CHAPTER 7

Connections
7.1 General
The objectives of connection design are

• to transfer loads resisted by structural members and systems to other

parts of the structure to form a “continuous load path”;
• to secure nonstructural components and equipment to the building; and
• to fasten members in place during construction to resist temporary
loads during installation (i.e., finishes, sheathing, etc.).

Adequate connection of the framing members and structural systems

covered in Chapters 4, 5, and 6 is a critical design and construction consideration.
Regardless of the type of structure or type of material, structures are only as
strong as their connections, and structural systems can behave as a unit only with
proper interconnection of the components and assemblies; therefore, this chapter
is dedicated to connections. A connection transfers loads from one framing
member to another (i.e., a stud to a top or bottom plate) or from one assembly to
another (i.e., a roof to a wall, a wall to a floor, and a floor to a foundation).
Connections generally consist of two or more framing members and a mechanical
connection device such as a fastener or specialty connection hardware. Adhesives
are also used to supplement mechanical attachment of wall finishes or floor
sheathing to wood.
This chapter focuses on conventional wood connections that typically use
nails, bolts, and some specialty hardware. The procedures for designing
connections are based on the National Design Specification for Wood
Construction (NDS) (AF&PA, 1997). The chapter also addresses relevant
concrete and masonry connections in accordance with the applicable provisions of
Building Code Requirements for Structural Concrete (ACI-318) and Building
Code Requirements for Masonry Structures (ACI-530)(ACI, 1999a; ACI 1999b).
When referring to the NDS, ACI-318, or ACI-530, the chapter identifies
particular sections as NDS•12.1, ACI-318•22.5, or ACI-530•5.12.

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For most connections in typical residential construction, the connection

design may be based on prescriptive tables found in the applicable residential
building code (ICC, 1998). Table 7.1 depicts a commonly recommended nailing
schedule for wood-framed homes.

TABLE 7.1 Recommended Nailing Schedule for a Wood-Framed Home1

Nailing Number Size of
Application Notes
Method of Nails Nail
Header to joist End-nail 3 16d
Toenail 2 10d
Joist to sill or girder

Toenail 3 8d
Header and stringer (band) joists to sill
Toenail 8d 16 inches on center

Board sheathing
Face-nail 2 or 3 8d To each joist

End-nail 2 16d At each stud

Stud to sole plate or top plate

Toenail 4 8d
Sole plate to joist or blocking
Face-nail 16d 16 inches on center
Face-nail,
Doubled studs
10d 16 inches on center
stagger
End stud of interior wall to exterior wall

Face-nail 16d 16 inches on center

stud

Upper top plate to lower top plate

Face-nail 10d 16 inches on center
Double top plate, laps and intersections
Face-nail 4 10d
Continuous header, two pieces, each edge
Face-nail 10d 12 inches on center
Ceiling joist to top wall plates
Toenail 3 8d
Ceiling joist laps at partition
Face-nail 4 16d
Rafter to top plate
Toenail 3 8d
Rafter to ceiling joist
Face-nail 4 16d
Rafter to valley or hip rafter
Toenail 4 10d
Endnail 3 16d
Rafter to ridge board
Toenail 4 8d
Collar beam to rafter, 2-inch member Face-nail 2 12d
Collar beam to rafter, 1-inch member Face-nail 3 8d
Diagonal let-in brace to each stud and
Face-nail 2 8d
plate, 1-inch member
Intersecting studs at corners Face-nail 16d 12 inches on center
Built-up girder and beams, three or more
Face-nail 10d 12 inches on center each ply
members, each edge
Maximum 1/2-inch-thick (or less) wood 6d at 6 inches on center at panel edges; 12 inches

Face-nail
structural panel wall sheathing on center at intermediate framing

Minimum 1/2-inch-thick (or greater) wood 8d at 6 inches on center at panel edges; 12 inches

Face-nail
structural panel wall/roof/floor sheathing on center at intermediate framing

1/2-inch-diameter anchor bolt at 6 feet on center

Wood sill plate to concrete or masonry

and within 1 foot from ends of sill members

Source: Based on current industry practice and other sources (ICC,1998, NAHB, 1994; NAHB, 1982).

Note:

1
In practice, types of nails include common, sinker, box, or pneumatic; refer to Section 7.2 for descriptions of these fasteners. Some recent

codes have specified that common nails are to be used in all cases. However, certain connections may not necessarily require su ch a nail or

may actually be weakened by use of a nail that has too large a diameter (i.e., causing splitting of wood members). Other codes allow box

nails to be used in most or all cases. NER-272 guidelines for pneumatic fasteners should be consulted (NES, Inc., 1997). However, the NER-

272 guidelines are based on simple, conservative conversions of various code nail schedules, such as above, using the assumption that the

required performance is defined by a common nail in all applications. In short, there is a general state of confusion regarding appropriate

nailing requirements for the multitude of connections and related purposes in conventional residential construction.

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The NDS recognizes in NDS•7.1.1.4 that “extensive experience”

constitutes a reasonable basis for design; therefore, the designer may use Table
7.1 for many, if not all, connections. However, the designer should consider
carefully the footnote to Table 7.1 and verify that the connection complies with
local requirements, practice, and design conditions for residential construction. A
connection design based on the NDS or other sources may be necessary for
special conditions such as high-hazard seismic or wind areas and when unique
structural details or materials are used.
In addition to the conventional fasteners mentioned above, many specialty
connectors and fasteners are available on today’s market. The reader is
encouraged to gather, study, and scrutinize manufacturer literature regarding
specialty fasteners, connectors, and tools that meet a wide range of connection
needs.

7.2 Types of Mechanical Fasteners

Mechanical fasteners that are generally used for wood-framed house
design and construction include the following:

• nails and spikes;

• bolts;
• lag bolts (lag screws); and
• specialty connection hardware.

This section presents some basic descriptions and technical information on

the above fasteners. Sections 7.3 and 7.4 provide design values and related
guidance. Design examples are provided in Section 7.5 for various typical
conditions in residential wood framing and foundation construction.

7.2.1 Nails
Several characteristics distinguish one nail from another. Figure 7.1
depicts key nail features for a few types of nails that are essential to wood-framed
design and construction. This section discusses some of a nail’s characteristics
relative to structural design; the reader is referred to Standard Terminology of
Nails for Use with Wood and Wood-Base Materials (ASTM F547) and Standard
Specification for Driven Fasteners: Nails, Spikes, and Staples (ASTM F 1667) for
additional information (ASTM, 1990; ASTM, 1995).

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FIGURE 7.1 Elements of a Nail and Nail Types

The most common nail types used in residential wood construction follow:

• Common nails are bright, plain-shank nails with a flat head and
diamond point. The diameter of a common nail is larger than that of
sinkers and box nails of the same length. Common nails are used
primarily for rough framing.

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• Sinker nails are bright or coated slender nails with a sinker head and
diamond point. The diameter of the head is smaller than that of a
common nail with the same designation. Sinker nails are used
primarily for rough framing and applications where lumber splitting
may be a concern.
• Box nails are bright, coated, or galvanized nails with a flat head and
diamond point. They are made of lighter-gauge wire than common
nails and sinkers and are commonly used for toenailing and many
other light framing connections where splitting of lumber is a concern.
• Cooler nails are generally similar to the nails above, but with slightly
thinner shanks. They are commonly supplied with ring shanks (i.e.,
annular threads) as a drywall nail.
• Power-driven nails (and staples) are produced by a variety of
manufacturers for several types of power-driven fasteners. Pneumatic-
driven nails and staples are the most popular power-driven fasteners in
residential construction. Nails are available in a variety of diameters,
lengths, and head styles. The shanks are generally cement-coated and
are available with deformed shanks for added capacity. Staples are
also available in a variety of wire diameters, crown widths, and leg
lengths. Refer to NER-272 for additional information and design data
(NES, Inc., 1997).

Nail lengths and weights are denoted by the penny weight, which is
indicated by d. Given the standardization of common nails, sinkers, and cooler
nails, the penny weight also denotes a nail’s head and shank diameter. For other
nail types, sizes are based on the nail’s length and diameter. Table 7.2 arrays
dimensions for the nails discussed above. The nail length and diameter are key
factors in determining the strength of nailed connections in wood framing. The
steel yield strength of the nail may also be important for certain shear
connections, yet such information is rarely available for a “standard” lot of nails.

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TABLE 7.2 Nail Types, Sizes, and Dimensions1

Nominal Size Length Diameter
Type of Nail
(penny weight, d) (inches) (inches)
6d 2 0.113
8d 2 1/2 0.131
10d 3 0.148
Common
12d 3 1/4 0.148
16d 3 1/2 0.162
20d 4 0.192
6d 2 0.099
8d 2 12 0.113
Box 10d 3 0.128
12d 3 1/4 0.128
16d 3 1/2 0.135
6d 1 7/8 0.092
8d 2 3/8 0.113
Sinker 10d 2 7/8 0.120
12d 3 1/8 0.135
16d 3 1/4 0.148
6d 1 7/8 to 2 0.092 to 0.113
8d 2 3/8 to 2 1/2 0.092 to 0.131
10d 3 0.120 to 0.148
Pneumatic2
12d 3 1/4 0.120 to 0.131
16d 3 1/2 0.131 to 0.162
20d 4 0.131
4d 1 3/8 0.067
Cooler 5d 1 5/8 0.080
6d 1 7/8 0.092

Notes
1
Based on ASTM F 1667 (ASTM, 1995).
2
Based on a survey of pneumatic fastener manufacturer data and NER-272 (NES, Inc., 1997).

There are many types of nail heads, although three types are most
commonly used in residential wood framing.

• The flat nail head is the most common head. It is flat and circular, and
its top and bearing surfaces are parallel but with slightly rounded
edges.
• The sinker nail head is slightly smaller in diameter than the flat nail
head. It also has a flat top surface; however, the bearing surface of the
nail head is angled, allowing the head to be slightly countersunk.
• Pneumatic nail heads are available in the above types; however, other
head types such as a half-round or D-shaped heads are also common.

The shank, as illustrated in Figure 7.1, is the main body of a nail. It

extends from the head of the nail to the point. It may be plain or deformed. A
plain shank is considered a “smooth” shank, but it may have “grip marks” from
the manufacturing process. A deformed shank is most often either threaded or
fluted to provide additional withdrawal or pullout resistance. Threads are annular
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(i.e., ring shank), helical, or longitudinal deformations rolled onto the shank,
creating ridges and depressions. Flutes are helical or vertical deformations rolled
onto the shank. Threaded nails are most often used to connect wood to wood
while fluted nails are used to connect wood to concrete (i.e., sill plate to concrete
slab or furring strip to concrete or masonry). Shank diameter and surface
condition both affect a nail’s capacity.
The nail tip, as illustrated in Figure 7.1, is the end of the shank–usually
tapered–that is formed during manufacturing to expedite nail driving into a given
material. Among the many types of nail points, the diamond point is most
commonly used in residential wood construction. The diamond point is a
symmetrical point with four approximately equal beveled sides that form a
pyramid shape. A cut point used for concrete cut nails describes a blunt point. The
point type can affect nail drivability, lumber splitting, and strength characteristics.
The material used to manufacture nails may be steel, stainless steel, heat-
treated steel, aluminum, or copper, although the most commonly used materials
are steel, stainless steel, and heat-treated steel. Steel nails are typically formed
from basic steel wire. Stainless steel nails are often recommended in exposed
construction near the coast or for certain applications such as cedar siding to
prevent staining. Stainless steel nails are also recommended for permanent wood
foundations. Heat-treated steel includes annealed, case-hardened, or hardened
nails that can be driven into particularly hard materials such as extremely dense
wood or concrete.
Various nail coatings provide corrosion resistance, increased pullout
resistance, or ease of driving. Some of the more common coatings in residential
wood construction are described below.

• Bright. Uncoated and clean nail surface.

• Cement-coated. Coated with a heat-sensitive cement that prevents
corrosion during storage and improves withdrawal strength
depending on the moisture and density of the lumber and other
factors.
• Galvanized. Coated with zinc by barrel-tumbling, dipping,
electroplating, flaking, or hot-dipping to provide a corrosion-
resistant coating during storage and after installation for either
performance or appearance. The coating thickness increases the
diameter of the nail and improves withdrawal and shear strength.

7.2.2 Bolts
Bolts are often used for “heavy” connections and to secure wood to other
materials such as steel or concrete. In many construction applications, however,
special power-driven fasteners are used in place of bolts. Refer to Figure 7.2 for
an illustration of some typical bolt types and connections for residential use.

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FIGURE 7.2 Bolt and Connection Types

In residential wood construction, bolted connections are typically limited

to wood-to-concrete connections unless a home is constructed in a high-hazard
wind or seismic area and hold-down brackets are required to transfer shear wall
overturning forces (see Chapter 6). Foundation bolts, typically embedded in
concrete or grouted masonry, are commonly referred to as anchor bolts, J-bolts,

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or mud-sill anchors. Another type of bolt sometimes used in residential

construction is the structural bolt, which connects wood to steel or wood to wood.
Low-strength ASTM A307 bolts are commonly used in residential construction as
opposed to high-strength ASTM A325 bolts, which are more common in
commercial applications. Bolt diameters in residential construction generally
range from 1/4- to 3/4-inch, although 1/2- to 5/8-inch-diameter bolts are most
common, particularly for connecting a 2x wood sill to grouted masonry or
concrete.
Bolts, unlike nails, are installed in predrilled holes. If holes are too small,
the possibility of splitting the wood member increases during installation of the
bolt. If bored too large, the bolt holes encourage nonuniform dowel (bolt) bearing
stresses and slippage of the joint when loaded. NDS•8.1 specifies that bolt holes
should range from 1/32- to 1/16-inch larger than the bolt diameter to prevent
splitting and to ensure reasonably uniform dowel bearing stresses.

7.2.3 Specialty Connection Hardware

Many manufacturers fabricate specialty connection hardware. The load
capacity of a specialty connector is usually obtained through testing to determine
the required structural design values. The manufacturer’s product catalogue
typically provides the required values. Thus, the designer can select a standard
connector based on the design load determined for a particular joint or connection
(see Chapter 3). However, the designer should carefully consider the type of
fastener to be used with the connector; sometimes a manufacturer requires or
offers proprietary nails, screws, or other devices. It is also recommended that the
designer verify the safety factor and strength adjustments used by the
manufacturer, including the basis of the design value. In some cases, as with
nailed and bolted connections in the NDS, the basis is a serviceability limit state
(i.e., slip or deformation) and not ultimate capacity.
A few examples of specialty connection hardware are illustrated in Figure
7.3 and discussed below.

• Sill anchors are used in lieu of foundation anchor bolts. Many

configurations are available in addition to the one shown in Figure
7.3.
• Joist hangers are used to attach single or multiple joists to the side
of girders or header joists.
• Rafter clips and roof tie-downs are straps or brackets that connect
roof framing members to wall framing to resist roof uplift loads
associated with high-wind conditions.
• Hold-down brackets are brackets that are bolted, nailed, or screwed
to wall studs or posts and anchored to the construction below (i.e.,
concrete, masonry, or wood) to “hold down” the end of a member
or assembly (i.e., shear wall).
• Strap ties are prepunched straps or coils of strapping that are used
for a variety of connections to transfer tension loads.
• Splice plates or shear plates are flat plates with prepunched holes
for fasteners to transfer shear or tension forces across a joint.

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• Epoxy-set anchors are anchor bolts that are drilled and installed
with epoxy adhesives into concrete after the concrete has cured and
sometimes after the framing is complete so that the required anchor
location is obvious.

FIGURE 7.3 Specialty Connector Hardware

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7.2.4 Lag Screws

Lag screws are available in the same diameter range as bolts; the principal
difference between the two types of connectors is that a lag screw has screw
threads that taper to a point. The threaded portion of the lag screw anchors itself
in the main member that receives the tip. Lag screws (often called lag bolts)
function as bolts in joints where the main member is too thick to be economically
penetrated by regular bolts. They are also used when one face of the member is
not accessible for a “through-bolt.” Holes for lag screws must be carefully drilled
to one diameter and depth for the shank of the lag screw and to a smaller diameter
for the threaded portion. Lag screws in residential applications are generally small
in diameter and may be used to attach garage door tracks to wood framing, steel
angles to wood framing supporting brick veneer over wall openings, various
brackets or steel members to wood, and wood ledgers to wall framing.

7.3 Wood Connection Design

7.3.1 General
This section covers the NDS design procedures for nails, bolts, and lag
screws. The procedures are intended for allowable stress design (ASD) such that
loads should be determined accordingly (see Chapter 3). Other types of fastenings
are addressed by the NDS but are rarely used in residential wood construction.
The applicable sections of the NDS related to connection design as covered in this
chapter include

• NDS•7–Mechanical Connections (General Requirements);

• NDS•8–Bolts;
• NDS•9–Lag Screws; and
• NDS•12–Nails and Spikes.

While wood connections are generally responsible for the complex, non-
linear behavior of wood structural systems, the design procedures outlined in the
NDS are straightforward. The NDS connection values are generally conservative
from a structural safety standpoint. Further, the NDS’s basic or tabulated design
values are associated with tests of single fasteners in standardized conditions. As
a result, the NDS provides several adjustments to account for various factors that
alter the performance of a connection; in particular, the performance of wood
connections is highly dependent on the species (i.e., density or specific gravity) of
wood. Table 7.3 provides the specific gravity values of various wood species
typically used in house construction.

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Common Framing Lumber Species and

TABLE 7.3
Specific Gravity Values
Lumber Species Specific Gravity, G
Southern Pine (SP) 0.55
Douglas Fir-Larch (DF-L) 0.50
Hem-Fir (HF) 0.43
Spruce-Pine-Fir (SPF) 0.42
Spruce-Pine-Fir (South) 0.36

The moisture condition of the wood is also critical to long-term

connection performance, particularly for nails in withdrawal. In some cases, the
withdrawal value of fasteners installed in moist lumber can decrease by as much
as 50 percent over time as the lumber dries to its equilibrium moisture content. At
the same time, a nail may develop a layer of rust that increases withdrawal
capacity. In contrast, deformed shank nails tend to hold their withdrawal capacity
much more reliably under varying moisture and use conditions. For this and other
reasons, the design nail withdrawal capacities in the NDS for smooth shank nails
are based on a fairly conservative reduction factor, resulting in about one-fifth of
the average ultimate tested withdrawal capacity. The reduction includes a safety
factor as well as a load duration adjustment (i.e., decreased by a factor of 1.6 to
adjust from short-term tests to normal duration load). Design values for nails and
bolts in shear are based on a deformation (i.e., slip) limit state and not their
ultimate capacity, resulting in a safety factor that may range from 3 to 5 based on
ultimate tested capacities. One argument for retaining a high safety factor in shear
connections is that the joint may creep under long-term load. While creep is not a
concern for many joints, slip of joints in a trussed assembly (i.e., rafter-ceiling
joist roof framing) is critical and, in key joints, can result in a magnified
deflection of the assembly over time (i.e., creep).
In view of the above discussion, there are a number of uncertainties in the
design of connections that can lead to conservative or unconservative designs
relative to the intent of the NDS and practical experience. The designer is advised
to follow the NDS procedures carefully, but should be prepared to make practical
adjustments as dictated by sound judgment and experience and allowed in the
NDS; refer to NDS•7.1.1.4.
Withdrawal design values for nails and lag screws in the NDS are based
on the fastener being oriented perpendicular to the grain of the wood. Shear
design values in wood connections are also based on the fastener being oriented
perpendicular to the grain of wood. However, the lateral (shear) design values are
dependent on the direction of loading relative to the wood grain direction in each
of the connected members. Refer to Figure 7.4 for an illustration of various
connection types and loading conditions.

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FIGURE 7.4 Types of Connections and Loading Conditions

The NDS provides tabulated connection design values that use the
following symbols for the three basic types of loading:

• W–withdrawal (or tension loading);

• Z⊥–shear perpendicular to wood grain; and
• Z||–shear parallel to wood grain.

In addition to the already tabulated design values for the above structural
resistance properties of connections, the NDS provides calculation methods to
address conditions that may not be covered by the tables and that give more
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flexibility to the design of connections. The methods are appropriate for use in
hand calculations or with computer spreadsheets.
For withdrawal, the design equations are relatively simple empirical
relationships (based on test data) that explain the effect of fastener size
(diameter), penetration into the wood, and density of the wood. For shear, the
equations are somewhat more complex because of the multiple failure modes that
may result from fastener characteristics, wood density, and size of the wood
members. Six shear-yielding modes (and a design equation for each) address
various yielding conditions in either the wood members or the fasteners that join
the members. The critical yield mode is used to determine the design shear value
for the connection. Refer to NDS•Appendix I for a description of the yield modes.
The yield equations in the NDS are based on general dowel equations that
use principles of engineering mechanics to predict the shear capacity of a doweled
joint. The general dowel equations can be used with joints that have a gap
between the members and they can also be used to predict ultimate capacity of a
joint made of wood, wood and metal, or wood and concrete. However, the
equations do not account for friction between members or the anchoring/cinching
effect of the fastener head as the joint deforms and the fastener rotates or develops
tensile forces. These effects are important to the ultimate capacity of wood
connections in shear and, therefore, the general dowel equations may be
considered to be conservative; refer to Section 7.3.6. For additional guidance and
background on the use of the general dowel equations, refer to the NDS
Commentary and other useful design resources available through the American
Forest & Paper Association (AF&PA, 1999; Showalter, Line, and Douglas, 1999).

7.3.2 Adjusted Allowable Design Values

Design values for wood connections are subject to adjustments in a
manner similar to that required for wood members themselves (see Section 5.2.4
of Chapter 5). The calculated or tabulated design values for W and Z are
multiplied by the applicable adjustment factors to determine adjusted allowable
design values, Z’ and W’, as shown below for the various connection methods
(i.e., nails, bolts, and lag screws).

[NDS•12.3 & 7.3]

Z ′ = ZC D C M C t C g C Δ for bolts
Z ′ = ZC D C M C t C g C Δ C d C eg for lag screws
Z ′ = ZC D C M C t C d C eg C di C tn for nails and spikes

[NDS•12.2&7.3]
W ′ = WC D C M C t C tn for nails and spikes
W ′ = WC D C M C t C eg for lag screws

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The adjustment factors and their applicability to wood connection design

are briefly described as follows:

• CD–Load Duration Factor (NDS•2.3.2 and Chapter 5, Table 5.3)–

applies to W and Z values for all fasteners based on design load
duration but shall not exceed 1.6 (i.e., wind and earthquake load
duration factor).
• CM–Wet Service Factor (NDS•7.3.3)–applies to W and Z values for all
connections based on moisture conditions at the time of fabrication
and during service; not applicable to residential framing.
• Ct–Temperature Factor (NDS•7.3.4)–applies to the W and Z values
for all connections exposed to sustained temperatures of greater than
100oF; not typically used in residential framing.
• Cg–Group Action Factor (NDS•7.3.6)–applies to Z values of two or
more bolts or lag screws loaded in single or multiple shear and aligned
in the direction of the load (i.e., rows).
• CΔ–Geometry Factor (NDS•8.5.2, 9.4.)–applies to the Z values for
bolts and lag screws when the end distance or spacing of the bolts is
less than assumed in the unadjusted design values.
• Cd–Penetration Depth Factor (NDS•9.3.3, 12.3.4)–applies to the Z
values of lag screws and nails when the penetration into the main
member is less than 8D for lag screws or 12D for nails (where D =
shank diameter); sometimes applicable to residential nailed
connections.
• Ceg–End Grain Factor (NDS•9.2.2, 9.3.4, 12.3.5)–applies to W and Z
values for lag screws and to Z values for nails to account for reduced
capacity when the fastener is inserted into the end grain (Ceg=0.67).
• Cdi–Diaphragm Factor (NDS•12.3.6)–applies to the Z values of nails
only to account for system effects from multiple nails used in sheathed
diaphragm construction (Cdi = 1.1).
• Ctn–Toenail Factor (NDS•12.3.7)–applies to the W and Z values of
toenailed connections (Ctn = 0.67 for withdrawal and = 0.83 for shear).
It does not apply to slant nailing in withdrawal or shear; refer to
Section 7.3.6.

The total allowable design value for a connection (as adjusted by the
appropriate factors above) must meet or exceed the design load determined for the
connection (refer to Chapter 3 for design loads). The values for W and Z are
based on single fastener connections. In instances of connections involving
multiple fasteners, the values for the individual or single fastener can be summed
to determine the total connection design value only when Cg is applied (to bolts
and lag screws only) and fasteners are the same type and similar size. However,
this approach may overlook certain system effects that can improve the actual

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performance of the joint in a constructed system or assembly (see Section 7.3.6).

Conditions that may decrease estimated performance, such as prying action
induced by the joint configuration and/or eccentric loads and other factors should
also be considered.
In addition, the NDS does not provide values for nail withdrawal or shear
when wood structural panel members (i.e., plywood or oriented strand board) are
used as a part of the joint. This type of joint–wood member to structural wood
panel–occurs frequently in residential construction. Z values can be estimated by
using the yield equations for nails in NDS 12.3.1 and assuming a reasonable
specific gravity (density) value for the wood structural panels, such as G = 0.5. W
values for nails in wood structural panels can be estimated in a similar fashion by
using the withdrawal equation presented in the next section. The tabulated W and
Z values in NDS•12 may also be used, but with some caution as to the selected
table parameters.

7.3.3 Nailed Connections

The procedures in NDS•12 provide for the design of nailed connections to
resist shear and withdrawal loads in wood-to-wood and metal-to-wood
connections. As mentioned, many specialty “nail-type” fasteners are available for
wood-to-concrete and even wood-to-steel connections. The designer should
consult manufacturer data for connection designs that use proprietary fastening
systems.
The withdrawal strength of a smooth nail (driven into the side grain of
lumber) is determined in accordance with either the empirical design equation
below or NDS•Table 12.2A.

[NDS•12.2.1]
5
W = 1380(G) 2 DL p unadjusted withdrawal design value (lb) for a smooth shank
nail
where,
G = specific gravity of the lumber member receiving the nail tip
D = the diameter of the nail shank (in)
Lp = the depth of penetration (in) of the nail into the member receiving the nail tip

The design strength of nails is greater when a nail is driven into the side
rather than the end grain of a member. Withdrawal information is available for
nails driven into the side grain; however, the withdrawal capacity of a nail driven
into the end grain is assumed to be zero because of its unreliability. Furthermore,
the NDS does not provide a method for determining withdrawal values for
deformed shank nails. These nails significantly enhance withdrawal capacity and
are frequently used to attach roof sheathing in high-wind areas. They are also used
to attach floor sheathing and some siding materials to prevent nail “back-out.”
The use of deformed shank nails is usually based on experience or preference.
The design shear value, Z, for a nail is typically determined by using the
following tables from NDS•12:

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 Chapter 7 - Connections

• Tables 12.3A and B. Nailed wood-to-wood, single-shear (two-

member) connections with the same species of lumber using box or
common nails, respectively.
• Tables 12.3E and F. Nailed metal plate-to-wood connections using
box or common nails, respectively.

The yield equations in NDS•12.3 may be used for conditions not

represented in the design value tables for Z. Regardless of the method used to
determine the Z value for a single nail, the value must be adjusted as described in
Section 7.3.2. As noted in the NDS, the single nail value is used to determine the
design value.
It is also worth mentioning that the NDS provides an equation for
determining allowable design value for shear when a nailed connection is loaded
in combined withdrawal and shear (see NDS•12.3.8, Equation 12.3-6). The
equation appears to be most applicable to a gable-end truss connection to the roof
sheathing under conditions of roof sheathing uplift and wall lateral load owing to
wind. The designer might contemplate other applications but should take care in
considering the combination of loads that would be necessary to create
simultaneous uplift and shear worthy of a special calculation.

7.3.4 Bolted Connections

Bolts may be designed in accordance with NDS•8 to resist shear loads in
wood-to-wood, wood-to-metal, and wood-to-concrete connections. As mentioned,
many specialty “bolt-type” fasteners can be used to connect wood to other
materials, particularly concrete and masonry. One common example is an epoxy-
set anchor. Manufacturer data should be consulted for connection designs that use
proprietary fastening systems.
The design shear value Z for a bolted connection is typically determined
by using the following tables from NDS•8:

• Table 8.2A. Bolted wood-to-wood, single-shear (two-member)

connections with the same species of lumber.
• Table 8.2B. Bolted metal plate-to-wood, single-shear (two-
member) connections; metal plate thickness of 1/4-inch minimum.
• Table 8.2D. Bolted single-shear wood-to-concrete connections;
based on minimum 6-inch bolt embedment in minimum fc = 2,000
psi concrete.

The yield equations of NDS•8.2 (single-shear joints) and NDS•8.3

(double-shear joints) may be used for conditions not represented in the design
value tables. Regardless of the method used to determine the Z value for a single
bolted connection, the value must be adjusted as described in Section 7.3.2.
It should be noted that the NDS does not provide W values for bolts. The
tension value of a bolt connection in wood framing is usually limited by the
bearing capacity of the wood as determined by the surface area of a washer used
underneath the bolt head or nut. When calculating the bearing capacity of the
wood based on the tension in a bolted joint, the designer should use the small

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 Chapter 7 - Connections

bearing area value Cb to adjust the allowable compressive stress perpendicular to

grain Fc⊥ (see NDS•2.3.10). It should also be remembered that the allowable
compressive stress of lumber is based on a deformation limit state, not capacity;
refer to Section 5.2.3 of Chapter 5. In addition, the designer should verify the
tension capacity of the bolt and its connection to other materials (i.e., concrete or
masonry as covered in Section 7.4). The bending capacity of the washer should
also be considered. For example, a wide but thin washer will not evenly distribute
the bearing force to the surrounding wood.
The arrangement of bolts and drilling of holes are extremely important to
the performance of a bolted connection. The designer should carefully follow the
minimum edge, end, and spacing requirements of NDS•8.5. When necessary, the
designer should adjust the design value for the bolts in a connection by using the
geometry factor Cρ and the group action factor Cg discussed in Section 7.3.2.
Any possible torsional load on a bolted connection (or any connection for
that manner) should also be considered in accordance with the NDS. In such
conditions, the pattern of the fasteners in the connection can become critical to
performance in resisting both a direct shear load and the loads created by a
torsional moment on the connection. Fortunately, this condition is not often
applicable to typical light-frame construction. However, cantilevered members
that rely on connections to “anchor” the cantilevered member to other members
will experience this effect, and the fasteners closest to the cantilever span will
experience greater shear load. One example of this condition sometimes occurs
with balcony construction in residential buildings; failure to consider the effect
discussed above has been associated with some notable balcony collapses.
For wood members bolted to concrete, the design lateral values are
provided in NDS•Table8.2E. The yield equations (or general dowel equations)
may also be used to conservatively determine the joint capacity. A recent study
has made recommendations regarding reasonable assumptions that must be made
in applying the yield equations to bolted wood-to-concrete connections (Stieda, et
al., 1999). Using symbols defined in the NDS, the study recommends an Re value
of 5 and an Rt value of 3. These assumptions are reported as being conservative
because fastener head effects and joint friction are ignored in the general dowel
equations.

7.3.5 Lag Screws

Lag screws (or lag bolts) may be designed to resist shear and withdrawal
loads in wood-to-wood and metal-to-wood connections in accordance with
NDS•9. As mentioned, many specialty “screw-type” fasteners can be installed in
wood. Some tap their own holes and do not require predrilling. Manufacturer data
should be consulted for connection designs that use proprietary fastening systems.
The withdrawal strength of a lag screw (inserted into the side grain of
lumber) is determined in accordance with either the empirical design equation
below or NDS•Table 9.2A. It should be noted that the equation below is based on
single lag screw connection tests and is associated with a reduction factor of 0.2
applied to average ultimate withdrawal capacity to adjust for load duration and
safety. Also, the penetration length of the lag screw Lp into the main member does

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not include the tapered portion at the point. NDS•Appendix L contains

dimensions for lag screws.

[NDS•9.2.1]
3 3
W = 1800(G) 2 D 4 L p unadjusted withdrawal design value (lb) for a lag screw
where,
G = specific gravity of the lumber receiving the lag screw tip

D = the diameter of the lag screw shank (in)

Lp = the depth of penetration (in) of the lag screw into the member receiving the

tip, less the tapered length of the tip

The allowable withdrawal design strength of a lag screw is greater when

the screw is installed in the side rather than the end grain of a member. However,
unlike the treatment of nails, the withdrawal strength of lag screws installed in the
end grain may be calculated by using the Ceg adjustment factor with the equation
above.
The design shear value Z for a lag screw is typically determined by using
the following tables from NDS•9:

• Table 9.3A. Lag screw, single-shear (two-member) connections

with the same species of lumber for both members.
• Table 9.3B. Lag screw and metal plate-to-wood connections.

The yield equations in NDS•9.3 may be used for conditions not

represented in the design value tables for Z. Regardless of the method used to
determine the Z value for a single lag screw, the value must be adjusted as
described in Section 7.3.2.
It is also worth mentioning that the NDS provides an equation for
determining the allowable shear design value when a lag screw connection is
loaded in combined withdrawal and shear (see NDS•9.3.5, Equation 9.3-6). The
equation does not, however, appear to apply to typical uses of lag screws in
residential construction.

7.3.6 System Design Considerations

As with any building code or design specification, the NDS provisions
may or may not address various conditions encountered in the field. Earlier
chapters made several recommendations regarding alternative or improved design
approaches. Similarly, some considerations regarding wood connection design are
in order.
First, as a general design consideration, “crowded” connections should be
avoided. If too many fasteners are used (particularly nails), they may cause
splitting during installation. When connections become “crowded,” an alternative
fastener or connection detail should be considered. Basically, the connection
detail should be practical and efficient.
Second, while the NDS addresses “system effects” within a particular joint
(i.e., element) that uses multiple bolts or lag screws (i.e. the group action factor
Cg), it does not include provisions regarding the system effects of multiple joints

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in an assembly or system of components. Therefore, some consideration of

system effects is given below based on several relevant studies related to key
connections in a home that allow the dwelling to perform effectively as a
structural unit.

Sheathing Withdrawal Connections

Several recent studies have focused on roof sheathing attachment and nail
withdrawal, primarily as a result of Hurricane Andrew (HUD, 1999a; McClain,
1997; Cunningham, 1993; Mizzell and Schiff, 1994; and Murphy, Pye, and
Rosowsky, 1995); refer to Chapter 1. The studies identify problems related to
predicting the pull-off capacity of sheathing based on single nail withdrawal
values and determining the tributary withdrawal load (i.e., wind suction pressure)
on a particular sheathing fastener. One clear finding, however, is that the nails on
the interior of the roof sheathing panels are the critical fasteners (i.e., initiate
panel withdrawal failure) because of the generally larger tributary area served by
these fasteners. The studies also identified benefits to the use of screws and
deformed shank nails. However, use of a standard geometric tributary area of the
sheathing fastener and the wind loads in Chapter 3, along with the NDS
withdrawal values (Section 7.3.3), will generally result in a reasonable design
using nails. The wind load duration factor should also be applied to adjust the
withdrawal values since a commensurate reduction is implicit in the design
withdrawal values relative to the short-term, tested, ultimate withdrawal
capacities (see Section 7.3).
It is interesting, however, that one study found that the lower-bound (i.e.,
5th percentile) sheathing pull-off resistance was considerably higher than that
predicted by use of single-nail test values (Murphy, Pye, and Rosowsky, 1995).
The difference was as large as a factor of 1.39 greater than the single nail values.
While this would suggest a withdrawal system factor of at least 1.3 for sheathing
nails, it should be subject to additional considerations. For example, sheathing
nails are placed by people using tools in somewhat adverse conditions (i.e., on a
roof), not in a laboratory. Therefore, this system effect may be best considered as
a reasonable “construction tolerance” on actual nail spacing variation relative to
that intended by design. Thus, an 8- to 9-inch nail spacing on roof sheathing nails
in the panel’s field could be “tolerated” when a 6-inch spacing is “targeted” by
design.

Roof-to-Wall Connections

A couple of studies (Reed, et al., 1996; Conner, et al., 1987) have

investigated the capacity of roof-to-wall (i.e., sloped rafter to top plate)
connections using conventional toenailing and other enhancements (i.e.,
strapping, brackets, gluing, etc.). Again, the primary concern is related to high
wind conditions, such as experienced during Hurricane Andrew and other extreme
wind events; refer to Chapter 1.
First, as a matter of clarification, the toenail reduction factor Ctn does not
apply to slant-nailing such as those used for rafter-to-wall connections and floor-
to-wall connections in conventional residential construction (Hoyle and Woeste,
1989). Toenailing occurs when a nail is driven at an angle in a direction parallel-
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to-grain at the end of a member (i.e., a wall stud toenail connection to the top or
bottom plate that may be used instead of end nailing). Slant nailing occurs when a
nail is driven at an angle, but in a direction perpendicular-to-grain through the
side of the member and into the face grain of the other (i.e., from a roof rafter or
floor band joist to a wall top plate). Though a generally reliable connection in
most homes and similar structures built in the United States, even a well-designed
slant-nail connection used to attach roofs to walls will become impractical in
hurricane-prone regions or similar high-wind areas. In these conditions, a metal
strap or bracket is preferrable.
Based on the studies of roof-to-wall connections, five key findings are
summarized as follows (Reed et al., 1996; Conner et al., 1987):

1. In general, it was found that slant-nails (not to be confused with toe-

nails) in combination with metal straps or brackets do not provide
directly additive uplift resistance.
2. A basic metal twist strap placed on the interior side of the walls (i.e.,
gypsum board side) resulted in top plate tear-out and premature
failure. However, a strap placed on the outside of the wall (i.e.,
structural sheathing side) was able to develop its full capacity without
additional enhancement of the conventional stud-to-top plate
connection (see Table 7.1).
3. The withdrawal capacity for single joints with slant nails was
reasonably predicted by NDS with a safety factor of about 2 to 3.5.
However, with multiple joints tested simultaneously, a system factor
on withdrawal capacity of greater than 1.3 was found for the slant-
nailed rafter-to-wall connection. A similar system effect was not found
on strap connections, although the strap capacity was substantially
higher. The ultimate capacity of the simple strap connection (using
five 8d nails on either side of the strap–five in the spruce rafter and
five in the southern yellow pine top plate) was found to be about 1,900
pounds per connection. The capacity of three 8d common slant nails
used in the same joint configuration was found to be 420 pounds on
average, and with higher variation. When the three 8d common toenail
connection was tested in an assembly of eight such joints, the average
ultimate withdrawal capacity per joint was found to be 670 pounds
with a somewhat lower variation. Similar “system” increases were not
found for the strap connection. The 670 pounds capacity was similar to
that realized for a rafter-to-wall joint using three 16d box nails in
Douglas fir framing.
4. It was found that the strap manufacturer’s published value had an
excessive safety margin of greater than 5 relative to average ultimate
capacity. Adjusted to an appropriate safety factor in the range of 2 to 3
(as calculated by applying NDS nail shear equations by using a metal
side plate), the strap (a simple 18g twist strap) would cover a multitude
of high wind conditions with a simple, economical connection detail.
5. The use of deformed shank (i.e., annular ring) nails was found to
increase dramatically the uplift capacity of the roof-to-wall
connections using the slant nailing method.

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Heel Joint in Rafter-to-Ceiling Joist Connections

The heel joint connection at the intersection of rafters and ceiling joists
have long been considered one of the weaker connections in conventional wood
roof framing. In fact, this highly stressed joint is one of the accolades of using a
wood truss rather than conventional rafter framing (particularly in high-wind or
snow-load conditions). However, the performance of conventional rafter-ceiling
joist heel joint connections should be understood by the designer since they are
frequently encountered in residential construction.
First, conventional rafter and ceiling joist (cross-tie) framing is simply a
“site-built” truss. Therefore, the joint loads can be analyzed by using methods
that are applicable to trusses (i.e., pinned joint analysis). However, the
performance of the system should be considered. As mentioned earlier for roof
trusses (Section 5.6.1 in Chapter 5), a system factor of 1.1 is applicable to tension
members and connections. Therefore, the calculated shear capacity of the nails in
the heel joint (and in ceiling joist splices) may be multiplied by a system factor of
1.1, which is considered conservative. Second, it must be remembered that the
nail shear values are based on a deformation limit and generally have a
conservative safety factor of three to five relative to the ultimate capacity.
Finally, the nail values should be adjusted for duration of load (i.e., snow load
duration factor of 1.15 to 1.25); refer to Section 5.2.4 of Chapter 5. With these
considerations and with the use of rafter support braces at or near mid-span (as is
common), reasonable heel joint designs should be possible for most typical design
conditions in residential construction.

Wall-to-Floor Connections

When wood sole plates are connected to wood floors, many nails are often
used, particularly along the total length of the sole plate or wall bottom plate.
When connected to a concrete slab or foundation wall, there are usually several
bolts along the length of the bottom plate. This points toward the question of
possible system effects in estimating the shear capacity (and uplift capacity) of
these connections for design purposes.
In recent shear wall tests, walls connected with pneumatic nails (0.131-
inch diameter by 3 inches long) spaced in pairs at 16 inches on center along the
bottom plate were found to resist over 600 pounds in shear per nail (HUD,
1999b). The bottom plate was Spruce-Pine-Fir lumber and the base beam was
Southern Yellow Pine. This value is about 4.5 times the adjusted allowable design
shear capacity predicted by use of the NDS equations. Similarly, connections
using 5/8-inch-diameter anchor bolts at 6 feet on center (all other conditions
equal) were tested in full shear wall assemblies; the ultimate shear capacity per
bolt was found to be 4,400 pounds. This value is about 3.5 times the adjusted
allowable design shear capacity per the NDS equations. These safety margins
appear excessive and should be considered by the designer when evaluating
similar connections from a practical “system” standpoint.

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7.4 Design of Concrete and

Masonry Connections
7.4.1 General
In typical residential construction, the interconnection of concrete and
masonry elements or systems is generally related to the foundation and usually
handled in accordance with standard or accepted practice. The bolted wood
member connections to concrete as in Section 7.3.4 are suitable for bolted wood
connections to properly grouted masonry (see Chapter 4). Moreover, numerous
specialty fasteners or connectors (including power driven and cast-in-place) can
be used to fasten wood materials to masonry or concrete. The designer should
consult the manufacturer’s literature for available connectors, fasteners, and
design values.
This section discusses some typical concrete and masonry connection
designs in accordance with the ACI 318 concrete design specification and ACI
530 masonry design specification (ACI, 1999a; ACI, 1999b).

7.4.2 Concrete or Masonry Foundation Wall to Footing

Footing connections, if any, are intended to transfer shear loads from the
wall to the footing below. The shear loads are generally produced by lateral soil
pressure acting on the foundation (see Chapter 3).
Footing-to-wall connections for residential construction are constructed in
any one of the following three ways (refer to Figure 7.5 for illustrations of the
connections):

• no vertical reinforcement or key;

• key only; or
• dowel only.

Generally, no special connection is needed in nonhurricane-prone or low- to

moderate-hazard seismic areas. Instead, friction is sufficient for low, unbalanced
backfill heights while the basement slab can resist slippage for higher backfill
heights on basement walls. The basement slab abuts the basement wall near its base
and thus provides lateral support. If gravel footings are used, the unbalanced backfill
height needs to be sufficiently low (i.e., less than 3 feet), or means must be provided
to prevent the foundation wall from slipping sideways from lateral soil loads. Again,
a basement slab can provide the needed support. Alternatively, a footing key or
doweled connection can be used.

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 Chapter 7 - Connections

FIGURE 7.5 Concrete or Masonry Wall-to-Footing Connections

Friction Used to Provide Shear Transfer

To verify the amount of shear resistance provided by friction alone, assume a

coefficient of friction between two concrete surfaces of µ = 0.6. Using dead loads
only, determine the static friction force, F = µ NA , where F is the friction force (lb),
N is the dead load (psf), and A is the bearing surface area (sf) between the wall and
the footing.

Key Used to Provide Shear Transfer

A concrete key is commonly used to “interlock” foundation walls to

footings. If foundation walls are constructed of masonry, the first course of masonry
must be grouted solid when a key is used.
In residential construction, a key is often formed by using a 2x4 wood board
with chamfered edges that is placed into the surface of the footing immediately after
the concrete pour. Figure 7.6 illustrates a footing with a key. Shear resistance
developed by the key is computed in accordance with the equation below.

[ACI-318•22.5]
Vu ≤ φVn

4
Vn = f c′ bh
3

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FIGURE 7.6 Key in Concrete Footings

Dowels Used to Provide Adequate Shear Transfer

Shear forces at the base of exterior foundation walls may require a dowel to
transfer the forces from the wall to the footing. The equations below described by
ACI-318 as the Shear-Friction Method are used to develop shear resistance with
vertical reinforcement (dowels) across the wall-footing interface.

[ACI-318•11.7]
Masonry Walls Concrete Walls
l be ≥ 12d b Vu ≤ φVn

350
4 f m′ A v 
0.2f
 c′ A c 




Vn = A vf f y µ ≤



B v =
minimumof 


800
A c 

0
.12A v f y 

Vu
A vf =
φf y µ
φ = 0.85

If dowels are used to transfer shear forces from the base of the wall to the
footing, use the equations below to determine the minimum development length
required (refer to Figure 7.7 for typical dowel placement). If development length
exceeds the footing thickness, the dowel must be in the form of a hook, which is
rarely required in residential construction.

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 Chapter 7 - Connections

[ACI-318•12.2, 12.5] Concrete Walls

Standard Hooks Deformed Bars
=
1200d b
where fy = 60,000 psi  
 αβγλ 
lhb
f c′  3f y
l db = 
 40 f ′  c + K TR 
 c  
 db 
c + K TR
≤ 2.5
db
fy  A s,required 
ξ= l d = l db   ≥ 12 ′′
60,000  A s,provided 
 
A s,required
ω=
A s,provided

[ACI-530•1.12.3,2.1.8] Masonry Walls

Standard Hooks Deformed Bars
l d = 0.0015d b Fs ≥ 12 in. l d = maximum {12d b }
l e = 11.25d b l d = maximum {12d b }

FIGURE 7.7 Dowel Placement in Concrete Footings

The minimum embedment length is a limit specified in ACI-318 that is not

necessarily compatible with residential construction conditions and practice.
Therefore, this guide suggests a minimum embedment length of 6 to 8 inches for
footing dowels, when necessary, in residential construction applications. In
addition, dowels are sometimes used in residential construction to connect other
concrete elements, such as porch slabs or stairs, to the house foundation to control
differential movement. However, exterior concrete “flat work” adjacent to a home
should be founded on adequate soil bearing or reasonably compacted backfill.
Finally, connecting exterior concrete work to the house foundation requires
caution, particularly in colder climates and soil conditions where frost heave may
be a concern.

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7.4.3 Anchorage and Bearing on Foundation Walls

Anchorage Tension (Uplift) Capacity

The equations below determine whether the concrete or masonry shear area
of each bolt is sufficient to resist pull-out from the wall as a result of uplift forces
and shear friction in the concrete.

[ACI-318•11.3, ACI-530•2.1.2]
Concrete Foundation Wall Masonry Foundation Wall
Vu ≤ φVc b a ≤ Ba
Vc = 4A v f c′ 0.5A p f m′ 

 

B a = minimumof  

0.2A b f y 
πl b 2  πl b 2 
  A p = minimum of 
A v = minimumof   
πl be 
2
πh 
2

Bearing Strength

Determining the adequacy of the bearing strength of a foundation wall

follows ACI-318•10.17 for concrete or ACI-530•2.1.7 for masonry. The bearing
strength of the foundation wall is typically adequate for the loads encountered in
residential construction.

[ACI-318•10.17 and ACI-530•2.1.7]

Concrete Foundation Wall Masonry Foundation Wall
Bc = factored bearing load
B c ≤ φ0.85f c′ A 1 f a ≤ Fa
P
fa =
A1
φ = 0.7 Fa ≤ 0.25f m′

When the foundation wall’s supporting surface is wider on all sides than the
loaded area, the designer is permitted to determine the design bearing strength on the
loaded area by using the equations below.

[ACI-318•10.7 and ACI-530•2.1.7]

Concrete Foundation Wall
A2 A2
B c = φ0.85f c′ A 1 where ≤2
A1 A1
Masonry Foundation Wall
P A2
fa = where ≤2
A1 A 2 A1 A1

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 Chapter 7 - Connections

7.5 Design Examples

EXAMPLE 7.1 Roof Sheathing Connections

Given
• Design wind speed is 130 mph gust with an open (coastal) exposure
• Two-story home with a gable roof
• Roof framing lumber is Southern Yellow Pine (G=0.55)
• Roof framing is spaced at 24 inches on center
• Roof sheathing is 7/16-inch-thick structural wood panel

Find 1. Wind load (suction) on roof sheathing.

2. Nail type/size and maximum spacing.

Solution
1. Determine the wind load on roof sheathing (Chapter 3, Section 3.6.2)

Step 1: Basic velocity pressure = 24.6 psf (Table 3.7)

Step 2: Adjust for open exposure = 1.4(24.6 psf) = 34.4 psf

Step 3: Skip

Step 4: Roof sheathing Gcp = -2.2 (Table 3.9)

Step 5: Design load = (-2.2)(34.4 psf) = 76 psf

2. Select a trial nail type and size, determine withdrawal capacity, and calculated
required spacing

Use an 8d pneumatic nail (0.113 inch diameter) with a length of 2 3/8 inches. The
unadjusted design withdrawal capacity is determined using the equation in Section
7.3.3.

W = 1380(G)2.5DLp

G = 0.55

D = 0.113 in

Lp = (2 3/8 in) – (7/16 in) = 1.9 in

W = 1380(0.55)2.5(0.113 in)(1.9 in) = 66.5 lb

Determine the adjusted design withdrawal capacity using the applicable

adjustment factors discussed in Section 7.3.2.

W’ = WCD = (66.5 lb)(1.6) = 106 lb

Determine the required nail spacing in the roof sheathing panel interior.

Tributary sheathing area = (roof framing spacing)(nail spacing)

= (2 ft)(s)
Withdrawal load per nail = (wind uplift pressure)(2 ft)(s)
= (76 psf)(2 ft)(s)

W’ ≥ design withdrawal load

106 lb ≥ (76 psf)(2 ft)(s)
s ≤ 0.69 ft
Use a maximum nail spacing of 8 inches in the roof sheathing panel interior.

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Notes:
1. If Spruce-Pine-Fir (G=0.42) roof framing lumber is substituted, W’ would be
54 lb and the required nail spacing would reduce to 4 inches on center in the
roof sheathing panel interior. Thus, it is extremely important to carefully
consider and verify the species of framing lumber when determining
fastening requirements for roof sheathing.
2. The above analysis is based on a smooth shank nail. A ring shank nail may
be used to provide greater withdrawal capacity that is also less susceptible to
lumber moisture conditions at installation and related long-term effects on
withdrawal capacity.
3. With the smaller tributary area, the roof sheathing edges that are supported
on framing members may be fastened at the standard 6 inch on center
fastener spacing. For simplicity, it may be easier to specify a 6 inch on
center spacing for all roof sheathing fasteners, but give an allowance of 2 to 3
inches for a reasonable construction tolerance; refer to Section 7.3.6.
4. As an added measure given the extreme wind environment, the sheathing nail
spacing along the gable end truss/framing should be specified at a closer
spacing, say 4 inches on center. These fasteners are critical to the
performance of light-frame gable roofs in extreme wind events; refer to the
discussion on hurricanes in Chapter 1. NDS•12.3.8 provides an equation to
determine nail lateral strength when subjected to a combined lateral and
withdrawal load. This equation may be used to verify the 4 inch nail spacing
recommendation at the gable end.

Conclusion

This example problem demonstrates a simple application of the nail withdrawal

equation in the NDS. The withdrawal forces on connections in residential construction
are usually of greatest concern in the roof sheathing attachment. In hurricane prone
regions, it is common practice to use a 6-inch nail spacing on the interior of roof
sheathing panels. In lower wind regions of the United States, a standard nail spacing
applies (i.e., 6 inches on panel edges and 12 inches in the panel field); refer to Table
7.1.

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EXAMPLE 7.2 Roof-to-Wall Connections

Given
• Design wind speed is 120 mph gust with an open coastal exposure
• One-story home with a hip roof (28 ft clear span trusses with 2 ft overhangs)
• Roof slope is 6:12
• Trusses are spaced at 24 in on center

Find 1. Uplift and transverse shear load at the roof-to-wall connection

2. Connection detail to resist the design loads

Solution
1. Determine the design loads on the connection (Chapter 3)

Dead load (Section 3.3)

Roof dead load = 15 psf (Table 3.2)

Dead load on wall = (15 psf)[0.5(28 ft) + 2 ft] = 240 plf

Wind load (Section 3.6)

Step 1: Basic velocity pressure = 18.8 psf (Table 3.7)

Step 2: Adjust for open exposure = 1.4(18.8 psf) = 26.3 psf

Step 3: Skip

Step 4: Roof uplift Gcp = -0.8

Overhang Gcp = +0.8

Step 5: Roof uplift pressure = -0.8(26.3 psf) = -21 psf
Overhang pressure = 0.8 (26.3 psf) = 21 psf

Determine the wind uplift load on the wall.

Design load on wall = 0.6D + Wu (Table 3.1)

= 0.6 (240 plf) + {(-21 psf)[0.5(28 ft) + 2 ft] – (21 psf)(2 ft)}
= - 234 plf (upward)

Design load per wall-to-truss connection = (2 ft)(-234 plf) = -468 lb (upward)

Determine the transverse shear (lateral) load on the roof-to-wall connection. The
transverse load is associated with the role of the roof diaphragm in supporting and
transferring lateral loads from direct wind pressure on the walls.

Design lateral load on the wall-to-truss connection

= 1/2 (wall height)(wall pressure)(truss spacing)

Adjusted velocity pressure = 26.3 psf

Wall GCp = -1.2,+1.1*

Wind pressure = 1.1(26.3 psf) = 29 psf

*The 1.1 coefficient is used since the maximum uplift on the roof and roof

overhang occurs on a windward side of the building (i.e., positive wall

pressure).

= 1/2 (8 ft)(29 psf)(2 ft)

= 232 lb

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Thus, roof-to-wall connection combined design loads are:

468 lb (uplift)

232 lb (lateral, perpendicular to wall)*

*The lateral load parallel to a wall is not considered to be significant in this example
problem, although it may be checked to verify the transfer of lateral wind loads on the
roof to shear walls; refer to Chapter 6.

2. Determine a roof-to-wall connection detail to resist the combined design load.

Generally, manufacturers publish loading data for metal connectors for multiple loading
directions. The designer should verify that these values are for simultaneous multi-
directional loading or make reasonable adjustments as needed. In this example problem,
the NDS will be used to design a simple roof tie-down strap and slant nail connection.
A tie down strap will be used to resist the uplift load and typical slant nailing will be
used to resist the lateral load. The slant nailing, however, does not contribute
appreciably to the uplift capacity when a strap or metal connector is used; refer to
Section 7.3.6.

Uplift load resistance

Assuming an 18g (minimum 0.043 inches thick) metal strap is used, determine the
number of 6d common nails required to connect the strap to the truss and to the wall top
plate to resist the design uplift load.

The nail shear capacity is determined as follows:

Z = 60 lb (NDS Table 12.3F)

Z’ = ZCD (Section 7.3.2)
= (60 lb)(1.6)
= 96 lb

The number of nails required in each end of the strap is

(486 lb)/(96 lb/nail) = 5 nails

The above Z value for metal side-plates implicitly addresses failure modes that may be
associated with strap/nail head tear-through. However, the width of the strap must be
calculated. Assuming a minimum 33 ksi steel yield strength and a standard 0.6 safety
factor, the width of the strap is determined as follows:

0.6(33,000 psi)(0.043 in)(w) = 468 lb

w = 0.55 in

Therefore, use a minimum 1-inch wide strap to allow for the width of nail holes and an
a staggered nail pattern. Alternatively, a thinner strap may be used (i.e., 20g or 0.033
inches thick) which may create less problem with installing finishes over the
connection.

Lateral load resistance

Assuming that a 16d pneumatic nail will be used (0.131 in diameter by 3.5 inches long),
determine the number of slant-driven nails required to transfer the lateral load from the
wall to the roof sheathing diaphragm through the roof trusses. Assume that the wall
framing is Spruce-Pine-Fir (G = 0.42).

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Z = 88 lb (NDS Table 12.3A)*

*A 1-1/4- inch side member thickness is used to account for the
slant nail penetration through the truss at an angle.
Z’ = ZCD** **The Ctn value of 0.83 is not used because the nail is slant driven
and is not a toe-nail; refer to Section 7.3.6.

Z’ = (88 lb)(1.6) = 141 lb

Therefore, the number of nails required to transfer the transverse shear load is
determined as follows:

(232 lb)/(141 lb/nail) = 2 nails

Conclusion

The beginning of the uplift load path is on the roof sheathing which is transferred to the
roof framing through the sheathing nails; refer to Example 7.1. The uplift load is then
passed through the roof-to-wall connections as demonstrated in this example problem.
It should be noted that the load path for wind uplift cannot overlook any joint in the
framing.

One common error is to attach small roof tie-straps or clips to only the top member of
the wall top plate. Thus, the uplift load must be transferred between the two members
of the double top plate which are usually only face nailed together for the purpose of
assembly, not to transfer large uplift loads. This would not normally be a problem if
the wall sheathing were attached to the top member of the double top plate, but walls
are usually built to an 8 ft – 1 in height to allow for assembly of interior finishes and to
result in a full 8 ft ceiling height after floor and ceiling finishes. Since sheathing is a
nominal 8 ft in length, it cannot span the full wall height and may not be attached to the
top member of the top plate. Also, the strap should be placed on the structural
sheathing side of the wall unless framing joints within the wall (i.e., stud-to-plates) are
adequately reinforced.

Longer sheathing can be special ordered and is often used to transfer uplift and shear
loads across floor levels by lapping the sheathing over the floor framing to the wall
below. The sheathing may also be laced at the floor band joist to transfer uplift load,
but the cross grain tension of the band joist should not exceed a suitably low stress
value (i.e., 1/3Fv); refer to Chapter 5, Section 5.3.1.

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EXAMPLE 7.3 Rafter-to-Ceiling Joist Connection (Heel Joint)

Given
• Rafter and ceiling joist roof construction (without intermediate rafter
braces)
• Roof horizontal span is 28 ft and rafter slope is 6:12 (26 degrees)
• Roof framing is Hem-Fir (G=0.43) with a spacing of 16 inches on-center
• Roof snow load is 25 psf
• Rafter & roofing dead load is 10 psf
• Ceiling dead load is 5 psf

Find 1. The tension load on the heel joint connection

2. Nailing requirements

Solution
1. Determine the tensile load on the heel joint connection

Using basic principles of mechanics and pinned-joint analysis of the rafter and
ceiling joist “truss” system, the forces on the heel joint can be determined. First,
the rafter bearing reaction is determined as follows:

B = (snow + dead load)(1/2 span)(rafter spacing)

= (25 psf + 10 psf)(14 ft)(1.33 ft)
= 652 lb

Summing forces in the y-direction (vertical) for equilibrium of the heel joint
connection, the compression (axial) force in the rafter is determined as follows:

C = (652 lb)/sin(26o) = 1,487 lb

Now, summing the forces in the x-direction (horizontal) for equilibrium of the
heel joint connection, the tension (axial) force in the ceiling joist is determined as
follows:

T = (1,487 lb)cos(26o) = 1,337 lb

2. Determine the required nailing for the connection

Try a 12d box nail. Using NDS Table 12.3A, the following Z value is obtained:

Z = 80 lb

Z’ = ZCDCd (Section 7.3.2)

CD = 1.25* (snow load duration, Table 5.3)

*NDS uses a factor of 1.15
Cd = p/(12D) (NDS•12.3.4)
p = penetration into main member = 1.5 inches
D = nail diameter = 0.128 inches
Cd = 1.5/[12(0.128)] = 0.98

Z’ = (80 lb)(1.25)(0.98) = 98 lb

In Section 5.6.1, a system factor of 1.1 for tension members and connections in
trussed, light-frame roofing systems was discussed for repetitive member
applications (i.e., framing spaced no greater than 24 inches on center). Therefore,
the Z’ value may be adjusted as follows:

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Z’ = (98 lb)(1.1) = 108 lb

The total number of 12d box nails required is determined as follows:

(1,337 lb)/(108 lb/nail) = 12.3

If a 16d common nail is substituted, the number of nails may be reduced to about
8. If, in addition, the species of framing lumber was changed to Southern Yellow
Pine (G = 0.55), the number of nails could be reduced to 6.

Conclusion

This example problem demonstrates the design of one of the most critical roof
framing connections for site-built rafter and ceiling joist framing. In some cases,
the ceiling joist or cross-tie may be located at a higher point on the rafter than the
wall bearing location which will increase the load on the joint. In most designs, a
simple pinned-joint analysis of the roof framing is used to determine the
connection forces for various roof framing configurations.

The snow load duration factor of 1.25 was used in lieu of the 1.15 factor
recommended by the NDS; refer to Table 5.3. In addition, a system factor for
repetitive member, light-frame roof systems was used. The 1.1 factor is
considered to be conservative which may explain the difference between the
design solution in this example and the nailing required in Table 7.1 by
conventional practice (i.e., four 16d common nails). If the slant nailing of the
rafter to the wall top plate and wall top plate to the ceiling joist are considered in
transferring the tension load, then the number of nails may be reduced relative to
that calculated above. If a larger system factor than 1.1 is considered (say 1.3),
then the analysis will become more closely aligned with conventional practice;
refer to the roof framing system effects discussion in Section 5.6.1. It should also
be remembered that the NDS safety factor on nail lateral capacity is generally in
the range of 3 to 5. However, in more heavily loaded conditions (i.e., lower roof
slope, higher snow load, etc.) the connection design should be expected to depart
somewhat from conventional practice that is intended for “typical” conditions of
use.

In any event, 12 nails per rafter-ceiling joist joint may be considered unacceptable
by some builders and designers since the connection is marginally “over-crowed”
with fasteners. Therefore, alternative analysis methods and fastener solutions
should be considered with some regard to extensive experience in conventional
practice; refer to NDS•7.1.1.4 and the discussion above.

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EXAMPLE 7.4 Wall Sole Plate to Floor Connection

Given
• A 2x4 wall bottom (sole) plate of Spruce-Pine-Fir is fastened to a wood floor
deck
• Floor framing lumber is Hem-Fir
• A 3/4-inch-thick wood structural panel subfloor is used
• The bottom plate is subject to the following design loads due to wind and/or
earthquake lateral loads:
250 plf shear parallel-to-grain (shear wall slip resistance)
120 plf shear perpendicular-to-grain (transverse load on wall)
• The uplift load on the wall, if any, is assumed to be resisted by other
connections (i.e., uplift straps, shear wall hold-downs, etc.)

Find A suitable nailing schedule for the wall sole plate connection using 16d pneumatic
nails (0.131inch diameter by 3.5 inches long).

Solution
It is assumed that the nails will penetrate the sub-flooring and the floor framing
members. It will also be conservatively assumed that the density of the sub-floor
sheathing and the floor framing is the same as the wall bottom plate (lowest
density of the connected materials). These assumptions allow for the use of NDS
Table 12.3A. Alternatively, a more accurate nail design lateral capacity may be
calculated using the yield equations of NDS•12.3.1.

Using NDS Table 12.3A, it is noted that the closest nail diameters in the table are
0.135 and 0.128 inches. Interpolating between these values, using a side member
thickness of 1.5 inches, and assuming Spruce-Pine-Fir for all members, the
following Z value is obtained:

Z = 79 + [(0.131-0.128)/(0.135-0.128)](88 lb – 79 lb) = 83 lb*

Z’ = ZCD = 83 lb (1.6) = 133 lb

*Using the NDS general dowel equations as presented in AF&PA Technical

Report 12 (AF&PA, 1999), the calculated value is identical under the same
simplifying assumptions. However, a higher design value of 90 pounds may be
calculated by using only the subfloor sheathing as a side member with G = 0.5.
The ultimate capacity is conservatively predicted as 261 pounds.

Assuming that both of the lateral loads act simultaneously at their full design
value (conservative assumption), the resultant design load is determined as
follows:

Resultant shear load = sqrt[(250plf)2 + (120 plf)2] = 277 plf

Using the conservative assumptions above, the number of nails per linear foot of
wall plate is determined as follows:

(277 lb)/(133 lb/nail) = 2.1 nails per foot

Rounding this number, the design recommendation is 2 nails per foot or 3 nails
per 16 inches of wall plate.

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Conclusion

The number of 16d pneumatic nails (0.131 inch diameter) required is 2 nails per foot of
wall bottom plate for the moderate loading condition evaluated. The number of nails
may be reduced by using a larger diameter nail or by evaluating the nail lateral capacity
using the yield equations of NDS•12.3.1.

As in Example 7.3, some consideration of extensive experience in conventional

residential construction should also be considered in view of the conventional fastening
requirements of Table 7.1 for wood sole plate to floor framing connections (i.e., one
16d nail at 16 inches on center); refer to NDS•7.1.1.4. Perhaps 2 nails per 16 inches on
center is adequate for the loads assumed in this example problem. Testing has
indicated that the ultimate capacity of 2 16d pneumatic nails (0.131 inch diameter) can
exceed 600 lb per nail for conditions similar to those assumed in this example problem;
refer to Section 7.3.6. The general dowel equations under predict the ultimate capacity
by about a factor of two. Using 2 16d pneumatic nails at 16 inches on center may be
expected to provide a safety factor of greater than 3 relative to the design lateral load
assumed in this problem (i.e., [600 lb/nail] x [2nails/1.33 ft]/277 plf = 3.2).

As noted in Chapter 6, the ultimate capacity of base connections for shear walls should
at least exceed the ultimate capacity of the shear wall for seismic design and, for wind
design, the connection should at least provide a safety factor of 2 relative to the wind
load. For seismic design, the safety factor for shear walls recommended in this guide is
2.5; refer to Chapter 6, Section 6.5.2.3. Therefore, the fastening schedule of 2-16d
pneumatic nails at 16 inches on center is not quite adequate for seismic design loads of
the magnitude assumed in this problem (i.e., the connection does not provide a safety
factor of at least 2.5). The reader is referred to Chapter 3, Section 3.8.4 for additional
discussion on seismic design considerations and the concept of “balanced” design.

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EXAMPLE 7.5 Side-Bearing Joist Connection

Given
• A 2x10 Douglas-Fir joist is side-bearing (shear connection) on a built-up wood
girder
• The design shear load on the side-bearing joint is 400 lb due to floor live and
dead loads

Find 1. The number of 16d box toenails required to transfer the side-bearing (shear)
load.
2. A suitable joist hanger

Solution
1. Determine the number of 16d box toenails required

Z’ = ZCDCdCtn

Z = 103 lb (NDS Table 12.3A)

CD = 1.0 (normal duration load)

Cd = 1.0 (penetration into main member > 12D)

Ctn = 0.83 (NDS•12.3.7)

Z’ = (103 lb)(0.83) = 85 lb

The number of toenails required is determined as follows:

(400 lb)/(85 lb/nail) = 4.7 nails

Use 6 toenails with 3 on each side of the joist to allow for reasonable construction
tolerance in assembling the connection in the field.

2. As an alternative, select a suitable manufactured joist hanger.

Data on metal joist hangers and various other connectors are available from a number
of manufacturers of these products. The design process simply involves the selection of
a properly rated connector of the appropriate size and configuration for the application.
Rated capacities of specialty connectors are generally associated with a particular
fastener and species of framing lumber. Adjustments may be necessary for use with
various lumber species and fastener types.

Conclusion

The example problem details the design approach for two simple methods of
transferring shear loads through a side-bearing connection. One approach uses a
conventional practice of toe-nailing the joist to a wood girder. This approach is
commonly used for short-span floor joists (i.e., tail joist to header joist connections at a
floor stairwell framing). For more heavily loaded applications, a metal joist hanger is
the preferred solution.

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EXAMPLE 7.6 Wood Floor Ledger Connection to a Wood or Concrete Wall

Given
• A 3x8 wood ledger board (Douglas-Fir) is used to support a side-bearing floor
system.
• The ledger is attached to 3x4 wall studs (Douglas-Fir) spaced at 16 inches on
center in a balloon-framed portion of a home; as a second condition, the ledger
is attached to a concrete wall.
• The design shear load on the ledger is 300 plf due to floor live and dead loads.

Find 1. The spacing of 5/8-inch-diameter lag screws required to fasten the ledger to
the wood wall framing
2. The spacing of 5/8-inch-diameter anchor bolts required to fasten the ledger to
a concrete wall

Solution
1. Determine connection requirements for use of a 5/8-inch-diameter lag screw

Z’ = ZCDCgCΔCd (Section 7.3.2)

Zs⊥ = 630 lb* (NDS Table 9.3A)

CD = 1.0 (normal duration load)

Cg = 0.98 (2 bolts in a row) (NDS Table 7.3.6A)

CΔ = 1.0**

Cd = p/(8D) = (3.09 in)/[8(5/8 in)] = 0.62 (NDS•9.3.3)

p = (penetration into main member) – (tapered length of tip of lag screw)***

= 3.5 in – 13/32 in = 3.09 in

*The Zs⊥ value is used for joints when the shear load is perpendicular to the grain
of the side member (or ledger in this case).
**A CΔ value of 1.0 is predicated on meeting the minimum edge and end
distances required for lag screws and bolts; refer to NDS•8.5.3 and NDS•9.4.
The required edge distance in the side member is 4D from the top of the ledger
(loaded edge) and 1.5D from the bottom of the ledger (unloaded edge), where D is
the diameter of the bolt or lag screw. The edge distance of 1.5D is barely met for
the nominal 3-inch-wide (2.5 inch actual) stud provided the lag screws are
installed along the center line of the stud.
***A 6-inch-long lag screw will extend through the side member (2.5 inches
thick) and penetrate into the main member 3.5 inches. The design penetration into
the main member must be reduced by the length of the tapered tip on the lag
screw (see Appendix L of NDS for lag screw dimensions).

Z’ = (630 lb)(1.0)(0.98)(1.0)(0.62) = 383 lb

The lag bolt spacing is determined as follows:

Spacing = (383 lb/lag screw)/(300 plf) = 1.3 ft

Therefore, one lag screw per stud-ledger intersection may be used (i.e., 1.33 ft
spacing). The lag screws should be staggered about 2 inches from the top and
bottom of the 3x8 ledger board. Since the bolts are staggered (i.e., not two bolts
in a row), the value of Cg may be revised to 1.0 in the above calculations.

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2. Determine connection requirements for use of a 5/8-inch-diameter anchor bolt in a

concrete wall

Z’ = ZCDCgCΔ (Section 7.3.2)

Z⊥ = 650 lb* (NDS Table 8.2E)

CD = 1.0 (normal duration load)

Cg = 1.0**

CΔ = 1.0***

* The Z⊥ value is used since the ledger is loaded perpendicular to grain

**The bolts will be spaced and staggered, not placed in a row.

***Edge and end distance requirements of NDS•8.5.3 and NDS•8.5.4 will be met

for full design value.

Z’ = (650 lb)(1.0)(1.0)(1.0) = 650 lb

The required anchor bolt spacing is determined as follows:

Spacing = (650 lb)/(300 plf) = 2.2 ft

Therefore, the anchor bolts should be spaced at about 2 ft on center and staggered
from the top and bottom edge of the ledger by a distance of about 2 inches.

Note: In conditions where this connection is also required to support the wall
laterally (i.e., an outward tension load due to seismic loading on a heavy concrete
wall), the tension forces may dictate additional connectors to transfer the load into
the floor diaphragm. In lower wind or seismic load conditions, the ledger
connection to the wall and the floor sheathing connection to the ledger are usually
sufficient to transfer the design tension loading, even though it may induce some
cross grain tension forces in the ledger. The cross-grain tension stress may be
minimized by locating every other bolt as close to the top of the ledger as
practical or by using a larger plate washer on the bolts.

Conclusion

The design of bolted side-bearing connections was presented in this design

example for two wall construction conditions. While not a common connection
detail in residential framing, it is one that requires careful design consideration
and installation since it must transfer the floor loads (i.e., people) through a shear
connection rather than simple bearing. The example also addresses the issue of
appropriate bolt location with respect to edge and end distances. Finally, the
designer was alerted to special connection detailing considerations in high wind
and seismic conditions.

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EXAMPLE 7.7 Wood Sill to Foundation Wall

Given
• The foundation wall is connected to a wood sill plate and laterally supported as
shown in the figure below.
• Assume that the soil has a 30 pcf equivalent fluid density and that the
unbalanced backfill height is 7.5 ft.
• The foundation wall unsupported height (from basement slab to top of wall) is
8 ft.
• The wood sill is preservative-treated Southern Yellow Pine.

Find 1. The lateral load on the foundation wall to sill plate connection due to the
backfill lateral pressure
2. The required spacing of ½-inch-diameter anchor bolts in the sill plate

Solution
1. Determine the lateral load on the sill plate connection

Using the procedure in Section 3.5 of Chapter 3 and the associated beam
equations in Appendix A, the reaction at the top of the foundation wall is
determined as follows:

Rtop = ql3/(6L) = (30 pcf)(7.5 ft)3/[6(8 ft)] = 264 plf

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2. Determine the design lateral capacity of the anchor bolt and the required spacing

Z’ = ZCDCMCtCgCΔ (Section 7.3.2)

Z⊥ = 400 lbs* (NDS Table 8.2E)

CD = 0.9 (life-time load duration, Table 5.3)
CM = 1.0 (MC < 19%)
Ct = 1.0 (temperature < 100oF)
Cg = 1.0 (bolts not configured in rows)
*The value is based on a recommended 6 inch standard embedment of the anchor
bolt into the concrete wall. Based on conventional construction experience, this
value may also be applied to masonry foundation wall construction when bolts are
properly grouted into the masonry wall (i.e., by use of a bond beam).

Z’ = (400 lb)(0.9) = 360 lb

Anchor bolt spacing = (360 lb)/(264 plf) = 1.4 ft

Note: According to the above calculations, an anchor bolt spacing of about 16

inches on center is required in the sill plate. However, in conventional residential
construction, extensive experience has shown that a typical anchor bolt spacing of
6 ft on center is adequate for normal conditions as represented in this design
example. This conflict between analysis and experience creates a dilemma for the
designer that may only be reconciled by making judgmental use of the “extensive
experience” clause in NDS•7.1.1.4. Perhaps a reasonable compromise would be
to require the use of a 5/8-inch-diamter anchor bolt at a 4 ft on center spacing.
This design may be further justified by consideration of friction in the connection
(i.e., a 0.3 friction coefficient with a normal force due to dead load of the
building). The large safety factor in wood connections may also be attributed to
some of the discrepancy between practice or experience and analysis in
accordance with the NDS. Finally, the load must be transferred into the floor
framing through connection of the floor to the sill (see Table 7.1 for conventional
toenail connection requirements). In applications where the loads are anticipated
to be much greater (i.e., taller foundation wall with heavier soil loads), the joint
may be reinforced with a metal bracket at shown below.

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Conclusion

This example demonstrates an analytic method of determining foundation lateral

loads and the required connections to support the top of the foundation wall
through a wood sill plate and floor construction. It also demonstrates the
discrepancy between calculated connection requirements and conventional
construction experience that may be negotiated by permissible designer judgment
and use of conventional residential construction requirements.

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EXAMPLE 7.8 Deck Header to Post Connection

Given
• A 2x8 preservative-treated header is attached to each side of a deck post in a
bolted, double shear connection to support load from deck joists bearing on the
headers.
• The deck post is a preservative treated 4x4.
• The deck framing lumber is preservative-treated Southern Yellow Pine.
• The design double shear load on the connection is 2,560 lb (1,280 lb per header).

Find Determine if two 5/8-inch-diameter bolts are sufficient to resist the design load.

Solution
Calculate the design shear capacity of the bolted joint assuming that the bolts are
located approximately 2 inches from the top and bottom edge of the 2x8 headers
along the centerline of the 4x4 post.

Z’ = ZCDCMCtCgCd (Section 7.3.2)

Zs⊥ = 1,130 lb* (NDS Table 8.3A)

CD = 1.0** (Normal duration of load)
CM = 1.0 (MC < 19%)
Ct = 1.0 (Temperature < 100oF)
Cg = 0.98 (2 bolts in a row) (NDS Table 7.3.6A)
CΔ = 1.0 (for the bottom bolt only)*** (NDS•8.5.3)
*The Zs⊥ value is used because the side members (2x8) are loaded perpendicular to grain and the

main member (4x4) is loaded parallel to grain.

**A normal duration of load is assumed for the deck live load. However, load duration studies for

deck live loads have not been conducted. Some recent research has indicated that a load duration

factor of 1.25 is appropriate for floor live loads; refer to Table 5.3 of Chapter 5.

***The top bolt is placed 2 inches from the top (loaded) edge of the 2x8 header and does not meet

the 4D (2.5 inch) edge distance requirement of NDS•8.5.3. However, neglecting the bolt entirely

will under-estimate the capacity of the connection.

Z’ = (1,130 lb)(0.98) = 1,107 lb (bottom bolt only)

If the top bolt is considered to be 80 percent effective based on its edge distance
relative to the required edge distance (i.e., 2 inches / 2.5 inches = 0.8), then the
design shear capacity for the two bolts in double shear may be estimated as
follows:

Z’ = 1,107 lb + 0.8(1,107 lb) = 1,993 lb < 2,560 lb NG?

Conclusion

The calculation of the design shear capacity of a double shear bolted connection is
demonstrated in this example. As shown in the calculations, the connection
doesn’t meet the required load in the manner analyzed. A larger bolt diameter or
3 bolts may be used to meet the required design load. However, as in previous
examples, this connection is typical in residential deck construction (i.e.,
supporting deck spans of about 8 ft each way) and may be approved by the
“extensive experience” clause of NDS•7.1.1.4. As additional rationale, the

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capacity of shear connections in the NDS is related to a yield (or deformation) limit
state and not capacity. On the basis of capacity, the safety margins are fairly
conservative for such applications; refer to Section 7.3.1. The use of a 1.25 load
duration factor for the deck live load will also increase the joint capacity to a value
nearly equivalent to the design load assumed in this example.

7-44 Residential Structural Design Guide

 Chapter 7 - Connections

EXAMPLE 7.9 Wood King and Jamb Stud to Floor or Foundation Connection

Given
• From Example 7.2, the net design uplift load at the roof-to-wall connection
was determined to be 234 plf for a 120 mph gust, open exposure wind
condition.
• Assume that the uplift loads at the top of the wall are adequately transferred
through interconnection of wall framing members (i.e. top plates, sheathing,
studs, headers to king and jamb studs, etc.) to the base of the upper story wall.
• The framing lumber is Hem-Fir

Find 1. The net uplift load at the base of the king and jamb studs adjacent to a 6 ft
wide wall opening
2. An adequate connection detail to transfer the uplift load

Solution
1. Determine the net design uplift load at the base of the king and jamb studs
supporting the 6 ft header using the ASD load combinations in Chapter 3.

Tributary load
= (1/2 header span + 1/2 stud spacing)[uplift load – 0.6(wall dead load)]
= [0.5(6 ft) + 0.5(1.33 ft)][234 plf – 0.6(64 plf)]
= 717 lb (uplift)

2. Determine the number of 8d common nails in each end of an 18g (0.043 inch
minimum thickness) steel strap

Z’ = ZCD (Section 7.3.2)

Z = 82 lb (NDS Table 12.3F)

CD = 1.6 (wind load duration)

Z’ = (82 lb)(1.6) = 131 lb

The number of nails required in each end of the strap is determined as follows:

(717 lb)/(131 lb/nail) = 6 nails

Note: As an option to the above solution, the same strap used on the layout studs
may be used on the jamb and king stud connection by using multiple straps. The
uplift strap on the layout studs would be required to resist 234 plf (1.33 ft) = 311
lb. Therefore, two or three of these straps could be used at wall opening location
and attached to the jamb and king studs. If the single strap is used as calculated in
the example problem, the jamb and king studs should be adequately
interconnected (i.e., face nailed) to transfer shear load from one to the other. For
example, if the header is strapped down to the top of the jamb stud and the king
stud is strapped at its base, then the two members must be adequately fastened
together. To some degree, the sheathing connections and other conventional
connections will assist in strengthening the overall load path and their
contribution should be considered or enhanced as appropriate.

Residential Structural Design Guide 7-45

 Chapter 7 - Connections

As another alternative design, the king/jamb stud uplift connection may serve a
dual role as a wind uplift strap and a shear wall hold-down restraint if the wall
segment adjacent to the opening is designed to be a part of the building’s lateral
force resisting system (i.e., shear wall segment). The method to calculate hold-
down restraint forces for a shear wall is detailed in Chapter 6, Section 6.5.2.4.
The uplift force due to wind would be simply added to the uplift force due to
shear wall restraint to properly size a hold-down bracket or larger strap than
required for wind uplift alone.

Regardless of whether or not the wall segment is intended to be a shear wall

segment, the presence of wind uplift straps will provide overturning restraint to
the wall such that it effectively resists shear load and creates overturning restraint
forces in the uplift straps. This condition is practically unavoidable because the
load paths are practically inseparable, even if the intention in the design analysis
is to have separate load paths. For this reason, the opposite of the approach
described in the paragraph above may be considered to be more efficient. In other
words, the wind uplift strap capacity may be increased so that these multiple
straps also provide multiple overturning restraints for perforated shear walls; refer
to Chapter 6, Section 6.5.2.2. Thus, one type of strap or bracket can be used for
the entire job to simplify construction detailing and reduce the potential for error
in the field. This latter approach is applicable to seismic design (i.e., no wind
uplift) and wind design conditions.

Conclusion

In this example, the transfer of wind uplift loads through wall framing adjacent to
a wall opening is addressed. In addition, several alternate design approaches are
noted that may optimize the design and improve construction efficiency – even in
severe wind or seismic design conditions.

7-46 Residential Structural Design Guide

 Chapter 7 - Connections

EXAMPLE 7.10 Concrete Wall to Footing (Shear) Connection

Given
Maximum transverse shear load on bottom of wall = 1,050 plf (due to soil)

Dead load on wall = 1,704 plf

Yield strength of reinforcement = 60,000 psi

Wall thickness = 8 inches

Assume µ = 0.6 for concrete placed against hardened concrete not intentionally

roughened.

f’c = 3,000 psi

Find • Whether a dowel or key is required to provide increased shear transfer capacity
• If a dowel or key is required, size accordingly

Solution
1. Determine factored shear load on wall due to soil load (i.e., 1.6H per Chapter 3,
Table 3.1)

V = 1,050 plf

Vu = 1.6 (1,050 plf)= 1,680 plf

2. Check friction resistance between the concrete footing and wall

Vfriction = µN = µ(dead load per foot of wall)

= (0.6)(1,704 plf) = 1,022 plf < Vu = 1,680 plf

Therefore, a dowel or key is needed to secure the foundation wall to the footing.

3. Determine a required dowel size and spacing (Section 7..2 and ACI-318•5.14)

Avf = Vu / (φfyµ)

= (1,680 plf)/[(0.85)(60,000)(0.6)] = 0.05 in2 per foot of wall

Try a No. 4 bar (Av = 0.20 in2) and determine the required dowel spacing as
follows:

Avf = Av/S
0.05 in2/lf = (0.2 in2)/S
S = 48 inches

Conclusion

This example problem demonstrates that for the given conditions a minimum of
one No. 4 rebar at 48 inches on center is required to adequately restrict the wall
from slipping. Alternatively, a key may be used or the base of the foundation wall
may be laterally supported by the basement slab.

It should be noted that the factored shear load due to the soil lateral pressure is
compared to the estimated friction resistance in Step 1 without factoring the
friction resistance. There is no clear guideline in this matter of designer
judgment.

Residential Structural Design Guide 7-47

 Chapter 7 - Connections

EXAMPLE 7.11 Concrete Anchor

Given
• 1/2-inch diameter anchor bolt at 4 feet on center with a 6 inch embedment
depth in an 8-inch thick concrete wall
• The bolt is an ASTM A36 bolt with fy = 36 ksi and the following design
properties for ASD; refer to AISC Manual of Steel Construction
(AISC,1989):
Ft = 19,100 psi (allowable tensile stress)
Fu = 58,000 psi (ultimate tensile stress)
Fv = 10,000 psi (allowable shear stress)
• The specified concrete has f’c = 3,000 psi
• The nominal design (unfactored) loading conditions are as follows:
Shear load = 116 plf
Uplift load = 285 plf
Dead load = 180 plf

Find Determine if the bolt and concrete are adequate for the given conditions.

Solution
1. Check shear in bolt using appropriate ASD steel design specifications (AISC,
1989) and the ASD load combinations in Chapter 3.

shear load 116 plf (4 ft)

fv = = = 2,367 psi
bolt area (0.196 in 2 )
Fv = 10,000 psi
fv ≤ Fv OK

2. Check tension in bolt due to uplift using appropriate ASD steel design
specifications (AISC, 1989) and the appropriate ASD load combination in
Chapter 3.

T = [ (285 plf) - 0.6 (180 plf)] (4 ft) = 708 lb

708 lb
ft = T = = 3,612 psi
A bolt 0.196 in 2
ft ≤ Ft

3,612 psi < 19,100 psf OK

3. Check tension in concrete (anchorage capacity of concrete) using ACI-318•11.3

and the appropriate LRFD load combination in Chapter 3. Note that the assumed
cone shear failure surface area, Av, is approximated as the minimum of π (bolt
embedment length)2 or π (wall thickness)2.

Vu = T = [1.5 (285 plf) - 0.9 (180 plf)] (4 ft) = 1,062 lb

π (6 in) 2 = 113 in 2
Av = minimum of 
π (8 in) 2 = 201 in 2
φVc = φ4Av f ’c = (0.85)(4)(113 in2) 3,000 psi = 21,044 lb

Vu ≤ φVc

1,062 lb ≤ 21,044 lb OK

7-48 Residential Structural Design Guide

 Chapter 7 - Connections

Conclusion

A 1/2-inch diameter anchor bolt with a 6 inch concrete embedment and spaced 4
feet on center is adequate for the given loading conditions. In lieu of using an
anchor bolt, there are many strap anchors that are also available. The strap anchor
manufacturer typically lists the embedment length and concrete compressive
strength required corresponding to strap gauge and shear and tension ratings. In
this instance, a design is not typically required−the designer simply ensures that
the design loads do not exceed the strap anchor’s rated capacity.

Residential Structural Design Guide 7-49

 Chapter 7 - Connections

7.6 References
ACI, Building Code Requirements for Structural Concrete and Commentary, ACI
Standard 318-99, American Concrete Institute, Farmington Hills, MI,
1999a.

ACI, Building Code Requirements for Masonry Structures, ACI Standard 530,
American Concrete Institute, Farmington Hills, MI, 1999b.

AF&PA, General Dowel Equations for Calculating Lateral Connection Values,

Technical Report 12, American Forest & Paper Association, Washington,
DC, 1999.

AF&PA, National Design Specification for Wood Construction (NDS), American

Forest & Paper Association, Washington, DC, 1997.

AISC, Manual of Steel Construction Allowable Stress Design, Ninth Edition,

American Institute of Steel Construction, Inc., Chicago, 1989.

ASTM, Standard Specification for Driven Fasteners: Nails, Spikes, and Staples
(ASTM F 1667), American Society of Testing and Materials, West
Conshohocken, PA, 1995.

ASTM, Standard Terminology of Nails for Use with Wood and Wood-Base
Materials (ASTM F 547), American Society of Testing and Materials,
West Conshohocken, PA, 1990.

Conner, H., Gromala, D., and Burgess, D., “Roof Connections in Houses: Key to
Wind Resistance,” Journal of Structural Engineering, Vol. 113, No. 12,
American Society of Civil Engineers, Reston, VA, 1987.

Cunningham, T.P., Roof Sheathing Fastening Schedules For Wind Uplift, APA
Report T92-28, American Plywood Association, Tacoma, WA, 1993.

Hoyle, R.J. and Woeste, F.R., Wood Technology in the Design of Structures, fifth
edition, Iowa State University Press, Ames, IA, 1989.

HUD, Reliability of Conventional Residential Construction: An Assessment of

Roof Component Performance in Hurricane Andrew and Typical Wind
Regions of the United States, prepared by the NAHB Research Center,
Inc., for the U.S. Department of Housing and Urban Development,
Washington, DC, 1999a.

HUD, Perforated Shear Walls with Conventional and Innovative Base Restraint
Connections, prepared by the NAHB Research Center, Inc., for the U.S.
Department of Housing and Urban Development, Washington, DC, 1999b.

7-50 Residential Structural Design Guide

 Chapter 7 - Connections

ICC, International One- and Two-Family Dwelling Code, International Code

Council, Inc., Falls Church, VA, 1998.

McClain, T.E., “Design Axial Withdrawal Strength from Wood: II. Plain-Shank
Common Wire Nails,” Forest Products Journal, Volume 47, No. 6,
Madison, WI, 1997.

Mizzell, D.P. and Schiff, S.D., Wind Resistance of Sheathing for Residential
Roofs, Clemson University, Clemson, SC, 1994.

Murphy, S., Pye, S., and Rosowsky, D., System Effects and Uplift Capacity of
Roof Sheathing Fasteners, Structures Congress, American Society of Civil
Engineers, New York, NY, 1995.

NAHB, Cost Effective Home Building: A Design and Construction Handbook,

prepared by the NAHB Research Center, Inc., for the National Association
of Home Builders, Washington, DC, 1994.

NAHB, Wood Frame House Construction, Second Edition, edited by Robert

Stroh, Ph.D., and Gerald Sherwood, P.E., Delmar Publications and NAHB
Home Builder Press, Washington, DC, 1982.

NES, Power-Driven Staples and Nails for Use in All Types of Building
Construction, NER-272, National Evaluation Service, Inc., Falls Church,
VA, 1997.

Reed, T.D., Rosowsky, D.V., and Schiff, S.D., Uplift Capacity of Rafter-to-Wall
Connections in Light-Frame Construction, Clemson University, Clemson,
SC, 1996.

Showalter, J., Line, P., and Douglas, P., Calculation of Lateral Connection Values
Using General Gowel Equations, Paper No. 994176, American Society of
Agricultural Engineers, St. Joseph, MI, 1999.

Stieda, C.K.A, et al., Lateral Strength of Bolted Wood-to-Concrete Connections,

Forintek Canada Corp., Vancouver, British Columbia, Canada, February
1999.

Residential Structural Design Guide 7-51

 Chapter 7 - Connections

7-52 Residential Structural Design Guide

 Appendix A

Shear and Moment

Diagrams and

Beam Equations

V 2
q = equivalent fluid density of soil (pcf)

L -h R 2
qh = soil presure (psf) at x = 0
− qh 3
V2 = − R 2 =
6L
1 2 h
V1 = R1 = qh (l − )
L 2 3L
h 1
Vx = V 1 − xq (2h − x) (where x < h)
2
x Vx = V2 (where x ≥ h)
R 1 1 1
Mx = V1x − qhx 2 + qx 3 (where x < h)
q h V 1
M m a x 2 6
S H E A R M O M E N T Mx = −V2 (L - x) (where x ≥ h)

2V1
x @ M max = h − h 2 −
q

qL3  hL L2 h 2 h3 
Δ max (at x ≅ L ) ≅  − − + 
2 EI 128 960 48 144L 
Figure A.1 - Simple Beam (Foundation Wall) - Partial Triangular Load

Residential Engineering Design Guide A-1

Appendix A – Shear and Moment Diagrams and Beam Equations

M max
P 1
P 2 V M M M
Vmax = R 2 =
m a x 1 2 m a x L
e 1 e R M 1 = P1e1
2
1
M 2 = P2 e 2

M max = M 2 − M 1 where M 2 > M 1

= M max = M 1 − M 2 where M 1 > M 2

L
x
M x = M max  
L
x
R 2

S H E A R M O M E N T

Figure A.2 - Simple Beam (Wall or Column) - Eccentric Point Loads

L R = Vmax =
wL
x 2

w L 
Vx = w  − x 
2 

R R M max =
wL2 L
(at x = )
L /2 L /2 8 2

Mx =
wx
(L − x )
2
V Δ max =
5wL4 L
(at x = )
384EI 2
S H E A R V Δx =
wx 3
24EI
(
L − 2Lx 2 + x 3 )
M m a x

M O M E N T
Figure A.3 - Simple Beam - Uniformly Distributed Load

A-2 Residential Structural Design Guide

 Appendix A - Shear and Moment Diagrams and Beam Equations

L R 1 = V1 =
w max

x 3

w m a x R 2 = V2 =
2w max
3
w max w 2
Vx = − max
R 1 R 2
3 L2

0 .5 8 L 0 .4 2 L L 2w max L
M max (at x = )=
3 9 3
V 1 w max x
Mx = (L2 − x 2 )
S H E A R V 3L2
2
8 w L3
Δ max (at x = L 1 − ) = max
M m a x
15 77 EI
w max x
Δx = (3x 4 − 10L2 x 2 + 7L4 )
180EIL2
M O M E N T

Figure A.4 - Simple Beam - Load Increasing Uniformly to One End

L
x P
Pb
R1 = V1 (max when a<b) =
L
Pa
R 1 R 2
R2 = V2 (max when a>b) =
L
a b Pab
Mmax (at point of load) =
L
V 1 S H E A R Mx (when x<a) =
Pbx
L
V 2 a (a + 2b) Fab (a + 2b) 3a (a + 2b)
Δmax [at x = when a<b] =
3 27EIL
Pa 2 b 2
M Δa (at point of load) =
m a x 3EIL
Pbx 2 2 2
Δx (when x<a) = (L - b - x )
M O M E N T 6EIL

Figure A.5 - Simple Beam - Concentrated Load at Any Point

Residential Engineering Design Guide A-3

Appendix A – Shear and Moment Diagrams and Beam Equations

L R1 = V1 =
P1 (L − a) + P2 b
L
x
P1a + P2 (L − b)
P 1
P 2
R2 = V2 =
L

Vx [when a<x <(L-b)] = R1 – P1

R 1 R 2
M1 (max when R1<P1) = R1a
a b
M2 (max when R2<P2) = R2b
V 1
Mx (when x<a) = R1x
S H E A R V 2
Mx [when a<x <(L-b)] = R1x - P1(x-a)

M M 2
1

M O M E N T
Figure A.6 - Simple Beam - Two Unequal Concentrated Loads Unsymmetrically Placed

L
R = Vmax = wL
w
Vx = wx
wL2
Mmax (at fixed end) =
x R 2
wx 2
Mx =
V m a x
2
S H E A R Δmax (at free end) =
wL4
8EI
M Δx =
w
M O M E N T m a x
24EI
(x4 – 4L3x + 3L4)

Figure A.7 - Cantilever Beam - Uniformly Distributed Load

A-4 Residential Structural Design Guide

 Appendix A - Shear and Moment Diagrams and Beam Equations

L
R=V=P
x P
Mmax (at fixed end) = Pb
R Mx (when x>a) = P(x-a)
a b
Pb 2
Δmax (at free end) = (3L-b)
6EI
V Pb 3
Δa (at point of load) =
S H E A R 3EI
Pb 2
Δx (when x<a) = (3L-3x-b)
M O M E N M m a x
6EI
P(L − x) 2
Δx (when x>a) = (3b-L+x)
6EI

Figure A.8 - Cantilever Beam - Concentrated Load at Any Point

L
3wL
w R1 = V1 =
8
5wL
R2 = V2 = Vmax =
8
R x R 2
Vx = R1 - wx
1 wL2
Mmax =
V 1
8
3 9
M1 (at x = ) = L= wL2
3 /8 L V 2
8 128
S H E A R wx 2
1 /4 L Mx = R1x ­
2
M 1 L wL4
Δmax (at x = (1 + 33 ) = 0.42L) =
M O M E N T M m a x
16 185EI
wx
Δx = (L3 – 3Lx2 + 2x3)
48EI

Figure A.9 - Beam Fixed at One End, Supported at Other - Uniformly Distributed Load

Residential Engineering Design Guide A-5

Appendix A – Shear and Moment Diagrams and Beam Equations

L R1 = V1 =
Pb 2
(a + 2L)
2L3
x P Pa
R2 = V2 = (3L2 - a2)
2L3
R 2 M1 (at point of load) = R1a
R 1 a b Pab
M2 (at fixed end) = (a + L)
2L2
V 1
Mx (when x<a) = R1x
Mx (when x>a) = R1x - P(x-a)
V 2 L2 + a 2 Pa (L2 − a 2 ) 3
S H E A R Δmax (when a<0.4L at x = L 2 ) =
3L − a 2 3EI (3L2 − a 2 ) 2
Pab 2
M 1
Δmax (when a>0.4L at x = L
a
)=
a
2L + a 6EI 2L + a
M O M E N T M Pa 2 b 3
2 Δa (at point of load) = (3L + a)
P a /R 2 12EIL3
Pa 2 x
Δx (when x<a) = 3
(3aL2 – 2Lx2 - ax2)
12EIL
Pa
Δx (when x>a) = 3
(L-x)2(3L2x - a2x - 2a2L)
12EIL

Figure A.10 - Beam Fixed at One End, Supported at Other - Concentrated Load at Any Point

L R=V=
wL
x w
2
L 
Vx = w  − x 
2 
R R Mmax (at ends) =
wL2
L /2 L /2 12
wL2
M1 (at center) =
24
V w
Mx = (6Lx - L - 6x2)
2
12
S H E A R V wL4
Δmax (at center) =
0 .2 L 384EI
wx 2
M 1 Δx = (L - x)2
24EI
M m a x M O M E N T M m a x

Figure A.11 - Beam Fixed at Both Ends - Uniformly Distributed Loads

A-6 Residential Structural Design Guide

 Appendix A - Shear and Moment Diagrams and Beam Equations

L R1 = V1 (max. when a<b) =

Pb 2
(3a + b)
x P L3
Pa 2
R R2 = V2 (max. when a>b) = (a + 3b)
1 R 2
L3
a b Pab 2
M1 (max. when a<b) =
L2
V 1 Pa 2 b
M2 (max. when a>b) =
S H E A R V 2
L2
2Pa 2 b 2
Ma (at point of load) =
L3
M p Pab 2
Mx (when x<a) = R 1 x −
M M L2
1 M E N T 2
2aL 2Pa 3 b 2
Δmax (when a>b at x = )=
3a + b 3EI (3a + b) 2
Pa 3 b 3
Δa (at point of load) =
3EIL3
Pb 2 x 2
Δx (when x<a) = (3aL - 3ax - bx)
6EIL3

Figure A.12 - Beam Fixed at Both Ends - Concentrated Load at Any Point

L R1 = V1 =
w 2 2
(L - a )
2L
x x 1 w
R2 = V2 + V3 = (L + a)2
w V2 = wa
2L

w 2 2
R 1
R 2
V3 =
2L
(L + a )
Vx (between supports) = R1 - wx
V 1 V
Vx1 (for overhang) = w(a - x1)
2 L  a2  w
M1 (at x = 1 − 2  ) = (L + a) 2 (L − a) 2
S H E A R V 2  L  8L2
3
wa 2
M2 (at R2) =
M 1
2
wx 2 2
M 2
Mx (between supports) =
2L
(L - a - xL)

M O M E N T Mx1 (for overhang) =

w
(a - x1)2
2
24EIL 4
Δx (between supports) = (L – 2L2x2 + Lx3 - 2a2L2 + 2a2x2)
wx
wx 1
Δx1 (for overhang) = (4a2L - L3 + 6a2x1 - 4ax12 + x13)
24EI

Figure A.13 - Beam Overhanging One Support - Uniformly Distributed Load

Residential Engineering Design Guide A-7

Appendix A – Shear and Moment Diagrams and Beam Equations

L R1 = V1 =
Pa
P L
x x 1 P
R2 = V1 + V2 = (L + a)
L
V2 = P
R 1
R 2 Mmax (at R2) = Pa
Pax
Mx (between supports) =
L
V 2 Mx1 (for overhang) = P(a - x1)
V 1 L PaL2
Δmax (between supports at x = )=
S H E A R 3 9 3EI
2
Pa
Δmax (for overhang at x1 = a) = (L + a)
M m a x
3EI
Pax 2 3
M O M E N T Δx (between supports) =
6EIL
(L - x )

Px 1
Δx (for overhang) = (2aL + 3ax1 - x12)
6EI

Figure A.14 - Beam Overhanging One Support - Concentrated Load at End of Overhang

2 L R1 = V1 = R3 = V3 =
3wL
8
x 10wL
R2 =
w 8
5wL
L L V2 = Vm =
8
R R wL2
1 R 2 3 Mmax = −
8
3L 9wL2
V V 2
M1 [at x = ]=
1 8 128
V V 3 3wLx wx 2
2 Mx [at x < L] = −
8 2
3 /8 L S H E A R 3 /8 L wL4
Δmax [at x ≅ 0.46L] =
185EI

M x
x M m a x

M O M E N T

Figure A.15 - Continuous Beam - Two Equal Spans and Uniformly Distributed Load

A-8 Residential Structural Design Guide

 Appendix A - Shear and Moment Diagrams and Beam Equations

2 L R1 = V1 =
7
wL
16
x 5
w R2 = V2 + V3 = wL
8
1
L L R3 = V3 = − wL
16
R 1 R 2
R 3
9
V2 = wL
16
7 49
Mmax [at x = L ] = wL2
V 1 V 16 512
3 1
V M1 [at R2] = − wL2
2 16
7 /1 6 L S H E A R Mx [at x < L] =
wx
(7L - 8x)
16
wL4
Δmax [at x ≅ 0.47L] =
M m a x 109EI
M 1
M O M E N T

Figure A.16 - Continuous Beam - Two Equal Spans with Uniform Load on One Span

x x 1 R1 = V1 =
M1
+
wL1
L1 2
w R2 = wL1 + wL2 - R1 - R3
M wL 2
L 1 L 2
R3 = V4 = 1 +
L1 2
R 1 R 2 R V2 = wL1 - R1
3
V3 = wL2 - R3
V 1 3 M1 [at x < L1 , max. at x =
R1
] = R1x =
wx 2
V w 2
V 2
4
wL 2 3 + wL1 3
M2 = −
S H E A R 8 (L 1 + L 2 )
R3 wx 1 2
M3 [at x1 < L2 , max. at x1 = ] = R3x1 -
w 2
M 1 M 3
M 2
M O M E N T

Figure A.17 - Continuous Beam - Two Unequal Spans and Uniformly Distributed Load

Residential Engineering Design Guide A-9

Appendix A – Shear and Moment Diagrams and Beam Equations

A-10 Residential Structural Design Guide

 Appendix B

Unit Conversions

The following list provides the conversion relationship between U.S. customary units and the International System
(SI) units. A complete guide to the SI system and its use can be found in ASTM E 380, Metric Practice.
To convert from to multiply by
Length
inch (in.) meter(µ) 25,400
inch (in.) centimeter 2.54
inch (in.) meter(m) 0.0254
foot (ft) meter(m) 0.3048
yard (yd) meter(m) 0.9144
mile (mi) kilometer(km) 1.6

Area
square foot (sq ft) square meter(sq m) 0.09290304
square inch (sq in) square centimeter(sq cm) 6.452
square inch (sq in.) square meter(sq m) 0.00064516
square yard (sq yd) square meter(sq m) 0.8391274
square mile (sq mi) square kilometer(sq km) 2.6

Volume
cubic inch (cu in.) cubic centimeter(cu cm) 16.387064
cubic inch (cu in.) cubic meter(cu m) 0.00001639
cubic foot (cu ft) cubic meter(cu m) 0.02831685
cubic yard (cu yd) cubic meter(cu m) 0.7645549
gallon (gal) Can. liquid liter 4.546
gallon (gal) Can. liquid cubic meter(cu m) 0.004546
gallon (gal) U.S. liquid* liter 3.7854118
gallon (gal) U.S. liquid cubic meter(cu m) 0.00378541
fluid ounce (fl oz) milliliters(ml) 29.57353
fluid ounce (fl oz) cubic meter(cu m) 0.00002957

Force
kip (1000 lb) kilogram (kg) 453.6
kip (1000 lb) Newton (N) 4,448.222
pound (lb) kilogram (kg) 0.4535924
pound (lb) Newton (N) 4.448222

Stress or pressure
kip/sq inch (ksi) megapascal (Mpa) 6.894757
kip/sq inch (ksi) kilogram/square 70.31
centimeter (kg/sq cm)

Residential Structural Design Guide B-1

Appendix B - Unit Conversions

To convert from to multiply by

pound/sq inch (psi) kilogram/square 0.07031

centimeter (kg/sq cm)
pound/sq inch (psi) pascal (Pa) * 6,894.757
pound/sq inch (psi) megapascal (Mpa) 0.00689476
pound/sq foot (psf) kilogram/square 4.8824
meter (kg/sq m)
pound/sq foot (psf) pascal (Pa) 47.88

Mass (weight)
pound (lb) avoirdupois kilogram (kg) 0.4535924
ton, 2000 lb kilogram (kg) 907.1848
grain kilogram (kg) 0.0000648

Mass (weight) per length)

kip per linear foot (klf) kilogram per 0.001488
meter (kg/m)
pound per linear foot (plf) kilogram per 1.488
meter (kg/m)

Moment
1 foot-pound (ft-lb) Newton-meter 1.356
(N-m)

Mass per volume (density)

pound per cubic foot (pcf) kilogram per 16.01846
cubic meter (kg/cu m)
pound per cubic yard kilogram per 0.5933
(lb/cu yd) cubic meter (kg/cu m)

Velocity
mile per hour (mph) kilometer per hour 1.60934
(km/hr)
mile per hour (mph) kilometer per second 0.44704
(km/sec)

Temperature
degree Fahrenheit (°F) degree Celsius (°C) tC = (tF-32)/1.8
degree Fahrenheit (°F) degree Kelvin (°K) tK= (tF+ 459.7)/1.8
degree Kelvin (°F) degree Celsius (°C) tC = (tK -32)/1.8

*One U.S. gallon equals 0.8327 Canadian gallon

**A pascal equals 1000 Newton per square meter.

The prefixes and symbols below are commonly used to form names and symbols of the decimal multiples and
submultiples of the SI units.

Multiplication Factor Prefix Symbol

1,000,000,000 = 109 giga G

1,000,000 = 106 mega M
1,000 = 103 kilo k
0.01 = 10-2 centi c
0.001 = 10-3 milli m
0.000001 = 10-6 micro µ
0.000000001 = 10-9 nano n

Residential Structural Design Guide B-2

 Index

A zone, 4-52
Dead load, 3-4, 3-24, 3-31, 3-32, 4-58, 4-61, 4-64,

Adhesive, 6-75
4-70, 4-72, 4-77, 4-80, 4-84, 5-49, 5-52, 5-72, 7-30,

Admixtures, 4-5, 4-6

7-47, 7-48

Allowable masonry stress, 4-35, 4-39

Decking, 5-5

Anchor bolt, 7-41

Defects, 1-17

Aspect ratio, 6-46

Deflection, 3-28, 3-38, 4-30, 4-32, 5-14, 5-16, 5-20,

Axial load, 4-20, 4-40, 5-64

5-21, 5-22, 5-55, 5-56, 5-80, 5-82, 5-83

Backfill, 4-34, 4-35, 4-47, 4-64, 4-70, 4-72, 4-80, 4-84

Deformation, 2-13, 3-40

Base shear, 6-42, 6-43, 6-49

Density, 3-6, 3-8, 3-9, 3-10, 3-18, 3-34, 4-4, 4-35,

Basement, 3-9, 5-70

4-64, 4-67, 4-70, 4-72, 4-80, 4-84, 4-87, 6-29

Beams and stringers, 5-5

Design load, 4-64, 5-72, 7-28, 7-30

Bearing, 4-8, 4-9, 4-12, 4-14, 5-11, 5-16, 5-17, 5-50,

Diaphragm, 6-11, 6-12, 6-14, 6-18, 6-38, 6-39, 6-40,

5-53, 5-55, 5-56, 5-63, 7-27

6-56

Bending, 4-14, 4-22, 4-31, 5-13, 5-14, 5-16, 5-17, 5-18,

Dimension lumber, 5-5

5-20, 5-53, 5-56, 5-74, 5-81, 5-84

Dowel, 4-24, 7-26, 7-50

Blocking, 6-24
Drainage, 4-34, 4-47

Board, 5-62, 6-24, 7-2

Drift, 6-35, 6-37

Bolt, 7-8, 7-9

Durability, 3-19, 5-6

Bottom plate, 6-27, 6-43

Earthquake (see Seismic also), 1-21, 1-22, 1-23, 1-25,

Box nail, 7-5

2-15, 2-17, 3-22, 3-24, 3-25, 3-29, 3-37, 3-39, 6-1,

Bracing, 1-20, 1-22, 1-23, 1-24, 4-2, 5-15, 5-19, 5-23,

6-2, 6-19, 6-75, 6-78

5-27, 5-34, 5-43, 5-44, 5-46, 5-48, 5-63, 5-72, 5-74,

Eccentricity, 4-26, 4-27, 4-82, 4-86

6-2, 6-9, 6-24, 6-26, 6-74

Engineered wood, 1-8, 5-16, 5-30

Bridging, 5-27, 5-83

Epoxy-set anchor, 7-17

Built-up beam, 5-28

Euler buckling, 4-25, 4-82, 5-15, 5-38

Built-up column, 5-38

Expansive soil, 3-30

Cantilever, 4-14, 5-55, 5-56, 5-57, 5-58, 6-60, 6-66

Exposure, 5-8

Capacity, 4-8, 4-21, 4-22, 4-23, 4-25, 4-32, 4-36, 4-37,

Failure, 1-20, 4-13, 6-3, 6-8

4-38, 4-39, 4-40, 4-42, 5-16, 6-25, 6-26, 6-29, 7-27,

Fastener, 3-34, 5-31, 6-24

7-51
Flexure, 4-14, 4-15, 4-17

Ceiling joist, 5-21, 5-40, 7-2

Flitch plate beam, 5-30

Checks, 5-16
Flood load, 2-4

Chord, 6-42, 6-49

Floor joist, 5-24

Cold-formed steel, 1-9, 5-26

Footing, 4-8, 4-10, 4-11, 4-14, 4-16, 4-47, 4-54, 4-58,

Collector, 6-8, 6-54, 6-67

4-61, 4-62, 7-23, 7-47

Column, 4-28, 5-11, 5-15, 5-18, 5-39, 5-70, 5-81

Foundation wall, 1-17, 3-4, 4-25, 4-34, 4-47, 4-85

Combined bending and axial load, 5-16

Free water, 5-6

Common nail, 7-4

Fungi, 5-6

Composite action, 2-4

Geometry, 1-13, 2-3, 3-11, 4-76, 5-79, 6-11, 6-20, 6-36

Compression parallel to grain, 5-10

Grade, 4-5, 4-6, 4-20, 4-42, 4-49, 4-50, 5-8, 5-55, 5-58,

Compression perpendicular to grain, 5-10

5-63, 5-70, 6-22, 6-23

Concentrated load, 3-6

Gravel footing, 4-11

Concrete masonry unit, 4-6, 4-7

Gravity load, 2-3, 3-31, 3-32

Concrete masonry, 1-10, 4-6, 4-7

Grout, 3-5, 4-8

Concrete, 1-6, 1-7, 1-10, 1-11, 1-25, 1-26, 3-5, 3-6,

Gypsum, 1-17, 3-6, 6-24, 6-78

3-38, 4-2, 4-4, 4-5, 4-6, 4-7, 4-10, 4-11, 4-13, 4-14,
Header, 5-14, 5-37, 5-67, 5-82, 7-2, 7-43

4-16, 4-20, 4-22, 4-23, 4-25, 4-28, 4-29, 4-30, 4-31,

Hold-down, 6-9, 6-27, 6-28, 7-9

4-32, 4-41, 4-44, 4-47, 4-48, 4-49, 4-50, 4-58, 4-64,

Horizontal diaphragm, 2-11, 6-6

4-68, 4-70, 4-72, 4-75, 4-77, 4-88, 4-89, 4-90, 7-1,

Horizontal reinforcement, 4-83

7-23, 7-24, 7-25, 7-26, 7-27, 7-38, 7-47, 7-48, 7-50

Horizontal shear, 5-53

Connection, 7-8, 7-9, 7-11, 7-30, 7-33, 7-35, 7-37,

Hurricane, 1-18, 1-19, 1-20, 1-21, 1-26, 1-27, 2-15,

7-38, 7-43, 7-45, 7-47, 7-50, 7-51

2-25, 7-20, 7-50

Cripple stud, 5-32

I-joists, 1-8, 5-22, 5-24, 5-25, 5-26, 5-28, 5-30, 5-54

Cyclic, 3-38
Impact, 3-18, 3-40, 5-12, 5-83

Cyclic, 6-74, 6-75

Insulating concrete form (ICF), 1-10, 4-51

Damage, 1-19, 1-22, 1-25, 1-26, 2-23, 3-39

Jetting, 4-52

Dampening, 3-25
Joist hanger, 7-9

Key, 1-18, 1-20, 1-23, 2-15, 3-29, 5-10, 6-18, 7-24,

7-25, 7-50

Residential Structural Design Guide

Index

Lag screw, 7-11, 7-18, 7-19

Risk, 1-27, 2-22

Lateral load, 2-4, 3-12, 3-15, 4-21, 4-36, 4-39, 7-31

Roof overhang, 3-19, 3-34

Lateral support, 4-34

Roof truss, 3-35, 5-41, 5-42, 5-43

Limit state, 2-15, 2-17, 5-9, 5-10, 5-51, 5-65, 5-66

Safety, 2-1, 2-14, 2-16, 2-17, 2-19, 2-21, 2-22, 2-24,

Lintel, 4-31, 4-32, 4-44, 4-77

3-39, 3-40, 5-16, 6-29

Live load, 3-6, 3-31, 3-32, 4-58, 4-61, 4-64, 4-70, 4-72,
Seismic (see Earthquake also), 1-25, 2-2, 2-3, 3-23,

4-77, 4-80, 4-84, 5-49, 5-52

3-24, 3-26, 3-39, 3-40, 4-34, 6-29, 6-41, 6-48, 6-60,

Load combination, 3-2, 4-87, 5-25

6-62, 6-63, 6-64, 6-67, 6-75, 6-76, 6-78

Load duration, 5-9, 5-11, 5-12, 5-36

Shakes, 3-5

Load sharing, 2-4

Shank, 7-7

Load-bearing wall, 5-35

Shear parallel to grain, 5-10

Machine stress rated, 5-5

Shear wall, 2-11

Minimum reinforcement, 4-77, 4-83

Sheathing, 5-31, 5-45, 5-62, 6-38, 6-74, 7-20, 7-28,

Model building code, 1-13

7-50, 7-51

Modular housing, 1-6

Shrinkage, 5-6, 5-16, 5-23, 5-51

Modulus of elasticity, 5-10

Single shear, 3-28, 6-9, 6-28, 6-30

Moisture, 5-6
Sinker nail, 7-5

Monolithic slab, 4-49

Site-fabricated beam, 5-30

Mortar, 4-7, 4-36, 4-88

Slab-on-grade, 4-49

Nail size, 5-31, 5-45, 6-30

Sliding, 6-35, 6-40

Nail, 5-31, 5-45, 6-22, 6-30, 6-38, 6-74, 7-2, 7-4, 7-5,
Slump, 4-5, 4-88

7-6, 7-28
Snow load, 2-17, 4-64

NBS, 2-4, 2-24, 6-14, 6-76

Softwood, 5-6, 5-83

Nonsway frame, 4-70

Soil bearing test, 4-8

One-way shear, 4-12

Sole plate, 7-2

Oriented strand board (OSB), 1-6, 1-8, 5-7, 5-8, 5-31,

Solid, 3-5, 4-7, 4-35, 4-36, 4-48

5-63, 6-23, 6-41, 6-42, 6-48, 6-67

Spaced column, 5-38

Overturning, 6-31, 6-33

Species, 5-4, 5-55, 5-59, 5-63, 5-67, 6-29, 7-12

Parallel shear, 4-21, 4-85

Specific gravity, 3-6, 6-25, 6-29, 6-36, 6-37, 6-41,

Partition, 5-44
6-48, 6-52

Permafrost, 3-39, 4-57

Splice, 7-9

Permanent wood foundation, 4-47

Static, 6-75

Perpendicular shear, 4-21, 4-23

Stiffness, 5-11, 6-14, 6-35, 6-40

Pile cap, 4-50

Strap tie, 7-9

Piles, 4-2, 4-50

Structural wood panel, 3-6, 5-7

Plate, 2-25, 5-23, 5-42, 5-44, 5-84, 7-35

Strut, 6-6

Platform framing, 1-1

Stucco, 6-23

Plywood box beam, 5-30

Stud, 4-47, 5-5, 5-14, 5-63, 5-84, 6-41, 6-48, 7-2, 7-45

Plywood, 1-26, 5-7, 5-8, 5-30, 5-31, 5-81, 5-83, 6-77,

Sway frame, 4-25

7-50
System, 2-2, 3-4, 3-26, 5-13, 5-14, 5-22, 5-25, 5-33,

Pneumatic nail, 7-6

5-37, 5-40, 5-67, 5-82, 5-83, 6-4, 7-19, 7-51

Portal frame, 6-37

Temperature, 3-30, 5-11, 7-43

Portland cement, 1-22, 1-23, 4-4, 4-6

Tension capacity, 5-63

Post-and-beam framing, 1-1

Tension parallel to grain, 5-10

Posts and timbers, 5-5

Termites, 5-7

Preservative-treated wood, 4-1, 4-45

Tie-down, 1-20, 3-16, 3-17, 3-19, 3-20, 3-34

Probability, 2-16, 2-23, 2-24, 3-38

Timber pile, 4-50

Punching shear, 4-12

Toenail, 3-34, 6-3, 7-2

Rafter, 3-35, 5-40, 5-43, 5-72, 5-76, 5-77, 5-78, 7-2,

Top plate, 6-27

7-9, 7-33
Topographic effect, 3-15

Rankine, 3-8
Tributary area, 6-11

REACH, 1-15
Tributary load, 7-45

Rebar, 4-6
Truss, 1-5, 1-7, 2-25, 2-9, 2-10, 3-17, 3-33, 3-35, 3-19,

Reinforcement, 4-5, 4-18, 4-30, 4-43, 4-49

4-87, 5-18, 5-23, 5-28, 5-41, 5-42, 5-43, 5-44, 5-45,

Reliability, 1-26, 2-16, 2-24, 2-25, 5-13, 5-14, 5-82,

5-46, 5-79, 5-23, 5-42, 5-44, 5-84, 6-18, 6-66

5-84, 7-50
V zone, 4-51

Resistance, 2-19, 2-21, 3-40, 5-81, 5-82, 6-1, 6-22,

Vibration, 5-22, 5-84

6-23, 6-25, 6-29, 6-75, 6-77, 6-78, 7-50, 7-51

Visually graded, 5-5

Ridge beam, 5-76

Water reducer, 4-5

Residential Structural Design Guide

 Index

Weight, 3-10, 4-4, 4-7, 4-80, 6-23, 6-74 Wood truss, 1-5

Wind load, 3-14, 3-15, 3-33, 5-63, 5-72, 7-28, 7-30 Yield,7-47

Withdrawal, 3-34, 6-66, 7-12, 7-16, 7-20, 7-28, 7-51

Residential Structural Design Guide

Index

Residential Structural Design Guide