5/8 inches or 4 inches in diameter and are flat plates
with a
flange extending from the face of plate

shear plates are particularly suited for construction that must be

Steel Connections

Bolting and welding are the two most common methods in use today for
making steel connections.


Bearing type

Bearing type connections resist the shear load on the bolt
through friction between surfaces.


critical connections are those where any amount of slip
would be detrimental to the serviceability of the s
tructure, such
as joints subject to fatigue loading or joints with oversized holes.

The entire load is carried by fricton

Bolts are further classified as to whether the bolt threads are
included or excluded from the shear plane.

The strength of conn
ection is affected because there is less area to
resist the load through the threaded portion.

Bolts may be in either single shear or double shear.

There are three basic types of bolts used in modern steel

Bolts designated with ASTM #A30

Called unfinished bolts

Have the lowest load
carrying capacity

Used only for bearing type connections

Bolts Designated A325 & A490

Called high
strength bolts

May be used in bearing
type connections

Must be used in slip
critical connections


The nuts are tightened to develop a high tensile stress in
the bolt which causes the connected members to develop a
high friction between them which resists the shear.

Bolts range in diameter from 5/8 inch to 1
1/2 inch in 1/8 inch

Most ty
pically used diameters are 3/4 inch and 7/8 inch

Standard codes for the condition of use:

SC: slip
critical connection

N: bearing
type connection with threads included in the
shear plane

X: bearing
type connection with threads excluded from the
shear plane

S: bolt in single shear

D: bolt in double shear

Factors in bolt selection

Diameter of bolt

Bolt designation

Type of hole being used

Standard round holes

larger than diameter of bolt

Oversize holes


5/16” larger than diameter of bolt
and may only be used with slip
critical connections

Short slotted holes

1/16” wider than the bolt diameter
and have a length that does not exceed the oversize ho
dimension by more than 1/16”. May be used in either
bearing or slip
critical connections.

Long slotted holes

1/16” wider than the bolt diameter
and a length not exceeding 2
1/2 times the bolt diameter.

Slotted holes are used where some amount of
is needed. Long slotted holes can only be used in one of
the connected parts of a joint. The other part must use
standard round holes or be welded.

Connection type

Loading condition

One of the most important considerations in bolted ste
connections is the spacing of bolts and the edge distance from
the last bolt to the edge of the members.


Absolute minimum spacing is 2
2/3 times the diameter of
the bolt being used with 3 times the diameter being the
preferred dimension.

Required ed
ge distances varies with the diameter of he
bolt being used. Typically, a dimension of 1.25 inches is
often used for all bolts up to 1 inch in diameter.


Welds are quite frequently used in lieu of bolts for several reasons:

The gross cross section of the members can be used instead of
the net section

Construction is often more efficint because there are no angles,
bolts, or washers to deal with and no clearance problems with

Welding is more practical for moment

Since members must be held in place until welding is completed,
welding is often used in combination with bolting.

The most common type of welding process used in building
construction is the electric arc process.

Penetration refers to t
he depth from the surface of the base metal to
the point where fusion stops.

Two types of electrodes are used commonly today:

E60: allowable shear stress is 18 kips per square inch

E70: allowable shear stress is 21 kips per square inch

Which electr
ode to use depends on the configuration of the joint, the
magnitude and direction of load, the cost of preparing the joint, and
what the erection process will be.

The three most common types of welded joints are the lap, the butt,
and the tee.

Plug or
slot welds are frequently used to join two pieces. In these
welds, a hole is cut or punched in one of the members and the area
filled with the weld.

The fillet weld is one of the most common types.

The perpendicular distance from the 90 degree corner
to the
hypotenuse of the triangle is called the throat.

Because the angles are 45 degrees, the dimension of the throat is
0.707 times the leg dimension.


For a butt joint, the throat dimension is the thickness of the material
if both pieces are the same

thickness, or the size of the thinner of two
materials if they are unequal.

There are common symbols used for welding. The full rage of
symbols gives information regarding the type, size, location, finish,
welding process, angle of grooves, and other i


The type of weld is indicated with one of the standard symbols
and placed below the line if the weld is on the side near the arrow
and above the line if it is on the side away from the arrow.

If the members are to be welded on both sides, the symbol is
repeated above and below the line.

Other data placed with the weld symbol are size, weld symbol,
length of weld, and spacing, in that order from left to right.

Field welds are indicated with a flag placed at the junction of the
horizontal line and the arrow line and pointing to the tail of the
reference line.

A circle at the same point indicates that the weld should be made
all around.

The perpendicular legs
of the filled, bevel, J, and flare bevel
welds must be at the left.

Loads in weld design:

For fillet welds, the stress is considered as shear on the throat
regardless of the direction of the load.

For butt welds, the allowable stress is the same as f
or the base

Weld requirements:

The maximum size of a fillet weld is 1/16 inch less than the
nominal thickness of the material being joined if it is 1/4 inch
thick or more. If the material is less than 1/4 inch thick, the
maximum size is the sam
e as the material.

The minimum size of fillet welds:

material thickness of the

minimum size of

thicker part joined, inches

fillet weld,

to 1/4 inclusive


over 1/4 to 1/2



over 1/2 to 3/4


over 3/4


The m
inimum length of fillet welds must not be less than 4 times
the weld size plus 1/4 inch for starting and stopping the arc.

Or two or more welds parallel to each other, the length must be at
least equal to the perpendicular distance between them.

For in
termittent welds, the length must be at least 1
1/2 inches.

Concrete Connections

In most cast
place concrete construction there are generally no
connectors as with wood or steel.

Different pours of concrete are tied together with reinforcing bars
or with
keyed sections.

cast concrete construction

there must be some way of rigidly
attaching one piece to another. This is accomplished with weld plates.

Rebars and keyed sections:

The most typical type of cast
place concrete joint is one

where the
reinforcing bars are allowed to extend past the formwork to become
part of the next pour.

These types of joints are found in many situations:

Footing to foundation wall

Walls to slabs

Beams to beams

Columns to beams

Reinforcing is only for the purpose of tying two pours of concrete
together rather than transmitting large loads, they are called dowels.

The length of the dowels or extensions of rebar from one section of
concrete to the next is determined by the minimu
m development length
required to transmit the loads or by the ACI code.

Keyed sections are used either alone or with rebars to provide a
stronger joint between teo pours of concrete. Keyed sections are often
used in footings and floor slabs.

Weld plat

Precast structures are built in sections require a way to transmit
horizontal, vertical, and moment forces from one piece to the next.
This is usually accomplished by casting weld plates, angles, and other
types of steel pieces into the concrete memb
ers at the factory.


At the site, the members are placed in position and corresponding plates
are welded together.

Shear Connectors

Shear connectors are not really conn
ectors in the usual sense, but are
use to tie steel and concrete together in composite sections so forces are
transmitted from one to the other.

One of the typical applications of shear connectors is with concrete slab
/ steel beam composite sections.

Connectors are welded to the top of the steel beam in the fabricating
shop at a fairly close spacing which is determined by engineering
calculations to transmit the forces created by the applied loads.

These are often called headed anchor studs and abbre
viated HAS on the

Building Code Requirements on Structural Design

Th code requires that any construction method be based on a rational analysis
in accordance with well
established principles of mechanics, and that such an
analysis provides a

path for all loads and forces from their point of origin to
the load resisting elements.

The analysis must include distribution of horizontal shear, horizontal
torsional moments, stability against overturning, and anchorage.

Horizontal torsional moment results from torsion due to eccentricity between
the center of application of a lateral force and the center of rigidity of the
resisting system.

Anchorage resists the uplift and sliding forces on a structure.

When the

building design is based on allowable stress or working stress
design, each component must be designed to resist the most critical effect
resulting from the combination of loads listed.

Live Loads

Some reductions in live loads are permitted by code.

Other provisions:

Designing floors to accommodate concentrated loads. If these loads,
acting on any space 2
1/2 feet square on an otherwise unloaded floor,
would result in stresses greater than those caused by the uniform load,
then the floor must b de
signed accordingly.

Practice Examination Answers

Long Spans do not provide better resistance to lateral loads


Long spans are not economical when compared to short spans

Modulus of Elasticity (E)

Ratio of unit stress to unit strain

Unit stress i
s the stress per unit area measured in psi

Unit strain is the total shortening or lengthening of a member divided
by its length

The higher the E value, the greater its stiffness or resistance to deformation

Simple Beams vs. Continuous Beams

beams have more deflection than continuous beams

Continuous beams require more complex calculations and connections

Simple beams generally have more maximum moment

Continuous beams usually have more maximum shear.

Continuous beams deflect less than simple beams.

Continuous beams are subject to negative bending moment over its

Simple beams never have negative moment.

For equal spans and loads, the maximum positive bending moment is
greater in the end spans of a continuous beam than in the center spans.


The full allowable unit bending stress is used in glulams up to 12 inches

Beams more than 12 inches

deep must reduce the allowable unit bending
stress by a size factor related to their depth.

Wood Species

Redwood is usually used when the structure will be exposed to the weather
and durability is the main consideration.

Douglas fir is the strongest

species and is commonly used in construction

Spruce is light weight with low strength

Cedar is durable when exposed to the weather, light weight and low in
strength, and is mainly used for siding and trim.

Deformation = PL/AE

P = the concentrated

L = the length

A = cross
sectional area


E = modulus of elasticity

Slump test

Is used to measure the consistency of concrete

Less slump means the mix is stiffer

More slump means the mix is wetter

4 inches of slump is the maximum accepta
ble for concrete used in

Deflection = KwL3/EI

K = load factor

W = the total uniform load

L = length

E = the modulus of elasticity

I = the moment of inertia

Dirt, oil, or other non
metalic coating must be removed before concrete is
placed so that the bond between the steel and concrete is not adversely

Rust and scale, often removed during the handling and placement of the
steel, actually improve th
e bond.

Wood Shrinkage

Wood shrinks the most in the direction of the annual growth rings

Wood shrinks less across the rings (radially)

Wood shrinks the least along the grain (longitudinally)

Studs and logs shrink very little compare
d with the shrinking of joists
across their depth

Glulams are made with seasoned lumber and are designed for very little

Braced Frames (K

Are constructed with steel members forming diagonal braces to act in both
tension and compress
ion between beams and columns.

Concrete is not used for braced frames because it is so weak in tension

Braced frames usually have bolted connections which are not rigid like
welded connections.

Braced frames are designed to create a triangulated syst
em of connections
to resist lateral shear and bending moments.


Since they effectively resist both vertical and lateral (seismic) loadings,
they are employed in both low
rise and high
rise construction.

Flat slabs

Concrete slab with reinforcement in t
wo directions and brings its load
directly to the supporting columns, generally without any beams or

Relatively thin and not economical in reiforcement, but economical in

For heavy live loads and bays which are approximately square,
flat slab
construction is often economical.

In the design of columns, the ratio of the effective length, l, to its least radius
of gyration, r, is known as the slenderness ratio.

Stirrups have a structural design purpose

to reinforce he concrete in areas
where shear stresses exceed the capability of concrete.


Simply supported beams deflect more than fixed
end beams

Concentrated loads cause more deflection than uniformly distributed loads

For a given load and span, the deflection of a beam varies inversely with its
moment of inertia (I).

The greater the I value of the beam, the lower its deflection.

Since I = bd3/12 for a rectangular section, the beam with the greatest
depth has the gre
atest I value and therfore will deflect the least.

Amount of deflection is determined by four factors:

The loads acting on the beams

The stiffness of the beam material (measured by its modulus of
elasticity (E))

The beam’s moment of Inertia (I)

he span of the beam

Inelastic material (wood and concrete) deflect when the load is intially
applied and continues to deflect through time (without an increase in load)

Elastic Material (steel) does not deflect more than its initial deflection
unless t
he load is increased.

All steel regardless of strength has the same stiffness as measured by its
modulus of elasticity (E).

The section modulus of a beam section is a measure of its ability to


resist flexural stress, not deflection.


A simp
ly supported beam will deflect more than a fixed
end beam with
the same span and load.

A concentrated load at mid
span will produce more deflection than the
same load uniformly distributed.

Summary of reinforced concrete beam design:

Select the speci
fied concrete compressive strength (f’c) and reinforcing
steel yield strength (fy). These values are constant for all the beams in the

For the given beam, determine the maximum bending moment (Mu) and
vertical shear (Vu), using the load factors 1.4 for the dead load and 1.7 for
the live load.

Select the width (b) and the effective depth (d) of the beam; these must be
adequate to resist
the maximum bending moment (Mu). In general, the
value of d should be about 1.5 times b. if the size of the beam is
predetermined, verify that it is adequate. Use T
beam action when

Compute the required area of tensile reinforcement (As) and

select the
bars. Verify that the steel area is at least the minimum required by the

If the depth of the beam is insufficient to resist the maximum moment,
provide compressive reinforcement.

Check the shear capacity and provide stirrups if neces

Verify that all reinforcing bars are extended at least their developmental
length beyond the point of peak stress.

Be sure that the beam is adequately sized for deflection.

Miscellaneous Notes:

Centroidal Axis

Locate centroids of individual

pieces that make up the whole

Select one of the bases as the X
X axis for the whole unit

Set up a chart

Area of each piece


distance from each individual pieces centroid to the X
X axis.

Area (Y)



All the areas together

All the Area(Y) together

The Centroidal Axis will be the result of dividing the total Area(Y) by
total Area. The distance is measured from the X
X axis.

Moment of Inertia around the centroidal axis (I)

Set up a chart

Area of each piece

Moment of inertia around each pieces own centroidal axis (bd3)/12

Y’ (Y prime) distance from each pieces own centroid to the
centroidal axis of the whole.

Y’ squared

Area(Y’ squared)

Io + Area(Y’squared)

Add up the “Io + Area(Y’squared)” for

the moment of inertia for the

After cutting a free
body diagram of a structure, if the calculated internal
forces are negative, then the internal forces act in the opposite direction
from that assumed.

If a load acts through a body’s center of
gravity, then the body

Has no tendency to rotate

Tends to translate in the direction of the applied force.

The yield point is the unit stress at which the material continues to
deform with no increase in load.

周攠Taxim畭⁳瑲 ss⁴桡琠a⁣ol畭渠捡渠r
depends on a column’s unbraced length and radius of

The flexural stress in a beam is maximum at the extreme fibers and is
a function of the beam’s section modulus.

The shear stress in a beam is maximum at the

neutral axis.

The carbon content of steel affects its strength and ductility.

The modulus of elasticity of steel:

Has a constant value


Is higher than that of any other structural material

Is a measure of the stiffness of steel

Roof Structures


a series of parallel arches which are skewed with respect to
the axes of a building and which intersect another series of skewed


a series of arches placed side by side to form a continuous

Way Truss

a series
of trusses which intersect another series of
perpendicular trusses to form a grid.

Space Frame

a series of inclined trusses which intersect another series
of inclined trusses.

Water weighs 62.4 pcf.

Thin Shell Structures

Is able to resist shear,
tension, and compression.

Too thin to have any significant resistance to bending moment, or


William LeBaron Jenney designed the Home Insurance Co. Building, the
first skyscraper in 1883.

Robert Maillart was a swiss engineer who des
igned arched concrete

Pier Luigi Nervi italian contractor and engineer who created soaring
concrete shell roofs of unusual elegance and refinement

Gustav Eiffel designed structures of great strength using steel and iron.

Fazlur Kahn designed
Sear’s Tower and John Hancock Building.

Skyscrapers were made possible by the invention of the elevator by Elisha
Graves Otis.

Louis Sullivan cast ironed framed buildings were among the first

Thermae were Roman public bathing establishme

Basilica was a Roman rectangular building used as a hall of justice and
public meeting place.

Amphitheater was a Roman oval arena surrounded by tiers of seats and
used in Rome for gladiatorial contests.


Stoa was a Greek colonnade used to provide
access to law courts,
gymnasiums, etc.

Joseph Paxton’s Crystal Palace (1851) was an immense prefabricated
glass and cast iron structure.

William LaBaron Jenney’
s Home Insurance company Building (1883) is
generally considered to be the first building completely framed in steel.

Burnham & Root’s Reliance Building (1890
95) completely expressed the
aesthetics of its steel skeleton.

H. H. Richardson’s Marshall Fi
eld Wholesale Store (1885
87) floors were
supported by timber framing and its exterior walls were largely of stone

French architect Perret was the first to use the reinforced concrete frame in
rise construction and to express it archit

One of Perret’s pioneering efforts was the Rue Franklin Apartment
Building (1903) in Paris, France.

Eiffel designed the Eiffel tower and several other steel structures as well as
the framework of the Statue of Liberty.

Freyssinet was one o
f the first engineers to develop and make use of
prestressed concrete.

Torroja was a Spanish engineer best known for his shell structures.

Pantheon (123 AD) is one of the greatest achievements in Roman
architecture. Its immense concrete dome is so thi
ck at its bottom that
tensile hoop stresses are resisted by the concrete, without any need for iron
reinforcing. The opening at the crown of the dome was desgned to act as a
compression hoop.


masterpiec of GREEK architecture

Adapted from the wood construction of early Greek temples to marble.

Subtle visual adjustments were made to the Parthenon to correct for
optical illusions.


a slight convexity of the columns so that they would not
appear concave.

The Romans
used arches in great profusion and for a variety of reasons.

Roman arches were always semi

They were constructed with scaffolding or centering which was
removed after the keystone was installed

the upper most masonry

The maximm span

of a Roman arch was about 100 feet.




Moment of Inertia, I: measure of the stiffness of a beam, its resistance to

Section Modulus, S: measure of the bending or flexural strength of a

Modulus of Elasticity
, E: determines stiffness of a material, or its
resistance to deformation.

Ductility: materials ability to deform without rupture.


Typically, structural systems in a building represent 25% of the total
construction cost.

If the spans of the structural bays are doubled, the costs for the structural
system would probably increase by about 20

In a solid sawn wood beam, the flexural stress is maximum at the top and
bottom fibers, and it passes through the neutral axis w
here it is zero.

Standard engineering practice calls for the resisting moment of the dead load
to be at least 1.5 times the overturning moment.

Widening the footing of a retaining wall is the simplest solution for
increasing the dead load and the resis
ting moment.

Several factors are used to determine the load bearing capacity of a wood

The cross
sectional area of the column is used and is calculated by the
dimensions of the column section

The ratio l/d is another factor, where l is the un
braced length of the column
and d is the smallest dimension in the column plan.

The modulus of elasticity is also considered, which is dictated by the
species of wood used.

The radius of gyration is used in determining the load bearing capacity of
l columns, NOT wood columns.

Open Web Steel Joists

Standardized, lightweight steel trusses which generally support uniform
loads from floor or roof decks

Steel joists ma have parallel chords or single or double pitched top chords
to provide roof drai

Joists have no fire
resistive ratings by themselves but ratings of one hour
or more may be obtained by using he proper floor or roof deck and ceiling.


Open web steel joists are always fabricated in the shop.

Glue Laminated Beams

Typically, glu
e laminated beams are manufactured from more than one
lamination grade.

The individual laminations are not required to be of the same species and
stress grade.

The higher grades are generally used at the top and bottom cross
where the flexural

(bending) stresses are maximum. Shear failure of a
beam is most likely to occur where the vertical shear is maximum, which is
adjacent to a support.

Horizontal shear stress in a beam varies from zero at the outermost fibers
to a maximum value at the mid
height of the beam.

Since the glue is generally stronger than the wood, failure is more likely to
occur within a lamination than between laminations.

When glue
laminated member is 12 inches or less in depth, the full
allowable stress may be used for d

For depths greater than 12 inches, a size factor is used, which has the effect
of reducing the allowable stress that may be used.


Plane scarf joints and finger joints can be made with adequate strength

Butt joints are not permitted for glue
laminated members because they
usually cannot transmit tensile stress and can transmit compressive
stress only after considerable deformation.

Camber is often built into glued laminated beams for the following

To avoid the appearance of sag

To eliminate the ponding of water

To compensate for deflection

Wood Columns

The capacity of a wood column is determined by several factors

The modulus of elasticity (E) of the wood, which depends on its species
and grade

The allowable compressive strength (Fc), which also depends on the
species and grade of the wood.

The ratio l/d, where l is the unbraced height of the column and d is t
least lateral dimension of the column.



The formulas used to design columns are based on idealized pin
conditions, where the end of the column are free to rotate, but not move
laterally (translate).

Actual building columns do not alwa
ys meet these conditions.

Their ends may be free to rotate

Or, they may permit no rotation

Their ends may be free to translate

Or, they may be fixed against translation.

To allow the column formulas to be used for all end conditions, the K

was devised.

This factor is multiplied by the actual unbraced length (l) to arrive at the
effective length (Kl), which is then used to design the column.

The shear stress in a column pad is essentially a function of the column
load, the column size, a
nd the thickness of the pad. It is not at all related to
the reinforcing steel, and only slightly affected by the pad size.

Increasing the pad thickness provides more area of concrete to resist the
shear load, and hence decreases shear stress.

The axial load carrying capacity of a steel column is determined by the
strength of the steel used in the column, and the tendency of the column to

The buckling tendency is a function of the length (l) of the column,
its radius of gyration ( r),
and the effective length factor (K).

In designing steel columns, the larger slenderness ratio is used because it
results in a smaller allowable axial stress.

Eccentrically loaded columns are columns which support vertical loads
applied at some distance from its centerline.

Concrete Columns

There are two types of concrete columns that differ in the kind of lateral
reinforcing they use:

Spiral columns

lose the longitudinal reinforcing bars with a
spaced continuous steel spiral, which braces the longitudinal
bars and confines the concrete.

Tied columns

have separate lateral ties which hold the longitudinal
bars in position, prevent them from
buckling outward, and also,
somewhat, confine the concrete.


Building codes require that reinforcement for shrinkage and temperature
stresses normal to the principal reinforcement must be provided in structural
floor and roof slabs, where the principal re
inforcement extends in one
direction. Such reinforcement is often called temperature steel.

Structural Steel Connections

The connections used in structural steel systems comprise a significant
part of the cost of these systems, and can even influence
the type of
structural steel system selected.

In some cases, bolted connections are more economical and in other cases,
welded connections are.

Usually shop connections are preferred over field because they are less

According to the building
code requirements for reinforced concrete, the
minimum concrete coverages are:







Maximum moment occurs where the vertical shear is equal to zero.

Reinforcing Bars

e ultimate tensile capacity of a reinforcing bar is the product of its area
and yield strength.

Grade 40 reinforcing steel has a yield strength of 40 ksi.

Grade 60 reinforcing steel has a yield strength of 60 ksi.

Splicing reinforcement bars:

One common method is the lap bars a sufficient amount; such lapped
bars are often wired together.

Welded butt and lap splices are acceptable.

Newer methods include mechanical couplers and end bearing, which is
acceptable for compression only.

cing bars are furnished with rolled
in markings

Identify the producing mill

The bar size

Type of steel

Additional marking for higher
strength steel

Bolts joining wood members have their greatest capacity when the load acts


parallel to the grain a
nd their least when the load acts perpendicular to the

When load acts at any other angle to the grain, the bolt capacity may be
determined by Hankinson’s formula, and the value thus obtained is less
than that parallel to the grain and greater than

that perpendicular to the

Composite Design

A concrete slab is connected to a steel beam with shear connectors

Shear connectors can develop the ultimate capacity of the concrete or
steel, whichever is less

Because the concrete and steel work together, a smaller size steel beam
may be used than in conventional steel framing, which generally results
in a more economical system.

When smaller steel beams are used, deflections tend to become greater,,
and thus
more critical, in composite design than in conventional steel

Conventional steel framing can always be designed to carry the required

Steel Beams

Shear Stress in a steel beam:

The unit shear stress f(v) is equal to V/dt.

The shear

stress should be checked for beams with a short span and a
heavy load

The shear stress should be checked for beams with a large concentrated
load near the support.


Strength Design Method

the internal stresses and strains in a r
concrete beam which is about to fail are used to determine the ultimate
moment capacity of the member.

Balanced Design

crushing of the concrete and yielding of the
reinforcement steel take place simultaneously.

It is desirable to keep the a
mount of reinforcing steel relatively small,
so that if the member were ever to be overstressed, it will fail gradually
by yielding of the steel, rather than the crushing of the concrete.

For this reason, the amount of reinforcing is limited to 75% of th
which would produce balanced design.


The principle factor that determines the strength of concrete is the
water ratio.

Concrete strength increases as the water
cement ratio decreases

Less water relative to cement results in stronger concret

More water relative to cement results in weaker concrete

Formwork (the following is the usual order for removal of concrete
formwork, from first removal to last):

Beam Side Forms

Slab Bottom Forms

Beam Bottom Forms

Wood Joists / Beams

narrow beams which tend to be laterally unstable

Bridging or blocking is used to prevent rotation or lateral displacement

Bridging and blocking also helps to distribute concentrated loads to the
adjacent joists

Horizontal shear is critical for wood b
eams with short spans and large

The following are generally ignored in the design and detailing of strctural
wood members:

Longitudinal shrinkage

Thermal expansion

Thermal contraction

Notching wood beams

A notch near the middle of a beam
’s span has practically no effect on its

The loss of shear strength caused by a gradual change in a beam’s cross
section is not as great as that caused by a square notch.

Concrete Beams

If the allowable concrete shear stress is exceeded, t
he shear capacity of the
beam ma be increased by adding shear reinforcing such as stirrups.

Other ways of increasing a beams shear capacity include increasing the
concrete strength, and increasing the width or depth of the beam.

Ways to reduce deflecti
on in concrete beams

周攠mom敮琠o映湥牴a ⡉⤠o映瑨攠扥bm may 扥b湣牥as敤eby mak湧


the beam wider or deeper.

周攠To摵d畳 o映flas瑩c瑹


周攠Tos琠敦晩捩e湴nway⁴o⁲敤 捥⁴桥c摥dl散瑩o渠ns⁴o⁤敥灥渠t桥
扥bmⰠs湣攠瑨攠I⁶al略映瑨攠扥am⁩ ⁰ o灯牴ronal⁴o⁴桥 瑨牤r


In fillet welds, the stress is always considered to be shear stress on the
minimum throat area,
regardless of the direction of the applied load.

The throat area is assumed to be equal to 0.707 times the weld size.

Concrete Members

Maximum size of aggregate that can be used depends on the size of
concrete members and the spacing of reinforcing b

Maximum size of aggregate should not exceed 1/5 of the dimension
between sides of forms or 3/4 of the clear spacing between reinforcing bars

Obtaining and handling aggregates larger than 2 or 2.5 inches is usually

The amount of water and cement required for concrete of a given
consistency decreases as the maximum size of coarse aggregate increases.

Reinforcing steel opposite the tension side of a reinforced concrete beam is
called compressive reinforcement, since it is located in the compression
side of the beam and resists compression.

The deflection of concrete members increases with time, beyond

the initial
deflection. This additional deflection, caused by shrinkage and creep, can
be reduced by using compressive reinforcement.

As with tensile longitudinal reinforcing, the compressive reinforcement
does not resist shear stress.

Belled Caisson

Belled caissons are frequently used when the soils near the surface are
relatively poor, but are underlain by dense soils having a high bearing

A special belling attachment is used to enlarge the hole to form a bell
having a diameter of up to
three times that of the drilled shaft.

The purpose of the bell is to provide sufficient bearing area to resist the
applied vertical load.


Prestressed Concrete

Is concrete which is permanently loaded so as to cause stresses opposite in
direction from
those caused by dead and live loads.

The entire cross
section becomes effective in resisting stress.

Two basic prestressing methods are used


high strength steel is stressed before the concrete is cast


the steel is st
ressed after the concrete is cast

Pretensioned members transfer the prestress force from the steel to the
concrete by bond and therefore require no end anchorages.

Shrinkage of the concrete and creep of the concrete and steel reduce the
prestressing fo
rce and must be considered in the design.

Tension / Compression

When a material is stressed in tension or compression, it deforms laterally
as well as longitudinaly.

Under tension, the member increases in length and its cross
sectional area

Under compression, the length of the member decreases and the
sectional area increases.

The ratio of the unit lateral strain to the unit longitudinal strain is called
Poisson’s ratio. For structural steel, the value of Poisson’s ratio is about




ability of a material to deform non
elastically without


refers to the capacity of a material to be molded or worked
into a shape.


the ability of a material to return to its original shape after
being deformed.


refers to a material’s resistance to deformation.


Strain Diagrams

Unit stress versus unit strain

Hooke’s Law states that up to the elastic limit, u
nit stress is directly
proportional to unit strain and the diagram will yield a straight line.

The constant ratio of unit stress to unit strain can also be expressed as the
tangent of angle theta

is called the modulus of elasticity.


The point in whic
h the sample continues to increase with no increase in
load is called the yield point.

Increasing the load on the sample will eventually reach the maximum unit
stress which develops before fracture. This is called ultimate strength.

engineered bui

Completely standardized, selected from a catalog, and factory built with
all the necessary components

Often used for single story industrial and warehouse occupancies.

A pre
engineered building is likely to be lower in cost than a custom
ned building.

Factory labor is generally less expensive than field labor.

Quality may be better because greater control is possible under factory

engineered buildings can also be built quicker.

Retaining Walls


Active Pressure

pressure exerted by retained earth against a retaining

Fluid Pressure

lateral pressure exerted by a fluid.

Passive Pressure

resistance to the movement of a retaining wall
provided by the earth in front of the wall and footin

Surcharge Pressure

is the increased lateral earth pressure caused by a
vertical load behind the wall or sloping ground surface.

A retaining wall is necessary whenever the ground elevation changes

The total earth pressure on the stem, for a one foot length of wall, is equal
to 30h(h)/2.

Lateral Forces



Hurricane wind speeds usually vary between 30 and 120 mph, with gusts
up to 180 mph.

Rotational speeds of a tornado is estimated

to be nearly 250 mph, and may
occasionally exceed 500 mph.

Measurement of Winds

Wind speed is measured by a device called a revolving cup anemometer.


The maximum average wind speed is called the fastest mile speed.

All wind speed data has been sta
ndardized to a height of 10 meters or 33

When using the wind speed contour map, great attention must be paid to
local wind records and conditions, which may indicate higher basic wind

Areas shown on the map as “special wind regions” have

basic wind speeds so different from those of the surrounding
geographic areas that they are specifically excluded from the map.

Wind speeds in “special wind regions” must be determined from local

A mean recurrence interval of 50 y
ears: means that the fastest mile wind
speed has a two percent probability of occurring in any one year.

Tornados, however, are NOT accounted for on the wind speed map.

Building Response to Wind

Wind creates a negative pressure, or suction, on the le
eward side of the
building, which is the side opposite the windward side, and the side walls
parallel to the wind direction.

The direct wind pressure is also called the stagnation pressure (in psf).

Formula: p = 0.00256(V)2

Doubling the wind velocity

increases the wind pressure four fold.

The terrain surrounding the building has an affect on wind velocity and

Building size and shape also affect wind velocity and pressure.

Code Requirements

Buildings of unusual shape, such as domes, o
r with unusual site
conditions, such as at the mouth of a canyon, are not covered by UBC
requirements. Wind tunnel testing may have to be done to determine the
applicable design loads.

The structure must be designed to resist the forces caused by EITHER

wind or earthquake, whichever is greater, in each direction, but not in both
directions acting at the same time.

Basic Formula for Static Analysis: wind pressure on the building (p)=


accounts for the height of the building, the
exposure, or
roughness of the terrain at the building site, and an increase to account
for the gusting effect.


Site exposure is classified as Exposure B, C, or D.

Exposure B

has terrain with buildings, forest, or surface
irregularities, covering at l
east 20% of the ground level area
extending one mile or more from the site.

Exposure C

has terrain which is flat and generally open, extending
half mile or more from the site in any full quadrant.

Exposure D

represents the most severe exposure
in areas with
basic wind speeds of 80 mph or greater and has terrain which is flat
and unobstructed facing large bodies of water over one mile or more
in width relative to any quadrant of the building site. Exposure D
extends inland from the shoreline 1/4

mile or 10 times the building
height, whichever is greater.


is a pressure coefficient for the structure or portion of the
structure under consideration.

The direct pressure on a windward wall is not the same as the suction or
uplift pressure on the roof.

Method 1

Normal Force Method, the wind pressures normal
(perpendicular) to all external surfaces are determined and are
assumed to act simultaneously.

May be used for any building, and must be used for gabled rigid

For windward walls, the pressure varies with the height.

For inward or outward pressures on roofs and leeward walls, the
factor (Ce) is evaluated at the mean roof height and results in
constant pressure.

Method 2

Projected Area Method, the wind pressures acting on the full
projected horizontal and vertical a
reas of the building are
determined and are assumed to act simultaneously.

Method 2 is limited to buildings less than 200 feet in height,
except those using gabled rigid frames.

(Ce) Factor includes the effects of external pressure or suction,

pressure or suction, and wind drag on the surfaces parallel
to the wind direction.

) factor is the wind stagnation pressure or direct wind pressure at a
standard height of 33 feet, determined from the basic wind speed, or


fastest mile speed, at that

) can be calculated = 0.00256V

(I) factor is the importance factor

similar to that used in earthquake

Dependant on the occupancy category.

Vertical Projected Area = Wall

Horizontal Projected Area = Roof / Floor

Lateral Loa
d Resisting Systems

Same as those used in earthquake design

Moment resisting frames

Shear walls

Braced frames

The concept of ductility, or the ability of a system to absorb energy in the
inelastic range, is less important for wind design than for earthquake

The stresses in wind design are expected to be in the elastic range, below
the yield point.


Dead load resisting moment must be at least 1
1/2 times the wind
overturning moment.

The wind overturning moment may not exceed 2/3 of the dead load
resisting moment.

If the columns are adequately anchored to the foundation, the weight of

foundation may be used to increase the dead load resisting moment.

Buildings with a high height
width ratio are most critical for
overturning from wind forces.

Deflection and Drift

The drift between adjacent stories is generally limited to 0.0025 times
the story height.

Diaphragms, collectors, and torsion

Torsion occurs in a rigid diaphragm when the center of mass does not
coincide with the center of rigidity.

Elements and comp
onents of Structures

Higher values for C

factor are used in the design of elements,


components, and discontinuities.