4.1

Chapter 4: Load Tracing

4.1 Load Tracing

During the initial stages of a project, the designer makes assumptions regarding

the way loads (forces) are transferred through the structure to the foundation

(ground).

• These loads (forces) travel along load paths.

• The analysis method is known as load tracing.

Definition: “Load tracing involves the systematic process of determining loads and

support reactions of individual structural members and how these loads are

transferred to other structural elements.”

Simple determinate structures are analyzed using the following.

• Free-body diagrams (FBDs).

• Basic equations of equilibrium.

• The process starts at the top (with the uppermost roof element), tracing the

loads down through the structure to the foundation.

Load Paths

The economy and efficiency of the structure is improved by the following.

• Minimizing the load path to the foundation.

• Involving fewer structural elements.

• Using the unique and inherent strengths of the materials (e.g. tension in steel,

compression in concrete)

Tributary Area

Loads uniformly distributed over an area of roof or floor are assigned to individual

members (rafters, joists, beams, girders) based on the concept of tributary area.

• This concept typically considers the tributary area that a member must support

as being halfway between the adjacent similar members.

Consider the wood floor framing

system shown at the right with a

uniform load over the entire deck

area of 50 psf.

• Each beam has a span length of 16’.

4.2

Beams A and D

Tributary width for edge Beam A = half the distance between A and B.

• The tributary width for edge Beam A = 2’.

• Similarly, the tributary width for edge Beam D = 2’.

Beams B and C

Tributary width for interior Beam B = half the distance between A and B plus half

the distance between B and C.

• Tributary width for interior Beam B = 2’ + 2’ = 4’

• Similarly, the tributary width for interior Beam C = 4’.

Beam load = distributed load (psf) times the tributary width.

• The load on Beams A and D:

wA = wD = 50 psf x 2’ = 100 lb/ft

• The load on Beams B and C:

wB = wC = 50 psf x 4’ = 200 lb/ft

Framing Design Criteria: Direction of Span

Architectural character

• Exposed structural framing can contribute to the architectural expression of

buildings.

• Differences in the depth of the structural elements can help define individual

structural bays of a building (e.g. short/shallow joists loading long/deep beams).

Structural efficiency and economy

Considerations for structural efficiency and economy should include the following.

• The appropriateness of materials (e.g. wood, steel, concrete) selected for the

structural system.

• The span capacity and intermediate supports.

• The availability of material and skilled labor locally.

• Standard sections and repetitive spacing of uniform members are generally

more economical.

4.3

Mechanical and electrical system requirements

The location and direction of mechanical systems should be coordinated with the

intended structural system.

• Layering the structural system provides space for ducts and pipes to cross

structural members, eliminating the need to cut openings in the beams.

• Flush or butt framing saves space in situations where it is desirable or

necessary to limit floor-to-floor dimensions.

Openings for stairs and vertical penetrations

Most framing systems accommodate openings.

• It is generally economical to make openings parallel to the principal spanning

direction.

• If openings are not parallel, additional headers and connections create point

loads on members that would otherwise be designed for light, uniform loads,

increasing their size.

Construction and Load Paths: Pitched Roof Systems

Figures 4.8 to 4.11 (pp. 200 - 201 of the textbook) illustrate the construction and

load paths of typical pitched roof systems.

Single-level framing

• Construction: Single-level framing construction is a common roof system for

residential structures.

- The single-level framing system

consists of sheathing (plywood, other

structural panels, or boards), roof

rafters, ridge board, and ceiling

joists.

- The roof rafters, ridge board, and

ceiling joists combine to form a simple

truss spanning between bearing walls.

• Load path

- Loads on the roof are initially supported by the sheathing.

- The sheathing transfers the loads to

the roof rafters.

- The roof rafters transfer the loads

to the ceiling joists and to the bearing

walls that support the trusses.

4.4

Double-level framing

• Construction: Double-level framing construction is another common roof framing

system.

- The double-level framing system consists

of decking or sheathing (plywood, other

structural panels, or boards), rafter

beams, and a ridge beam.

- The rafter beams are supported at one

end by the ridge beam (usually at the

peak of the roof) and supported at the

other end by a bearing wall or by a

header beam.

- The ridge beam is supported at each end by a column or by a bearing wall.

• Load path

- Loads on the roof are initially supported by the decking or sheathing.

- The decking or sheathing transfers the loads to the rafter beams.

- The rafter beams transfer the loads

to the ridge beam at one end and to a

bearing wall or header beam at the

other end.

- The ridge beam transfers the loads to the supporting column or bearing wall.

Notice that each level of the structural framing spans in a perpendicular direction

to the next layer.

• The sheathing is perpendicular to rafters.

• The rafters are perpendicular to ridge beam and bearing walls.

Three-level framing

• Construction: A third method makes use of heavier roof beams (rather than

roof rafters or rafter beams).

- The three-level framing system

consists of decking, purlins, roof

beams, and a ridge beam.

- The center-to-center spacing between

the roof beams ranges from 4’ to 12’

(compared to 16” to 24” for roof

rafters or rafter beams).

4.5

- The ridge beam is supported at each end by a column or by a bearing wall.

- The purlins, spaced 1’-6” to 4’-0” on centers, are installed between the roof

beams and support the decking.

- The roof beams are supported by the ridge beam at one end (generally at

the peak of the roof) and supported by a bearing wall or header beam at the

other end.

• Load path

- Loads on the roof are initially supported by the decking.

- The decking transfers the load to the purlins.

- The purlins transfer the loads to the

roof beams as concentrated loads.

- The roof beams transmit the loads to the

ridge beam at one end and a bearing wall

or header beam at the other.

- Columns or wall framing support the ends of the ridge beam.

Load Paths: Wall Systems

Figures 4.12 to 4.17 (pp. 202 - 203 of the textbook) illustrate the load paths for

various types of loads acting on typical wall systems.

Bearing wall

A bearing wall is a vertical support system that transmits compressive forces

through the wall plane and to the foundation.

• Bearing wall systems can be constructed with masonry, cast-in-place concrete,

pre-cast concrete panels, or studs (wood or light-gauge metal framing).

Load Paths

Uniform distribution

Uniform compressive forces acting along the length of the wall result in a

relatively uniform distribution of force.

• Roof or floor joists (in typical light-wood framing) are closely spaced at 16” or

24” on center.

• This regular, close spacing is assumed as a uniformly distributed load along the

top of the wall.

• If there are no openings to disrupt the load path from the top to the bottom of

the wall, a uniform load will result on top of the footing.

4.6

Non-uniform distribution

Concentrated loads develop at the top of a wall when beams are spaced at wide

intervals.

• The effect of the concentrated load

spreads out as it moves down the wall.

- Depending on the wall material, the

area of influence of the concentrated

load is generally defined by an angle

of 45° or 60°.

• The resulting footing load will be non-

uniform with the largest forces directly

under the applied load.

• Disruptions in the structural continuity of the wall (e.g. a large window or door

opening) result in a non-uniform distribution of the compressive forces on the

footing.

“Arching action” over an opening

Openings in walls redirect the loads to either side of the opening.

• The natural stiffness of a concrete wall under compression produces an “arching

action” that contributes to the lateral distribution of the loads.

Openings in a stud wall Stud walls (wood and metal) are generally idealized as monolithic walls (except for

openings) when loaded uniformly from above.

• Openings require the use of headers (beams) that redirect the loads to either

side of the opening.

• Concentrated loads from the header reactions must be supported by a buildup

of studs resembling a column.

Concentrated loads – pilasters

In special cases where the concentrated loads are very large, walls may need to be

reinforced with pilasters directly under the beam.

• Pilasters are essentially columns and carry the large concentrated loads directly

to the footing.

• The walls between the pilasters are now considered as non-bearing walls except

for carrying their own weight.

4.7

Example Problems - Load Tracing

Problems 4.1 and 4.2

These homework problems will be worked together in class using the homework

problem worksheet available from the website.

4.8

Load Paths: Roof and Floor Systems

Figures 4.18 to 4.23 (pp. 204 - 205 of the textbook) illustrate the load paths for

common roof and floor systems.

One-level framing

• Construction: Pre-cast hollow-core

concrete planks or heavy timber-plank

decking is used to span closely spaced

bearing walls or beams.

- This is not a common framing system.

- Spacing of the supports (the distance between the bearing walls) is based on

the span capability of the concrete planks or timber decking.

• Load path

- Loads acting on the concrete planks or

timber-plank decking are transmitted

directly to the bearing walls.

Two-level framing

• Construction: Two-level framing is a very common type of floor system.

- The two-level framing consists of decking with closely spaced beams (called

joists) to support the deck.

- The decking is laid perpendicular to the

beam (joist) framing.

- Efficient structural sections of wood or

steel beams (joists) allow relatively long

spans between bearing walls.

- Lighter deck materials such as plywood

panels can be used to span between the

closely spaced beams (joists).

- Span (distances) between bearing walls and beams affect the size and

spacing of the joists.

• Load path

- Loads on the decking are transmitted to

beams (joists).

- The beams transmit loads to the bearing

walls.

4.9

Notice, again, that each level of structural framing spans in a perpendicular

direction to the next layer.

• The decking is perpendicular to the beams/joists, and the beams/joists are

perpendicular to the bearing walls.

Three-level framing

• Construction: This type of construction is used for buildings requiring large

open floor areas.

- The three-level framing consists of

decking or sheathing, joists, beams,

and girders, trusses, columns, or

bearing walls.

- Floor space is free of bearing walls

and with a minimum number of

columns.

- Construction typically relies on the

long span capacity of joists supported

by trusses or girders.

- The spacing of the primary structure and the layering of the secondary

structural members establish regular bays that subdivide the space.

• Load path

- Loads on the decking or sheathing are supported by the joists.

- The decking transfers the loads to

the joists.

- The joists transfer the loads to the

beams.

- The beams transfer the loads to

girders or trusses.

- The girders or trusses transfer the loads to columns or bearing walls.

Each level of framing is arranged perpendicular to the level directly above it.

4.10

Example Problems - Load Tracing

Problems 4.3 and 4,.4

These homework problems will be worked together in class using the homework

problem worksheet available from the website.

4.11

Load Paths: Foundation Systems

Figures 4.24 to 4.29 (pp. 206 - 207 of the textbook) illustrate common foundation

systems.

The foundation system for a particular structure or building depends on the

following.

• The use and size of the structure.

• Subsurface soil (geology) conditions at the site.

- A geologist or soils engineer will likely be part of the project team.

• The cost of the foundation system to be used.

A large building with heavy loads can often be supported on relatively inexpensive

shallow footings if the subsurface soils are dense and stable.

A large building constructed at a site with soft soils, compressive clay soil, or poorly graded soils (e.g. beach sand or “sugar” sand) may require expensive

foundations or soil stabilization.

• One such stabilization technique might be over-excavation and refill with

“borrow” material (such as stone) and the use of geo-textiles (geo-grids).

- This technique requires the removal, hauling, and dumping of poor materials.

- This technique requires the purchase, hauling, spreading and compaction of

“borrow” materials.

- This technique requires the purchase, handling, and placing of the geo-

textile materials.

• Chemical stabilization (using lime or cement) may provide a remedy for shallow

foundations.

• Pile or caisson foundations may be necessary in areas where poor soils are

present for significant depths below the ground surface.

Foundations are generally divided into two major categories: shallow foundations

and deep foundations.

Shallow foundations

• Shallow foundations essentially obtain their support on soil or rock.

- Soils with moderate to high soil-bearing capacities can provide adequate

support for most construction.

- Rock located just below the bottom of the structure can provide support in

direct bearing.

4.12

- Rock located just below the structure may offer challenges and increase the

costs of extending underground utilities.

• Vertical loads are transmitted from walls or columns to a footing.

- The footing then distributes the load over a large enough area so that the

allowable load-carrying capacity of the soil is not exceeded and settlement

(including differential settlement) is minimized.

Shallow foundations are of three basic types.

1. Spread footings support an individual column.

• The spread footing is usually square or circular in plan.

• The spread footing is generally simple and

economical for moderate to high soil-bearing

capacities.

- The footings are generally shallow.

- Simple wood framed forms are used.

- Pedestals and footings are reinforced

with little to no steel.

• The purpose of this footing is to distribute

the load over a large area of soil.

2. Wall footings (continuous strip footings) support bearing walls.

• Continuous strip footings are one of the most common types of footings used

to support a bearing wall.

- For example, a continuous strip footing is

commonly used to support a concrete

block foundation wall for a typical

residential structure.

- Continuous strip footings usually support

uniform bearing wall loads.

• The continuous strip footing is simple and

economical for moderate to high soil-bearing

capacities.

- The footings are generally shallow.

- Simple wood framed forms or metal forms are used.

- Pedestals and footings are reinforced with little to no steel.

• The wall footing width remains constant throughout its length if no large

concentrated loads occur.

4.13

3. Mat or raft foundations cover the entire plan area of the building.

• Mat foundations are used when soil

bearing is relatively low or where

loads are heavy in relation to soil-

bearing capacities.

• This foundation type is essentially one

large footing under the entire building

and the load is distributed over the

entire mat.

• A mat foundation is referred to as a raft foundation when it is placed deep

enough in the soil that the soil removed during excavation equals most or all

of the building’s weight.

Deep foundations

Deep foundations are generally piles, piers, or caissons installed in a variety of

ways.

• The function of a deep foundation is to carry building loads beneath a layer of

unsatisfactory soil to a satisfactory bearing stratum.

• Building loads are distributed to the soil in contact with the surface area of the

pile through skin friction (friction piles), in direct end-bearing (bearing piles) at

the bottom of the pile on a sound stratum of earth or rock, or a combination of

skin friction and direct bearing.

Deep foundations are of three basic types.

1. Pile foundations are the most common deep-foundation system.

• Piles are driven into the earth by pile-driving hammers powered with drop

hammers, compressed air, or diesel engines.

• Friction piles: Timber piles are

normally used as friction piles;

however, timber piles can rot if the

water table fluctuates.

• Bearing piles: Concrete and steel piles

are generally used as bearing piles.

- A combination of steel and

concrete is used when bearing piles

must be driven to great depths to

reach suitable bearing.

4.14

- Hollow steel casings are driven into the ground to a predetermined

bearing point, reinforcing steel (cages) may be placed within the casing,

and then the casings are filled with concrete.

◦ As each hollow steel casing section (typically 20’ long) is driven into

the ground, additional sections are welded to the end and then driven.

2. Pile caps are used when individual building columns are supported by more than a

single pile.

• The thick reinforced concrete cap that is

poured on top of a pile group distributes

the column load to all the piles in the

group.

3. Grade beams are used to transfer the loads from a building wall to a group of

piles.

• Piles or piers supporting bearing walls

are generally spaced at regular

intervals and are connected with a

continuous reinforced concrete grade

beam.

4.15

Example Problems - Load Tracing

Problems 4.5 and 4.6

These homework problems will be worked together in class using the homework

problem worksheet available from the website.

4.16

4.2 Lateral Stability Load Tracing

Geometric stability refers to a configuration property that preserves the

geometry of a structure.

• Geometric stability is achieved by the way the structural elements are

strategically arranged.

• Geometric stability is achieved by the way the structural elements interact to

resist loads.

All building structures require a bracing system.

• A bracing system provides the stability for the entire structure.

• The type and location of the bracing system directly affects the organizational

plan of the building and its final appearance.

The primary concerns in the design of any structure include the following.

• To provide sufficient stability to resist collapse.

• To prevent excessive deformation (deflection and racking), which may result in

the cracking of brittle surfaces and glass.

• To be adequately stiffened against gravity-induced loads.

• To be stable against horizontal forces (e.g. wind and seismic forces) coming

from two perpendicular directions.

The use of horizontal diaphragms (i.e. roof and floor planes) is the most common

system to resist lateral loads in wood-frame buildings.

• The roof sheathing can be designed economically to serve as both a vertical-

load and lateral-load carrying element.

Ways to achieve stability

There are several ways of achieving stability and counteracting the racking of the

frame under vertical and/or horizontal loading.

• Each solution has architectural implications.

• The selection of the bracing system must be made for reasons beyond being the

“most efficient structurally.”

- The “most efficient” systems may interfere with openings (such as doors,

windows, and internal passages).

Figures 4.37 to 4.42, 4.44, 4.46 - 4.48 (pp. 234 - 237 of the textbook) illustrate

common ways of achieving stability.

4.17

Diagonal Truss Member

A simple way of providing lateral stability is to introduce a simple diagonal member

connecting two diagonally opposite corners.

• In effect, a truss is created, and stability is

achieved through triangulation.

- If a single diagonal member is used, it must

be capable of resisting both tension and

compression forces, since lateral loads are

assumed to occur in either direction.

- The members need to be sized similarly to truss members in compression.

◦ Members subjected to compression have a tendency to “buckle.”

X-Bracing Members

Another strategy involves the use of two cross-bracing members with smaller

cross-sectional areas.

• These X-braces are also known as diagonal tension counters (discussed in Section 3.3).

- Only one counter is effective in resisting

the directional lateral load.

Knee-Bracing

A commonly used arrangement in carports and elevated wood decks is knee-bracing.

• This stiffening method triangulates the beam-column connection to provide a

degree of rigidity at the joint.

- The larger the knee-braces are, the more

effective their ability to control racking.

- Bracing is usually placed as close to 45° as

possible but will sometimes range between

30° and 60°.

• Knee-braces develop tension and compression

forces (like truss members) depending on the

lateral force direction.

• Some movement will still occur because of the pin connections at the base of

the columns.

4.18

Gusset Plates

Large gusset plates at each beam-column connection can also provide the required

rigidity to stabilize the frame.

• Some movement will occur because of the pin

connections at the base of the columns.

• Modifying the base into a more rigid connection

can add to the rigidity of the frame.

- Rigid connections induce bending moments in

the beams and columns.

Rigid Base Condition

Columns placed at some depth into the ground and set in concrete can provide a

rigid base condition.

• Resistance to lateral loads comes through the

columns acting as large vertical cantilevers.

• The horizontal beam transfers loads between

the columns.

Combination Knee-Brace and Rigid Column Base

Knee-braces may be used in conjunction with rigid column bases.

• All connections of the frame are rigid.

• The lateral loads are resisted through the

bending resistance offered by the beam and

columns.

• The lateral displacements are less than the

three previous examples (i.e. knee bracing,

gusset plates, and rigid base).

Rigid Beam/Column Joints

Connections may be made so that the beam and column form a rigid type of

connection.

• Steel-framed structures: The connections

may be made using bolts, welds, and

stiffener plates in specific arrangements.

4.19

• Concrete structures: A rigid connection may

be formed using reinforcing steel and

monolithically cast beams and columns.

Knee-Braced Structure with Roof Truss

A truss supported on two pin-connected columns is unstable.

• Knee-braces provide stability for

the truss to develop resistance to

racking.

Shear walls

Many residential and small- to mid-scale commercial buildings depend on the walls

(bearing and non-bearing) of the structure to develop the necessary resistance to

lateral forces.

• This type of lateral restraint, referred

to as a shearwall, depends on the vertical

cantilever capacity of the wall.

• Commonly used materials for shear walls

are concrete, concrete blocks, bricks,

and wood sheathing products such as

plywood, oriented strand board (OSB),

and wafer boards.

4.20

Example Problems – Lateral Stability

Problem 4.9 (p. 249)

Given: The frame with the lateral

load shown.

Find: The reaction forces at A and

B, and all other member forces.

Assume Ax = Bx

Solution

Find the reactions at the supports.

FBD: Entire frame

∑MA = 0 = - 1200 (16) + By (14)

14 By = 1200 (16) = 19,200

By = + 1371.4 lb

By = 1371.4 lb ↑

∑MB = 0 = - 1200 (16) - Ay (14)

14 Ay = - 1200 (16) = - 19,200

Ay = - 1371.4 lb Ay = 1371.4 lb ↓

∑Fx = 0 = Ax + Bx + 1200 (Assume Ax = Bx)

0 = Bx + Bx + 1200

2 Bx = - 1200

Bx = - 600 Ax = Bx = 600 lb ←

Find the forces acting on members AHG and FH.

FBD: Member AHG

∑MG = 0 = - 600 (16) + (1/ 2 ) HF (4)

0 = - 600 (16) + 2.828 HF

2.828 HF = 600 (16) = 9600

HF = + 3394.6 lb

HF = 3394.6 lb (T)

4.21

∑Fx = 0 = Gx + (1/ 2 ) HF – 600 + 1200

0 = Gx + 0.707 (3394.6) – 600 + 1200

Gx = - 2400 + 600 – 1200 = - 3000

Gx = 3000 lb ← on AHG

∑Fy = 0 = Gy + (1/ 2 ) HF - 1371.4

0 = Gy + 0.707 (3394.6) – 1371.4

Gy = - 2400 + 1371.4 = - 1028.6

Gy = 1028.6 lb ↓ on AHG

Find the forces acting on members BCD and CE.

FBD: Member BCD

∑MD = 0 = - 600 (16) - (1/ 2 ) CE (4)

0 = - 600 (16) – 2.828 CE

2.828 CE = - 600 (16) = - 9600

CE = - 3394.6

CE = 3394.6 lb (C)

∑Fx = 0 = Dx - (1/ 2 ) CE – 600

0 = Dx – 0.707 (- 3394.6) – 600

Dx = 0.707 (- 3394.6) + 600

Dx = - 2400 + 600 = - 1800

Dx = 1800 lb ← on BCD

∑Fy = 0 = Dy + (1/ 2 ) CE + 1371.4

0 = Dy + 0.707 (- 3394.6) + 1371.4

Dy = - 0.707 (- 3394.6) - 1371.4

Dy = + 2400 – 1371.4 = + 1028.6 lb

Dy = 1028.6 lb ↑ on BCD

4.22

Multiple bays

The previous discussion of frame stability from lateral loads was limited to single-

bay (panel) frames; however, most buildings contain multiple bays in the horizontal

and vertical directions.

• The principles that apply to single-bay frames also hold true for multiple-bay

frame structures.

• Often only one panel needs to be braced for the entire frame to be stabilized.

- It is rarely necessary for every panel to be braced to achieve stability.

Figure 4.50 (p. 238 of the textbook) illustrates the following common ways of

achieving stability in structures with multiple horizontal bays.

• Shear walls, diagonal tension counters, and diagonal truss brace.

Multistory and Multi-bay Structures

Multistory and multi-bay structures also use the same bracing principles as

previously discussed with some modifications.

• As the structures become taller, only certain types of bracing systems and

materials of construction remain practical from a structural and/or economic

standpoint.

- For example, knee-braces, although appropriate for smaller one- or two-

story structures, are not nearly as effective for larger structures.

◦ The horizontal force component within the knee-brace acts on the column

and produces a significant bending moment, which requires a larger

column size.

• Larger diagonal braces that go across an entire panel from opposite diagonal

points are found to be much more effective structurally.

- Bracing techniques are generally limited to the exterior wall planes of the

building to permit more flexibility for interior spaces.

- Diagonals, X-bracing, and K-trussing on multistory frames essentially form

vertical cantilever trusses that transmit lateral loads to the foundation.

• Reinforced concrete (or masonry) and braced steel framing used for stairwells

and elevators are often used as part of the lateral force strategy.

• Bracing systems must be provided at each story level.

Combinations of bracing, shear wall, and/or rigid frames are used in many buildings.

• Larger multi-story buildings contain utility/service cores, which include

elevators, stairs, ducts, and plumbing chases.

4.23

- These utility cores are strategically placed to meet functional and structural

criteria.

- Because these cores are generally solid to meet fireproofing requirements,

they can often function as excellent lateral resisting elements, in isolation or

as part of a larger overall strategy.

Figure 4.51 (p. 239 of the textbook) illustrates the following common ways of

achieving stability in multistory structures.

• X-bracing, eccentric braced frame, K-trussing, shear walls, and rigid frame.

Three-Dimensional Frames

Buildings are three-dimensional frameworks, as indicated in Figure 4.53 (p. 240 of

the textbook).

• Each planar frame represents just one of several (or many) frames that

constitute the structure.

• A fundamental requirement of geometric stability for a three-dimensional

structure is its ability to resist loads from three orthogonal directions (i.e.

vertically and both directions horizontally).

• A three-dimensional frame can be stabilized by use of bracing elements or

shear walls in a limited number of panels in the vertical and horizontal planes.

- In multistory structures, these bracing systems must be provided at each

and every story level.

The exterior walls of a building transfer the wind forces to the roof and floors,

which in turn direct them to the lateral load resisting system (e.g. shear walls or

braced frames).

• In wood-framed buildings or buildings with wood roof and floor systems, the

roof and floor sheathing is designed to connect to the supporting framing

members to function as horizontal diaphragms capable of transferring lateral

loads to the lateral load resisting system.

• In buildings with concrete roof and floor slabs, the slabs are designed to

function as diaphragms.

If the wood sheathing or reinforced concrete slab is designed to function as a

horizontal diaphragm for lateral forces in one direction, it probably can be

designed to function as a diaphragm for forces applied in the other direction.

4.24

• If the roof or floor sheathing is too light or flexible and unable to carry the

diaphragm forces, the horizontal framework must be designed with bracing

similar to braced walls or shear walls.

- Horizontal bracing may consist of tension counters, trusses, or stiff panels

in strategic locations (ref. Figure 4.53, p. 240 of the textbook).

Bracing Configurations

Once the roof plane (or floors) has been configured to function as a diaphragm, a

minimum requirement for stabilizing the roof is three braced (or shear) walls that

are neither all parallel nor concurrent to a common point.

• The arrangement of the walls is crucial in resisting loads from multiple

directions.

- More than three braced (or shear) walls are usually provided increasing the

structural stiffness of the framework in resisting lateral displacements.

• Braced (or shear) walls are located strategically throughout the structure to

minimize the potential of torsional displacements and moments.

- A common solution is to have two shear walls parallel to one another (a

reasonable distance apart) and a third wall (or perhaps more) perpendicular

to the other two.

- Figure 4.54 (p. 241 of the textbook) illustrates various shear wall

arrangements – some stable and others unstable.

Multistory Structures

In multistory structures, lateral loads (from wind and earthquake forces) are

distributed to each of the roof and floor (diaphragm) levels.

• At any given floor level, there must be an adequate number of braced (shear)

walls to transfer the cumulative lateral forces from the diaphragms above.

- Each story level is similar to the simple structures examined previously, in

which the diaphragm load was transferred from the upper level (roof) to the

lower level (ground).

Multistory structures are generally braced with a minimum of four braced planes

per story, with each wall being positioned to minimize torsional moments and

displacements.

• Although it is often desirable to position the braced walls in the same position

at each floor level, it is not always necessary.

- The transfer of shear through any one level may be examined as an isolated

problem.

4.25

Example Problems - Lateral Stability/Diaphragms and Shear walls

Problems 4.11 and 4.12

These homework problems will be worked together in class using the homework

problem worksheet available from the website.