Forces on Structures
Building Structural Systems
Structure
is an essential part of architecture.
Definition:
the way parts are combined or arranged to form a whole.
Structures
must assure stability against gravity, wind, and earthquake.
Structures must be designed to be
resistant to all of the forces that are anticipated to act upon them during
their entire existence.
The function of a structure is to
resist forces in equilibrium. Forces in equilibrium = a stable structure - the
basis of design.
For most of history, man built
intuitively. For the last 200 years or so, the science of structures has
evolved and now most structures are designed using rigorous mathematical
calculations or models.
Structures
must be built to resist forces; forces acting on a structure are called loads
Forces
Force
is defined as a push or a pull exerted on an object.
All
forces have magnitude, direction, and point of application.
Forces are depicted in engineering
diagrams by using arrows that indicate direction of the force or the "line
of action"
Drawn
to scale the length of arrow indicates the magnitude of-the force.
Example
1 " = 1000 Ib = arrow 1"
length 2000 Ib = 2" arrow length
Force is measured in units of
weight.
Example: 1000 Ib = 1 kp or kip.
(Metric:
11bf (pound force) = 4.448
The
most important force - the basic force - in building design is gravity.
Determining the magnitude,
direction, and point or points of application of forces, is the first step in
structural design.
Force
applied to a body is called an external force or load.
The
resistance of the body to the load is called internal force or stress.
Concentrated
Load is a force applied to a small area of a body
Distributed
load is a force applied to a large area
The
"line of action" of a force, is a line parallel to and in line with
the force.
Concurrent forces = if lines of
action of several forces pass through a common point.
Non-concurrent
forces = if lines of action do not have a common point.
A resultant force is = one force
that will produce the same effect on a body as two or more other forces - or
forces that meet at a point.
Forces on the same line of action
may added together to produce a resultant that is the sum of the forces.
Forces with the same line of
action, but opposing directions may be subtracted from each other. The
remainder of the force is the resultant in the direction of the larger force.
Concurrent forces cannot be added
directly because they are on different lines of action - they may be added
together vectorially by diagramming the forces.
Example #1 for computing the
resultant of two forces (P 1-4)
Begin at the intersection of the
two forces.
Extend the each line of action through their intersection
to scale.
Add parallel lines to form a parallelogram.
The distance diagonally across the parallelogram is the
resultant.
This known as a parallelogram of force.
Insert force
Parallelogram image from AutoCAD
Example #2
for computing the resultant three or more forces: (P 1-5)
Resultant
is computed by using a force polygon.
Force
Polygon
1. Start at any point and layoff
one of the forces to scale and in the correct direction.
2. From
it's arrowhead end, layoff another force to scale and in the correct direction.
3. Layoff all forces in the same
manner.
4. Draw an arrow AWAY from the
starting point to the arrowhead end of the final force.
5. This arrow is the resultant both
in magnitude and direction.
Insert multi vector force image from AutoCAD
Force Polygon rules:
1. the order in which the forces are drawn
makes no difference.
2. the resultant is directed away from the
starting point.
3. the resultant is concurrent with the
original forces. (passes through the same point.
Equilibrant
(the opposite of a
resultant) = a force equal to the resultant, opposite in direction, on the same
line of action as the resultant.
This principal is used to balance
forces within a structure and results in equilibrium or stability.
Resolving
forces - replacing the
original force with two or more forces which produce the same result as the
original
Useful for structures because
forces on structures are often resolved into vertical and horizontal components
or forces that are at right angles to the
Original force. These forces are
called components of the
original force.
To resolve use the parallelogram of force.
See Example #3, (P 1-6)
The analytical method can also be used to resolve forces using
trigonometry. Principle of parallel
forces - the see-saw is a simple example.
The distance times the weight of
each occupant must be equal in order to achieve equilibrium.
Reverse the see-saw example: this
is similar to a beam with a load in the middle.
If we want to know the magnitude of
stress working on any given point on a beam we multiply the magnitude of the
force times the distance to the point on the beam. The result is a moment of
force.
Moment - a tendency of a force to cause
rotation around a given point.
The point is called center of
moments
The distance is called the moment
arm or lever arm.
Moment magnitude - the magnitude of the force
multiplied times the distance from the center of moments.
Units of moments - foot-pounds, inch-pounds,
foot-kips
Metric - Newton-meters
Moment is not the rotation itself,
but the tendency to rotate.
See see-saw diagram page 1-9.
Couple (or mechanical couple) two forces
equal in magnitude but opposite in direction and acting at some distance from
each other.
The moment produced by a couple is
equal to one of the forces x the distance -- between them.
Couple, example:
Use lug wrench diagram page 1-9.
Equilibrium
- A building must have no unbalanced forces acting on it.
The sum of all forces acting to the
right must equal forces acting to the left.
The sum of all downward forces must
equal all upward forces.
The sum of all forces acting
counterclockwise must equal forces acting clockwise.
Stresses - stress in a body is
internal resistance to external forces.
Total stress - total internal force
Unit stress - stress per unit of
area
Three types of stresses most
commonly found in building design. Tension, Compression, and Shear
Tension - tends to stretch or pull
apart a member.
Compression - tends to crush or
shorten a member.
Shear - 2 members tend to slide
past one another.
The unit stress (f) is equal to the
load (P) divided by the cross sectional area (A). F= P/A
See Example #12 (P 1-16)
What is the tensile stress on the
cable?
P = 10,000 10000 ~ <ZL,lPA:
A = .4417 square inches ~ t
F = 22,640 psi
Another example:
2" x 2" bar under tension supports a load of 2000
lb.
What is the unit tensile stress in the bar? (500 psi)
P = 2000 lb A = 4
square inches F = 500 psi
Example
#13 (P 1-17)
A 10" square concrete post has an allowable unit
stress of 1750 psi (very weak concrete).
How much load can it support? (P= FA)
P = 1750 psi x 100 square inches
= 175,000 Ibs
Another example:
A 12" square concrete post has an allowable unit
stress of 4000 psi.
How much load can it support?
P = 4000 psi x 144 square inches
= 576,000 Ibs
Example
#14 (P 1-17)
Shear
Two angles connected by two bolts.
The area subject to shear is equal to the cross sectional
area of the two bolts. Area of each bolt = .306 square inches
Total area of bolts = .612 square inches
F = PIA = 6000 Ibs/.612 = 9803.92 Ibs
Strain - the deformation or change in physical
size of a body (componenet) caused by external load
or stress.
Total strain - the total elongation or shortening
of a body Unit strain – total strain divided by the original length.
Hookes law - unit stress is equal to unit strain (up to the elastic limit of the material)
Unit stress/unit strain = E = Modulus
of elasticity
E is expressed in psi and but is not a stress - it is a measure of stiffness
of the material.
Steel
- E = 29,000,000 psi
Concrete
(depending on mix design) E = 3,000,000 to 5,000,00 psi Wood - depends on species - Douglas Fir - E = 1,300,000
to 1,900,000 psi
Other
types of stresses
Bending - a complex force state associated
with bowing under transversely applied loading.
Bending causes tension on one side of beam and compression on the other. The stress in a specific cross section cannot
be expressed by the stress = force/area formula
Torsion
– torsion or
twisting.
Bearing - forces that act perpendicular to
the face of the member at the interface of two members. Columns
on footings. Beams on walls or columns.
Lateral
Stability Refer to Schodek (pages 15 - 17)
Unstable structures can be made
stable by introducing structural elements into the design.
Diagonal Bracing - places crossing/diagonal members
under tension ( used in timber or steel construction)
Shear Walls - Uses a rigid planar element
placed to resist lateral load.
Wood
frame with plywood skin
Masonry
Concrete
Rigid Frames - Usually steel but can be built
from reinforced concrete beams/columns
Lateral stabilizing elements:
can be used in combinations
can be placed within a building
usually placed along a perimeter of a
building
should be used symmetrically
(illustrate)
As the height of the structure
increases the lateral support must increase.
Building Loads
Refer
to ALS, ST2 Bui/ding Loads" pages 1-] to 1-7
Loads
- may be
distributed or concentrated forces acting on a structure.
Dead loads - vertical loads of the structure
and weight of permanent elements
Live loads - may not be present all of the
time, movable items, occupants, furnishings, snow
Wind loads - multidirectional, complex, and lateral.
Loads are computed laterally.
Earthquake forces - are multidirectional but are
often computed as lateral loads
A buildings structure must be
designed for all contingencies and all loads that may be reasonable expected to
act upon it over it's ENTIRE life.
Building codes usually subscribe
uniform loads and concentrated loads for structures. i.e.
As each element of a building's
structure is loaded, it's supporting elements must react
with equal but opposite forces
Miscellaneous loads - Special loads that may be
required for specific portions of the building.
Retained Earth - retaining walls
Hydrostatic pressure - structures
that contain water or other fluids
Forces caused by temp. change
Railings - balconies and stairs
Impact loads - moving machinery
like elevators
Vibration - caused by machinery or
vehicles or dancing Blast - designed to resist explosion
Wheel loads - loads from vehicle
wheels
Structural Systems-
Three
types - Linear, Planar, and Composite
Linear - composed primarily of columns and
beams and form a skeleton.
Columns - transmit compressive forces along
their length vertically.
Columns
thickness/shape/material affect its capacity to carry
loads.
Thicker
columns carry more load without compressing or
buckling.
Beams - defined as members which support
loads perpendicular to its
longitudinal axis.
Transfers
loads laterally along its length to it's supports.
Beams are loaded they're subject
bending.
If the length is doubled it carry's
only half the load.
Planar - utilize rigid planes vertically
and horizontally to provide stability
Vertical walls - can be load bearing or shear
plane
Floor planes - rigid horizontal diaphragms.
Transfer lateral loading from wind and seismic forces to the vertical planar
elements.
Composite - utilize linear and planar
elements in combination to form a stable structure.
Composite structures allow more
flexibility in design and are the most common type used.
Structural Systems
Refer
to ALS, ST2 pages 1-16 and 1-17
Wood
Joist System
Trussed
Rafter Roof System
Wood
plank and beam system
Steel
joist system
Steel
beam and girder system
Stub
girder system