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Structures Test Review Notes:

Selection of Structural Systems

Standard Structural Systems





relativel y strong in compression and tension,

easy to work with

easy to fasten to

used primarily in ONE
WAY structural systems where the load is
transmitted through structural members in one direction at a time.

JOISTS are a common use of wood

Light, closely spaced members that span between beams or bearing

Typical sizes are 2x6, 2x8, 2x10, and 2x12

Typical spacings are 12”, 16”, and 24” on center

Typical maximum normal span is about 20 feet, but spa
ns up to 25 feet
are often used.

Plywood or particle board usually span the top of joists as sheathing

Joists must be laterally supported due to their slenderness

Avoids twisting or lateral displacement

Bridging supports the bottom edge of the jois
ts while the sheathing
supports the top

Maximum intervals of not more than 8 feet are recommended for

Either solid or cross bridging may be used.

WOOD BEAMS are not available in the sizes they once were.

Solid wood beams for longer spans
have generally been replaced with


laminated construction.

Most common use of solid wood beams is with plank

Members are 4 to 6 inches wide nominal

Spaced at 4, 6, or 8 feet on center

Maximum normal span is about 10 to 20 feet

Wood decking is typically used as sheathing

GLUED LAMINATED construction is a popular method of wood

These structural members are made up of individual pieces lumber 3/4”
or 1
1/2” thick glued together in a factory

Standard widths are

1/8”, 5
1/8”, 6
3/4”, and 8

Typical spans range from 15 feet to 60 feet

Aesthetically pleasing structure

Can be manufactured in:

Tapered beams

Tapered and curved beams

Various styles of arches


sist of a top and bottom chord of solid or laminated wood separated
by a plywood web

Used in residential and light commercial construction

Allows longer spans than are possible with a wood joist system

This product is stronger and stiffer than a wood


PARALAM WOOD BEAM is made up of many veneers glued together to
form a beam

Used primarily as a header over openings

Has a higher modulus of elasticity than a standard wood joist

Has an allowable stress in bending about twice that of a Dou
glas Fir


wood joist

WOOD TRUSS is made up of standard wood members connected with
metal plates

Typical spans range from 24 to 40 feet

Typical depths of members range from 12 to 36 inches

Typical member spacing is 24 inches on center

Useful for residential and light commercial construction

Allow for passage of mechanical systems between webs of joists

due to difficulty in fabrication

BOX BEAM is made of plywood panels glu
ed and nailed to solid wood

Solid wood members are usually 2x4s

Typically used where depth of members is not critical

Used where other types of manufactured beams cannot be brought
to the building site

STRESSED SKIN PANELS same construction

as a box beam but used
for floor and roof structures

Solid wood members are usually 2x4s


Steel is one of the most used structural materials

High strength


Ability to adapt to a wide variety of structural conditions

Ductile material

Can undergo some deformation and return to its original shape

It will bend before it breaks

giving notice prior to failure

Well suited for multifloor construction

High strength


Structural continuity

Two of the most common str
uctural systems are:


Larger members span between vertical supports

Smaller beams frame into larger members

Girders span the shorter distance

Beams span the longer distance

Typical spans range from 25 to 40 feet

Typical beam sp
acing from 8 to 10 feet on center

Steel framing is typically covered with metal decking which spans
between the beams

A concrete floor may be poured over the decking to form a floor


Span between beams or bearing walls

al spans range from 60 to 96 feet

Typical depths range from 8 to 30 inches in 2 inch increments

Deep long
span joists can span up to 144 feet

Deep long span joist depths range from 18 to 72 inches

Typical floor joist spacing is 2 to 4 feet on center

Typical roof joist spacing is 4 to 6 feet on center

Efficient structural members

Commonly used for low
rise commercial construction

Can span long distances

Are non

Mechanical sys
tems can be run through the webs



Require formwork and are constructed in the field

Generally take longer to build than precast

Can conform to an almost unlimited variety of shapes, sizes, design


intentions, and structural

Majority of cast
place systems utilize only mild steel reinforcing

Some times post
tensioning steel is used

LIFT SLAB construction is sometimes used.

Two general types of cast
place concrete structures

way system

Slabs and beams are designed to transfer loads in one direction

A common one
way system is the beam
girder system
which functions similar to a steel system in which the slab is
supported by intermediate beams which are carried by larger

Typical spans range from 15 feet to 30 feet


Economical for most applications

Relatively easy to form

Allows penetrations and openings to be made in the slab

Concrete Joist System

Comprised of members spaced 26 or 36 inches apart

in one direction, which frame into larger beams

Typical spans range from 20 to 30 feet

Joist depths range from 12 inches to 24 inches

This system is easy to form since prefabricated metal pan
forms are used.

This system is good for light o
r medium loads where
moderate distances must be spanned.

way system

There are three principal two
way concrete systems

Flat plate

Flat slab

Waffle slab

All are designed for use in rectangular bays where the distance
between columns is the same (or close to the same) in both



Flat Plate

Simplest of the three

Slab is designed and reinforced to span in both directions
directly into the column

Because loads increase near the columns and there is no
provision to increase the thickness of the concrete or the
reinforcing at the columns this system is limited to light loads
and short spans.

Typical spans up to 25 feet

Typical slab thickness range from 6 to 12 inches

Very useful in situations where floor
floor height must be
kept to a minimum or an un
cluttered underfloor appearance
is desired.

Flat Slab

When spans of the flat plate are large or the loads heavie

flat plates will require drop panels

Drop panels are thickened slabs at the columns

Drop panels provide greater resistance against punching
shear failures

Truncated pyramids or cones are often called column capitals
and are used to handle punching

shear as well as large
bending moments.

This system can accommodate fairly heavy loads

Typical spans are up to 30 feet

Waffle slab system

Supports heavier loads than flat plate and flat slab

Support longer spans than the flat slab system

al spans up to 40 feet are possible within economical

Typically formed of prefabricated, reusable metal or
fiberglass forms

Typically faster construction due to standardized formwork

Often left unexposed with lighting integrated into the coffe



Usually formed in a plant under strictly controlled conditions

Quality control is better

Erection proceeds quickly

Especially if structure is composed of a limited number of repetitive

Majority of precast systems are prestressed

Some times mild steel reinforcing is used

Some times precast is done on the site

Typically limited to wall panels (referred to as tilt
up panels)

Precast structural members

Come in a variety of forms:

Rectangular beam

Inverted tee beam

Shaped beam

Single tee

Double tee

Hollow core slab

cast column

Can be used as structural members or wall panels

Precast concrete members are connected in the field using welding
plates cast into mem
bers at the plant

Structural Precast Concrete Members

Precast concrete is typically prestressed

High strength steel cables are stretched in the precasting forms
before the concrete is poured

After the concrete cures to a desired level, the cables are released
and they transfer compressive stresses to the concrete.

When the members are completely cured, the concrete member has
a built
in compressive stress which resists the tension forces cau
by the member’s own weight plus the live loads acting on the


Single Tee or Double Tee beams

Simultaneously serve as structural supports as well as floor or roof

Are easy and fat to erect

Topping concrete (usually about 2 inches

thick) is placed over the
tees to provide a uniform, smooth floor surface

Topping also provides increased strength when the tees are designed
to ac as composite beams.

Unloaded beams from the plant have camber built into them due to
the prestressing c
aused by the reinforcement

Camber is to disappear when live and dead loads are placed on the

Post Tensioned Concrete

Post tensioning steel

often called tendons

is stressed after the
concrete has been poured and cured

Tendons are:

l high strength wires

wire strands

Solid bars

Tendons are stressed with hydraulic jacks pulling on one or both

Hydraulic jack pressures:

100 to 250 psi for slabs

200 to 500 psi for beams

post tensioned concrete structural systems are useful where high
strength is required and where it may be too difficult to transsport
precast to the job site


Masonry as a structural system is generally limited to bearing walls

Masonry has hi
gh compressive strength

Masonry’s unitized nature makes it inherently weak in tension and bending

There are three basic types of masonry bearing wall construction:


Single wythe

Have no provisions for reinforcing or grouting

Double wythe

Both la
yers may be of the same material or different

May be grouted and reinforced or un


May be grouted and reinforced or un

Advantages of Masonry Bearing Walls:


Design flexibility


Resistance to weathering

Fire resistance

Sound insulation

Their mass makes them ideal for may passive solar energy applications

Joints in masonry must be reinforced horizontally at regular intervals

Strengthens the wall

Controls shrinkage crac

Ties multi
wythe walls together

Provides a way to anchor veneers to the back
up structure

Comes in a variety of forms and is generally placed at 16 inche o.c.

Vertical Reinforcement

Standard reinforcing bars sized and spaced in accordance wi
th the
structural requirements of the wall.

Horizontal bars are also used and are tied to the vertical bars

Entire assembly is set in grout

In single
wythe construction only vertical reinforcing is used with fully
grouted wall cavities

Thickness o
f walls determines three important properties:


Slenderness ratio

Ratio of the wall unsupported height to its thickness

Indication of the walls ability to resist buckling due to compressive
loads being applied to it

Flexural strength

Important property when the wall is subjected to lateral forces such as

Fire resistance

Depends on the material of the wall and its thickness

Composite Construction

Any structural system consisting of two or more materials designed to act
ether to resist loads

Composite construction is employed to utilize the best charachteristics of
each of the individual materials

Reinforced concrete construction is the most typical of composite

Other types of systems:

Composite steel

deck and concrete

Steel deck is designed with deformations or wires welded to the deck to
transfer load between steel and concrete

Concrete slab and steel beam systems

Headed stud anchors are used to transfer load between concrete and


them act as one unit

Open web steel joists with wood chords

Provide a nailable surface for the floor and ceiling while using the high
weight ratio of steel for the web members

Less frequently used composite systems:

Trusses with wood for compression members and steel rods for tension

Concrete filled steel tube sections

Walls and the Building Envelope

Non load bearing walls are not considered part of the structural system of a


There are 2 important structural considerations that non
load bearing walls do
have to withstand

Weight of the envelope that will need to be supported by the structure

Exterior loads placed on the envelope such as wind that will need to be

to the structure

Typical Attachment by system

Panels and curtain wall systems are attached with clips on the mullions at
the structural frame

Stone and masonry facings are attached with clip angles, continuous
angles, or special fastenings and are a
ttached to the structural framing at
the floor lines

Lightweight facings such as wood siding, shingles, and stucco need to be
applied over continuous sheathing firmly secured to the structural wall

One of the most important considerations is to

allow for movement such as
expansion and contraction

Movement can be provided for

Clip angles with slotted joints

Slip joints

Flexible sealants

Movement considerations:

Steel framed building do not present many problems with movement of
the st
ructural frame itself

Concrete structures are subject to creep over time and need special
connections to exterior envelope systems

Wood structures also deform over time due to wood shrinkage and long
term deflection

Complex Structural Systems


Trusses are structures comprised of straight members forming a number of
triangles with the connections arranged so that the stresses in the members are
either in tension or compression

Trusses can be used:





Trusses are primarily tension/compression structural systems

Some amount of bending is present in many of the members

This bending is due to loads applied between the connections and secondary
bending and shear stresses at the connections themsel
ves caused by minor
eccentric loading

Trusses can be field fabricated or assembled in the factory

Such as with open web steel joists and wood trussed rafters

Primary limiing factor is the ability to transport them from factory to the


Arches may have hinged or fixed supports

hinged and fixed arches are staically indeterminate

Hinged arches are primarily subjected to compressive forces

Allows arch to remain flexible and avoid high bending stresses under:

Live loading

Loading due to temperature changes

Foundation settlement

To resist loads in only compression the arch has to have a funicular

Funicular shape can be found by suspending the anticipate loads from a
cable and then turning the shape of the cable u
pside down.

Antonio Gaudi used this method of analysis in may of his structural

For a hinged arch supporting a uniform load across its span the
resultant shape is a parabola

There are two reactions at the supports of a hinged arch


Horizontal reactions or thrust

Thrust is inversely proportional to the rise or height of the arch

If rise is reduced by one
half the thrust will be doubled

Sometimes arches have hinges at their apex


This is called a three
hinged arch

Makes the structure statically determinate

Arches can be constructed of : (each with inherent limitations)


span 50 to 500 feet


span 20 to 320 feet


span 50 to 240 feet


Variety of shapes:

Classic half round
arch of the romans

Pointed gothic arches

Decorate arabic arches

Functional parabolic shapes

Rigid Frames

A rigid frame is constructed so that the vertical and horizontal members work
as a single structural unit.

This is a more efficient struct
ure because all three members resist vertical
and lateral loads together

There are forces and reactions in a rigid frame unlike post
beam due to
the members being rigidly attached to one

Columns are subjected to both compressive and bending


Columns are subjected to thrust similar to an arch

Attachement of columns to foundation may be hinged or rigid

This connection will result in slightly different loads on the columns

Fixed frame is stiffer than the hinged frame

Thrust in t
he fixed frame is greater then in the hinged frame

When a horizontal beam is not required

the rigid frame takes on the
appearance of a gable frame

This shape decreases the bending stresses in the two inclined members

This shape increases the compression in the two inclined members

Because rigid frames develop a high moment at the connections between
the horizontal and vertical members

the amount of material is often
increased near these points.


Space Frames

A space frame is a structural system consisting of trusses in two directions
rigidly connected at their intersections

More common type of space frame is a triangulated space frame

where the
bottom chord is offset from the top chord

Space frames are v
ery efficient structures for enclosing large rectangular

Typical spans up to 350 feet

depth ratios range from 20:1 to 30:1

Light weight

Repetitive nature reduces fabrication and erection time

A computer is needed for analysis and de

Folded Plates

Loads are transferred in two directions

First in the transverse direction

Second in the longitudinal direction

Plates act a beams between supports

There are compressive stresses above the neutral axis

There are tensile str
esses below the neutral axis

Folded plates are usually constructed of reinforced concrete

3 to 6 inches thick

typical spans of 30 to 100 feet (longer spans possible with reinforced

Thin Shell Structures

Curved surface that resists loads through tension, compression, and shear in
the plane of the shell only

Theoretically, there are no bending or moment stresses in a thin shell strucure

Material is practically always reinforced concrete 3 to 6 inches th

Forms can be:



Barrel vaults


Saddle shaped hyperbolic paraboloid

Typical spans from 40 feet to over 200 feet

Hyperbolic paraboloids span 30 to 160 feet

Stressed Skin Structures

Comprised of sheathing sandwiching interm
ediate members

Typically made of wood

Typical spans of 12 to 35 feet

Suspension Systems

Most commonly seen on bridge design

Some large stadiums have utilized suspension systems to suspend roofs

Federal Reserve Bank in Minneapolis is a suspende
d building

Cable suspension systems are similar to arches

Loads they support must be resisted by both vertical reactions and
horizontal thrust reactions

In suspension systems vertical reactions are up and horizontal thrust
reactions are outward since

the sag tends to pull the ends together

Shallow sags result in high reactions

Deep sags result in lower reactions

Suspension systems can only resist loads with tension

The shape of the cable will change as the load changes

No bending stresses are possible

Disadvanage: instability due to wind and other types of loading

Suspension systems must be stabilized or stiffened with a heavy infill material

Inflatable Structures

Similar to suspension systems

can only resist l
oads in tension

Held in place with constant air pressure which is greater than the outside air

skin inflatable structure

Created by inflation of a series of voids (like an air mattress)

This type of system elliminates the need for a
n “air
lock” for entry and


Inflatable structures are inherently unstable in the wind and cannot support
concentrated loads

Used for temporary enclosures and for large, single space buildings such as
sports arenas

Structural System Selection Cri

Resistance to loads

Primary consideration

Anticipated loads

Weight of the structure (dead load)

External forces such as wind, snow, earthquakes

Loads caused by use of the building such as people, furniture, and
equipment (live loads)

Calculated from known weights of equipment and materials and
building code requirements

anticipated loads

Difficult to plan for

Include changes in use of the facility

Overloading caused by extra people or equipment

Unusual snow loads


of water on the roof

Degradation of the structure itself

Very unusual loads will be the primary determinate of the structural

Building Use and Function

Type of occupancy

Example: office building works well with spans in the 30 to 40 foot


In a location where building height is limited, a client may want to squeeze as
many floors into a multi
story building as possible

Integration with other building systems

Mechanical electrical and plumbing systems and how they integrate wit
h the


Exterior cladding systems

Cost Influences

Selecting materials and systems that are most appropriate for the

loads proposed

spans required

style desired

integration needed

fire resistance called for

all other factors

refining the selected sstem so that the most economical arrangement and use
of materials is selected

Fire Resistance

Building codes dictate the fire resistance of materials based on building use

Ratings range from 1 to 4 hours

Range is the indicat
ion of how long a member can withstand a standard
fire test before it becomes dangerously weakened

Two considerations

Combustibility of the member itself

Loss of strength anticipated due to heat

Construction Limitations

Time, material, and labor



International Style

steel post and beam construction

Consider fire proofing requirements

Social and Cultural Influences

Look at surrounding buildings and materials used

Chapter 2

Loads on Buildings



Probable magnitudes of building loads have been determined over a long
period of time based on successful experience and the statistical probability
that a particular situation will result in a given load.

Building loads are also based on the worst case

Loads are defined by building codes and by common practice

Codes provide:

Live load requirements

Wind values

Earthquake values

Standard published tables provide accepted weights of building materials for
dead load calculations.

t loads on buildings are static

Loads determined to be dynamic, such as wind loads, are considered to be
static so calculations are easier to perform.

Gravity Loads

Dead Loads are vertical loads due to the weight of the buildin and any
permenant equi

Dead loads include:


Exterior walls

Interior walls


Mechanical equipment

Weight of structure must be assumed to

make a preliminary calculation of
the size of the structural member; then the actual weight can be used for
checking the calculation.

Most dead loads are easily calculated from published lists of weights of
building materials found in standard referenc
e sources.

UBC requires that floors in office buildings and other buildings where
partition locations are subject to change be designed to support an extra 20
psf of dead load

Live Loads


Live loads are those imposed on the building by its particular use and

Live loads are generally considered movable or temporary




Movable equipment


Does not include

Wind loadig

Earthquake loading

Live loads are established by building codes for different occupancies

The code also requires that floors be designed to support concentrated
loads if the specified load on an otherwise unloaded floor would produce
stresses greater than those caused by the uniform load.

The concentrated load is assumed to be located on any
space 2.5 feet

Live Load reductions

When a structural member supports more than 150 square feet

Except floors in places of public assembly

Excpet for live loads greater than 100 psf

Where there is snow load greater than 20 ps
f on any pitched roof over
20 degrees

Loads on sloped surfaces are assumed to act vertically on a horizontal plane
projected from the slope

Combination Loads

It is generally agreed that when calculating all the loads acting on a
building, all of them

will probably not act at once.

Acceptable combination of loads are as follows:

Dead load plus floor live load plus roof live load (snow)

Deal load plus floor live load plus wind (or seismic)

Dead load plus floor live load plus wind plus 1/2 snow


Dead load plus floor live load plus snow plus 1/2 wind

Dead load plus floor live load plus snow plus seismic

Lateral Loads


Wind loading is a dynamic process

Pressure, direction, and timing are constantly changing

To aid in calculations, wind is considered a static force

Variable that effect wind loading

Wind velocity

Pressure on a building varies as the square of the velocity


Height of the wind above the ground

Slower near the ground and increases with height

Wind values are taken at 33 feet above the ground


Prarie vs. city



Size of building

Shape of building

Surface texture of building


Positive pressure
on the windward side

Negatve pressure on leeward side and roof

Greater pressure at

Building corners



Other projections

Special concerns:

Building shapes


Design features

Closely spaced buildings

Small openings at ground level

Wind is fluid

Building drift

The distance a building moves from side to side in the wind

A building should be designed stiff enough so that the maximum
drift does not exceed 1/500 of the height of the building.


Earthquake produces dynamic loads

Ground moves both vertically and horizontally (laterally)

Lateral movement is considered most significant

Some tall buildings or structures require a dynamic structural analysis
(requires a computer to calcu

Building codes allow a static analysis of the loads produced by an
earthquake to simplify structural design

With static analysis, the total horizontal shear at the base of the building
is calculated according to a standard formula

This total fo
rce is distributed to the various floors of the building so
the designer knows what force the structure must resist.

Miscellaneous Loads

Dynamic loads

Dynamic loads are loads that are applied suddenly or changes rapidly

When a force is only applied suddenly it is often called an impact load

Examples of dynamic loads:

Moving automobiles

Elevators travelling in a shaft

Helicopter landing on the roof of the building

Dynamic loads do not occur on every building

C lists minimum requirements for many of these types of loads

In many cases, dynamic loads are static loads multiplied by an impact


A uniques type of dynamic load is a resonant load

Rhythmic application of a force to a structure with the same
fundamental period as the structure itself.

Fundamental period is the time it takes the structure to complete one
full oscillation

Resonant loads start small and slowly build up over time

A tuned dynamic damper can be placed at the top of tall buildi
ngs to
dampen the effects of wind sway

Temperature induced loads

Expansion and contraction of materials

Measured in the coefficient of expansion in/foot/degree F

Soil Loads

Retaining walls required to resist the lateral pressure of retained

Code allows walls retaining drained earth to be designed for pressure
equal to that exerted by a fluid weighing 30 pcf and having a depth
equal to that of the retained earth

This is in addition to surcharge of vertical loads on the surface and any
other lateral loads

Must resist sliding by at least 1.5 times the lateral force

Must resist overturning by at least 1.5 times the overturning moment


Water tanks, swimm
ing pools, retaining walls that are undrained will
have water loads

Water weighs 62 pcf

Force exerted by water is called hydrostatic pressure

Chapter 3

Structural Fundamentals

Statics and Forces

Statics deals with bodies in a state of equilibri

Equilibrium is said to exist when the resultant of any number of forces
acting on a body equal zero.

Three fundamental principals of equilibrium apply to buildings:


The sum of all vertical forces acting on a body must equal zero

The sum of all the horizontal forces acting on a body must equal zero

The sum of all the moments acting on a body must equal zero

Forces are actions applied to an object.

External forces are called loads

The internal structure of a building materia
l must resist external loads with
internal forces that are equal in magnitude and opposite in sign (equal and

Internal forces are called stresses

The structural design of buildings is primarily concerned with selecting the
size, co
nfiguration, and material components to resist, with a reasonable
margin of safety, external forces acting on them.

A force has both direction and magnitude and is called a vector quantity.

Line of action of a force is a line concurrent with the force

The principal of transmissibility says you can consider a force acting
anywhere along the line of action as long as the direction and magnitude
don’t change.

There are several types of forces:

Colinear Forces

vectors lie along the same stra
ight line

Concurrent Forces

lines of action meet at a common point

concurrent Forces

lines of action do not pass through a common

Coplanar Forces

lines of action all lie within the same plane

coplanar Forces

lines of action do

not lie within the same plane

Structural forces in buildings can be any combination of these types

The simplest combination of forces are colinear forces.

Concurrent and non
concurrent forces, the effect of the direction of the
force must b
e taken into account.


Stress is the internal resistance to an external force.

There are three basic types of stress






stress in which the particles of the member tend to pull apart
under load


stress in which the particle of the member are pushed
together and the member tends to shorten


stress in which the particles in a member slide past eachother

Tension and Compression

force acts perpindicular


force acts

Other types of stresses


is a type of shear in which the member is twisted


is a combination of tension and compression


can occur in many situations

Thermal Stresses

Changes in temperature, an increase in e
xpansion when heat is added or,
contraction when it is cooled.

Coefficients of linear expansion is the dimension an object will expand or
contract per degree change

If the material is restrained at both ends, a change in temperature causes an
thermal stress.

Unit stress is independent of the cross
sectional area of the member IF
there are no other loads being applied to the member while it is undergoing
thermal stress.

Strain and Deformation

Strain is the deformation of a material caused
by external forces.

As a frorce is applied to a material:

The strain (deformation) is directly proportional to the stress up to a
certain point.

This si known as Hooke’s Law after mathmetician Robert Hooke

At this stage, the material will return to its original size if the force is

At the elastic limit the material will begin to change length at a faster
ration than the applied force.

At this stage, the material will be permanently deformed, even

if the
force is removed.


At the yield point, the material continues to deform with very little
increase in load

At ultimate strength this is the point prior to rupture or failure.

The most important portion from a practical standpoint is where the s
and strain are directly proportional up to the elastic limit.

Sound engineering practices establish working stresses to be used in
calculations at some point below the yield point.

The modulus of elasticity is the ratio of stress to strain for a

This is the materials resistance to deformation or its stiffness = E

Actual values of E to be used in calculations should be derived from
building codes or accepted tables of value.


A moment is the tendancy of a force to cause rota
tion about a point.

It is the product of the force times the distance to the point about which it is

If the rotation is clockwise in direction

it is considered positive

If the rotation is counter
clockwise in direction

it is considered ne

Properties of Sections

The most common properties of sections:



Statical moment

Moment of inertia

Section modulus

Radius of gyration


in all bodies there is a point at which the mass of the body can be
considered concentrated

Center of Gravity

The point on a plane surface that corresponds to the center of gravity is
called the centroid.

Statical Moment

used to find the centroid
in unsymetrical areas.

Th statical moment of a plane area with respect to an axis is the product of
the area times the perpindicular distance from the centroid of the area to
the axis.

The statial moment of the entire area is equal to the sum of the st


moments of the parts.

If there is a hole in the figure, treat the statical moment of the hole as a
negative number.

Moment if Inertia

is a measure of the bending stiffness of a structural
member’s cross
sectional shape, similar to how the modu
lus of elasticity is
the measure of the stiffness of the material of a structural member.

The moment of inertia about a certain axis of the section is the summation
of all the infinitely small areas of the section multiplied by the square of
the distance

from the axis to each of these areas.

Common designaton “I” and its units are inches to the fourth power.

The axis passing through the centroid is the most commonly used for this
calculation and is otherwise known as the neutral axis.

In order to fi
nd the moment of inertia for composite areas, you must
transfer the moment of inertia of each section about its centroid to a new

The moment of inertia is dependant on the area of a section and the
distance o the area rom the neutral axis

The mom
ent of inertia is the summation of the areas times the square of the
distances of those areas from the neutral axis.

The depth of a beam has a greater bearing on its resistance to bending than
its width or total area.

Structural Analysis

Resultant Forces

The resulatant force is the combination of two or more concurrent forces
into one force that produces the same effect as the individual forces.

If the forces are colinear

the resultant is just the sum of the forces.

If the forces are concurrent, both the magnitude and direction must be
taken into account.

For magnitude

use the law of cosines

For direction

use the law of sines

Components of Force

The reactions of the force would be equal in magnitude but opp
osite in
direction to the vertical and horizontal components of the force.

Three or more forces can be resolved by resolving each one into their
horizontal and vertical components, summing these components, then
finding the resultant of the horizontal an
d vertical components with
pythagorean theorem.


Body Diagrams

Used in analyizing structures

Allows a portion of the structure to be studied using principals of

Chapter 4

Beams and Columns


Basic Principles

At the neut
ral axis, or centroid, which is in the geometric center of the beam if
it is rectangular or symmetrical, the beam does not change length so no
compressive or tension stresses are developed.

If the beam is in equilibrium, then all the moment forces must c
ancel out;
those acting in a clockwise rotation must equal those acting in a
counterclockwise rotation.

R x d = (C x c) + (T x t)

this formula represents the basic theory of bending,
that the internal resisting moments at any point in a beam must equal

bending moments produced by the external loads on the beam.

The moment increases as the distance from the reaction increases or as the
distance from the neutral axis increases.

In the case of a simply supported beam, the maximum moment occur at the
center of the span and the beam is subjected to its highest bending stresses at
the extreme top and bottom fibers.

In order for a beam to support loads, the material, size, and shape

of the beam
must be selected to sustain the resisting moments at the point on the beam
where the moment is greatest.

The section modulus is the ratio of the beams moment of inertia to the
distance from the neutral axis to the outermost part of the secti
on (extreme

Another fundamental type of stress in beams is shear.

Shear is the tendancy of two adjacent portions of the beam to slide past
eachother in a vertical direction.

Horizontal shear

two adjacent portions of a beam to slide past eac
h other
in the direction parallel to the length of the beam.

Usually horizontal shear is not a problem except in wood beams where the
horizontal fibers of the wood make an ideal place for the beam to split and
shear in this direction.

Another importan
t aspect of the behavior of beams is their tendency to


deflect under the action of external loads.

Types of Beams

There are several types of beams:

Simply supported

Overhanging beam

Continuous beam

Cantilever beam

Fixed end beam

Simply supp
orted, overhanging, and continuous beam all have ends that
are free to rotate as the load is applied

Cantilever and fixed end beams have one or both sides restrained against

Continuous beam is one that is held up by more than two supports

o typical kinds of loads on building structures:

Concentrated loads

Uniformly distributed loads

The resultant of unifomly distributed loads is at the center of the

Simply supported, overhanging, and cantilever beams are statically
eterminate which means that the reactions can be found using the
equations of equilibrium

Continuous and fixed end beams are statically indeterminate and
require more complex calculation methods to find the reactions.

Basic requirements for the structural design of a beam is to determine
what the stresses due to bending moment and vertical shear will be that
are caused by the particular loading conditions.

The reactions at the supports must be calculated first.

ection is the change in vertical position of a beam due to a load

The amount of deflection depends on :


Beam length

Moment of inertia

Modulus of elasticity


The amount of allowable deflection is limited by building code
requirements or prac
tical requirements such as how much a beam can
deflect before ceiling surfaces begin to crack or before the spring of the
floor becomes annoying to occupants.

The deflection due to live load is limited to L/360

The deflection due to total load (dead pl
us live) is limited to L/240


Basic Principles


the tendency of a long slender column to buckle under a


combined loading (compressive plus lateral loads)

Flexural stress caused by eccentricity is given
by the flexural formula.

Radius of Gyration

Ability of a column to withstand a load is dependant on its length,
sectional area, and its moment of inertia.

Radius of gyration is the combination of area and moment of inertia.

In non
symmetric sections there are two radii of gyration, one for each

Most interest in column design is the least radius of gyration

in this axis
the column will fail.


Basic Principles

A truss is a structure generally formed of st
raight members to form a number
of triangles with the connections arranged so that the stresses in the members
are either tension or compression.

Typical depth to span ratios range from 1:10 to 1:20

Flat trusses require less overall depth than pitched

Spans generally range from 40 to 200 feet.

Roof loads on a truss are transferred from the decking to purlins, which are
attached to the truss at the panel points to avoid putting any bending stresses
in the top chord of the truss.

If concentr
ated loads are placed between panel points, or uniform loads are
applied directly to the top chords, the member must be designed for the axial
loading as well as for bending.

Trusses act much like beams in that there is usually compression in the top


rds and tension in the bottom chords, with the web members being either
in compression or tension, depending on the loading and type of truss used.

The forces in a parallel chord truss increase toward the center.

Individual truss members are designed a
s columns if they are in compression.

If truss members are in tension, they must have adequate net area to resist the
unit tensile stress allowed by the material being used.

If concentrated loads or uniform loads are placed on any chord member
the panel points, the member must also be designed to resist bending

The effective length of chord members in compression is important

Kl in which K is determined by the restraint of the ends of the members

For steel trusses, K is usually t
aken as 1.0 so the effective length is the
same as the actual length

The ratio of length to least radius of gyration, l/r, should not exceed 120 for
main members and 200 for secondary and bracing members.

Designing steel trusses with double angles

by knowing the compressive
load, the length of the member, and strength of steel, you can determine the
size and thickness of a double angle combination.

For members in tension, the net area must be determined. This is the
actual area of the member le
ss the area of bolt holes which is taken to be
1/8 inch larger than the diameter of the bolt.

Truss members should be designed so they are concentric; so the member
is symmetric on both sides of the centroid axis in the plane of the truss.

The centroi
dal axes of all intersecting members must also meet at a point
to avoid eccentric loading.

Standard practice for steel joists made up of angles is to have gage lines
rather then centroidal axes meet at a common point.

The gage line is a standard dimension from the corner edge of an angle to
the centerline of the bolt hole or holes.

Gage line value depends on the size of the angle.

Truss Analysis

First step in designing a truss is to determine the loads in the vari

The following are general guidelines for truss analysis

The sum of the vertical forces at any point equal zero

The sum of the horizontal forces at any point equal zero


The sum of the moments about any point equal zero

Forces in each m
ember are shown going away from the joint if in
tension and toward the joint if in compression

Forces acting up or to the right are positive

Forces acting down or to the left are negative

For analysis, trusses are assumed to have pivoting or rolling
supports to
avoid other stresses at these points

Three methods that can be used to determine the forces in truss members:

Method of joints

Method of sections

Graphic method

Method of Joints

Each joint is considered separately as a free body diagram to which the
equations of equilibrium are applied.

Method of Sections

A portion of the truss is cut through three members, one member of
which is under analysis.

Cut section is drawn as a fre
e body diagram and forces are foud by
using sum of moments.

Graphic Method

Drawing a stress diagram to scale showing all the force polygons for
each joint on one drawing.

Not very accurate


Since the truss is in equilibrium, the force polygo
n of each joint
must close

When developing the force polygon for a joint, work in a clockwise
direction around the joint. Do this consistently or every joint.

To determine if a member is in compressions or tension, trace the
rays of the force polygon.

Imagine that the ray was transposed onto
the truss diagram. If the direction of the ray is toward the joint, the
member is in compression. If it is away from the joint, the member
is in tension.

There will be as many sides to each force polygon as th
ere are truss
members entering a joint.


Soil and Foundations

The foundation is the part of the building that transmits all the gravity and
lateral loads to the underlying soil.

Selection and design of foundations depends on two primary elements:

The required strength of the foundation to transmit the loads on it

The ability of the soil to sustain the loads without excessive total
settlement or differential settlement among different parts of the

Soil Properties

Soil is t
he material that supports the building

Soil is classified into four groups

Sands and gravels

Granular material that is non


Small particles that have some cohesion, or tensile strength, and are
plastic in their behavior



intermediate size between clays and sands and behave as
granular material but are sometimes slightly plastic in their behavior


Are materials of vegetable or other organic masterials

Solid Rock is another type and has the highest bearing cap
acity of all soil

Subsurface Exploration

Two most common methods of subsurface exploration are:


Core borings, undistrubed samples of the soil are removed at
reagular intervals

Type of material recovered is recorded in a boring log

Shows the material

The depth at which it was encountered

Standard soil designation


Moisture content


Other tests’ results observed on site

Most common bore hole test is the Standard Penetration Test

Measure of the density of gr
anular soils and consistancy of
some clays

2” diameter sampler is driven into the bottom of the bore hole
by a 140 pound hammer falling 30 inches.

The number of blows N required to drive the cylinder 12
inches is recorded

Laboratory test performed on

recovered borings:

Strength tests of bearing capacity

Resistance to lateral pressure

Measure slope stability


Grain size

Specific gravity

Density tests

Usually, a minimum of four borings are taken, one near each
corner of t
he proposed building.

Test pits

Trenches dug at the jobsite that allow visual inspection of the soil
strata and direct collection of undisturbed samples

Practical limit on depth is about ten feet

soil below that cannot
be directly examined.

Soil Types and Bearing Capacities

Classified according to the Unified Soil Classification System (USC)

System divides soils into major divisions and subdivisons based on grain
size and laboratory tests of physical characteristics

System provides standardized names and symbols.

Bearing capacities are generally specified by code.

Water in Soil

Water in soil can cause several problems for foundations


Water can reduce the load carrying capacity of soil

Differential settlement

may occur causing cracking and weakening of
structural and non
structural componenets

Hydrostatic pressure:

Puts additional loads on the structural elements

Makes waterproofing more difficult

Ways to minimize the problems caused by excess soil moi

Slope the ground away from the building

Drain storm water away from the building

Foundation drains

web matting against the foundation wall breaks water pressure

Layers of large gravel

Soil Treatment

Drainage: can increase the strength of soils and prevent hydrostatic

Fill: used to replace unacceptable soils

needs to be compacted

Proctor test measures moisture to density for optimum strength/bearing

Compaction: simple compacti
on of some soil types provides the desired
bearing capacity

Densification: vibration, dropping of heavy weights, pounding piles into
the ground and filling the voids with sand

Surcharging: pre
loading the soil with fill to compact the soil or “train”

Other Considerations:


Expansive Soils (bentonite clay)


typically 45 degrees

Foundation Systems

Two broad divisions of foundations:

Spread footings

Pile or caisson foundations

Spread footings spread the load from the stru
cture and the foundation walls
over a large area so that the load bearing capacity of the soil is not exceeded


and settlement is minimized.

One of the most common is the wall footing which is placed under a
continuous foundation wall which in turn suppor
ts a bearing wall.

The joint between the footing and foundation wall is strengthened with a
keyed joint.

Types of spread footings:

Wall footing

Independent column footing

Combined footing

Strap footing

Mat or raft foundation

Independent column footing is similar in concept but supports only one

Required size of both wall and independent column footings is found by
dividing the total load on the footing by the load carrying capacity of the
soil. A safety factor is of
ten used as well. For wall footings, design is
based on a linear foot basis.

Combined footings support two or more columns in situations where the
columns are spaced too close together for separate ones, or where one
column is so close to the property l
ine that a symmetrically loaded footing
could not be poured.

A strap footing or cantilever footing which uses a concrete strap beam to
distribute the column loads to each footing to equalize the soil pressure on
each footing.

Strap footings are also us
ed where the exterior column is next to the
property line but the footing cannot extend beyond the property line.

A mat or raft foundation is used when soil bearing is low or where loads
are heavy in relation to soil pressures. One large footing is desi
gned as a
way slab and supports the columns above it.

Pile and caisson foundations distribute the load from the building to the ends
of the piles which often bear on bedrock, or to the surrounding soil in contact
with the pile through skin friction o
r a combination of both.

When soil near grade level is unsuitable for spread footings, pile
foundations are used.

Piles are either driven or drilled

Driven piles may be of timber or steel and are placed with pile
hammers powered with drop ham
mers, compressed air, or diesel



Drilled piles or caissons are usually called piers.

Drilled piers are formed by drilling out a hole to the required depth and
then filling it with concrete.

A metal lining is used to keep the soil from caving
in during drilling. It
is removed as the concrete is poured or may be left in.

If the soil pressure is not sufficient for a drilled pie of normal
dimensions, the bottom is “belled” out to increase the surface area for

Piles are usually placed

in groups or in a line under a bearing wall with the
loads from the building transferred to them with pile caps.

The piles are embedded from 4 to 6 inches into the pile cap which is
designed and reinforced to safely transmit the loads and resist shear a
moment stresses developed.

When two or more piles are used to support one column, the centroid of
the pile group is designed to coincide with the center of gravity of the
column load.

Grade beams are designed and reinforced to transfer the loads from the
building wall to the piles.

Grade beams are often used where expansive soils or clay, such as
bentonite, are encountered near the surface.

The use of carton forms to support concret
e during pouring are used
and disintegrate and form a void shortly after the concrete is cured.

Designing Footings

Three factors when designing footings:

Unit loading

the allowable bearing pressure of the soil is not exceeded
and differential settl
ement is eliminated as much as possible.


Punching (two
way shear) when the column or wall load punches
through the footing.

Fail in flexural shear or diagonal tension the same as regular beams


when the lower surface cracks under
flexural loading.

Simple spread footings act much like inverted beams with the upward soil
pressure being a continuous load that is resisted by the downward column

This tends to cause bending in the upward direction which induces


compression near

the top of the footing and tension near the bottom of
the footing.

The area of a spread footing is determined by dividing the total wall or
column load on it plus its own weight plus any soil on top of the footing by
the allowable soil bearing pressure.

The footing itself is designed for shear, moment, and other loads with
factored loads as required by the American Concrete Institute.

Wall footing design considerations:

Two critical sections

Face of the wall where bending moment is the greatest

At distance, d, from the face of the wall in the footings where
flexural shear is of most concern

The critical two
way shear section for column footings is a
distance d/2 from the face of the wall.

(d) is the distance from the top of the footing to the cntroid of the
reinforcing steel, called the effective depth of the footing since the
concrete below the steel does not contribute any structural properties.

(d) for masonry is different than (d) for

concrete walls. For concrete
walls it is measured to the face of the wall.

Maximum allowable flexural shear governs the design depth of wall

Individual column footings are subject to two
way action much like flat
slabs near columns, as well

as one way shear.

Both types of shear must be calculated and the depth of the footing
designed to resist these shear forces.

When both are calculated, the greater shear value is used for design.

way shear at distance (d) from the face of column,

the factored
soil design pressure is calculated over the rectangular area indicated
by the shear line and the outside face of the footing.

way shear is calculated a distance (d)/2 from the face of
concrete in a rectangular area around the pier.

ttom reinforcing in both directions is required to resist the
moment forces at the face of the column.

Concrete weighs approximately 150 pounds per cubic foot (a one foot
section weighs 1050 pounds)

Soil weighs approximately 100 pounds per square foot
per foot of



The ACI code requires the design soil pressure be calculated based on
factored loads according to the following formula: U=1.4D + 1.7L.

Types of Retaining wall

Three types of retaining walls

Gravity wall

Gravity wall resist
s the forces on it by its own weight and by soil
pressure and soil friction against its surface opposite to the earth

Commonly used for low retaining walls up to about 10 feet where
forces on it are not too great.

Cantilever wall

Most common type

Constructed of reinforced concrete

Resists forces by the weight of the structure as well as by the weight
of the soil on the heel at the base slab.

Often constructed with a key projecting from the bottom of the slab
to increase the w
all’s resistance to sliding.

The toe is omitted if the wall is next to a property line or some other

The arm, heel, and toe act as cantilevered slabs, the thickness and
reinforcement increase with increased length because of the larger
ents developed.

Cantilevered walls are economically limited to about 20

25 feet in

Counterfort wall

Walls higher than 20
25 feet.

Similar to cantilevered walls but with counterforts placed at
distances equal to or a little larger than one
half the height.

Counterforts are simply reinforced concrete webs that act as
diagonal bracing for the wall.

Forces on Retaining Walls

Force on a retaining wall results from the pressure of the earth retained
acting in a horizontal direction to the

Earth pressure increases proportionally with the depth from the surface.


The coefficient of earth pressure depends on the soil type and the
method of backfilling and compacting it.

Coefficient of earth pressure may range from 0.4 for uncompacte
soils like sands and gravels to 1.0 for cohesive, compacted soils.

Pressure acts in a triangular form.

Total pressure against the wall can be assumed to be acting through the
centroid of the triangle

or one
third the distance from the base of the

Assumed equivalent weight of soil is 30 PCF

Additional loads called sur
charges may result from driveways or other
forces being imposed on the soil next to the wall.

If the ground behind the wall becomes wet, there is additional pressure
resulting from the water which must be added to the soil pressure

Design Considerations

A retaining wall may fail in two ways

As a whole by overturning or sliding

Individual co
mponents may fail such as when the arm or stem
breaks due to excessive moment.

In order to prevent failure due to overturning or sliding, the resisting
moment or forces that resist sliding are generally considered sufficient
if there is a safety factor o
f 1.5.

To prevent sliding, the friction between the footing and surrounding
soil and the earth pressure in front of the toe (and key, if any) must be
1.5 times the pressure tending to cause the wall to slide.

The thickness, width, and reinforcing of th
e retaining wall must be
designed to resist the moment and shear forces induced by soil
pressures, surcharges, and any hydrostatic pressures,

Design retaining walls to eliminate or reduce the build
up of water
behind them.


The majority of

structural failures occur in the connection of members.

Either the incorrect types of connectors are used, they are undersized, too few
in number, or improperly installed.

Wood Connections

Variable that effect the design of wood connections


Load c
arrying capacity of the connector

Species of wood

Type of load

Condition of the wood

Service conditions

Whether or not the wood is fire
retardent treated

Angle of load to the grain

Critical net section

Type of shear the joint is subjected to

Spacing of the connectors

End and edge distance to connectors

Species of wood

Species and density of wood affects holding power of connectors

Species are classified into four groups

There is one grouping

for timber connectors

Split ring connectors and shear plates

Four groups for timber connectors are designated A, B, C, and D

Another grouping

Lag screws, nails, spikes, wood screws, metal plate connectors

Four groups for these connectors are des
ignated I, II, III, and IV

Type of Load

Wood can carry greater maximum loads for short durations than for
long durations

Tables of allowable connector loads are for normal duration of ten

Other conditions

multiply by the following factors

0.90 for permanent loading over 10 years.

1.15 for 2 months’ duration (snow loads for example)

1.25 for 7 days’ duration

1.33 for wind and earthquake loads

2.00 for impact loads


Condition of Wood

Tabulated values are based on fastening to woo
d seasoned to a moisture
content of 19% or less.

Partially seasoned or wet wood reduces the holding power of the

Service Conditions

The environment in which the wood joint will be used.

Are they? Dry, wet, exposed to the weather, subject

to wetting and

Any service conditions other than dry or continuously wet reduce the
holding power of the connector.

retardant treatment

Wood that has been fire
retardant treated does not hold connectors as
well as wood that has not been

treated. The adjustment factor for
fastener design loads is 0.90.

Angle of Load

One of the most important variable affecting allowable loads carried by
connectors is the angle of the load to the grain, which is defined as the
angle between the direct
ion of load acting on the member and the
longitudinal axis of the member.

Wood connectors can carry more load parallel to the grain than
perpendicular to it.

If the load is acting other than parallel or perpendicular to the grain, it
must be calculated

using the Hankinson formula or by using one of the
graphs that gives the same results.

Critical Net Section

When a wood member is drilled for one of the many types of
connectors, there is a decrease in area of wood to carry the imposed

The section where the most wood has been removed is called the
critical net section.

It may be necessary to increase the size of the member just to
compensate for this decrease in area.

Type of Shear

Connectors such as bolts and lag screws can be in
single shear, double
shear, or multiple shear.


The type of shear condition and the relative thickness of each piece to
the others are especially important when designing bolted connections.

Spacing Connectors

Connector spacing is the distance between

centers of connectors
measured along a line joining their centers.

End and Edge Distances to connectors

End distance is the distance measured parallel to the grain from the
center of the connector to the square
cut end of the member.

Edge distance is the distance from the edge of the member to the center
of the connector closest to the edge of the member measured
perpendicular to the edge.


Nails are the weakest of wood connectors

Nails are the most common for light frame co

For the same penny weight:

Box nails have the smallest diameter

Common wire nails have the next largest diameter

Wire spikes have the greatest diameter

The preferable orientation is to have the fastener loaded laterally in side
where the holding power is the greatest.

If one of the pieces is metal rather than wood, allowable values may be
increased by 25 percent.

Fasteners loaded in withdrawal from end grain are not allowed by
building codes.


Wood screws used for structural purposes are available in sizes from #6
to #24 in lengths up to five inches.

Also like nails, screws are best used laterally loaded in side grain rather
than in withdrawal from side grain. Withdrawal from end is not

Design values given in tables are for a penetration into the main
member of approximately 7 diameters.

In no case should the penetration be less than 4 diameters.

Like nails, design values can be increased by 25% if a metal side plate
is used.


Lag Screws

Lag screws are also called lag bolts.

Sizes range from 1/4 inch to 1
1/4 inch in diameter and from 1 inch to
16 inches in length.

Diameters are measured at the non
threaded shank portion of the screw.

Design values for lateral loading
and withdrawal resistance depend on

Species group

Angle of load to grain

Diameter of the lag screw

Thickness of the side member

Length of the screw

If the load is other than at zero degree or 90 degree angle, the design
value must be determined

using the Hankinson formula.


Bolts are one of the most common forms of wood connectors for joints
of moderate to heavy loading.

Variables such as the following affect the allowable design values and
the spacing of the bolts:

Thickness of the

main and side members

Ratio of bolt length in main member to bolt diameter

The number of members joined

Two typical conditions are joints in single shear and double shear

Design values given in tables are usually for conditions where the side
members in double shear joints are one
half the thickness of the main

When steel plates are used for side members or main members loaded
parallel to the grain, the tabulated
values can be increased 75% for
joints made with bolts 1/2 inch or less, and 25% for joints made with
bolts 1
1/2 inch with intermediate diameter values interpolated.

No increase is allowed for loading perpendicular to the grain.

Timber Connectors

There are two types of timber connectors:

Split rings


Either 2
1/2 inches or 4 inches in diameter and are cut through in
one place in the circumference to form a tongue and slot

Shear plates