STRUCTURAL MODULE 1
STRUCTURAL
ENGINEERING
MECHANICS AND
STRENGTH OF
MATERIALS
ENGINEERING MECHANICS
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Branch of engineering that deals
with the analysis of the external
effects of forces on rigid bodies.
BRANCHES OF ENGINEERING
MECHANICS
RIGID BODIES
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Do not deform under load.
A basic requirement for the study
of the mechanics of deformable
bodies and the mechanics of fluids.
(Advanced courses).
FORCE
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Is an action, a push or pull upon an
object.
CHARACTERISTICS OF FORCE
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Magnitude, F
o Amount of force
Direction, 𝜽
o Orientation of the path
where force is imposed.
STATICS
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Deals with the study of the external
effects of forces on rigid bodies at
rest and remain at rest before
and after the application.
TENSION
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DYNAMICS
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TENSION VS. COMPRESSION
Deals with the motion of bodies
under action of forces, the
mathematical analysis of the
motion as a result of impressed
forces.
KINEMATICS
Calculates the
trajectory of particles or
bodies
Does not consider the
mass of each particle in
the system
Can be considered a
branch of mathematics
KINETICS
Calculates the motion
and the causes of that
motions
Considers the mass of
each particle in the
system
Is a branch of physics
and cannot be regarded
as branch of
mathematics.
An external force that creates a
pulling or stretching action on a
material
COMPRESSION
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An external force that creates a
push or squeezing action on a
material.
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STRUCTURAL MODULE 1
RESULTANT FORCE
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JOINT METHOD
Is a single force whose effect is
representative of the cumulative
effects of each force in the system.
SECTION METHOD
REACTION
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CENTER OF GRAVITY
Is a reactive force developed by a
body on which a force or system of
forces acts.
SYSTEM OF UNITS
KINDS OF LOADS (FORCES)
TRUSSES
UNIFORMLY DISTRIBUTED LOAD
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Loads applied on the entire span
or at a specified portion of a
structure.
BAY: distance between trusses
SPAN: distance between supports
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STRUCTURAL MODULE 1
CONCETRATED LOADS
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Loads concentratedly imposed at a
point or on a very small are shown
in the FBD.
UNIFORMLY VARYING LOAD
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Load applied on the entire span or
at a specified portion of a structure
which varies from zero or any
minimum amount of load to any
maximum value.
FORMULA
UNIFORMLY DISTRIBUTED LOAD
TRAPEZOIDAL LOAD
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W = area of rectangular shape
=w*L
= wL in N
UNIFORMLY VARYING LOAD
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W = area of triangular shape
=½w*L
= ½ wL in N
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STRUCTURAL MODULE 1
FREE BODY DIAGRAM
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Is an isolation of a force or system
of forces that acts at specific parts
of a structure or machine element
in consideration.
COUPLE
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Two parallel forces equal in
magnitude but oppositely directed.
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A couple produces a rotation or
moment;
The moment (M) is F x d
The unit of a moment is product of
F and d.
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EQUILIBRIUM
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Is a state in which the resultant of
the force system that acts on a
body vanishes. Equilibrium means
that both the resultant force and
the resultant couple are zero.
Static equilibrium satisfies the
following conditions:
FOR 3 AXES:
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STRUCTURAL MODULE 1
FRICTION
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CENTROID / CENTER OF GRAVITY
Defined as the contact resistance
developed by a body upon another
body due to the actions of a force
that moves or tends to move the
two bodies past each other.
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STRUCTURAL MODULE 1
STRENGTH OF MATERIALS
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MOMENT OF INERTIA OF COMMON
SHAPES
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Branch of engineering that deals
with the internal effects of forces
on the body.
Is a branch of applied mechanics
that deals with the behavior of solid
bodies subjected to various types
of loading.
STRESS & STRAIN RELATIONSHIP
STRESS
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It is the unit of strength of element.
STRAIN
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It is the unit deformation of a
materials when loaded.
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STRUCTURAL MODULE 1
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F = force
L = original length
A = cross sectional area
E = modulus of elasticity
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Rise = Stress
Run = Strain
STRAIN GAUGE
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Also called extensometer.
Instrument used to measure a
minute deformation.
Used to determine elongation or
shortening.
𝐸 (𝑚𝑜𝑑𝑢𝑙𝑢𝑠 𝑜𝑓 𝑒𝑙𝑎𝑠𝑡𝑖𝑐𝑖𝑡𝑦) =
𝜎 (𝑠𝑡𝑟𝑒𝑠𝑠)
𝜀 (𝑠𝑡𝑟𝑎𝑖𝑛)
PROPORTIONAL LIMIT (HOOKE’s LAW)
STRESS & STRAIN RELATIONSHIP
ROBERT HOOKE (HOOKE’S LAW)
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Stress, 𝜎: is the unit strength of
element.
𝐹
o 𝜎=𝐴
Strain, ∈: is the unit deformation of
a material subjected to an applied
load.
𝜹
o 𝜺=𝑳
“Stress is proportional to Strain”
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STRUCTURAL MODULE 1
ELASTIC AND PLASTIC RANGES
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The region in the stress-strain
diagram from O to P is called the
elastic range. The region from P to
R is called that plastic range.
PROPORTIONAL LIMIT
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Is the greatest stress that a
material is capable of withstanding
without deformation/deviation and
obeys Hooke’s Law.
ELASTIC LIMIT
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Is the limit beyond which the
materials will no longer go back to
its original shape when the load is
removed, or it is the maximum
stress that e may developed such
that there is no permanent or
residual deformation where load is
entirely removed.
YIELD POINT
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Is the stress in a material at which
an increase in strain occurs
without an increase in stress.
ULTIMATE STRESS
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MODULUS OF RESILIENCE
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Modulus of resilience is the work
done on a unit volume of material
as the force is gradually increased
from O to P, in N x m / m3 . This
may be calculated as the area
under the stress-strain curve from
the origin O to up to the elastic
limit E (the shaded area in the
figure).
The resilience of the material is its
ability to absorb energy without
creating a permanent distortion.
MODULUS OF TOUGHNESS
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A point wherein a material is about
to rupture.
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Modulus of toughness is the work
done on a unit volume of material
as the force is gradually increased
from O to R, in N x m / m3. This
may be calculated as the area
under the entire stress-strain curve
(from O to R).
The toughness of a material is its
ability to absorb energy without
causing it to break.
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STRUCTURAL MODULE 1
YOUNG’s MODULUS
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The Young’s Modulus (E) is a
property of the material that tells
us how easily it can stretch and
deform and is defined as the ratio
of tensile stress, 𝜎 to tensile strain,
𝜀.
o 𝐸=
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RESILIENCE
𝑠𝑡𝑟𝑒𝑠𝑠
𝑠𝑡𝑟𝑎𝑖𝑛
=
𝜎
𝜀
The modulus of elasticity for most
concretes at 28 days, ranges from
15 – 40kN/mm2.
MODULUS OF RIGIDITY
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Is the ratio of shear stress to the
displacement per unit sample
length, (shear strain).
Shear modulus
Is the coefficient of elasticity for a
shearing force.
In materials science, shear
modules or modulus of rigidity,
denoted by G defined as the ratio
of shear stress to the shear strain,
𝜏
i.e. 𝐺 = 𝑦
PROPERTIES OF MATERIALS
ELASTICITY
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Ability of a material to return to its
original shape and size upon
removal of load.
PLASTICITY
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Is the property of a material, by
virtue of which, a permanent
deformation (without fracture)
takes place whenever it is
subjected to action of external
forces or load. It is inelastic strain
in a material.
TOUGHNESS
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Is the property of a material that it
does not break under a sudden
shock.
It is the ability of a material to
withstand shock loading.
The ability to absorb energy before
rupturing.
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Is the capacity of a material to
absorb energy elastically. It is the
max energy which can be stored in
a material up to elastic limit. It is
the capacity of a material to bear
shocks and vibrations.
TENSILE STRENGHT
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Is the ability of a material to stretch
without breaking or snapping.
YIELD STRENGTH
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The stress a material can withstand
without permanent deformation.
IMPACT STRENGTH
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Is the reaction of a stationary
object to a collusion with a moving
body.
It is the energy required to fracture
a material under an impact force.
DUCTILITY
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Is a measure of deformation at
fracture.
Is it defined by percent elongation
or percent reduction in area
Property that enables the material
to deform under tensile load.
HARDNESS
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Is the property of a material that
enables it to resist plastic
deformation, usually by
penetration.
FATIGUE STRENGTH
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Is the stress at which a material
fails under repeated loading.
Fatigue: is progressive fracture
under repeated loading.
CREEP
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Continuous deformation of
concrete with time under loads.
Time-dependent deformation
which occurs at elevated
temperature.
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STRUCTURAL MODULE 1
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Plastic flow may occur.
Ability to flow like fluid.
TEMPERATURE EFFECT
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WEAR RESISTANCE
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It is the capacity of a material to
resist abrasion.
RUPTURE STRENGTH
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The strength in which material
breaks or cracks.
EFFECTS OF FORCES
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MALLEABILITY
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Is the quality of something that can
be shaped into something else
without breaking, like the
malleability of clay.
The ability to deform under
compressive stress or load.
OTHER TERMS
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MODULUS OF ELASTICITY
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The brittle behavior low
temperature can cause in a
normally ductile material.
It is the ratio between the unit
stress and unit deformation caused
by stress.
Derived from Hooke’s Law
𝜎=𝐸𝜀
When a material is loaded with
force, it produces stress.
Strain is the response of a system
to an applied stress. Engineering
strain is defined as the amount of
deformation in the direction of the
applied force divided by the initial
length of the material.
Stress is expressed in Newtons per
square meter, or Pascal.
1 Pascal (symbol Pa) is equal to
1N/m2.
In imperial units, stress is
measured in pound force per
square inch, which is often
shortened to psi.
SHEAR MODULUS OF ELASTICITY
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Also called modulus of rigidity,
modulus of torsion;
The ratio between shearing stress
and the shearing strain.
POISSON’s RATIO
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Is the ratio of the transverse
contraction strain to longitudinal
extension strain in the direction of
stretching force.
∈𝑙𝑎𝑡
𝑣 = − ∈𝑙𝑜𝑛𝑔
STRAIN RATE EFFECT
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The behavior an increased rate of
load application can cause in
normally ductile material.
TYPES OF STRESS
AXIAL STRESS
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A stress that tends to change the
length of material:
o Compressive Stress: is
the axial stress that tends
to cause a body to become
shorter along the firection
of applied force.
o Tensile Stress: is axial
stress that tends to cause a
body to become longer
along the direction of
applied force.
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STRUCTURAL MODULE 1
SHEARING STRESS
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A stress produced when on body
slides the other.
Is also devvevloped in the figures
below. Sheared area is parallel to
the applied force.
BEARING STRESS
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A stress produced when on body is
in contact normal to the other.
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STRUCTURAL MODULE 1
TORSIONAL STRESS
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A stress produced when the force
applied tends to twist the body.
THERMAL STRESS
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Thermal strain does not produce
stress if a structure is not
constrained as in the case of
statically determinate structures. If
a structure is constrained statically
indeterminate structures, thermal
stress will be developed and is
calculated by:
BOND STRESS
CIRCUMFERENTIAL STRESS
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A stress produced at the thinwalled cylinders.
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The force of adhesion per unit area
of contact between two bonded
surfaces, such as between
concrete and a steel reinforcing
bar.
BOARD EXAM:
BENDING STRESS
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Also called flexural stress; tends to
cause of materials like beams.
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SHEAR AND MOMENT DIAGRAM
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Example: bottom chord &
some web members of
trusses
Transverse
o Act of bending a structure
o Effect: deflection
o Example: Beam
Torsion
o Act of twisting/bending
o Effect: Shear
deformation/deflection
o
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TYPES & SOURCES OF LOADS
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Can be found in NSCP
o At the beginning and end of
every chapter, study the
terms for the board exam.
DEAD LOAD
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Weight of materials and any
permanent loads imposed on it.
LIVE LOAD
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Movable loads applied on a
material.
WIND LOAD
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LOADS
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Cause of stress in a material
Ultimate
Small
probability of
being
exceeded in
50 years
Nominal
Small
probability of
ebing
exceeded in
1 year
Service
Loads act on
the structure
at an
Arbitrary
point in time
TYPES OF LOADS
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Compression
o Act of shortening or state of
pushing together
o Effect: shortening
o Example: Columns
Tension
o Act of stretching or state of
pulling apart
o Effect: elongation
Force on structure arising from the
impact of wind on it. It depends on
the location (exposure) and
typhoon signal.
SEISMIC LOAD
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Force on structure arising from the
impact of earthquake on it. It
depends on the epicenter and
magnitude of earthquake.
IMPACT LOAD
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Abrupt application of load. Its is an
additional load based on the
weight applied on the materials
(NSCP)
HYDROSTATIC PRESSURE
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Force on structure exerted by
water.
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STRUCTURAL MODULE 1
SOIL PRESSURE
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Force on structure exerted by soil.
206.9 CRANE LOADS
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LOAD FROM TEMPERATURE CHANGE
MOVING LOADS
SNOW LOAD
ICE LOAD
LIVE LOADS (NSCP)
The crane load shall be the rated
capacity of the crane. Design loads
for th runway beams, including
connections and support brackets,
of moving bridge cranes and
monorail cranes shall include
maximum wheel loads of the crane
and the vertical impact, lateral, and
longitudinal forces, induced by the
moving crane.
206.10 HELIPORT & HELISTOP
LANDING AREAS (NSCP)
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SPECIAL LOADS
OTHER MINIMUM LOADS (NSCP)
206.3 IMPACT LOADS
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The live loads specified in Sections
205.3 shall be assumed to include
allowance for ordinary impact
conditions. Provisions shall be
made in the structural design for
used and loads that involve
unusual vibration and impact
forces.
Section 206.9.3 for impact loads
for cranes, and Section 206.10 for
heliport and helistop landing areas.
In addition to other design
requirements, heliport and helistop
landing or touchdown areas shall
be designed for the following
loads, combined in accordance
with Section 203.3 or 203.4:
o Dead load plus actual
weight of the helicopter
o Dead load plus a single
concentrated impact load,
L, covering 0.1m2 of 0.75
times the fully loaded
weight of the helicopter if it
is equipped with hydraulictype shock absorbers, or
1.5 times the fully loaded
weight of the helicopter if it
is equipped with a rigid or
skid-type landing gear.
207.1.4.1 MAIN WIND-FORCE
RESISTING SYSTEM (NSCP)
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The wind load to be used in the
design of the MWFRS for an
enclosed or partially enclosed
building or other structure shall not
be less than 0.5 kPa multiplied by
the area of the building or structure
projected onto a vertical plane
normal to the assumed wind
direction. The design wind force
for open buildings and other
structures shall not be less than
0.5kPa multiplied by the area Af as
defined in Section 207.3
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STRUCTURAL MODULE 1
207.1.4.2 COMPONENTS AND
CLADDING
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The design win pressure for
component and cladding of
buildings shall not be less than a
net pressure of 0.5 kPa acting
either direction normal to the
surface.
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BASIC WIND SPEED
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Three-second gust speed at 10m
above the ground in Exposure C.
203.3 LOAD COMBINATIONS USING
STRENGTH DESIGN
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1.4(D+F)
1.2(D+F+T)+1.6(L+H)+0.5(Lr or R)
0.9D + 1.6W + 1.6H
0.9D + 1.0E + 1.6H
1.2D + 1.6D(Lr or R)+(f1 L or 0.8W)
1.2D + 1.6W + f1L + 0.5(Lr or R)
1.2D + 1.0E + f1L
F1 = 1.0 for floors in places of
public assembly, for live loads in
excess of 4.8 kPa and for garage
live load.
F1 = 0.5 for other live loads
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L = live load, except roof live load,
inclusion any permitted live load
reduction.
Lr = roof live load, including any
permitted live load reduction
P = ponding load
R = rain load on the undeflected
roof
T = self-straining force and effects
arising from contraction or
expansion resulting from
temperature change, shrinkage,
moisture change, creep in
component materials, movement
due to differential settlement, or
combinations thereof.
W = load due to wind pressure
TYPES OF STRUCTURES
BEAMS
TRUSSES / PURLINS
LOAD COMBINATIONS USING
ALLOWABLE STRESS DESIGN
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D+F
D+H+F+L+T
D + H + F + (Lr or R)
D + H + F + 0.75 [L + T + (Lr or R)]
𝐸
D + H + F + (W or 1.4)
NOTATION
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D = dead load
E = earthquake load set forth in
Section 208.5.1
Em = estimated maximum
earthquake force that can be
developed in the structure as set
forth in Section 208.5.1 .1
F = load due to fluids with welldefined pressures and maximum
heights.
H = load due to lateral pressure of
soil and water in soil.
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STRUCTURAL MODULE 1
WALLS (Retaining Wall)
COLUMNS/PEDESTALS/PIERS/BRIDGES
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SLABS
PILES
FOUNDATIONS
PUNCHING SHEAR
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Arises when a concentrated load is
applied to a small area of a slab or,
most commonly, the reaction of a
column against a slab.
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