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: Newton = one kilogram pushing one meter per second)

11bf (pound force) = 4.448 Newtons

 

     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. Anchorage area snow load is 50 Ibs/sf

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