts are assembled with integral
attachments, has also been studied and developed for use as an open-source product which
consumers can easily access. Saul et al. (2011) developed the program SketchChairto allow
consumers to design their own chair which is laser cut by the manufacturer and shipped. Of
particular interest in this work is the ability for the software to test the chair for ergonomic
performance through a rigid-body physics simulator (Fig. 2.19). By testing the effect of gravity
on the stability of the chair during the design phase, time, material, and cost of production is
reduced. Again, however, the performance of the attachment geometry under applied loads is not
part of the research question.
Figure 2.19 Physics simulation prompts design corrections for improved stability (Saul, 2011)
Computation projects have created tools which optimize attachment design for
interlocking planar structures and have even provided a means for evaluating the stability of the
final 3D shapes. Thankfully, structural intuition is used in each of the design projects to produce
globally rigid objects. Yet there remains the question as to how the mechanical connections
between pieces behave under applied loads, which is a question of both the attachment geometry
and the material properties. This thesis intends to delve into this open research question by
examining yourHouse as a specific model of friction-fit, interlocking planar parts. Much more
than with tables, chairs, and toys, the structural performance of the embedded joinery must be
able to meet load demand to ensure the safety of the consumer. For this reason, systematic
analysis of the structural connections is required.
28
2.5 Chapter Summary
This chapter introduced the process of digital fabrication for creating 3D geometries
composed of interlocking planar surfaces. The precision of the CNC mill allows integral
attachments to achieve tight friction fits with its mate. Use of CNC-milled parts with embedded
joinery to create functional objects such as chairs and building blocks is presented in the context
of furniture-making and full-scale residential construction. Contributions to the optimization of
the attachment design for complex geometries have been made through development of
computation tools. yourHouse serves as a case study of a purely friction-fit construction system
which requires systematic analysis of the structural performance of the attachment design, as no
such research is currently available.
29
30
Chapter 3. Structural Analysis of Sheathing Ties: Methodology
This chapter presents the physical test performed on the tension tie, referred to as a
"Jack," between plywood sheathing panels. The variably sized panels are CNC cut from 4' x 8'
sheets of V" plywood and attached to the building studs. Without a mechanical fastener between
the panels, bending moment demand is difficult to meet when loads are present (Sass, 2014). The
function of the jack is to transform the wall of staggered panels into a single plane, rigidifying
the system. Of course, the effect and bending moment capacity is dependent on the strength of
the jack. In turn, the strength of the jack is dependent on its geometry. The primary goal of the
following test is to explore the strength of the jack and the wall system's bending moment
capacity across a spectrum of geometric variation. The methodology for fabrication, setup and
testing is presented here. Chapter 4 will present the results and observations of the test, as well as
a discussion of the results.
3.1 Theoretical Calculations
To begin the process of fabrication, the original AutoCAD files for the MoMA house in
New Orleans were acquired from Professor Lawrence Sass. Because of proprietary concerns,
these files are only available upon request from Professor Sass. With his permission, the files are
consulted to identify the accurate dimensions of the jack used in fabrication of the complete
house. These dimensions were nearly the same for the previous version of the jack, which was
referred to as a "biscuit" for its shape. The biscuit is the same height and width as the jacks in the
file, but with rounded bulbs on each end, rather than squared off rectangles. With the correct
dimensions, modes and loads of failure are able to be calculated using allowable stress equations.
When loaded in direct tension, the jack has three possible modes of failure: tension,
compression, and in-plane shearing. Figure 3.1 illustrates which areas of the jack and biscuit are
susceptible to each failure mode. Tension is expected to occur across the neck (w) of the jack in
plies whose grain is oriented perpendicular to the applied force. Compression, or bearing, is
expected to occur between the interface of the hammerhead and the plywood panel (x). In-plane
shearing is expected to occur along the height of the hammerhead (b) and along the height
between the hammerhead and the edge of the sheet (y) in plies whose grain is oriented parallel to
the applied force. Each of these parameters are multiplied by the thickness of the plywood, t, to
find the area across which load is transferred. When multiplied by the allowable stress, the
31
estimated maximum load before failure occurs can be calculated. The allowable tensile and
compressive capacity for plywood is equivalent to 4500 psi, while the in-plane shear capacity is
900 psi (Matweb). The governing failure load for both the jack and the biscuit is determined
using these figures and the allowable stress equation, Stress = Force/Area. Because of symmetry,
the failure loads calculated with b, x, and y are doubled. The tension tie dimensions are found in
Table 3.1 and the allowable load calculations are in Table 3.2.
Jack
b
b
4
X
y
Panel
'_ -
W
W
kaersectlon
Biscuit
b, in
I
1.7
y, in
2
2
x, in
.75
.5
w, in
of Applied
Force
Figure 3.1 Standard Jack and Biscuit Design Parameters
Table 3.1 Standard Jack and Biscuit Dimensions
Capacitv, Ibs.
Failure Mode
Load Equation, lbs
t, in
twat
.7
4500
2*txac
.75
4500
Tension
Compression
Jack
Biscuit
5063
3375
2297
.75,
Shear of Tie
Shear of Panel
(- allowable, Psi
2*tya,
900
.75
2697
2697
Table 3.2 Calculating failure load from allowable stress calculation
Table 3.2 tells us that the governing failure mode for the standard jack and the biscuit
version is in-plane shear of the tie, parameter b. Under direct tension loading, the fibers in the
parallel grain plies will slide out of place before other modes of failure occur. This governing
parameter is used in the next step of the experiment: altering the jack dimensions to identify their
optimal proportions.
3.2 Alternate Designs
While the ultimate failure load is able to increase with larger areas to transmit force, the
size of the jack is restricted by the inner grid of studs. The jack cannot become infinitely tall nor
32
infinitely wide. Therefore, the design requirement for the alternative jack designs is to meet
current performance without exceeding the current length and width. Three variations are
designed, each with a specific consideration: a "curved jack," a "small jack," and a "skinny
jack."
The curved jack model (c) intends to avoid a stress concentration at sharp corners. By
curving the turn from the neck to the hammerhead of the specimen, the force flow through the
material is allowed a smoother transition and space to redistribute, though the stress calculations
do not account for variation within the material. Removing the sharp corner reduces the stress
concentration, which can be 2 to 3 times higher than the stress experienced throughout the rest of
the material (Furlong, 2012). A transition with no curvature can easily become the weakest link
in a system. Furthermore, by curving the inner turns, the CNC process becomes more natural. A
3/8" drill bit used on the CNC router will leave the same radius when attempting to cut inner
corners. A 1/8" drill bit will make a sharper turn, but will also wear out much faster when
required to cut through the tough plywood. Even with the smaller drill bit, drill holes are required
at every inner corner so that it can be matched with its companion corner. Figures 3.2 and 3.3
illustrate this concept by highlighting where corners are meant to fit precisely and the CNC
router tool path with and without drill holes.
Figure 3.3 Drill holes cut in plywood
Figure 3.2 CNC Toolpath and location of necessary drill holes
Just as a sharp corner in the jack would result in a high stress concentration, so does the
notch caused by the drill hole. Furthermore, by drilling a 1/8" hole at the inner corners of the
joint, 1/8" width is removed from both the tension and bearing parameters, lowering the expected
failure load. By curving the highlighted turn, the need for notches is trumped. This same
reasoning is applied to the next two jack iterations.
33
The second alternative jack (d) adjusts all parameters to fail at the same governing load
as the standard jack. This small jack is expected to meet the standard jack performance with
minimum dimensions. The third jack design is a skinny jack (e); the length is set at the standard
jack length, 6 inches, while other parameters are adjusted to share the same failure load, which
would be in-plane shear. By designing these versions, not only can theoretical calculations be
tested, but there is also the prospect of conserving material. Although the cutouts in the large
sheathing panel do not allow any conservation of useable material, the cuts around the smaller
jacks do. Accounting for the 3/8" drill bit tool path around the jack, which is lost material, the
small jack uses 60% less material than the standard jack, while the skinny jack uses 30% less.
For a house such as that constructed by Lawrence Sass, which used about 400 jacks (a
conservative estimate made from consulting the structural plans provided by Professor Sass), this
translates to saving a full 4' x 8' sheet of plywood and a half 4' x 8' sheet of plywood for the
small jack and the skinny jack, respectively. The goal of these two designs is to conserve
material while preserving structural performance. Figure 3.4 depicts a side by side comparison of
the 5 models to be tested.
-t-~
+
1.7
RO.25
(c)
(b)
(a)
(d)
(e)
Figure 3.4 (a) Standard Jack (b) Biscuit (c) Curved Jack (d) Small Jack (e) Skinny Jack
Canacitv. lbs.
Fail Mode
Standard Jack
Biscuit
Curved Jack
Small Jack
Skinny Jack
4806
3204
4806
1280
1920
2560
1280
1920
Tension, w
Compression, x
Shear of Tie, b
Shear of Panel, y
2 76
2560
2560
Table 3.3 Expected Failure Load in Pounds for Each Model. Measured Plywood Thickness = 0.712"
34
3.3 Testing Procedure
In order to test these 5 models in direct tension, a rigging system is required that can grip
and pull the plywood panels without reaching failure before the specimens themselves. With the
input of Stephen Rudolph, MIT's Department of Civil and Environmental Engineering's
technical instructor, a system of steel bars and plates was developed. Four 3"x6"x 1/4" steel
plates are attached the MTS 60 Kip Load Cell with
2" diameter
steel rods. The other ends of the
steel plates sandwich the plywood panel, and a 1" diameter steel rod is passed through the 3
layers (Figure 3.5). The diameter of the steel rod passing through the plywood is most
significant. If the rod is too thin, it will likely split the wood. Furthermore, the width of the rod
will bear on the plywood with the applied force. This area needs to meet or exceed the bearing
area being tested between the jack and panel. However, by moving the rod hole far from the edge
of the plywood panel, the rod is not expected to experience any displacement. The holes in the
plywood panels where the steel rod passes are modeled a fraction larger to account for
tolerances. Rather than 1" holes, they must be modeled as 1.1" holes. When this setup was
agreed upon, Stephen Rudolph was able to proceed with production of the steel parts.
Figure 3.5 Test Setup and Steel Plate aoseup
After the specimens have been modeled in AutoCAD@ and the locations of the bar holes
decided, the 3D geometry must be flattened into 2D polylines. The polylines are arranged within
a bounding box of dimensions 48" x 96". These dimensions correspond to the plywood sheet
stock which was ordered through Christopher Dewart, the MIT Department of Architecture's
woodshop instructor. Three of each specimen is produced for testing. A minimum distance of
35
5/8" must be left between polylines to allow the CNC drill bit to pass by without disturbing
adjacent geometry. Once the 2D cut file is complete, it was imported into Rhino so that point
objects could be added at 90' turns. These point objects tell the CNC router where drill holes are
required (as discussed above). The Rhinoceros@ geometry is then imported into Mastercam@,
where the CNC router tool path code is generated. Like all software, Mastercam@ is best learned
with practice. This section will not describe the software use step by step. However, it is very
important to cut the drill holes first, inner geometry second, and so on. This will assure that these
smaller cuts are made in the correct position before larger cuts possibly shift the material. The
material is secured to the CNC bed with suction, but the order of the cuts assures maximum
accuracy.
Once the code is generated, it is loaded into the CNC router computer through a sequence
of setup steps and the machine is started (Fig. 3.6). When the machine is finished, tabs are
removed on a band saw. On a flat surface, the jacks are struck into their respective panels with
the use of a rubber mallet (Fig. 3.7). No other tools or fasteners are required. The jacks and their
cutouts are meant to be exact matches, with no material loss. Through friction, the jacks are held
in place. However, this extremely precise method of fabrication requires a large force to be
applied during assembly. Friction must first be fought to attain the perfect fit. For this reason,
many of the jacks experienced damage during the assembly process. These damages were
expected to affect the structural performance of the jacks. A thorough discussion of this
construction issue will be given in Section 5.1.
'Figure 3.6 Finished sheet of CNC cuts
Figure 3.7 Assembly of Jack and panel with rubber mallet
36
Finally, each specimen is rigged as shown in Figure 3.5. A digital camera was set up on a
tripod with a remote shutter control. The machine is set to a zero load and zero displacement. A
picture is taken in sync with the start of the machine, so that each subsequent photograph can be
paired with a specific load and time data point. The specimen is then loaded to failure at a rate
0.1 inch per minute, which is achieved when the load data starts to decrease. In some cases, the
machine is allowed to continue running until a minimum 1/8" displacement is noticeable in the
model.
3.4 Chapter Summary
This chapter described the fabrication process and methodology for testing the jack's
ability to transfer tension between sheathing panels. Several variations on the current jack design
were presented to illustrate the effect of geometry on the sheathing tie's performance. It was
shown that the construction method can cause significant damage to the plywood parts. Chapter
4 will present data and observations of the direct tension load tests.
37
38
Chapter 4. Structural Analysis of Sheathing Ties: Results
4.1 Test Results
This section will present the data collected during the direct tension test carried out on
March 25, 2014. The summarized data for each model will be given. Data and observations for
each individual test are provided in Appendix B. The next section will provide a comparison
analysis across the 5 different models.
4.1.1 StandardJack
Specimen
Load at 1/8"
Displacement, lbs.
Ultimate
Expected Failure
Average Ultimate
SD,
Load, lbs.
Load, lbs.
Load, lbs.
lbs
2
1156
1255
1280
960
367
3
PF
442
Table 4.1 Standard
Jack Test Data. PF = post failure
Standard Jack
2500
2000
1500
-1.
1000
500
... um-3
I
0
0.00
0.05
0.10
0.15
iplacement,In.
Chart 4.1 Load vs Displacement Plot for each Specimen
39
0.20
0.25
SD/Avg
0.38
(3)
(2)
(1)
Figure 4.1 Damage to each specimen after being loaded to failure
Shear failure consistently occurred prior to other modes of failure. Tension failures
followed, always between the 90 degree turns in the jack. Damage incurred during construction
caused the third test to perform poorly, though the first and second performed close to
expectations. This third test is not discarded because it illustrates the impact of the construction
method on structural performance.
4.1.2 Biscuit
Load at 1/8"
Displacement, lbs.
Ultimate
Load, lbs.
Expected Failure
Average Ultimate
SD,
Specimen
Load, lbs.
Load, lbs.
lbs
2
1848
2215
2176
1625
419
3
PF139
Table 4.2 Biscuit Test Data. PF =post failure
Biscuit
2500
2000
'.0
j 1500
I,
AW
AOV
-- 1
-00-Wi
1000
-
500
0
.0
0.05
0.15
Displacement In.
0.10
Chart 4.2 Load vs. Displacement Plot for each Specimen
40
0.20
0.25
2
SD/Avg
0.26
(3)
(2)
(1)
Figure 4.2 Damage to each specimen after being loaded to failure
The smoother transition between the neck and the ends of the jack allowed bearing
behavior to occur. While shear occurred in interior layers, the adjacent plies were allowed to slip,
delaying a sharp drop in the carried load.
4.1.3 CurvedJack
Specimen
Load at 1/8"
Displacement, lbs.
Ultimate
Upeimate
Load, lbs.
Expected F~ dilure
EnceF
Load, lbS.
2
PF
608
1280
3
PF92
Table 4.3 Curved Jack Test Data. PF
=post failure
Curved Jack
2500
Chart 4.3 Load vs. Displacement Plot
41
Average Ultimate
SD,
Load, lbs.
lbs
772
130
SD/Avg
0.17
(3)
(2)
(1)
Figure 4.3 Damage to each specimen after being loaded to failure
Bearing between the jack and the panel was noticed first in each test, followed by shear
failure in the jack. Tension failure occurred last because the layers were allowed to displace
through crushing due to the smooth turns.
4.1.4 Small Jack
Load at 1/8"
Ultimate
Expected Failure
Average
Displacement, lbs.
Load, lbs.
Load, lbs.
Ultimate Load
2
PF
739
1280
748
3
PTV52
Table 4.4 Curved Jack Test Data. PF =post failure
Small Jack
2000
-
-
2500
1500
1000
Chart 4.4 Load vs. Displacement Plot
42
D/Avg
234
0.31
1
(3)
(2)
(1)
Figure 4.4 Damage to each specimen after being loaded to failure
The small jack was susceptible to construction damage of the top plies, which caused
rapid failure in tension. Where shear occurred first, the perpendicularly oriented plies were
allowed to bear on the panel before tension occurred. This is because of the curved transition.
4.1.5 Skinny Jack
Specimen
Load at 1/8"
Displacement, lbs.
Ultimate
Load, lbs.
Expected Failure
Load, lbs.
Average
Ultimate Load
SD, lbs
SD/Avg
2
PF
819
1920
526
L5:
U.34
3
P6-2,2,
Table 4.5 Curved Jack Test Data. PF = post failure
Skinny Jack
2500
2000
Chart 4.5 Load vs. Displacement Plot
43
(1)
Figure 4.5 Damage to each specimen after being loaded to failure
(2)
(3)
Construction defects in the top plies caused the jack to fail almost immediately in tension.
A modest amount of load was able to be picked up through bearing and shear. The brittle failure
in the second and third test indicates when shear failure occurred.
4.2 Discussion of Results
The preceding section presented data and observations for each model and test. This
section will compare and contrast the different models' general behavior. To start this
comparison, Table 4.6 compares their average load, primary failure mode, time to failure, and
standard deviation. Table 4.7 provides each model's average modulus of elasticity. Table 4.8
lists the pros and cons observed in each model. Finally, Chart 4.6 and 4.7 will present the most
representative load-displacement and stress-strain plot for each model. These items will be used
to generate a design recommendation for future versions of the jack and offer a preliminary wind
load specification for the current version of the jack.
Model
Standard
jack
Biscuit
Primary Failure
Expected Failure Load,
Avg. Ultimate
Standard
Mode
lbs.
Load, lbs.
Deviation
1625
419
748
526
234
28-5
SD/Avg
I-P lane Sheacie Perform36anc
Compression
2176
207210
Copeso
Curved Jack
1280
In-Plane Shear
Small jack
Tens Ion:12
Skinny jack
Table 4.6 Summary of Average Specimen Performance
44
0.26
017
0.31
0.54
Standard Jack
Biscuit
Curved Jack
Standard Jack
42,200
Biscuit
Curved Jack
Small Jack
Small Jack
Skinny Jack
123,600
58,200
26,600
86,0W
Standard Dev.
8095
11324
3409
7857
39187
SD's /oAvg.
19
Model
Model
I
Avg. Modulus of
Elasticity, psf
Skinny Jack
30
Table 4.7 Modulus of Elasticity calculated from Load-Displacement data
Model
Cons
Pros
U
Standard Jack
*npI*.Ane er is 00. siMeoty pyk-fary
*
Dalb
es
Anseduce
S Temna f.Wum consditntly occmr at,
Biscuit
Curved Jack
Highest ultimate average load
Compression continues to pick up load
after shear failure
m Fit into sheathing with less resistance
P
*
Bearing on surrounding panel does not
allow replacement of just biscuit
*
Lower average ultimate ad thm
standard jact
Most linwatbehavior due to bearing
S Sudde.:bril
alr
*ossftnt loo 4 plaement plot shape
Small Jack
'
Uses 60% less material than standard
*
jack
* Consistent load-displacement plot shape
Skinny Jack
Usps 30%less mAerg l than sWArd.
Table 4.8 Pros and Cons of Each Model Type
45
*
Easily damaged when hit with mallet
during assembly
Assembly defects contribute
significantly to failure
ultita load
- Load
Model Comparison
- ---1400
I
1200
1000
Standard Jack
---
.* 800
--
.9 600
--
400
Biscu it
Curved Jack
-Small
200
Jack
.- Skinny Jack
n -I
0.15
0.10
0.05
0.00
Mipbocement, In.
Chart 4.6 Comparison of Each Model's Representative Load-Displacement Plot
Model Comparison - Stiffness
61
2000
1800
1600
1400
1200
1000
800
600
400
20D
-
IL
A
-A
---
Standard Jack
-
Small Jack
-Biscuit
0
0.02
0.04
0.06
0.08
--
Curved Jack
--
SkinnyJack
0.1
Strain
Chart 4.7 Comparison
of representative stress-strain plot
The biscuit and the standard jack were the highest and second highest performing models,
respectively. Contrary to expectations, the curved jack underperformed. The curvature created a
more direct load path between the sheathing and joint where bearing occurred, followed by
shearing. The top plies of both the joint and sheathing were oriented perpendicular to the applied
force. This orientation results in crushing of the wood fibers. The portions that are not crushed
pull adjacent layers through lamination. Parallel oriented plies, however, are better at resisting
46
crushing. Their fibers resist the displacement, failing in shear instead. The standard jack, on the
other hand, does not pick up load through bearing and crushing, instead relying on tension for
strength. When the applied load overcomes the shear capacity, the parallel fibers slide out of
place, pulling the adjacent plies with it. However, the three curved jack specimens had more
homogenous behavior. The standard deviation for the curved jack's data was only 17% of the
average ultimate load, while the standard jack's was 38%. Furthermore, while the curved jack
performed worse than the standard jack in average failure load, it performed better than the
standard jack in modulus of elasticity. The curved jack is stiffer and, again, displays much more
regular behavior with a mere 6% standard deviation of the average modulus of elasticity.
Reliable performance is desirable and necessary to assure occupant safety. A curved jack with a
higher in-plane shear capacity and the standard jack's bearing capacity could exceed the standard
jack and biscuit performance with a better guarantee of structural performance. More testing
should be done on a larger set of specimens to evaluate this claim.
Theoretical calculations cannot account for construction inconsistencies. This becomes
apparent with the small jack and the skinny jack. The parameters of the small jack were all set to
fail at the same load as the standard jack, 1280 pounds. While two of the standard jacks came
close to this expected load, none of the small jacks exceeded a 1,000 pound load. The skinny
jack was given a higher shear capacity and expected ultimate load, 1920 pounds, yet none of the
specimens carried even half of that load Table 4.9 summarizes the expected results versus the
observed behavior. Two of each model sustained damage during assembly. Plies were split or
delaminated because of the force required to position the jack. The specimens whose plot is
included in Charts 4.6 and 4.7 did not have any assembly defects. Therefore these data are
representative of the geometry's actual behavior, which is still poorer than the standard jack's. It
is not recommended that the jacks be designed so slim, as the construction method tends to
damage these much easier.
Model
Observed Avg. Load, lbs.
Expected Load, lbs.
Observed/Expected
Biscuit
1625
2170
0.75
Curved Jack
772
1290
0.60
Small Jack
748
1280
0.58
Skinny Jack
526
1920
0.27
Standard Jack
Table 4.9 Observed versus Expected Behavior of Jacks
47
Because none of the alternative jacks exceeded the standard jack's performance, the
average ultimate load of the standard jack is used to make a rough estimate of the system's load
capacity. For the wall, this would be a wind load. For the floor, this would be dead load and
occupancy load. A strip of the wall and floor is taken and approximated as a simply supported
beam (Fig. 4.6). The width taken is the largest distance between jacks, as this is the largest area a
jack would be responsible to transmit force across. In the floor, two jacks are provided for this
same width, one on either side of the stud.
7.25"
Psf25
0,ps
Figure 4.6 Strip of wall and floor area under distributed load
The configuration of wall studs and sheathing panels resembles the structural I-beam.
The sheathing and jacks must carry the tension and compression force couple, behaving as
stiffening flanges. Using the average ultimate load for the standard jack acquired in the direct
tension test enables the use of equilibrium equations to reverse calculate an allowable distributed
load. The force couple equation, T=C=M/d, begins these calculations, with the force equaling the
average ultimate load of the standard jack (multiplied by 2 for the floor which has two jacks per
stud). The bending moment found is set equal to the maximum bending moment for a linear load,
o pounds per foot. Finally, o is divided by the strip width to find an allowable distributed load in
pounds per square foot. Figure 4.7 accompanies the following equations for clarity.
48
Wall Section Allowable Load
F = Max Moment , d = 7.2 5in = 0.6 ft
2.
=
8Mmax
, L = 166 in = 13.8ft
Mmax =
Mmax = (960lbs)(0.6 f t) = 576 lb -f t
_
(8)(576 lb-t)
L2
(13.8 ft)
_
2
2
lb
ft
lb
3.
J2 -
=-
width
6 s
f
1.5 ft
Floor Section Allowable Load
1.
2F =
2.
Mmax =-,L
3.
f2
Max Moment
d
, d = 9.25in = .8 ft => Mmax = (2)(960lbs)(0.8ft) = 1536 lb -ft
= 8Mmax = (8)(1536 lb-ft)
2
= 180 in= 15ft
8
L2
(15 ft)
Max Shear
W2
54
Lb
ft
5. lb
'
-
ft
width =1.5 f t=3
36_s
f
da
V
U
Max
Bnding a iaL/8
Momefit
Figure 4.7 Shear and Moment diagram for simply supported beam
The distributed loads found here are low for a typical, single family home. When a safety
factor of two is imposed on the calculations, the system's capacity for carrying distributed loads
falls far below design standards. However, these preliminary distributed load estimates assume
that the jack is transmitting all of the flange forces between panels. In reality, the tabs which
connect the sheathing to the studs are also working to transmit the tension and compression force
couple across the flanges through the studs. This behavior will be studied in the next chapter,
which presents the three point bending test performed on the stud-sheathing assembly. Data and
49
analysis in this chapter must be considered in conjunction with the next test to attain a more
comprehensive understanding of friction-fit structural performance.
4.3 Test Summary
The sheathing ties are intended to strengthen the system against applied loads, such as
wind and occupancy. An analysis on several geometric variations of the jack was able to identify
strengths and weaknesses associated with each. It is the conclusion that the current jack design is
sturdy enough to withstand damage during construction and performs better than smaller,
theoretically sound versions. However, the consistency of its structural performance is lacking,
and can be improved through smoother transitions, which will also streamline the fabrication
process. Finally, an increase in the shear capacity of the joint, parameter b, will increase the
jack's ultimate failure load.
50
Chapter 5. Structural Analysis of Assembled System: Methodology
A three point bending test was performed on a section of the sheathing-contour assembly.
Slots in the sheathing panels are paired with protruding tabs along the contours ("Contour" and
"stud" are used interchangeably). When hammered into position with the use of a mallet, the tabs
support the weight of the panels and restrict movement in all directions. Friction prevents the
panels from sliding off of the tabs, while compression and shear resist panel displacement around
the tab. At the same time, the %" plywood panels provide rigidity to system, tying the contours
together. The goal of the test presented in this chapter is to observe the behavior of the tabs and
calculate an allowable distributed load based on empirical data.
5.1 Model Configuration
To begin developing the test, an original AutoCAD file for the MoMA house in New
Orleans was acquired from Lawrence Sass. With his permission, I used the file to identify the
assembly configurations present throughout the house, and acquire accurate dimensions. The
same connections and configurations are used in the walls, floor, and roof, only varying by
assembled depth. Along every stud there is a five inch long tab midway between intersecting
studs (Fig. 5.1).
5" Tab
<
Figure 5.1 Stud and Bracing Grid w/ Tab Location
(section of digital model acquired from Lawrence
Sass)
51
Four configurations were developed to test different properties of the structure. The top
two models (A and B) in Figure 5.2 explore the effect of stud continuity on the load capacity of
the system. The first model uses two continuous studs and the second tests the hammerhead
joints used to splice shorter pieces into a single contour. The bottom two models (C and D) split
the sheathing panels at mid-span, one using jacks as a bridging load path and the other providing
no sheathing tie. The system of studs and sheathing panels acts as a series of parallel I-beams
with regular perpendicular bracing. Therefore the approach to the system was to isolate a typical
section of the assembly and test it as a simply supported beam. The bridging element in the
middle of each model served to prevent rotational displacement of the two adjacent I-beams.
P
A
C
1D
Figure 5.2 Four Assembly Configurations Developed for Fabrication and Testing
The digital model provided necessary information regarding proportions and design
dimensions. However, the dimensions of the load machine bed restricted the length of the
specimens to 30 inches. Because of this, the test subjects were modeled at a smaller depth than
the eight inch wall and ten inch floor in order to preserve the aspect ratio of the "beam" and
accurately reproduce the system's behavior.
52
The four assembly configurations were modeled in AutoCAD and converted to a 2D
polyline cut file. The polylines are arranged within a bounding box of dimensions 48 inches by
96 inches. These dimensions correspond to the plywood sheet stock which was ordered through
Christopher Dewart, the MIT Department of Architecture's woodshop instructor. Two of each
specimen are produced for testing. A minimum distance of 5/8" must be left between polylines to
allow the CNC drill bit to pass by without disturbing adjacent geometry. A minimum %" space
between all polylines accounted for any necessary scaling. Three sheets of plywood were needed
to produce all parts. Once the 2D cut file is complete, it is imported into Rhino so that point
objects could be added at 9( turns. These point objects tell the CNC router where drill holes are
required (as discussed in chapter 3). As mentioned, scaling of the cut file may be necessary due
to variation in actual sheet stock thickness. Many wood products are sold at nominal sizes, so it
is good practice to get an accurate measure of the material being used. This is especially crucial
in the case of friction-fit construction, where the structure is dependent on the precise mating of
pieces. Measured with a dial caliper, the three sheets of plywood were 0.712 inches thick, a 5%
difference from the nominal sheet thickness. In order to update all sheathing and contour slots,
the entire cut file (minus the bounding region) was scaled down by 5%.
The Rhino geometry is then imported into MasterCAM, where the CNC router tool path
code is generated. Once the tool paths are created for each sheet, starting with drill holes and
ending with the outermost cuts on all geometry, the CNC mill is run. The pieces were passed
through a band to remove all tabs left by the CNC mill code. Each model is then assembled on a
flat surface with the use of a rubber mallet. Unfortunately, model D was unable to be assembled
without absolutely destroying the jacks. These small pieces were attempted to be inserted last
into already tightly assembled parts, which was the case in the construction of the MoMA house.
Difficulty in construction and the brute force required to fit certain parts together will be
discussed in more depth in Chapter 5, as it can majorly affect the performance of the proposed
system.
Specimens were loaded on a Baldwin-Tate-Emery 60K Universal load machine, operated
by Stephen Rudolph in MIT's department of Civil and Environmental Engineering, at a rate of
0.1 inches per minute. Initially, a smaller machine was planned to be used, and the model was
fabricated at only 16 inches wide. However, the bed dimensions of the machine used are 30
53
inches by 30 inches, which allowed for a wider model. I would suggest that four inches be added
to each side of the top and bottom panels to create a more accurate, likely stiffer, model.
In order to test the models as simply supported beams, the specimen was raised up on two
four inch square wood studs, allowing space for deflection of the model under loading. The
location of the support reactions was taken to be at the centroid of wood studs, two inches
inwards from the model ends (Fig 5.3, drawn in red). Support blocks were selected so that they
were strong enough to provide the vertical reactions yet not overlap with the location of the tabs,
which would have possibly altered the results significantly. The test setup also included a two
inch by four inch stud oriented with the long edge vertically, intended to distribute the applied
force across the middle of the model. Each test was extended past a peak load to identify
secondary load paths. Figure 5.3 illustrates the described setup.
Figure 5.3 Three point bending test configuration
5.2 Theoretical Calculations
Expectations for load capacity were calculated using both stress and force couple equations.
Bending stress is an accurate means of estimating continuous beam-like behavior because it
takes into account the specific geometry of the specimen. The stiffness of the beam is assessed as
a function of the second moment of inertia about the X-axis divided by half of the beam depth.
This value is known as the section modulus, which changes with any change in dimension. The
54
following analysis considers the two studs as independent I-beams connected by the top and
bottom panels. By considering each individual section's stiffness, this is a conservative
approach. The failure load for one half is doubled because the two beams each carry half of the
load. The distance from the supports is taken at the furthest tab location, where stresses can be
carried through the assembly. The maximum shear and moment used in the equations are
illustrated in Figure 5.4. Figure 5.5 gives the dimensions of the beam section to accompany the
bending stress calculations.
Form.
p
C
TI
P/2p
P/1
2 4
4-5
-x axis-
162.41
M
-
Amawun
X~
Figure 5.5 I-beam Section Modulus about X-axis
Figure 5.4 Flange forces transmitted through stud tabs
Vmax =
lbs
M(x) = (Vm
* X) = 2-* x lb - in
Where x is the distancefrom the support in inches
g lobal =
'local is
in, A = bh, and dy = distancefrom x - axis
Ilocal + Ady'), where Ix =
negligible and thus not calculatedin
'global;
Ad2 term goes to Zero for vertical areas
4
2
Iglobal = 2(4.5 in)(.712 in)(1.6 in) = 16 in
-
y = 1.6 in,
,
Section Modulus, S,
S =
y
Benin Stes,
Bending
Stress,2So =Moment =Px =in
Pfailure = (2)
=
x
PX
2)(10)
16 in4
= 10 in
1.6 in
psi , rearrangeto solve for P
lbs , set a equal to allowable stress values for tab in compression and shear
Pfailure,shear =
(20 in 3 )(900 psi)
7. in
2*
7.25 in
Pfaiture,compression = 2 *
=
(20 in3 )(4500 psi)
7.25 in
55
4,980 lbs
= 24,800 lbs
The previous equations assume a beam connected continuously along its span. That is not
the case for the friction fit system. The only points where flange forces can be transmitted is
through the tabs. The force couple equation for beams says tension and compression in the
flanges is equal to the bending moment divided by the beam depth. This particular equation is
useful in hypothesizing how the tabs will perform when the model is loaded, because they
transmit the flange forces through the assembly by compression and shear. Figures 5.6 and 5.7
demonstrate how the tabs are expected to be loaded and how they resist force. When the flange
force, T=C, is set equal to the maximum load that can be carried by the tabs, we then find an
expected Pfalure. The force able to be carried by compression of the tab is the compression area
multiplied by the allowable compressive stress of plywood. The force carried through shear is
the shear area of the tab multiplied by the plywood's in-plane shear capacity. The model has two
sets of tabs, thus the load is expected to be doubled. The distance "x" is taken at the point
labeled "c" closest to mid-span in figure 5.6, where the bending moment is greater and thus
governs. The following equations reveal that the tab is expected to crush before shear failure
occurs.
Compression Area
Force
C
Formr-
c
Shear Area
--------d=3.25'
T
P/2
P12
Figure 5.7 Areas available on tab to transmit Flange forces
Figure 5.6 Inner forces acting on tabs under loading
T(-
I~F
T(x) = C(x) = F
M
x_ 2dF
lbs
PfaUure =
lbs
Compressionmax = ( 2 )(Acomp.xcomp.) = (2)(.712in) 2 (4500 psi) = 4562 lbs
(6.5 in)(4562 lbs)
=bs
Pfalure,compression=
Shearmax =
7.25 in
(2)(Ashear)(Ushear) =
P.
f ailureslear
-
,
(2)(.712 in)(4.75 in)(900 psi) =6087 lbs
(6.5 in)(6087 lbs) -5450
7.25 in
lbs
56
For comparison, we make the assumption that the model behaves as a single
continuous, hollow beam. Thus the section modulus is calculated for the full cross section and
the failure loads are recalculated using the areas illustrated in Figure 5.8. Table 5.1 summarizes
the range of failure loads for the model.
P
15.7"-
x-axis
2.4"
Figure 5.8 Section Modulus calculated for Full Cross Section area
I. = 57 in
a
=
;
Sx
P
psi
35 in3
1.6 in
y
lbs
Pfailure =
)
(900 psi)(70 in3
7.25 in
Pfailureshear -
=
)
(4500 psi)(70 in3
8,700 lbs
Pfailure compression
=
7.25 in
= 43,400
lbs
Calculated Failure Load by Method, Kips
Mechanism
T
C
=
Md
=
2*
M/Sxj ndependent
S
=
In-Plane Shear
S.
5
8.7
Compression
4
25
43
Table 5.1 Range of failure loads calculated by various approaches
57
Conservatively, the system will begin to fail at 4 Kips according to these calculations.
The test results will reveal which method best describes the behavior of the system. The section
modulus in the previous calculations assumes that the flanges are continuous along the beam.
When the bottom panel is not continuous then it cannot transmit any tension force. The tension is
then carried through a much smaller area at the bottom of the vertical stud. That area and its load
capacity are found by first locating the centroid of the T-beam, calculating a new section
modulus, and solving for the expected failure load. Figure 5.9 illustrates this approach and
accompanies the following calculations.
4.5"
0. 1~-/
~'
0.9"
"
. 4-
2. 8"
FXa
y=2.2"
1. 2"
Figure 5.9 T-beam section modulus contributing area
y = (Ay)/
Centroid:
,/ A
Iglobal:
'global
(0.712 in)(2.4 in)(1.2 in)+(4.5 in)(0.712 in)(2.8 in)
(0.712)(2.4 in)+(4.5 in) (0.712 in)
= E(Ilocal + Ad2)
=
(4.5in)(0.712in)(0.9in)
-
2.2 in
(Adz flange + (Ilocai)vertical
2
+ (.712in)(2.4in)
12
3
= 3.4 in4
Section Modulus:
Iglobal
y
3.4 in4 -
1.5 in 3
2.2 in
Bending Stress:
=
=
PL
\X4\sI
=>
Ptwo stds =2
= 2 *2n
L
(4)(1.5
24.5 in
in3)(soo psi) =2200 lbs
Removing the tension capacity of the bottom flange by splitting the panel reduces the
expected failure load by a factor of two. This model examines the behavior of the system without
any mechanism for tying adjacent sheathing panels together. Unfortunately, the model with jacks
(D) at mid-span was not able to be assembled and tested. However, its failure load can be
58
calculated using the average failure load of the standard jack found in Chapter 3. This load
represents the jack's capacity for transmitting the flange force in tension. In these calculations,
the moment is calculated at mid-span, where the jacks would have to transmit the largest flange
force. Clearly, the jack will fail in tension before the stud of the T-Beam configuration would
split, and thus does not theoretically contribute to the capacity of the system.
Where x =
F=T=C=-=-
L
M
d
; Mmax =
PL
4d
Px
=
PL
T
for a point load
solveforP=*
4Fd
L
P1sd=--
Where F=960 lbs, d=3.2 in, L=24.5 in P2 studs = 2 * (4)(96024.5
lbs) (3.2 in) = 1000 lbs
in
5.3 Chapter Summary
This chapter presented four types of stud and sheathing panel configurations for testing.
However, only three types of models will be tested (A, B, and C), as model D was unable to be
constructed without serious damage. Because of this same reason, only one model B will be
tested. The models were then analyzed as simply supported beams. Equilibrium and bending
moment equations were used to calculate the expected failure load for various assumptions.
Chapter 6 will present data and observations from the three point bending tests, as well as give a
discussion of the results. The results will reveal which analytic approach is most accurate for the
friction-fit system under bending.
59
60
Chapter 6. Structural Analysis of Assembled System: Results
6.1 Test Results
This section will present the data collected during the three-point bending tests carried
out on April 1, 2014. Data and observations for each test are provided in Appendix C. The next
section will provide a discussion of each model's behavior and a comparison analysis across the
5 different models.
6.1.1 Continuous Stud & Panel (A)
Model
2
Load at 1/8"
Ultimate
Min. Expected
Average Ultimate
Displacement, lbs.
Load, lbs.
Failure Load, lbs
Load, lbs.
992
4850
Table 6.1 Continuous Section Test Data
Continuous Stud & Panel
6000
5000
4000
Chart 6.1 Load vs Displacement plot for each specimen
61
SD, lbs.
SD/Avg.
Figure 6.1 Continuous model post failure
(a)
Figure 6.2 Details from failure of Continuous model
(b)
(c)
The tabs experience crushing where expected. The failure loads confirm that the model
behaves as two individual I-beams. Crushing of the tabs and splitting of the bottom panel
occurred simultaneously, allowing for an even load distribution and softer failure.
62
6.1.2 Non-Continuous Stud (B)
Model
Load at 1/8"
Ultimate
Min. Expected
Average Ultimate
Displacement, lbs.
Load, lbs.
Failure Load, lbs.
Load, lbs.
SD, lbs.
SD/Avg
Table 6.2 Non-Continuous Stud Test Data
Non-Continuous Stud
6000
5000
_'00
4000
%
3000
2000
1000
0
0
1
0.5
Dbsoacsrent, Iin
rhnrt A3
7 nari we iceniaromant PInt
mgure D.s Non-onuinuous stua at rawure
63
1.5
(a)
(b)
Figure 6.4 Details of failure from Non-Continous Stud model
(c)
Only one test specimen was available for this particular model, as the construction
method caused extensive damage to the stud. This model showed an increased amount of
flexibility, likely due to the joints in the studs, but behaved very similarly to the continuous
model. The joints in the stud did not experience any observable failure during the test, as the
shear force in the stud near mid-span is low.
64
6.1.3 Non-Continuous Sheathing (C)
Model
2
Load at 1/8"
Ultimate
Expected Failure
Average Ultimate
Displacement, lbs.
Load, lbs.
Load, lbs.
Load, lbs.
SD
369
Table 6.3 Split Sheathing Test Data
Non-Continuous Sheathing
6000
5000
4000
3000
-1
2000
--- 2
1000
0
0
0.5
1
Displacement, In.
Chart 6.3 Load vs Displacement plot for each specimen
Figure 6.5 Non-Continuous Sheathing model at start of test
65
1.5
SD's /oAvg.
(a)
(b)
Figure 6.6 Details from failure of Non-Continuous Sheathing model
(c)
As expected, this model failed at a much lower load than the other models at mid-span, as
the discontinuous bottom panel cannot contribute any flange capacity for carrying bending
moment. The studs split at the bottom and the top panel crushed the tabs.
6.2 Discussion of Results
This section will compare and contrast the different models' general behavior and discuss
their relation to the expected results. Table 6.4 lists the average data across the model types for
comparison. Table 6.5 summarizes the observed failure mode for each model and assigns the
model an accurate analytic approach. Chart 6.4 contains a representative load versus
displacement plot for each model. These three items will be used to offer a load specification for
the current dimensions of the friction fit system.
Model
Primary
Failure Mode
Expected Failure
Load, Kips
Avg. Ultimate
Load, Kips
Standard
Deviation
SD's /oAvg.
Ultimate
Load
43
Continuous
Non-Cont. Stud
Compression
Non-Cont.
Sheathing
Table 6.4 Summary of Average Specimen Performance
66
Model
Continuous Stud & Sheathing
Non-continuous Stud
P Middle of stud appeared more
horizontal than stud ends under
loading
P Crushing at tabs and splitting of
bottom sheathing
* No stress noticed in stud splice
ioints
* Similar behavior to
Continuous model, softening
of graph around 3 Kips
Non-continuous Sheathing
Table 6.5 Behavior and Appropriate Approach to Models
Model Comparison
6000
5000
4000
11111114
k
A,,,,,Iliilllllllllll111111111111
67
M
T = C =d
Where the sheathing panels are continuous, splicing of the studs does not diminish the
system's load capacity. The two models behave very similarly, with crushing of the tabs and
splitting of the bottom panel occurring simultaneously. The data and observations for each model
confirm that the calculations using the flange forces is appropriate for this system as it accounts
for the actual area of the tab that can transmit force. On the other hand, an overestimate is
calculated assuming continuous I-beam behavior. The non-continuous sheathing model was
unable to resist bending through tension of the bottom panel. Crushing of the tab barely occurred
on the top panel before the studs split in tension. The average failure load was between the
calculated load for one stud and two, although load was taken on after one of the studs broke.
This indicates that the theoretical calculation for the stud's load capacity is below the actual
capacity of the stud for carrying bending moment.
The average failure load of the continuous beam is used to calculate bending moment at
the innermost tab location (see Fig 5.4). Bending moment is then divided by the beam depth to
find the load at which the tabs ultimately failed in compression by transmitting flange forces (I).
This compression failure represents the flange force capacity for the wall and floor assembly,
and can be used to determine the allowable distributed load for each (II). However, using the
failure load of the standard jack as the maximum flange force for the same section results in a
much lower allowable distributed load (III) While the wall has only one jack aligned with each
vertical stud, the floor has a jack on either side of the studs, doubling the potential flange force
for the same tributary width. Figure 6.7 depicts the two areas under consideration with
dimensions. Figure 6.8 illustrates the shear and moment diagrams for a beam under a distributed
load.
I. Flange ForceCapacityfor Tab:
M = VMax *X =
, where x = 7.25 in = 0.6 ft ,P = Avg Ult Load = 5100 lbs
(5100 lbs)(0.6 ft)
2M
M
Where d =3.2 in = 0.3ft;
F
T= C =
d
53153
b-
= 1530
b ft = 5100 lbs
0.3 ft
II. DistributedLoad for a ContinuousSheathing Model:
Wall:
Mmax = F * d = (5100 lbs)(0.6 ft) = 3060 lb -ft; where d = 7.25 in = 0.6 ft
Mmax = 0)13
8
= B*Mmax
L2
ft)
(8)(3060
(13.8 f t) 2
68
-
where L = 166 in = 13.8
128 L;
ft
ft
w-_ _
width
Floor:
128 lbj
1
Lft
-
1.5 ft
85 psf
Mmax = F * d = (5100 lbs)(0.8 ft) = 4080 lb - ft; where d = 9.25 in = 0.8 ft
8 *Mmax
Mmax
2=
L2
8
849
W width
1.5
_ (8)(4080
lb-ft) - 145 ' ; where L = 180 in = 15 ft
(15 ft)2
ft
-f
-997 psf
ft
III. DistributedLoad for Non-ContinuousSheathing Model with Jack:
Wall:
Mmax = F * d = (960 lbs)(0.6 ft) = 576 lb -ft; where d = 7.25 in = 0.6 ft
8
maxWLZ
L2
24 lb/ft 1.5 ft
width
*Mmax
-
(8)(576 lb-ft)
(13.8 ft)
2
lb
ft
l6psf
Floor: Mmax = 2F * d = (2)(960 lbs)(0.8 ft) = 1536 lb -f t; where d = 9.25 in = 0.8 f t
Mmax
12 =
-8
-d--
width
2
=>
.5 ft
1.5 f t
w _ 8*Mmax
0
-
Mma
lb-ft)
(15 ft)2
_ (8)(1536
54 Lb ; where L = 180 in = 15 ft
ft
36 psf
2 5"
6"
Ill. Wall
.
'Y 1 6
Figure 6.7 Floor and wall strip under distributed load (shown as point load for clarity), tributary area in red
69
WIbItt
Jz
U
12
L
/2
d
Max Shear z UL12
V
Max
Bending
Moment
=
X'/8
Figure 6.8 Shear and Bending moment diagrams for a beam under Linear Load
The ultimate failure load of a section of the floor or wall where the sheathing is
discontinuous based can be roughly estimated based on the bending test data. The average failure
load of the discontinuous sheathing model was exactly one-third of the continuous beam's
average failure load. By extending this observed behavior to the full scale model, a
straightforward assumption might be made that the wall and floor would only be able to support
one-third of the distributed load calculated for the continuous section. However, this assumption
cannot be directly proven. In the wall case where the jack is responsible for transmitting flange
forces across sheathing gaps, the maximum distributed load that can be carried is extremely low.
Furthermore, when a safety factor of two is introduced into the design considerations, the actual
allowable design load is a mere eight pounds per square foot. In the floor case, where two jacks
are responsible for transmitting flange force for each beam section, the allowable design load
would be 18 psf. Table 6.6 summarizes these findings.
Section
L, ft.
Wall
Floor
15
Flange Force, lbs.
Load Capacity,
Psf.
With Safety
Factor of 2
T-Beam
1/3 Tab
29
14
Tab
5100
97
48
2 Jacks
1920
36
18
d, ft.
Flange Type
J1
Tb50
0.8
Table 6.6 Summary of Distributed Load Calculations
70
The assembled friction-fit house is in fact a combination of the tab and jack conditions.
Throughout the house, the sheathing panels are staggered, so that no gap in the sheathing extends
from one end of the wall or floor to the other. All sheathing edges are flanked by continuous
panels, imparting stiffness to the discontinuous sections. Therefore the actual allowable design
load is between 8 and 43 pounds per square foot for the wall and between 18 and 48 pounds per
square foot for the floor. Panels in the floor are tied together with more jacks than the wall panels
are and there are supports along the floor mid-span. In addition to the larger depth, these two
features are likely intended to allow the floor to carry a higher distributed load than the walls.
However, one concerning aspect of the sheathing layout on the house's underbelly is the nearly
continuous split across the mid-span. Clearly, continuous panels provide a better resistance to
bending moments and should be located at high stress concentration areas whenever possible.
Figures 6.9 and 6.10 illustrate the staggered panel layout of the floor and wall, respectively.
Sections considered for the earlier calculations are highlighted in red. Supports are in blue. The
more frequent spacing of the floor supports likely allows the floor to carry a distributed load
closer to the continuous section value of 48 pounds per square foot. The dimensions of the wall,
on the other hand, need to be reconsidered if the current jack is used.
IiIIIIII I
I
3-0
I
~L~j
II
I
-r~
I
d
II
a-4
I
~a
--
I
-~
-a
I
I
-1-a
IILJI
rn-a
LUa
~E~L~L
rn~a'
a
0C
0-0
I'
I~
II
J
WI
-K-I -4
a
'A
I
T
I
Figure 6.9 Underbelly Sheathing Panel Layout (Sass, 2008). Bold lines added
71
I
1 L
::
I
o
1 1 112
11)
--
~
..
_ _ _ ......
..
.
.
w:fj-.1:
11
'-I-,
Figure 6.10 Exterior Side Sheathing Panel Layout (Sass, 2008). Bold lines added
6.3 Test Summary
The bending tests described in this chapter, combined with the data from Chapter 3,
reveal the clear disparity in load capacity between the continuous sheathing sections and the
discontinuous sections which rely on jacks to transmit flange forces. The jacks will always fail
before the stud tabs even begin to crush. While the data and analysis can only provide a range of
allowable design loads for the system, it is clear where improvement and alterations can and
should be made in the dimensions of the system. Several design variations will potentially
increase the capacity of the wall to carry wind load. One option is to provide two jacks per stud,
as in the floor, and shorten the wall to ten feet, thus allowing a distributed load of 31 pounds per
square foot, accounting for the safety factor of two. Another option would be to also provide two
jacks per stud and increase the assembled depth from eight inches to ten inches, increasing the
distributed load capacity to 21 pounds per square foot. In any case, the designer should take care
to provide continuous panels as much as possible, decreasing the need for the use ofjacks.
Chapter 7 will further explore the effect of various depths and spans on the capacity of the
friction fit system to carry loads.
72
Chapter 7. Design Recommendations
The goal of this chapter is to apply the results of the tests performed on the friction-fit
components in order to provide preliminary structural guidelines and a discussion on the
practicality of the proposed system. Section 7.1 will discuss alternatives to the current jack
design which have the potential to improve the component's structural contribution. Section 7.2
will consider the system's capacity for carrying distributed loads for a range of spans and depths.
The same equations can be used to determine minimum spans and depths for a given design load.
Section 7.3 will then address fabrication and construction topics which have the potential to
affect the structural performance of the friction-fit system.
7.1 Jack Design and Use
The friction-fit system derives its stiffness from the beam-like configuration of the studs
and sheathing panels. When a force is applied to the structure, the sheathing must transfer flange
forces to counter the bending moment. This is achieved through compression of the tabs which
protrude from the studs and are inserted into the sheathing. Where the sheathing is discontinuous,
jacks are required to transfer flange forces across adjacent panels. Therefore these are the two
mechanisms which determine the capacity of the system to support live loads. However,
previous chapters showed that the jack not only demonstrated unreliable behavior as is, but that it
also far underperforms when compared to the continuous panel configuration. This leads to
several suggestions for the jack's use that can potentially improve the performance of
discontinuous sheathing areas.
First, in order to give the sheathing tie more consistent behavior, reduce stress
concentrations, and streamline the fabrication process, curving the jack transitions is
recommended. These points are discussed in Chapter 3. Second, to improve the load capacity of
the jack, the area which can transmit shear force, the governing mode, should be increased.
Currently, the standard jack provides a one inch length on each side of the hammerheads for inplane shear to be carried, and a two inch length between the jack's hammerhead and the edge of
the surrounding panel. These two distances can be adjusted so that they are equal in height,
immediately increasing the shear capacity of the jack without exceeding the overall height.
Alternatively, these same dimensions can be made equivalent by adding an inch to either end.
Furthermore, the area which compression force can be transmitted between the jack and the
73
sheathing panel should be the same as the standard jack. These dimensions should be measured
between the curved edges. Figure 7.1 illustrates the suggested alterations to the sheathing tie,
which should undergo their own series of load tests.
2'
(a)
(c)
(b)
Figure 7.1 (a) Standard Jack (b) Alternative 1(c) Alternative 2
A third recommendation for the use of the jacks is directly derived from the analysis of
the test data, which demonstrated that the jack is only able to transmit about 1 Kip of flange
force when the assembly is subjected to a live load. Chapter 3 and 4 concluded that this only
amounts to about 16 pounds per square feet of live load capacity when only one jack is present
along each contour. When two are provided, the capacity is doubled, allowing the system to
carry more moderate and in some cases typical live loads. This double jack scheme is present
throughout the floor panel layout, but not the walls. It is suggested that double jacks be provided
throughout the entire building. According to allowable stress calculations for in-plane shear
capacity, the model in Figure 7.lc would provide the same flange force capacity as the tab and
sheathing configuration if two are provided per stud (see calculations below).
Force
Oshear = Area => F = oshear -4ht = (900psi)(4)(2in)(. 75in) = 5.4 Kips
where h = height of shear paramter,t = plywood thickness
the area is multiplied by 4 because of symmetry in the jack and 2 are provided per stud
However, with only double standard jacks, the continuous sheathing areas which rely on
compression of the tabs and tension in the plywood panel are able to carry nearly three times
more live load. Therefore, the final recommendation regarding the jacks would be to ideally limit
74
their need where ever possible by using larger sheathing panels. The feasibility of this, however,
is unlikely, as the size of the panels is limited not only by the plywood sheet stock, but also by
the dimensions of the CNC mill bed. The following section will show how the assembled depth
and spans can help bring the system at its weakest points up to a more reasonable live load
capacity.
7.2 Designing with Distributed Loads
7.2.2 Findinga Relationship
Analysis of the data acquired from the load tests will be used here to offer basic
guidelines for designing homes of the friction-fit system. It is important to first note that the
following information should not be taken as the final word on the structural performance of a
building. Rather, the analysis is intended to contribute load data and systematic observations to
future, comprehensive structural queries. Furthermore, the research here focused primarily on the
local behavior of two structural connections in the system, and can only be cited as such. There
remains to be completed a larger, global behavior study.
In Section 4.1.1 it was determined that a single standard jack can transmit about I Kip of
flange force. Section 6.2 found that the stud tab can transmit about 5 Kips of flange force. These
two values are taken as the limiting flange force where bending moment is greatest for a beam
under a distributed load. The equation for the flange force couple (1) and the equation for
maximum bending moment for a simply supported beam under a linear load (2) can be
rearranged to find a relation between the beam depth, the beam span, and a distributed load (3).
This relationship is derived below.
F=
Mmax
where F = flange force, d = beam depth
(1)
When (1)is rearranged: Mma = F * d
Mma
=
(OL
2
; where w = linearload
F* d
OLa 2
l
'
, L = span, ft
(2)
(3)
75
The depth used in equation (3) is measured between the centerlines of the sheathing
panels, not the full assembled beam depth (Fig 7.2). In the plots where the assembled depth is set
as the design parameter, it is first reduced by three-quarters of an inch and converted to feet.
Similarly, when the minimum design depth is the product of the calculations, it is converted to
inches and increased by three-quarters of an inch to give the minimum assembled depth.
Assembled
Depth, in
d
D
Design
Depth, in
Figure 7.2 Assembled Depth versus Design Depth
The linear load, o, in equation (3) is equivalent to the distributed load times the tributary
width, w, which is one and half feet. Therefore, equation (3) can be re-written in terms of the
distributed load, noted as K2 (4). Equation (4) is the final relationship used to produce the graphs
in this section.
Fd= 8-
-
8
(4)
For each flange condition, tab and jack, equation (4) can be used to determine the
maximum load capacity when the span and depth are given. Similarly, the maximum span and
minimum assembled depth can be prescribed with a given design load. When these relationships
are plotted, the various flange conditions can be compared and analyzed for their suitability as a
structural connection. In addition to the tab and jack flange conditions, the graphs include a plot
for a double jack scheme to illustrate the effect this simple design change would have on the load
capacity.
Each of the graphs to follow highlights the region of parameters which are typically
found in contemporary residential design. For instance, the assembled depth of the floor and wall
in the house used for study is eight inches and ten inches, respectively. This is also typical of
homes built in conventional, "stick built" construction. Floor joists and beams of similar depths,
when spaced according to residential building codes, are expected to safely span around 15 feet
76
with 40 pounds per square foot occupancy load capacity. In fact, 40 pounds per square foot is the
typical minimum occupancy load required for single family homes. Wall and floor depths
exceeding 12 inches are uncommon for single family residential construction, which is reflected
in the graphs. Though dependent on many topographic and safety factors, typical wind load
demand for residential construction is estimated between 20 psf and 50 psf (ASCE, 2010). This
region is highlighted in the graphs which plot allowable design loads. The given design loads and
allowable design loads in the following charts include a safety factor of two. The full tables of
data and accompanying calculations, as well as more charts, can be found in Appendix D.
One final note to make regarding the design charts is that when the floor load capacity is
being considered, it includes the load due to self-weight. The dead load of the floor, which is also
carried through bending, is calculated by finding the volume of material in a 18 inch by 12 inch
section of the floor. That volume is then multiplied by the plywood density to find the weight of
the material. Finally, when divided by the floor area taken, the dead load comes out to be seven
pounds per square foot (see steps below). Therefore, when the graphs are being referenced to
find the occupancy load capacity of the floor, the allowable load must be reduced by 7 pounds
per square foot.
Weight = Area * thickness * p = (695in2 )(0.75in) (34
=
(521 int) (3
(0.3 ft3 ) (34t) = 10 lb
Dead Load
=
weight
floor area
10 lb
(1.5 ft)(1ft)
7
7.2.2 Given Span
Suppose an architect would like to design a house of the friction-fit system which spans
15 feet and has ten feet tall walls. Chart 7.1 can be used to determine at which assembled depth
the floor and wall can carry practical occupancy and wind loads.
77
=
Set Span
100
.--- Tab/Continuous
10 ft
_hPathing
90
-
80
2 Jacks
Jack
-
70
is
-01-0--
60
10 ft.
40
4
10 ft.
15 ft.
20
0
6
7
8
9
10
11
12
Anablod Dapth, in.
Chart 7.1 Distributed Load Capacity of system with a given span and depth
The chart shows that the ten foot tall walls, when provided two jacks per one and half
foot of width, can carry a wind load of 20 pounds per square foot for a wall six inches deep.
Many factors and classifications are incorporated into the wind pressure calculation for
buildings, so it is impossible without information on the location of the building to determine
what basic wind speed this load would correspond to. However, this is a typical lower bound for
low-rise, residential buildings. Furthermore, according to a survey of building codes, industry
standards, etc., wood stud walls of 2x6 studs spaced 24 inches on center are used to reach heights
up to about 20 feet (Allen & lano 1995, 51). In the design case of the friction-fit system, the
studs are spaced at most 18 inches on center and are only 10 feet tall with the same depth. Chart
7.1 also shows that by increasing the depth, the 10 foot tall wall approaches the upper bound of
typical residential wind loads. However, this is dependent on the use of a double jack scheme.
Using a single jack, the 10 foot wall would need to be over 10 inches deep to support a low
conservative 20 pounds per square foot of wind load.
According to Chart 7.1, a 15 foot floor span is impossible, even with a double jack
scheme. While it shows that the tabs and continuous sheathing can support a full 50 pounds per
78
square foot gravity load (7 psf. dead load and 40+ psf. occupancy load) with a span of 15 feet
and a ten inch depth, the sheathing layout clearly does not allow this case to be realistic. The
discontinuity of the sheathing panels requires jacks at several locations along the span of the
floor, prompting the conservative approach of reducing the capacity of the system to that of the
jack condition. Therefore, with two jacks, the floor span must be reduced to 10 feet and given a
minimum depth of 12 inches.
7.2.3 Given Design Load
+
The following charts consider a situation where the wind load and gravity load (DL
LL) are given at 30 psf. and 50 psf, respectively. The designer then presents the span and wall
height designs. Chart 7.2 allows the designer to select the correct depth for wall height.
Similarly, chart 7.3 allows the designer to select the appropriate depth for the floor span. Chart
7.2 illustrates that wall can reach up to about 13 feet tall while remaining within a reasonable
range of assembled depth using a double jack scheme. However, chart 7.3 shows that the floor
cannot span more than ten feet without exceeding a 12 inch depth.
Wind Load=30psf
30
-
-
2 Jacks
1 Jacky
25
---
---
-
7-----
Chart 7.2 Minimum Required Depth for wind load and span
79
--
-J
Gravity Load=50psf
-
30
2 Jacks,
1 Jack
25
Tab/Sheathing
-
--
-
-
-
-
-
-
-
-
-
15
10
C
8
10
12
16
14
$paN,
18
20
ft
Chart 7.3 Minimum Required Depth for gravity load and span
Each of the preceding charts reveals that the friction-fit system, when given continuous
sheathing panels, actually has sufficient strength to support the typical wind and occupancy loads
of dominant, conventional wood construction even with similar spans and depths. This reiterates
the recommendation that sheathing panels be made larger where possible. The charts also
reinforce another recommendation previously made, which is to provide two jacks per stud rather
than just one. Of course, one jack can be used if its capacity for carrying direct tension loads is
increased. Ideally, the jack would be able to support 5.1 Kips, which is the flange capacity of the
sheathing and tab configuration. However, it may not be necessary to exactly match the jack
capacity to the tab/sheathing capacity. This research and analysis has been conservative in that
the stud's capacity for carrying bending through its depth has not been included in the
discontinuous sheathing calculations. It has been ignored because this study focused on the local
behavior of the structural connections. While much light has been shed on the behavior of the
connections, further study is required to understand the global behavior of the system.
80
7.3 Constructability
Ease of on-site construction is noted as one of the advantages to the friction-fit house.
There are no fasteners, adhesives, expensive tools or carpentry experts required to assemble the
kit of parts. The high-quality, precisely cut parts are able to be assembled by any nonprofessional with the use of rubber mallet. While this feature undoubtedly reduces the cost of onsite labor and machinery, the shear force required to fit the parts together is concerning. During
assembly of the specimens for the load tests in chapters 3 and 4, the impact of the mallet on the
plywood parts resulted in damage of some of the pieces. Most of the damage was incurred by the
jacks when they were being inserted into place. Figure 7.3 shows several examples of ruptured
plies in the jack which occurred during assembly.
While the most damage was incurred by the skinny and the small jack because of the
slender necks, even the standard jack and the wider biscuit experienced damage due to
construction. In each of the load tests with damaged specimens, the defects were the cause of
either immediately failure or peeling of the plies. Figure 7.4 demonstrates how the construction
defects contributed to the failure of the specimen.
(a)
(c)
(b)
Figure 7.3 Construction defects due to mallet Impact
81
(d)
(a)
(b)
(c)
(d)
Figure 7.4 Failures due to construction defects
The effectiveness of the jacks and all connections in the house relies on friction between
parts cut with zero tolerance. Getting the parts into place by hand means applying enough force
to first overcome the desired friction. From the above images, it is clear that plywood cannot
always remain intact under such impact. The jacks are especially susceptible to construction
damage because they are last to be added to an already tightly assembled wall or floor. In fact,
one model intended to be part of the load test in Chapter 5 was unable to be built because the
force required to insert the jacks resulted in completely damaged parts. While the simplicity of
construction is admirable, the average person who is expected to assemble the kit of parts has no
means of assuring that the jacks will not be destroyed during construction, nor are they able to
produce replacements for damaged jacks.
Friction during construction also becomes an issue when the length of the jack is
considered. Once any portion of the jack is inserted into place, impact from the mallet at another
point on the jack will cause the inserted portion to attempt to retract (Fig. 7.5). As the jack tries
to slide back out of its position, friction grips the plies which are already inserted, causing them
to potentially delaminate. If the delamination occurs, then the jack loses its ability to behave as a
single element, reducing its load capacity and causing behavior such as in figure 7.4b and 7.4d.
Force of
Mallet
-Withdrawal
7 -- LFriction
Figure 7.5 Potential delamination of plywood as Jacks are inserted into place
82
The concern with the brute force of construction suggests that a more controlled method
of inserting the jacks be developed. Additionally, the issues experienced during assembly further
support the recommendation to reduce the use of the jacks wherever possible, as their function
can be nearly negated through the construction method.
7.4 Chapter Summary
This chapter presented the recommendations and considerations for future iterations of
the friction-fit house which uses tabs and jacks to carry bending moment forces under applied
loads. Analysis of the data and observations from the load tests identifies the sheathing ties as the
governing point in the system. It is also clear that the construction method can negatively impact
the already mediocre performance of the jacks. A construction method which distributes the
force of impact and allows for a more even insertion of the jacks is worth further consideration.
Additionally, if the jacks are redesigned to improve in-plane shear capacity and reliability of
their behavior, as well as provided in pairs, there is the possibility that they can perform at the
same level as the rest of the system. On the other hand, the analysis was able to provide a first
approximation of the load capacity of the tabs and sheathing, proving that their composite
structural performance is on par with contemporary wood frame construction under typical
distributed loads.
83
84
Chapter 8. Conclusions
This final chapter summarizes the findings of the load tests performed on the structural
connections in the plywood friction-fit home design yourHouse. The purpose of these tests was
to investigate the performance of integral attachments under an applied load and evaluate their
effectiveness in transmitting forces throughout the assembly. Motivation for this thesis project
comes from the lack of study into the load capacity of the proposed system, which is crucial for
its implementations as an inhabitable structure.
8.1 Summary of Contributions
This thesis was conducted with the goal of completing a specific set of tasks which can
be contributed to future structural analysis investigations. These goals reiterated here along with
their solutions.
i. Characterizethe local behavior of the structuralconnections
Chapter 4 and 6 presented test results which revealed the behavior of the sheathing ties
and stud tabs under an applied load. The jacks function as tension ties between panels where
sheathing is discontinuous. It was shown that the geometry of the jack significantly affects its
performance with regards to load capacity and stiffness. The primary observed failure mode for
each jack design was in-plane shear, and should thus be designed to maximize this parameter.
Tabs which connect the sheathing panels to the bilateral stud frame primarily transmit flange
force through compression as a means of carrying bending moment. However, the tests showed
that there is a distribution of flange force amongst the tabs and the continuous sheathing panels,
resulting in a soft failure.
2.
Identify the governingfailure mechanism and its associatedload capacity
The test data was used to calculate the maximum bending moment which could be
supported due to a distributed load. It was shown that a single standard jack can only provide
1/5' of the load capacity of the stud tab and continuous sheathing condition. Once the jack fails,
the depth of the wall stud will be responsible for carrying tension forces. For the current wall
height and depth, the standard jack design can only transmit flange force for a bending moment
resulting from 8 pounds per square foot of distributed load (includes a safety factor of 2). For the
current floor span and depth, the two jacks which are provided per stud can still only carry
85
bending moment from a maximum gravity load of 18 pounds per square foot. These loads are far
below residential load demands.
s. Providerecommendationsfor component design and configurationto improve structural
performance where needed
The recommendations for component design and configuration are heavily focused on
sheathing tie. As a structural member in their current form, they have proven to be inadequate for
meeting minimum load demands. Their continued use requires that they be redesigned to match
the capacity of a continuous sheathing element. This can be achieved by increasing their in-plane
shear capacity and providing two per stud. However, efforts should also be made to reduce their
need by thoughtful placement of larger sheathing panels.
4.
Generate aidesfor designing with wind andgravity loads
Equilibrium equations were used to apply the test data to full scale design conditions. The
charts and tables in Chapter 7 and Appendix D allow any designer to include the friction-fit
attachments' structural performance in the early design phase. As a quick example of a design
which can meet minimum wind and gravity load demands using the current jack design and
layout (1 per wall stud and 2 per floor stud) and the current assembled depth, the charts reveal
the following information:
* An 8 inch deep wall with a 20 psf wind loadcapacity can be at most 9feet tall
-
A 10 inch deepfloor with a 7 psf dead load and 40 psf occupancy load can span at most
9feet
The same charts can be used to show that the current 15 feet floor span and 10 inch depth
can only support an 18 psf. gravity load, which includes the load due to self-weight. In other
words, the current floor design provides 11 psf. occupancy load capacity, which can
accommodate about 22 people. This number, however, considers a house with no furniture,
appliances, or fixtures. Actual load demand in residential construction will quickly surpass this
load capacity. Thus, the tables assist the designer in considering final load demands in the early
design phase decision-making.
86
8.2 Future Research
This thesis intentionally chose a narrowly focused research question, so as to provide a
thorough discussion and offer clear, useful data. Because this research project is one of the first
documents to investigate the structural performance of full-scale plywood friction-fit
construction, it was important to the author to concentrate on local behavior as a means of
approximating more global behavior. Therefore, the research presented in this thesis leads to
several options for future research endeavors.
The recommendations made regarding the jack design call for a second round of direct
tension tests to evaluate the claims made. This study would ideally include a larger population of
test specimens, reducing the potential for anomalies to skew the performance expectations.
Another useful research aim could be to perform load tests on jacks designed in different
materials, such as plastics and isotropic wood products. These or design studies would be
beneficial in improving the performance of the jacks, as they are currently a weak link in the
system.
This research was limited in scale by the load cell machinery available. With larger
machinery, this local behavior study could be carried over to a global behavior study to further
examine the performance of assembled parts. Such a project would be helpful to gauge the
accuracy of the span tables delivered in this thesis.
Furthermore, the test results of this thesis could be used as input data into a computation
tool which evaluates the structural performance of the 3D design as planar parts are added and
subtracted. This would allow typical load demands to be imposed as a constraint on the final 3D
form.
As in CNC-milled furniture design, contouring of the studs can be studied as a means for
conserving material and designing for specific load conditions. Trading ergonomics for wind and
gravity load, sculpting of the friction-fit studs can lead to both intriguing and structurally
efficient building profiles. The computation software StructureFIT (Mueller, 2013) exists to
integrate structural needs with design and material conservation possibilities, and would be an
ideal tool with which to carry out this possible research path.
Finally, the durability of the friction between parts could be another possible research
direction. Over time, and under repeated loading, the tight fit and the coefficient of friction
between the plywood surfaces may degrade. The fatigue life, as defined by ASTM (2013), of the
87
friction-fit parts can be determined through a cyclical loading scenario. A study of this sort
would contribute valuable information on the life expectancy of a friction-fit planar structure.
8.3 Closing Remarks
The possibilities for producing low-cost, rapid, durable housing through digital
fabrication make the proposed friction-fit system an innovative and altruistic endeavor.
Therefore, it is the author's pleasure and honor to conduct research that can potentially assist in
the full implementation of the friction-fit housing system. Without guarantees of occupant safety,
it would be irresponsible to present these buildings as inhabitable. It was the intention of this
thesis to begin the necessary conversation about the structural performance of a novel
construction method. Though this project attempted to provide the most accurate and useful
analysis possible, all data analysis and design aides are meant as first approximations, and thus
should not be used as a guarantee of performance without final consultation from a professional
engineer. Finally, it is the author's hope that this conversation and investigation will continue,
working out imperfections and improving the performance of planar structure houses so that they
will reach the implementation phase.
88
References
ASTM Standard E1823, 2013. "Standard Terminology Relating to Fatigue and Fracture Testing,"
ASTM International, West Conshohocken, PA, 2013, DOI: 10.1520/E1823-13,
www.astm.org
Building Performance Assessment Team (BPAT). Oklahoma and Kansas Midwest Tornadoes of
May 3, 1999: Observations, Recommendations, and Technical Guidance. Federal
Emergency Management Agency, 1999.
Davis, Noel R. (2006). Design ofa CNC Routed Sheet Good Chair(Undergraduate Thesis).
Retrieved from DSpace@MIT database. (UMI No. 872270731).
Digital Design and Fabrication Group. yourHouse. MIT Design Lab, n.d. Web. 27 Feb. 2014.
Eentileen. Web. 16 May 2014.
FacitHomes. Facit Homes Limited. 2014. Web. 16 May 2014.
France, Anna Kaziunas. "Open-Source Furniture." Make:. Maker Media, Inc., 18 March 2014.
Web. I May 2014.
Furlong, Cosme. "Stress Analysis." Worcester Polytechnic Institute. Worcester, MA. 07 Feb
2012. Web. 25 April 2014. <http://users.wpi.edu/~cfurlong/es2502/lect15/Lecti 5.pdf>
Hildebrand, Kristian, Bernd Bickel, and Marc Alexa. "crdbrd: Shape fabrication by sliding
planar slices." Computer Graphics Forum. Vol. 31. No. 2pt3. Blackwell Publishing Ltd,
2012.
"LaN @ MoMA 'HOME DELIVERY'." Photograph. LaN/Live Architecture Network. Web. 15
May 2014.
Larsen, Knut Einar, and Christoph Schindler. "From Concept to Reality: Digital Systems in
Architectural Design and Fabrication." InternationalJournalofArchitectural
Computing 6.4 (2008): 397-413. Web. 1 May 2014.
Minimum Design Loads for Buildings and Other Structures. Reston, VA: American Society of
Civil Engineers, Structural Engineering Institute, c2010.
Mueller, Caitlin. InteractiveEvolutionary Framework. Caitlin Mueller, 2013. Web. 25 Feb.
2014.
"Plywood." MatWeb MaterialPropertyData. MatWeb, LLC, n.d. Web. 20 Feb. 2014
Postell, Jim. FurnitureDesign (2nd ed.). Somerset, NJ: Wiley, 2012. Web. 1 May 2014.
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Prevatt, David 0. et al. Joplin, Missouri, Tornado of May 22, 2011: Structural Damage Survey
and Case for Tornado-Resilient Building Codes. Reston, VA: American Society of Civil
Engineers, 2013.
Sass, Lawrence. "Home Delivery: Fabricating the Modern Dwelling." MoMA. 10 July 2008.
Web. 27 Feb. 2014.
Sass, Lawrence. Personal Interview. 2 March 2014.
Sass, Lawrence. "Synthesis of design production with integrated digital fabrication." Automation
in Construction 16.3 (2007): 298-3 10. Web. 27 Feb. 2014.
Saul, Greg, et al. "SketchChair: an all-in-one chair design system for end users." Proceedingsof
the fifth internationalconference on Tangible, embedded, and embodied interaction.
ACM, 2011.
Schwartzburg, Yuliy, and Mark Pauly. "Design and optimization of orthogonally intersecting
planar surfaces." ComputationalDesign Modelling. Springer Berlin Heidelberg, 2012.
191-199. Web. 27 Feb. 2014
Schwartzburg, Yuliy, and Mark Pauly. "Fabrication-aware Design with Intersecting Planar
Pieces." Computer GraphicsForum. Vol. 32. No. 2.3. Blackwell Publishing Ltd, 2013.
WikiHouse. Web. 16 May 2014.
90
Appendix A. Simpson Strong Tie Test and Results (reproduced)
Product Testing:
Metal Plate Connectors
Mali Wagner
4.491 - Independent Study
January 2014
Contents...................................pg#
Introduction ................................
92
Test Setup...............................
93
Test Results.............................96
Conclusion..................................100
91
Introduction
From the analysis of failure modes for different hurricane strap geometries and features, I hope
to learn about the behavior of the roof-to-wall intersection when in uplift and the metal connector
plates when in tension to identify specific vulnerabilities which to focus research efforts on. The
purpose of this project is to provide data for comparison as part of the larger research
project/thesis of developing a technology to reinforce homes against total failure from EF3
tornadoes using digital fabrication. Post-disaster surveys performed by the Federal Emergency
Management Agency and by the American Society of Civil Engineers, as well as several
controlled experiments performed in wind tunnels, indicate that the integrity of the roof- to-top
wall connection is critical in maintaining the home's stability'. Providing a continuous load path
in home construction is crucial to preventing structural failure, such as a roof truss separating
from the top of the wall from uplift forces. In light of this information, the current phase of the
thesis research project aims to evaluate current products in the market for reinforcement at this
intersection in traditional home construction. Hurricane straps in particular have been
recommended as an effective solution to resisting uplift loads on the roof of a home when in the
path of a tornado. For this study, I have selected Simpson Strong-Ties products as a
comprehensive representation of hurricane strap design.
The Simpson Strong-Tie@ Company provides a range of product designs to accommodate
regional variety in home construction. The two product categories I chose to analyze are rafterto-double top plate connectors and rafter-to-stud connectors. While the rafter-to-stud connector
may provide a more direct load path across the rafter, top plate, and stud components, not all
wood frame construction line up the wall stud to the roof truss". For this reason I chose two
models from each category. The HIOA and the MTS12 models connect the rafter to the top plate,
while the HIOS and the LGT2 models tie together the rafter, top plate, and wall stud (Fig. la-i b).
Specifications for each model are listed in Table 1.
~4for latera
(a)
b)
(c)
Figure 1. (a) HGA (b) MTS12 (c) H1OA (d) LGT2
(images from Simpson Strong-Tie website www.stronftae.com)
92
(d)
Table 1. Product Specifications
Model
Gauge
Uplift Capacity, lbs
(Design Load)
HlOA
MTS12
HiOS
LGT2
18
16
18
14
1015
860
870
1785
Fasteners to
Fasteners to
Fasteners to Wall
Rafter
9 - 10dx
Top Plate
9 - l0dx2
Stud
2
7 - 10dx 2
8 -8dxV 2
16 - 16d Sinkers
7 - l0dxlV2
8 -8dx12
Optional
N/A
N/A
8 -8d
16 - 16d Sinkers
Test Setuo
In order to test the hurricane straps in uplift conditions, an appropriate test apparatus had to be
developed. Fortunately, the manufacturer made available test reports on each of the four models.
These reports include schematics and photographs of the test setup used in the product
certification process. The International Code Council Evaluation Service was the certifying
agency and also provides publications on the accepted criteria for testing of metal connector
plates. The hurricane straps fall under the category ofjoists hangers and similar devices, and it is
the Acceptance Criteria for Joist Hangers and Similar Devices (AC 13) publication which the
manufacturer adhered to in their product testing. "'While considering the machinery available for
this project, the test apparatus attempted to be as close to the manufacturer's plan as possible in
an attempt to achieve similar results and understand the process of failure rather than simply the
final failure state. Furthermore, each test report included data from 6 or 12 test specimens (2 per
load test), while this test will only collect results on 2 specimens of each model.
The frames which the hurricane straps are attached to are approximations of the rafter-top platewall stud intersection (Fig. 2). While the rafter
:-Rafter
is generally inclined, the test frame assumes a
non-inclined rafter attached to the top plate. The
frames are constructed of 2" x 4" studs of
Prespruce pine fir. However, the top plate
fabricated
components are sections of 2"x6" studs of
Roof Truss
spruce pine fir. Though roof trusses are strictly
manufactured from 2"x4" wood sections, 2"x6"
stud construction is a common practice in the
United States Midwest, where tornadoes are
most prevalent." The test frames attempt to be
representative of this regional trend, yet must
also consider the loading machine dimensions.
Therefore, the wall stud components of the test
Double Top
Plate
*Wall
Figure 2. Portion of Roof Truss and Wall Intersection
frame are 2"x4" sections, enabling the machine
head to fit between them.
Figures 3 through 7 illustrate the test apparatus and test setup.
93
Stud
23
247
18"
__
U
LNj
Figure 3. Test Frame for Models H10A and MTS12. Elevation (left) and Plan (right).
[1
23
____
12"
____
11
24"
L
Figure 4. Test Frame for Model H10S. Elevation (left) and Plan (right).
23"
12"
-F
24
[~J
Figure 5. Test Frame for Model LGT2. Elevation (left) and Plan (right).
94
1
4 Figure 6. Full View of Loading
Machine, Illustrating Frame Orientation.
Machine Head Lowered at 0.100in/min
After Contact is Made with Test
Apparatus
'
Figure 7. Close-up of Steel Box
in Place Between Machine Head and
Rafter Component
The frames are approximations of the roof to top wall intersection, inverted. This allows a force
to be applied onto the rafter component from above, creating a concentrated "uplift" force. The
hurricane straps are thereby able to be tested in tension. Two hurricane straps are attached to
each test frame, one at each end of the rafter component, as shown in Figure 7. Additionally, the
entire frame is supported on two 5"x5" wood blocks to elevate the frame above the machine bed,
allowing the rafter component room for displacement.
95
Test Results
For each test, the ultimate failure was observed when the wood failed to carry the applied load.
This is in contradiction to the observed failure mode reported by the manufacturer, where the
metal plates split or the fasteners were dislodged from the wood. However, prior to the failure of
the wood, minor deformations in the hurricane straps were observed. Splitting of the wood was
also observed at fastener locations. While these are general observations made for all of the
specimens, each model and test frame had unique behavior leading up to failure.
HOA
1
2.
The HIOA model ties together the rafter and the double
top plate using 1 Odxl %2" nails. Ultimate failure occurred
at 4,257 pounds. Just prior to the rafter splitting (seen in
images 1 and 3) the top plate began to split where a nail
was in place. I was unable to capture an image of the gap
before the rafter violently split. Image 2 instead shows a
faint line circled in red where the top plate split was
observed. Had the rafter not split, it is my assumption
that the nail would have pulled out of the wood at this
point. The existence of a knot at the rafter mid-span no
doubt contributed to the significant beam split.
Furthermore, the decision to approximate the rafter as a
perpendicular element resulted in fasteners being much
closer to the edge of the wood than they would be in an
inclined rafter. This resulted in the wood splitting in this
3.
manner.
MTS12
The MTS12 model ties together the rafter and double top plate using lOdx1/ 2" nails. Ultimate
failure occurred at 3,580 pounds. The strap also folds over the rafter and under the top plate to
96
take full advantage of the steel's strength. However, it is this same feature that gave way to the
first noticeable material deformation: the metal strap dug into the top of the rafter (circled in
image 1). This not only compresses and weakens the wood in the rafter, but also allows for
displacement of the rafter. The machine head continued to lower, in part to compression of the
wood where load was applied, but also because of the digging of the metal strap. There was also
a significant gap between the rafter and the top plate due to stretching and bending of the metal
strap at the 90 degree bend. The bend allows for the strap to wrap around the two components,
yet also becomes a point of concentrated deformation. However, if the load ceased to be applied
at this time, the intersection would still be salvageable and a new strap could be installed. The
ultimate failure mode was splitting of the rafter around a knot in the wood seen in image 2.
Nearing the ultimate failure load, the fasteners began to split the wood, particularly in the rafter
component. Had the knot not been present, it is possible that the splitting at the end of the wood
beam would lead to the nails being pulled out.
1.
2.
The HIOS model provides a continuous load path across the rafter, double top plate, and wall
stud. Ultimate failure occurred at 3,523 pounds. Like its counterpart, the HIOA, this model
sandwiches the rafter, but extends approximately 5 inches down the outer face of the wall stud. It
was expected that this model would be better performing because of the added layer of resistance
to uplift on the wall stud material. However, a knot near the edge of the rafter caused the wood to
fail at about 750 pounds less than the H1OA ultimate load (image 3). Some stretching of the
metal strap may be responsible for the gap that developed between the rafter and the top plate
depicted in image 1. Splitting also developed near the bottom face of the top plate, seen circled
in image 2. This leads me to believe that the wall stud component in this test was not a key
performer. Seeing as the wall stud was not anchored as it would be in the actual home frame, it
seems clear now that it would not behave as a third line of defense against structural failure. I
97
believe that it was the location of the knot that caused this test to fail sooner than the previous
examples had.
1.
3.
2.
LGT2
The LGT2 model bridges across the rafter to the wall stud using 16d sinkers. This model is
designed for use with a double roof truss and double wall stud. The thicker steel, doubled wood
material, and the thicker coated nails make this model carry the most load. Ultimate failure
occurred at 8,147 pounds. Again, the final failure mode was the rafter splitting. However,
because the applied load was distributed over two components, the achieved load was nearly
doubled. Additionally, clamps were added across the top of the wall stud components, shown in
image 1. This stiffened the frame and allowed the wall stud members to carry load rather than
simply pivoting as load was applied. Image 2 depicts the specimen before load was applied.
Image 3 depicts the same specimen just prior to failure. A comparison between the two images
clearly shows that the metal strap experienced stretching along the inner curved edges (red
arrow). Furthermore, the images reveal that stretching also occurred in the region bridging across
the double top plate. No fasteners were present in the top plate, as the manufacturer asserts that
fasteners here would not contribute to uplift resistance, only lateral load resistance. Therefore,
the metal is freer to deform in this region, as it surely did. The same red line drawn in image 2 is
much lower in image 3. These two observed deformations can account for the rafter
displacement seen in image 3.
98
1.
2.
3.
Table 2 compares the observed failure loads with each model's published design load and
manufacturer's test results.
Table 2. Comparison of Test Results to Manufacturer's Results
Model
H1OA
MTS12
HIOS
LGT2
'Design
Load, lbs
1015
860
870
1785
Simpson Strong-Tie
Avg. Ultimate
'Average 1/8"
Load, lbs
Displ. Load, lbs
7044
5900
6070
12683
5458
3673
3608
6003
Lab Test
Ultimate
Load, lbs
4257
3580
3523
8147
1/8" Displ.
Load, lbs
3% Ult.
-1500
2650
3600
60
60
58
64
Load
Displ.
Load
4%
-40
73
60
1. Design Loads are taken from www.strongtie.com . The number represents the lowest ultimate failure load
observed in testing divided by 2 and then divided by a safety factor of 3. There are some variations that are not
accounted for.
2. The manufacturer reports recorded deflection data. The test machine used for this project produced data on the
machine head displacement, not material deflection. The 1/8" displacement load in the test data reflects the load at
which there was a 1/8" gap between the rafter and top plate components.
3. % Ultimate Load = 100 * (Lab Test Ultimate Load, lbs) / (SST Average Ultimate Load, lbs)
4. % Displacement Load =100 * (Lab Test 1/8" Displacement Load, Ibs) / (SST Average 1/8" Displacement Load,
lbs)
99
Conclusion
Failure of the wood occurred before any hurricane strap failure was observed in each case. This
was the case for two very clear reasons. The first reason was imperfections in the wood, such as
the knots in the rafters. During construction of these wood frames, I was concerned about not
placing fasteners in any knots, yet neglected to notice that knots were present at mid-span in 3 of
the 4 frames. In real-life uplift conditions, the load is not nearly as concentrated as it was in our
tests. The concentrated load overwhelmed the wood and amplified the wood's weak points. Test
reports from the manufacturer indicate that failure was achieved in the metal plates, not in the
wood. Though the listed wood species are the same as the one used in this test, it is very likely
that the wood selection process was much more rigorous.
The second reason that failure occurred in the wood before any significant deformations were
observable in the metal straps is because of the placement of the straps. Because the test attempts
to recreate the wood frame geometry, where load is applied relative to the placement of the
straps becomes a significant parameter. The overhang of a roof adds about 25 psf to the uplift
force for wind speeds of 135 mph. The largest concentration of force is under the overhang. The
manufacturer requires installation of the hurricane straps on the outer surface of the wall, directly
under the overhang. Therefore, the metal straps should have been placed on the inner side of the
top plate, closer to the machine head. This would have required the metal straps to carry the load
more directly. Moreover, by placing the metal straps on the interior of the wood frame, the span
of the rafter member would be decreased by eleven inches. Decreasing the span from eighteen
inches to 7 inches would decrease the bending moment at mid-span by a factor of approximately
4, thus decreasing the stress for the same P by a factor of 4 (see justification below).
P
a= M/S = (PL/2)/S = PL/2S
S is constant section modulus
For L/2 (approximate change in span)
L
0=
P/2
M/S = (PL/8)/S = PL/8s
P/2
While a better wood sample or moving the metal straps closer to the applied load would provide
results more representative of the manufacturer's tests and more observable deformations in the
metal straps, the results from this test prove that the hurricane straps are more than sufficient for
carrying over 2000 pounds when loaded gradually. The metal straps' behavior when an impact of
load of over 2000 pounds is yet to be determined, which would be more representative of an EF3
tornado load (the load increases much more rapidly but only last for several minutes). These
considerations lead to at least 3 options for further development of the project.
100
Building Performance Assessment Team (BPAT). Oklahoma and Kansas Midwest Tornadoes of May 3, 1999:
Observations, Recommendations, and Technical Guidance. Federal Emergency Management Agency, 1999.
3
http://www.fema.gov/media-library-data/20130726-1443-20490-7720/fema 42.pdf. ; Haan, F. L., Balaramudu,
Vasanth K., Sarkar, P. P. "Tornado-Induced Wind Loads on a Low-Rise Building." Journal of Structural Engineering,
ASCE 2010, 106-116. DOI: 10.1061/(ASCE)ST.1943-541X.0000093. ; Kumar, N., Dayal, V., Sarkar, P. "Failure of
Wood-Framed Low-Rise Buildings Under Tornado Wind Loads." Engineering Structures 39 (2012), 79-88. DOI:
10.1016/j.engstruct.2012.02.011.; Mitigation Assessment Team (MAT). Tornado Outbreak of 2011: Alabama,
Georgia, Mississippi, Tennessee, and Missouri. Federal Emergency Management Agency, 2013, 4-1 through 4-38.
http://www.fema.gov/media-library-data/20130726-1827-25045-9156/tornado mat chapter4 508.pdf. ; Prevatt,
David 0. et al. Joplin, Missouri, Tornado of May 22, 2011: Structural Damage Survey and Case for Tornado-Resilient
Building Codes. Reston, VA: American Society of Civil Engineers, 2013.
I I spoke on the telephone with Shane Vilasineekul, Engineering Manager at Simpson Strong-Tie about the use of
rafter to stud versus rafter to top plate model. Also the reports that are mentioned in this document refer to four
test reports that he emailed to me as protected documents, not allowed to be shared.
I This publication is on order with the-MIT library. The document is inaccessible for reference without purchase.
'v Discussion with Chris Dewart in the MIT architecture wood shop on home construction.
101
102
Appendix B. Complete Sheathing Tie Test Results
Standard Jack
Test 1
2500
2000
:
1500
1
M 1000
500
0
0.00
0.05
0.10
0.15
0.20
0.25
Displacement, in.
The specimen had a brittle failure in both shear and tension. A gap
began to develop between the plywood panels before the tension
failure was noticed. This suggests a shear failure in the plies oriented
parallel to the applied force, which contributed to a tension failure in
adjacent, perpendicularly oriented plies. When one mode of failure
occurs and displacement occurs, the lamination between plies causes
the displaced plies to pull on adjacent layers.
Test 2
2500
2000
1500
1000
lb.
500
0
0.00
0.05
0.10
0.15
0.20
Displacement, in.
103
0.25
The plies with grain parallel to the applied force experienced
shear failure. As the fibers slid out of place, the lamination pulled
the adjacent layers with it. The layers with grain perpendicular to
the applied force bore on the surrounding panel, causing plies to
split. A soft failure is indicated on the load-displacement graph
because of the bearing failure.
Test 3
2500
2000
1500
1000
50
442 1bs
0
0.00
0.05
0.10
0.15
0.20
0.25
Displacement, in.
This specimen experienced splitting and peeling in layers that
were not flush with the surrounding panel. These layers were
not able to resist displacement through bearing. Like the other
tests, lamination caused displaced layers to pull on adjacent
plies, leading to subsequent tension and shear failures. The
construction defects caused this specimen to drastically
underperform.
104
Biscuit
Test 1
2500
2000
1249 lbs
1500
I e00
1000
500
0
0 .00
0.05
0.10
0.15
0.20
0.25
Displacement, in.
In-plane shear occurred along the inner plies. A tension
failure followed along the neck of the specimen. The
smoother transition at the bulb on this model allows for
more bearing behavior to occur. There is a second peak in
the graph as a result of this.
Test 2
2500
.215
lbs
2000
e 1500
0
1000
500
0
0 .00
0.05
0.10
0.15
0.20
Displacement, in.
105
0.25
The geometry of this model allows more bearing action to occur
between the specimen and the panel. The graph shows a steady
softening because of the slippage that occurs. In the panel, plies
oriented perpendicular to the applied force were crushed by the
biscuit. Plies oriented parallel to the applied force experienced
shear failure and were pushed out of the sheet.
2500
-
Test 3
2000
1500
1389 lbs
-
:e 1000
1000
0
-
500
0.00
0.05
0.10
0.15
0.20
0.25
Displacement, in.
In the third test, the bulb of the biscuit experienced
compression. As the surrounding panel crushed the bulb,
the outer plies were peeled out of plane. Softening in the
graph corresponds to the crushing stage of failure. The
sharp drop in the graph relates to the separation of the
plywood layers, when lamination failed.
106
Curved Jack
Test 1
2000
-
-2 1500
-
2500
784 lbs
M
1000
0
-j
0
-
500
2
0.00
,
0.05
0.10
0.15
0
0
0.20
0.25
Displacement, in.
The top portion of this specimen was not completely flush with
the panel. Because of this, those plies were quick to separate
from the lower layers. Lower layers experienced a clean shear
failure and subsequent tension failure.
Test 2
2000
-
2500
:0 1500
*0
S1000
bID
-
500
0
0.00
0.05
0.10
0.15
0.20
0.25
Displacement, in.
107
Compression between the joint and sheet was noticed
first, quickly followed by a shear failure in the joint.
Tension failure occurred only after the machine was
allowed to keep running post shear failure. The smooth
transitions allow the perpendicularly oriented plies to
crush the sheet before splitting.
Test 3
2500
2000
M1 1000
0
-
1500
50 0
0
0.00
0.05
0.10
0.15
0.25
0.20
Displacement, in.
The curved jack took on load primarily through
compression. This is reflected in the mostly curved incline
in the graph. Shear failure is responsible for the sharp drop
in load noticed on the graph. No tension failure was
observed.
108
Small Jack
Test 1
2500
2000
1500
984 lbs
0
,
MU1000
500
0.00
0.05
0.10
0.15
0.20
0.25
Displacement, in.
A shear failure occurred, causing adjacent plies to also
displace. The perpendicularly oriented plies were able to
bear on the surrounding panel before being split in tension
at two places.
-
2000
:9 1500
-
2500
-
Test 2
-
1000
500
0.00
0.05
0.10
0.15
0.20
0.25
Displacement, in.
109
Construction defects caused a rapid tension failure to
occur. Shearing in the joint ensued, followed by a
shearing of the panel's inner plies. These inner plies were
pulled past the edge of the sheet. This type of behavior
indicates intact plies within the joint, which bear on the
panel's inner plies, causing the shearing behavior.
Test 3
2000
-
2500
1500
100
00.00
0.05
0.10
0.15
0.20
0.25
Displacement, in.
These smaller jacks were more susceptible to construction defects.
Missing top plies, which carry tension, led to a more rapid shear failure
in the joint. However, as seen in the picture at the left, the portion of
the top ply that remained was pulled with the sheared plies and
compressed the surrounding panel. The curved corners allow this
bearing behavior.
110
Skinny Jack
Test 1
0.10
0.15
0.20
0.25
Displacement, in.
The top ply of the joint was split during assembly.
The loss of this load carrying ply caused the other
perpendicularly oriented layers to fail nearly
immediately in tension. All of these plies exhibit a
clear gap across the middle of the neck.
Test 2
2500
2000
U,
.0
1500
(U 1000
a
-J
500
0
819 lbs
0.00
,
.
10
2500
2000
1500
1000
138 lbs
500
0
0 .00
0.05
0.05
0.10
0.15
0.20
Displacement, in.
111
0.25
This second test experienced a similar tension failure
across the middle of the neck. However, bearing
behavior was noticed first, which allowed the jack to
slowly pick up load before the brittle failure.
Test 3
2500
2000
1500
1000-
U22
.9500
0.00
0.05
S
0.10
0.15
0.25
0.20
Displacement, in.
During the test, displacement was proceeding without any
noticeable tension or bearing behavior. The assembly process
damaged the outer, tension carrying plies. Therefore, the only
path for load to be transmitted was through shear. The brittle
failure indicates when the plies gave in shear.
112
Appendix C. Assembled System Test Results
Continuous Stud and Sheathing
Compression of the tabs was
Test 1
6000
noticeable at 2 Kips.
Displacement allowed by
534 lbs
5000
2Kp
2 Kips
3000
bottom sheathing panel to also
,
.-
crushing of the tabs allowed the
Softening at
S4000
split slowly rather than suddenly.
S2000
Compression of the tabs resulted
1000
10.2
0
0.0
in a soft failure.
0.5
1.0
Displacement, in.
1.5
113
Top and bottom panels counter
Test 2
hinge behavior of the stud.
6000
tension in the sheathing and
Softening
at
. 4000
-
Distribution of forces between
4850 lbs
5000
crushing of the tabs allows for a
3000
soft failure rather than a
2000
concentrated, brittle failure in the
1000
sheathing panel.
0.25
0
0
1.5
1
0.5
Displacement, in.
114
Non-Continuous Sheathing
A gap developed between the
Test 1
bottom panels immediately. All
6000
tension carried by stud. Failure
5000
occurred in stud at mid-span.
' 4000
3000
o
2000
Some plies appeared to have
2
7 Ibs
split but beam was still picking
1000
up load perhaps through other
0*
0
0.5
1
Displacement, in.
1.5
115
plies.
The studs split on opposite sides
Test 2
of the middle brace. While the
6000
beams were not able to pick up
5000
any more load, the model was
v 4000
.0
held together by the bridge
10-3000
q 2000
-
1267 lbs
0
1
0.5
Displacement, in.
through friction.
1000
1.5
116
Non-Continuous Stud
The joints in the studs did not
Test 1
6000
experience any observable stress.
bs
Even with the splice, the studs
acted as a continuous element.
3000
Crushing of the tabs and splitting
a 20001000
0
of the bottom panel occurred
simultaneously, allowing for a
0.
0
0.5
1
Displacement, in.
1.5
117
soft, flexible system.
118
Appendix D. Span Tables and Charts
Equations
F = Flange Force
d = Design Depth
12 = DistributedLoad
w = Tributary Width
L = Span(or Height)
w = 1.5 feet
Fsingle Jack
= 960 lbs
FDouble Jack =
1920 lbs
FTab/sheathing =
5100 lbs
Safety Factorof 2 included in all DistributedLoads
1ft
Depthdesign(ft) = (Depthassembled - 0.75 in) - 12 in
F-d
f2wL 2
8
Chart Legend
Doubleuble
Jack thJack
T-a-b-/She
--
Tab/Sheathing Flange Force
119
Given Span - FindDistributedLoadfor a Range ofAssembled Depths
SetSpan
10ft
15 ft
80
0
V
V50
.0
40
30
20
-
-
-
-
-
-
---
-
-
-
-
-
- - - - - - 77
-
-
-
-
-
-
-
10
- -
n
6
7
8
9
- -
10
- -
- -
-
- -
11
- -
-
ILL
12
Assembled Depth, in.
Single Jack
Span,
ft
Assembled
Depth, in
Design
Depth, ft
Distributed
Load, psf
W/
SF=2
7
27
13
31
15
9
0.5
0.6
0.7
35
18
10
0.8
39
20
11
0.9
44
12
0.9
7
0.5
0.6
0.7
0.8
0.9
0.9
8
--
E
Assembled
Depth, in
Design
Depth,
Distributed
Load, psf
w/
SF=
0.5
0.6
22
7
8
9
10
11
48
24
12
12
6
14
7
16
8
18
9
19 ~
10
21
11
7
8
9
10
11
12
4
4
5
6
6
7
8
3
4
45
5
6
2
2
2
3
3
3
4
.460 5
8
9
10
11
12
Span
ft
25
0.8
0.9
0.9
A;.
7
8
9
10
11
12
120
0.7
0.5
0.6
0.7
0.8
0.9
0.9
Double Jack
Span,
ft
Assembled
Depth, in
Design
Depth, ft
Distributed
Load, psf
W/
SF=2
Span,
ft
Assembled
Depth, in
Design
Depth,
ft
Distributed
Load, psf
W/
SF=2
10
6
0.4
45
22
20
6
0.4
11
6
7
0.5
53
27
7
13
7
8
0.6
62
31
8
15
8
9
0.7
70
35
9
0.5
0.6
0.7
18
9
10
0.8
79
39
10
0.8
20
10
11
0.9
87
44
11
0.9
22
11
12
0.9
96
48
12
0.9
24
12
6
0.4
20
10
6
0.4
7
4
7
0.5
24
12
7
0.5
9
4
8
0.6
27
14
8
0.6
10
5
9
0.7
31
16
9
0.7
11
6
10
0.8
35
18
10
0.8
13
6
7
25
11
0.9
39
19
11
0.9
14
12
0.9
43
21
12
0.9
15
8
Tab/Sheathing
Span,
ft
Assembled
Depth, in
Design
Depth, ft
Distributed
Load, psf
W/
SF=2
Span,
ft
Assembled
Depth, in
Design
Depth,
ft
Distributed
Load, psf
W/
SF=2
10
6
0.4
119
:60
20
6
0.4
30
15
35
18
41
21
15
7
0.5
142
71
7
8
0.6
164
82
8
0.5
0.6
9
0.7
187
94
9
0.7
47
23
26
10
0.8
210
105
10
0.8
52
11
0.9
232
116
11
0.9
58
29
12
0.9
255
128
12
0.9
64
32
6
04
N
6
0.4
7
0.5
63
31
7
0.5
8
0.6
73
37
8
25
10
23
11
0.6
26
13
15
9
0.7
83
42
9
0.7
30
10
0.8
93
47
10
0.8
34
17
11
0.9
103
52
11
0.9
37
19
12
0.9
113
57
12
0.9
41
20
121
Given Assembled Depth - FindDistributedLoadfor a Range of Spans
12 in
10 in
Set Assembled Depth
-8 in
6 in
100
90
80
K \
X\
70 4-
XN44
NN NN4%
60
0
VI
50
40
30
20
-
=
10
----------------------------------------------
14
0
8
10
12
14
----------------------------------------------------
16
20
18
Span, ft
Single Jack
Assembled
Depth, in
Design
Depth, ft
Span,
ft
Distributed
Load, psf
W/
SF=2
10
22
11
12
16
8
14
11
6
16
9
4
18
7
3
20
6
10
Assembled
Depth, in
Design
Depth, ft
Span,
ft
Distributed
Load, psf
W/
SF=2
10
39
20
12
27
14
14
20
10
16
15
8
18
12
6
3
20
10
5
31
15
10
48
24
12
21
11
12
33
17
14
16
8
14
24
12
16
12
6
16
19
9
18
10
5
18
15
7
20
8
4
20
12
6
122
Double Jack
Assembled
Depth, in
Design
Depth, ft
Span,
ft
Distributed
Load, psf
WI
SF=2
6__ 0.48 7035
10
8
0.6
45
Assembled
Depth, in
Design
Depth, ft
Span,
ft
Distributed
Load, psf
W/
SF=2
10
0.8
8
123
62
10
79
39
27
22
12
31
16
12
55
14
23
11
14
40
20
16
18
9
16
31
15
12
18
14
7
18
24
20
11
6
20
20
10
8
97
48
8
150
75
48
12
0.9
10
62
31
10
96
12
43
21
12
67
33
14
32
16
14
49
24
38
19
16
24
12
16
18
19
10
18
30
15
20
15
8
20
24
12
Tab/Sheathing
9 199
_
Assembled
Depth, in
Design
Depth, ft
Span,
ft
Distributed
Load, psf
W/
SF=2
Assembled
Depth, in
Design
Depth, ft
Span,
ft
Distributed
Load, psf
W/
SF=2
6
0.4
8
186
93.
10
0.8
8
328
164
10
119
60
10
210
105
12
83
41
12
146
73
14
61
30
14
107
53
16
46
23
16
82
41
18
37
18
18
65
32
20
52
26
__0.6
15
20
30
8
257
Z8
10
164
82
10
255
128
12
114
57
12
177
89
14
84
42
14
130
65
16
64
32
16
100
50
39
32
12
3
0.9
18
51
25
18
79
20
41
21
20
64
123
i
T40
Given Design Load - Find Minimum Assembled Depthfor a Range ofSpans
50 psf
Given Design Load
I
I
psf
30 psf
20 psf
-
30
I
I
/
I
I
25
I
I
I
I
I
1
/
I
-
-
I
-
20
-
I
CL
-
/
I
-
4.)
a. 15
I
I
-
10
-
I
I
mo
5
0
10
8
20
18
16
14
12
Span, ft
Single Jack
W/
SF=2
Distributed
Load, psf
Span,
ft
Design
depth, ft
Assembled
Depth, in
10
0.8
10
W/
SF=2
Distributed
Load, psf
Design
depth,
ft
Assemble
d Depth,
in
10
1.6
20
28
Span,
ft
12
1.1
14
12
2.3
14
1.5
19
14
3.1
38
16
2.0
25
16
4.0
49
18
5.1
62
18
2.5
31
20
3.1
38
10
1.2
15
10
2.0
24
12
1.7
21
12
2.8
35
14
2.3
28
14
3.8
47
61
20 6.3
76_
16
3.0
37
16
5.0
18
3.8
46
18
6.3
77
20
4.7
57
20
7.8
95
124
Double Jack
W/
SF=2
Distributed
Load, psf
Span,
ft
Design
depth, ft
Assembled
Depth, in
20
40,
8
10
0.3
0.4
4
5
12
0.6
14
30
60
W/
Distributed
SF=2
Load, psf
80
Span,
ft
Design
depth,
ft
Assemble
d Depth,
S
10
0.5
in
7
0.8
10
8
12
1.1
14
0.8
10
14
1.5
19
16
1.0
13
16
2.0
25
18
1.3
16
18
2.5
31
20
8
10
1.6
0.4
0.6
20
5
8
20
3.1
38
0.6
12
0.8
11
40.
50
10
1.0
8
12
12
1.4
18
24
100
14
1.1
15
14
1.9
16
1.5
19
16
2.5
31
18
1.9
24
18
3.2
39
20
2.3
29
20
3.9
48
Design
depth, ft
Assembled
Depth, in
W/
SF=2
Distributed
Load, psf
Span,
ft
Design
depth,
ft
Assembke
d Depth,
in
40
80
8
10
0.2
0.3
3
4
Tab/Sheathing
W/
SF=2
Distributed
Load, psf
Span,
ft
20
40
8
10
01
0.1
2:
3
12
0.2
3
12
0.4
6
14
0.3
4
14
0.6
8
16
0.4
5
16
0.8
10
12
30
18
0.5
6
18
1.0
20
0.6
8
20
1.2
$
082
15
4
50
012
60
100
10
0.2
3
10
0.4
5
12
5
12
0.5
7
6
14
0.7
9
8
16
0.9
12
18
0.3
0.4
0.6
0.7
9
18
1.2
15
20
0.9
11
20
1.5
18
14
16
125