WHAT IS THE DIFFERENCE BETWEEN AN ENGINEER AND AN ARCHITECT?

The major distinctions between architects and engineers run along generalist and specialist lines. The generalists are ultimately responsible for the overall planning.

It is for this reason that an architect is generally employed as the prime professional by a client. On some special projects, such as dams, power plants, wastewater treatment, and research or industrial installations, where one of the engineering specialties becomes the predominant feature, a client may select an engineering professional or an E/A firm to assume responsibility for design and construction and taken on the lead role.

On certain projects, it is the unique and imaginative contribution of the engineer that may make the most significant total impact on the architectural design.

The overall strength of a dynamic, exposed structure, the sophistication of complex lighting systems, or the quiet efficiency of a well-designed mechanical system may prove to be the major source of the client’s pride in a facility. In any circumstance, the responsibilities of the professional engineer for competence and contribution are just as important to the project as those of the
architect.

Engineers, for example, play a major role in intelligent building system design, which involves mechanical-electrical systems. However, a building’s intelligence is also measured by the way it responds to people, both on the inside and outside.

The systems of the building must meet the functional needs of the occupants as well as respect the human response to temperature, humidity, airflow, noise, light, and air quality. To achieve the multifaceted goals, an intelligent building requires an intelligent design process with respect to design and system formulation as well as efficient and coordinated execution of design and technical documentation within the management structure.

An intelligent building begins with intelligent architecture—the shape, the building enclosure, and the way the building appears and functions. Optimal building solutions can be achieved through a design process that explores and compares varying architectural and engineering options in concert.

Sophisticated visualization and analytical tools using three-dimensional computer modeling techniques permit architects and engineers to rapidly evaluate numerous alternatives. Options can be carefully studied both visually and from a performance standpoint, identifying energy and life-cycle cost impact. This enables visualization and technical evaluation of multiple schemes early in the design phase, setting the basis for an intelligent building.

In all cases, the architect’s or engineer’s legal responsibilities to the client remain firm. The prime professional is fully responsible for the services delivered. The consultants, in turn, are responsible to the architect or engineer with whom they contract.

Following this principle, the architect or engineer is responsible to clients for performance of each consultant. Consequently, it is wise for architects and engineers to evaluate their expertise in supervising others before retaining consultants in other areas of responsibility.

THE UNIFIED SOIL CLASSIFICATION SYSTEM (USCS) BASIC INFORMATION TUTORIALS

The Unified Soil Classification System is based on the airfield classification system developed by A. Casagrande during World War II. With some modification it was jointly adopted by several U.S. government agencies in 1952. Additional refinements were made and it is currently standardized as ASTM D 2487-93. It is used in the U.S. and much of the world for geotechnical work other than roads and highways.

In the unified system soils are designated by a two-letter symbol: the first identifies the primary component of the soil, and the second describes its grain size or plasticity characteristics. For example, a poorly graded sand is designated SP and a low plasticity clay is CL. Five first-letter symbols are used:

G for gravel

S for sand

M for silt

C for clay

O for organic soil

Clean sands and gravels (having less than 5% passing the No. 200 sieve) are given a second letter P if poorly graded or W if well graded. Sands and gravels with more than 12% by weight passing the No. 200 sieve are given a second letter M if the fines are silty or C if fines are clayey.

Sands and gravels having between 5 and 12% are given dual classifications such as SP-SM. Silts, clays, and organic soils are given the second letter H or L to designate high or low plasticity. The specific rules for classification are summarized as follows and described in detail in ASTM D 2487.

Organic soils are distinguished by a dark-brown to black color, an organic odor, and visible fibrous matter. For soils that are not notably organic the first step in classification is to consider the percentage passing the No. 200 sieve.

If less than 50% of the soil passes the No. 200 sieve, the soil is coarse grained, and the first letter will be G or S; if more than 50% passes the No. 200 sieve, the soil is fine grained and the first letter will be M or C.

For coarse-grained soils, the proportions of sand and gravel in the coarse fraction (not the total sample) determine the first letter of the classification symbol. The coarse fraction is that portion of the total sample retained on a No. 200 sieve.

If more than half of the coarse fraction is gravel (retained on the No. 4 sieve), the soil is gravel and the  first letter symbol is G. If more than half of the coarse fraction is sand, the soil is sand and the first letter symbol is S.

ATTERBERG LIMITS AND PLASTICITY BASIC INFORMATION AND TUTORIALS

Atterberg limits, named after the Swedish soil scientist A. Atterberg, are water content values at which notable changes in soil behavior occur. The liquid limit , denoted LL or wL, marks the transition between liquid and plastic behavior.

At water contents above the liquid limit the soil behaves as a viscous liquid; below the liquid limit the soil behaves as a plastic solid. The liquid limit is determined in the laboratory by partly filling a standard brass cup with wet soil and cutting a groove of a standard dimension in the soil.

The liquid limit is taken as the water content at which the groove closes a specified amount when the cup is lifted and dropped 1 cm exactly 25 times. The details of the test are given in AASHTO T 89 and ASTM D 4318-93.

The plastic limit, denoted PL or wp, is the transition between plastic and brittle behavior. It is determined in the laboratory as the water content at which a 1/8-inch diameter thread of soil begins to crumble when rolled under the palm of the hand.

Details of the liquid limit and plastic limit tests are provided by AASHTO T 90 and ASTM D 4318-93. The shrinkage limit, denoted SL or wS, is the water content below which the soil no longer reduces in volume when the water content is reduced.

Although Atterberg limits are water contents and are properly decimals or percentages, they are usually expressed as an integer percentage without a percent sign. Thus, a liquid limit of 40% is usually reported as LL = 40.

The plasticity index, denoted PI or IP, is the difference of the liquid limit and the plastic limit:

PI = LL – PL

The liquidity index, denoted LI or IL , is a measure of the natural water content (w) relative to the plastic limit and the liquid limit:

LI = Il = (W-pl)/ (LL-PL)

CONSTRUCTION CONTRACT BASIC DEFINITION AND TUTORIALS

Construction projects are done under a variety of contract arrangements for each of the parties involved. They range from a single contract for a single element of the project to a single contract for the whole project, including the financing, design, construction, and operation of the facility. Typical contract types include lump sum, unit price, cost plus, and construction management.

These contract systems can be used with either the competitive bidding process or with negotiated processes. A contract system becoming more popular with owners is design-build, in which all of the responsibilities can be placed with one party for the owner to deal with.

Each type of contract impacts the roles and responsibilities of each of the parties on a project. It also impacts the management functions to be carried out by the contractor on the project, especially the cost engineering function.

A major development in business relationships in the construction industry is partnering. Partnering is an approach to conducting business that confronts the economic and technological challenges in industry in the 21st century.

This new approach focuses on making long-term commitments with mutual goals for all parties involved to achieve mutual success. It requires changing traditional relationships to a shared culture without regard to normal organizational boundaries.

Participants seek to avoid the adversarial problems typical for many business ventures. Most of all, a relationship must be based upon trust. Although partnering in its pure form relates to a long-term business relationship for multiple projects, many single project partnering relationships have been developed, primarily for public owner projects.

Partnering is an excellent vehicle to attain improved quality on construction projects and to avoid serious conflicts. Partnering is not to be construed as a legal partnership with the associated joint liability. Great care should be taken to make this point clear to all parties involved in a partnering relationship.

Partnering is not a quick fix or panacea to be applied to all relationships. It requires total commitment, proper conditions, and the right chemistry between organizations for it to thrive and prosper.

The relationship is based upon trust, dedication to common goals, and an understanding of each other’s individual expectations and values. The partnering concept is intended to accentuate the strength of each partner and will be unable to overcome fundamental company weaknesses; in fact, weaknesses may be
magnified.

Expected benefits include improved efficiency and cost effectiveness, increased opportunity for innovation, and the continuous improvement of quality products and services. It can be used by either large or small businesses, and it can be used for either large or small projects.

Relationships can develop among all participants in construction: owner-contractor, owner-supplier, contractor-supplier, contractor-contractor. (Contractor refers to either a design firm or a construction company.)

SIMEON DENIS POISSON BASICS AND TUTORIALS

SIMEON DENIS POISSON BASIC INFORMATION
Who Is Siméon Denis Poisson?

Siméon Denis Poisson is mathematician famous and responsible for an important mathematical expression known as Poisson's Ratio.


He was born on 21-Jun-1781 at Pithiviers, France.

Siméon Poisson was a protégé of Laplace. Poisson was an extremely prolific researcher and also an excellent teacher. In addition to important advances in several areas of physics, Poisson made important contributions to Fourier analysis, definite integrals, path integrals, statistics, partial differential equations, calculus of variations and other fields of mathematics.

The Poisson Distribution is a discrete distribution is also named after Poisson. He published its essentials in a paper in 1837. The Poisson distribution and the binomial distribution have some similarities, but also several differences.

Among the books he authored:

Traité de Mécanique (1811, science)
Théorie Nouvelle de l'Action Capillaire (1831, science)
Théorie Mathématique de la Chaleur (1835, science)
Recherches sur la Probabilité des Jugements en Matière Criminelle et en Matière Civile (1837)

FLY ASHES CIVIL ENGINEERING CONSTRUCTION PURPOSE BASICS AND TUTORIALS

FLY ASHES CIVIL ENGINEERING CONSTRUCTION PURPOSE BASIC INFORMATION
What Are Fly Ashes?


Fly ash meeting the requirements of ASTM C618, ‘‘Specification for Fly Ash and Raw or Calcined Natural Pozzolan for Use as a Mineral Admixture in Portland Cement Concrete,’’ is generally used as a cementitious material as well as an admixture.

Natural pozzolans are derived from some diatomaceous earths, opaline cherts and shales, and other materials. While part of a common ASTM designation with fly ash, they are not as readily available as fly ashes and thus do not generate the same level of interest or research.

Fly ashes are produced by coal combustion, generally in an electrical generating station. The ash that would normally be released through the chimney is captured by various means, such as electrostatic precipitators. The fly ash may be sized prior to shipment to concrete suppliers.

All fly ashes possess pozzolanic properties, the ability to react with calcium hydroxide at ordinary temperatures to form compounds with cementitious properties. When cement is mixed with water, a chemical reaction (hydration) occurs.

The product of this reaction is calcium silicate hydrate (CSH) and calcium hydroxide [Ca(OH)2]. Fly ashes have high percentages of silicon dioxide (SiO2). In the presence of moisture, the Ca(OH)2 will react with the SiO2 to form another CSH.

Type F ashes are the result of burning anthracite or bituminous coals and possess pozzolanic properties. They have been shown by research and practice to provide usually increased sulfate resistance and to reduce alkali-aggregate expansions.

Type C fly ashes result from burning lignite or subbituminous coals. Because of the chemical properties of the coal, the Type C fly ashes have some cementitious properties in addition to their pozzolanic properties. Type C fly ashes may reduce the durability of concretes into which they are incorporated.

SAINT - VENANT PRINCIPLE BASICS AND CIVIL ENGINEERING TUTORIALS

SAINT - VENANT PRINCIPLE BASIC INFORMATION
What Is The Saint - Venant Principle?


Saint-Venant’s principle states that in a body under the action of a system of forces which are applied in a limited region of its boundary, the stresses and strains induced by those forces in another region of the body, located at a large distance from the region where the forces are applied, do not depend on the particular way the forces are applied, but only on their resultant.

This “large distance” may be considered, in most cases, as the largest dimension of the region where the forces are applied.

This principle does not have a formal, general and exact demonstration as yet, but it has been verified in so many cases, both experimentally and numerically, that it is accepted as valid by the generality of authors on this subject.

It is a very useful principle, since complex force systems may be reduced to their resultants, which substantially simplifies and reduces the computation effort in practical problems. Besides, it is a very helpful tool in the theoretical development of solutions for problems in Theory of Elasticity and Strength of Materials.

As an example, let us consider the prismatic bar represented in Fig. 56 under the action of three systems of forces with equal resultants: the stresses at a grater distance than the transversal dimension 2b from the upper end of the bar may be accepted as equal in the three cases.

This principle is also valid in the cases of non-isotropic materials, nonlinear material behaviour, plastic and viscous deformations and material heterogeneity. Furthermore, the validity of this principle is not limited to small deformations.

FIELD FABRICATION OF STRUCTURAL COMPONENTS (MIXTURE AND COMPONENTS) BASIC AND CIVIL ENGINEERING TUTORIALS

FIELD FABRICATION OF STRUCTURAL COMPONENTS (MIXTURE AND COMPONENTS) BASIC INFORMATION
What Are Field Fabrication Of Structural Components?


Structural components that are fabricated on site by trades people constitute the greatest risk for a catastrophic failure. This is due to the fact that control of putting parts together in the field is not done with the same diligence and controlled environment as a factory-made component.

Thus, great care must be taken to ensure that proper testing is performed so that a failure will not occur. The erection of a concrete structure is an excellent example where the use of a mixed type material must have adequate testing.

Concrete is a very viable construction material if placed according to the standards established by the organizations. However, due to the complexity of mixing the ingredients at the plant and transporting it to the site, placing the concrete at the site requires numerous controls to obtain an excellent final product.

The testing of concrete should include:

1. A trial concrete mix approved by the owner’s engineer
2. Proper mixing procedures at the concrete plant
3. Timing for the transportation of the concrete mix
4. Designed and properly installed form work and shoring so that they will not collapse or deflect
5. Temperature monitoring of the concrete at the site (to make sure that flash setting will not occur)
6. Ambient temperature monitoring (too hot for flash setting and too cold for freezing)
7. Slump test to confirm water/cement ratio of the concrete
8. Supervision for concrete vibration and dropping height for the actual placement of the concrete
9. Monitoring the thickness of a concrete slab
10. Assurance that all the concrete encapsulates the reinforcing bars, especially when
pouring columns
11. Placement of a sample of the concrete into concrete cylinders to determine the compressive strength of the concrete at 7, 14, and 28 days (via testing in the laboratory). This will be accomplished for design strength conformance and to know when the forms can be stripped
12. Checking the number and location of the reinforcing bars required for the pour
13. Proper curing of the concrete
14. Assurance that reinforcing bars are properly lapped
15. Assurance that all exterior exposed concrete is covered by 3 inches of concrete
(2 inches for interior concrete) over the reinforcing steel

Even though steel sections are fabricated in a controlled environment at a plant, the steel members must be connected in the field by iron workers with bolts and/or welding.

Thus, stringent testing is also required for a steel structure. Some of the tests that would have to be considered when erecting steel are the following:
1. Proper bolts are being utilized.
2. Required tightening (torque) of the bolts needs to be accomplished by code standards.
3. Steel sections as indicated on the approved shop drawings are in fact being installed.
4. Welds have to be checked for proper thickness and continuity.
5. All welders have to be certified.
6. Shear stud connectors have to be attached to the steel with proper spacing and welds.
7. The steel has to be fireproofed with approved material that will have proper thickness, adhesion, and density.
8. All columns are perfectly aligned (plumbed).
9. Correct steel is being used (i.e., A36).
10. Proper steel camber has been placed on the steel as specified by the consultants.
11. Splice plates must be of the approved thickness.
12. Inspection at the fabricator’s shop would be helpful for checking beam camber and obtaining coupons.

METHODS OF JOINT TRUSS MEMBERS ANALYSIS BASICS AND CIVIL ENGINEERING TUTORIALS

METHODS OF JOINT TRUSS MEMBERS ANALYSIS BASIC INFORMATION
How To Do The Methods Of Joint Truss Members Analysis?


This method for finding the forces in the members of a truss consists of satisfying the conditions of equilibrium for the forces acting on the connecting pin of each joint. The method therefore deals with the equilibrium of concurrent forces, and only two independent equilibrium equations are involved.

We begin the analysis with any joint where at least one known load exists and where not more than two unknown forces are present. The solution may be started with the pin at the left end. Its free-body diagram is shown in Fig. 4/7.

With the joints indicated by letters, we usually designate the force in each member by the two letters defining the ends of the member. The proper directions of the forces should be evident by inspection for this simple case.

The free-body diagrams of portions of members AF and AB are also shown to clearly indicate the mechanism of the action and reaction. The member AB actually makes contact on the left side of the pin, although the force AB is drawn from the right side and is shown acting away from the pin.

Thus, if we consistently draw the force arrows on the same side of the pin as the member, then tension (such as AB) will always be indicated by an arrow away from the pin, and compression (such as AF) will always be indicated by an arrow toward the pin.

The magnitude of AF is obtained from the equation ΣFy = 0 and AB is then found from ΣFx = 0. Joint F may be analyzed next, since it now contains only two unknowns, EF and BF. Proceeding to the next joint having no more than two unknowns, we subsequently analyze joints B, C, E, and D in that order.

Figure 4/8 shows the free-body diagram of each joint and its corresponding force polygon, which represents graphically the two equilibrium conditions ΣFx = 0 and ΣFy = 0. The numbers indicate the order in which the joints are analyzed.

We note that, when joint D is finally reached, the computed reaction R2 must be in equilibrium with the forces in members CD and ED, which were determined previously from the two neighboring joints. This requirement provides a check on the correctness of our work.

Note that isolation of joint C shows that the force in CE is zero when the equation ΣFy = 0 is applied. The force in this member would not be zero, of course, if an external vertical load were applied at C.

It is often convenient to indicate the tension T and compression C of the various members directly on the original truss diagram by drawing arrows away from the pins for tension and toward the pins for compression.

This designation is illustrated at the bottom of Fig. 4/8. Sometimes we cannot initially assign the correct direction of one or both of the unknown forces acting on a given pin. If so, we may make an arbitrary assignment. A negative computed force value indicates that the initially assumed direction is incorrect.

EQUILIBRIUM CATEGORIES BASICS AND CIVIL ENGINEERING TUTORIALS

EQUILIBRIUM CATEGORIES BASIC INFORMATION
What Are The Equilibrium Categories?


The categories of force systems acting on bodies in two-dimensional equilibrium are summarized in Fig. 3/3 and are explained further as follows.

Category 1, equilibrium of collinear forces, clearly requires only the one force equation in the direction of the forces (x-direction), since all other equations are automatically satisfied.

Category 2, equilibrium of forces which lie in a plane (x-y plane) and are concurrent at a point O, requires the two force equations only, since the moment sum about O, that is, about a z-axis through O, is necessarily zero.

Included in this category is the case of the equilibrium of a particle.

Category 3, equilibrium of parallel forces in a plane, requires the one force equation in the direction of the forces (x-direction) and one moment equation about an axis (z-axis) normal to the plane of the forces.

Category 4, equilibrium of a general system of forces in a plane (x-y), requires the two force equations in the plane and one moment equation about an axis (z-axis) normal to the plane.

FREE BODY DIAGRAM CONSTRUCTION BASICS AND TUTORIALS

TIP ON HOW TO CONSTRUCT FREE BODY DIAGRAM

Construction of Free-Body Diagrams Tutorials

The full procedure for drawing a free-body diagram which isolates a body or system consists of the following steps.

Step 1. Decide which system to isolate. The system chosen should usually involve one or more of the desired unknown quantities.

Step 2. Next isolate the chosen system by drawing a diagram which represents its complete external boundary. This boundary defines the isolation of the system from all other attracting or contacting bodies, which are considered removed. 

This step is often the most crucial of all. Make certain that you have completely isolated the system before proceeding with the next step.

Step 3. Identify all forces which act on the isolated system as applied by the removed contacting and attracting bodies, and represent them in their proper positions on the diagram of the isolated system. Make a systematic traverse of the entire boundary to identify all contact forces. 

Include body forces such as weights, where appreciable. Represent all known forces by vector arrows, each with its proper magnitude, direction, and sense indicated. Each unknown force should be represented by a vector arrow with the unknown magnitude or direction indicated by symbol. 

If the sense of the vector is also unknown, you must arbitrarily assign a sense. The subsequent calculations with the equilibrium equations will yield a positive quantity if the correct sense was assumed and a negative quantity if the incorrect sense was assumed. 

It is necessary to be consistent with the assigned characteristics of unknown forces throughout all of the calculations. If you are consistent, the solution of the equilibrium equations will reveal the correct senses.

Step 4. Show the choice of coordinate axes directly on the diagram. Pertinent dimensions may also be represented for convenience. 

Note, however, that the free-body diagram serves the purpose of focusing attention on the action of the external forces, and therefore the diagram should not be cluttered with excessive extraneous information. 

Clearly distinguish force arrows from arrows representing quantities other than forces. For this purpose a colored pencil may be used.

CENTER OF GRAVITY & MASS MOMENT OF INERTIA OF HOMOGENEOUS SOLIDS TUTORIALS

CENTER OF GRAVITY & MASS MOMENT OF INERTIA OF HOMOGENEOUS SOLIDS
Tutorials On Center of Gravity and Mass Moment of Inertia of Homogeneous Solids

This is a reference on the center of gravity and mass moment of inertia for typical homogeneous solids. These are helpful reference in solution of civil engineering problems.

CENTER OF GRAVITY & MASS MOMENT OF INERTIA OF SPHERE

CENTER OF GRAVITY & MASS MOMENT OF INERTIA OF HEMISPHERE

CENTER OF GRAVITY & MASS MOMENT OF INERTIA OF CIRCULAR DISK

CENTER OF GRAVITY & MASS MOMENT OF INERTIA OF THIN RING

CENTER OF GRAVITY & MASS MOMENT OF INERTIA OF CYLINDER

CENTER OF GRAVITY & MASS MOMENT OF INERTIA OF CONE

CENTER OF GRAVITY & MASS MOMENT OF INERTIA OF THIN PLATE

CENTER OF GRAVITY & MASS MOMENT OF INERTIA OF SLENDER ROD

STRUCTURAL COLUMN CURVES REFERENCE AND CIVIL ENGINEERING TUTORIALS

STRUCTURAL COLUMN CURVES BASIC REFERENCE
What Are Structural Column Curves?

Curves obtained by plotting the critical stress for various values of the slenderness ratio are called column curves. For axially loaded, initially straight columns, the column curve consists of two parts: (1) the Euler critical values, and (2) the Engesser, or tangent-modulus critical values.

Column curves: (a) stress-strain curve for a material that does not have a sharply defined yield pont: (b) column curve for this material; (c) stress-strain curve for a material with a sharply defined yield point; (d ) column curve for that material.

The latter are greatly affected by the shape of the stress-strain curve for the material of which the column is made, as shown in Fig. 5.44.

The stress-strain curve for a material, such as an aluminum alloy or high-strength steel, which does not have a sharply defined yield point, is shown in Fig. 5.44a.

The corresponding column curve is drawn in Fig. 5.44b.

In contrast, Fig. 5.44c presents the stress strain curve for structural steel, with a sharply defined point, and Fig. 5.44d the related column curve.

This curve becomes horizontal as the critical stress approaches the yield strength of the material and the tangent modulus becomes zero, whereas the column curve in Fig. 5.44b continues to rise with decreasing values of the slenderness ratio.

Examination of Fig. 44d also indicates that slender columns, which fall in the elastic range, where the column curve has a large slope, are very sensitive to variations in the factor k, which represents the effect of end conditions.

On the other hand, in the inelastic range, where the column curve is relatively flat, the critical stress is relatively insensitive to changes in k.

Hence the effect of end conditions on the stability of a column is of much greater significance for long columns than for short columns.

WISS AND PARMELEE RATING FACTOR FOR TRANSIENT VIBRATIONS BASICS AND TUTORIALS

WISS AND PARMELEE RATING FACTOR FOR TRANSIENT VIBRATIONS BASIC INFORMATION
What Is The Wiss And Parmelee Rating Factor?


Wiss and Parmelee also conducted research to refine the findings of Lenzen’s research. In particular, they attempted to quantify, in a more scientifically rigorous manner, human perception to transient floor motion.

They subjected 40 persons, standing on a vibrating platform, to transient vibration episodes with different combinations of frequency (2.5 to 25 Hz), peak displacements (0.0001 to 0.10 in), and damping (0.1 to 0.16, expressed as a ratio of critical).

After each episode, the subject was asked to rate the vibration on a scale of 1 to 5 with the following definitions: (1) imperceptible, (2) barely perceptible, (3) distinctly perceptible, (4) strongly perceptible, and (5) severe. Using regression analysis, an equation was perception ratings.

This equation is presented below. Wiss and Parmelee rating factor:

R= 5.08 (FA/ D^0.217)^0.265

where
R= response rating; 1= imperceptible; 2= barely perceptible; 3= distinctly perceptible; 4= strongly perceptible; 5= severe.
F= frequency of the vibration episode, Hz
A= maximum displacement amplitude, in
D= damping ratio, expressed as a ratio of critical

A graph of this subjective rating system is shown in Fig. 5.115. It should be noted that the lines represent a mean for that particular rating. The authors suggest that the boundaries for each rating lie halfway between the mean lines.

The boundaries defining R= 1 and R= 5 are not identified by the authors. These ratings are unbounded; therefore, a mean line cannot be computed.

AXIAL LOADING; NORMAL STRESS BASICS AND TUTORIALS

AXIAL LOADING; NORMAL STRESS TUTORIALS
What Is Axial Loading? What Is Stress?

The deformation caused in a body by external forces or other actions generally varies from one point to another, i.e., it is not homogeneous. In fact, a homogeneous deformation is rare. It occurs, for example, in a body with isostatic supports under a uniform temperature variation or in a slender member under constant axial force.

Rod BC of the example considered in the preceding section is a two-force member and, therefore, the forces FBC and F'BC acting on its ends B and C (Fig. 1.5) are directed along the axis of the rod. We say that the rod is under axial loading.

An actual example of structural members under axial loading is provided by the members of the bridge truss shown in Photo 1.1.

Returning to rod BC of Fig. 1.5, we recall that the section we passed through the rod to determine the internal force in the rod and the corresponding stress was perpendicular to the axis of the rod; the internal force was therefore normal to the plane of the section (Fig. 1.7) and the corresponding stress is described as a normal stress.

Thus, formula (1.5) gives us the normal stress in a member under axial loading:

σ =P/A 

We should also note that, in formula (1.5), s is obtained by dividing the magnitude P of the resultant of the internal forces distributed over the cross section by the area A of the cross section; it represents, therefore, the average value of the stress over the cross section, rather than the stress at a specific point of the cross section.

To define the stress at a given point Q of the cross section, we should consider a small area DA. Dividing the magnitude of DF by DA, we obtain the average value of the stress over DA. Letting DA approach zero, we obtain the stress at point Q:

σ = lim dF/dA      as dA approaches infinity (1.6)

In general, the value obtained for the stress s at a given point Q of the section is different from the value of the average stress given by formula (1.5), and s is found to vary across the section. In a slender rod subjected to equal and opposite concentrated loads P and P' , this variation is small in a section away from the points of application of the concentrated loads, but it is quite noticeable in the neighborhood of these 

It follows from Eq. (1.6) that the magnitude of the resultant of the distributed internal forces is

∫dF = ∫σ dA     lower limit = A

But the conditions of equilibrium of each of the portions of rod require that this magnitude be equal to the magnitude P of the concentrated loads. We have, therefore,

P = ∫dF = ∫σ dA    lower limit = A

which means that the volume under each of the stress surfaces must be equal to the magnitude P of the loads. This, however, is the only information that we can derive from our knowledge of statics, regarding the distribution of normal stresses in the various sections of the rod. 

The actual distribution of stresses in any given section is statically indeterminate. To learn more about this distribution, it is necessary to consider the deformations resulting from the particular mode of application of the loads at the ends of the rod.

In practice, it will be assumed that the distribution of normal stresses in an axially loaded member is uniform, except in the immediate vicinity of the points of application of the loads. The value s of the stress is then equal to save and can be obtained from formula (1.5). 

However, we should realize that, when we assume a uniform distribution of stresses in the section, i.e., when we assume that the internal forces are uniformly distributed across the section, it follows from elementary statics† that the resultant P of the internal forces must be applied at the centroid C of the section. 

This means that a uniform distribution of stress is possible only if the line of action of the concentrated loads P and P' passes through the centroid of the section considered. This type of loading is called centric loading and will be assumed to take place in all straight two-force members found in trusses and pin-connected structures, such as the one considered in Fig. 1.1. 

However, if a two-force member is loaded axially, but eccentrically we find from the conditions of equilibrium of the portion of member that the internal forces in a given section must be equivalent to a force P applied at the centroid of the section and a couple M of moment M = Pd. The distribution of forces—and, thus, the corresponding distribution of stresses—cannot be uniform. Nor can the distribution of stresses be symmetric.

HOOKE’S LAW; MODULUS OF ELASTICITY BASICS AND TUTORIALS

HOOKE’S LAW; MODULUS OF ELASTICITY BASIC INFORMATION
What Is Hooke's Law? How To Apply Hooke's Law?


Most engineering structures are designed to undergo relatively small deformations, involving only the straight-line portion of the corresponding stress-strain diagram. For that initial portion of the diagram, the stress s is directly proportional to the strain P, and we can write

σ = ΞE

This relation is known as Hooke’s law, after Robert Hooke (1635–1703), an English scientist and one of the early founders of applied mechanics. The coefficient E is called the modulus of elasticity of the material involved, or also Young’s modulus, after the English scientist Thomas Young (1773–1829). 

Since the strain P is a dimensionless quantity, the modulus E is expressed in the same units as the stress s, namely in pascals or one of its multiples if SI units are used, and in psi or ksi if U.S. customary units are used.

The largest value of the stress for which Hooke’s law can be used for a given material is known as the proportional limit of that material. In the case of ductile materials possessing a well-defined yield poin, the proportional limit almost coincides with the yield point. 

For other materials, the proportional limit cannot be defined as easily, since it is difficult to determine with accuracy the value of the 63 stress s for which the relation between s and P ceases to be linear. But from this very difficulty we can conclude for such materials that using Hooke’s law for values of the stress slightly larger than the actual proportional limit will not result in any significant error.

Some of the physical properties of structural metals, such as strength, ductility, and corrosion resistance, can be greatly affected by alloying, heat treatment, and the manufacturing process used. For example, we note from the stress-strain diagrams of pure iron and of three different grades of steel (Fig. 2.11) that large variations in the yield strength, ultimate strength, and final strain (ductility) exist among these four metals. 

All of them, however, possess the same modulus of elasticity; in other words, their “stiffness,” or ability to resist a deformation within the linear range, is the same. Therefore, if a high-strength steel is substituted for a lower-strength steel in a given structure, and if all dimensions are kept the same, the structure will have an increased load-carrying capacity, but its stiffness will remain unchanged.

For each of the materials considered so far, the relation between normal stress and normal strain, s 5 EP, is independent of the direction of loading. This is because the mechanical properties of each material, including its modulus of elasticity E, are independent of the direction considered. Such materials are said to be isotropic.

Materials whose properties depend upon the direction considered are said to be anisotropic. An important class of anisotropic materials consists of fiberreinforced composite materials. These composite materials are obtained by embedding fibers of a strong, stiff material into a weaker, softer material, referred to as a matrix. 

Typical materials used as fibers are graphite, glass, and polymers, while various types of resins are used as a matrix. Figure 2.12 shows a layer, or lamina, of a composite material consisting of a large number of parallel fibers embedded in a matrix.

An axial load applied to the lamina along the x axis, that is, in a direction parallel to the fibers, will create a normal stress sx in the lamina and a corresponding normal strain Px which will satisfy Hooke’s law as the load is increased and as long as the elastic limit of the lamina is not exceeded. 

Similarly, an axial load applied along the y axis, that is, in a direction perpendicular to the lamina, will create a normal stress sy and a normal strain Py satisfying Hooke’s law, and an axial load applied along the z axis will create a normal stress sz and a normal strain Pz which again satisfy Hooke’s law. 

However, the moduli of elasticity Ex, Ey, and Ez corresponding, respectively, to each of the above loadings will be different. Because the fibers are parallel to the x axis, the lamina will offer a much stronger resistance to a loading directed along the x axis than to a loading directed along the y or z axis, and Ex will be much 

larger than either Ey or Ez.

A flat laminate is obtained by superposing a number of layers or laminas. If the laminate is to be subjected only to an axial load causing tension, the fibers in all layers should have the same orientation as the load in order to obtain the greatest possible strength. But if the laminate may be in compression, the matrix material may not be sufficiently strong to prevent the fibers from kinking or buckling. 

The lateral stability of the laminate may then be increased by positioning some of the layers so that their fibers will be perpendicular to the load. Positioning some layers so that their fibers are oriented at 308,

45 deg, or 60 deg to the load may also be used to increase the resistance of the laminate to in-plane shear. 

STRESS - STRAIN CURVE FOR BRITTLE MATERIALS BASICS AND TUTORIALS

STRESS - STRAIN CURVE FOR BRITTLE MATERIALS BASIC INFORMATION
What Is The Stress-Strain Curve Of Brittle Materials?


Many of the characteristics of a material can be deduced from the tensile test. It is more convenient to compare materials in terms of stresses and strains, rather than loads and extensions of a particular specimen of a material.

The stress at any stage is the ratio of the load of the original cross-sectional area of the test specimen; the strain is the elongation of a unit length of the test specimen.

For stresses up to about 750 MN/m2 the stress-strain curve is linear, showing that the material obeys Hooke’s law in this range; the material is also elastic in this range, and no permanent extensions remain after removal of the stresses.

The ratio of stress to strain for this linear region is usually about 200 GN/m2 for steels; this ratio is known as Young’s modulus and is denoted by E. The strain at the limit of proportionality is of the order 0.003, and is small compared with strains of the order 0.100 at fracture.

FIG 1.5

We note that Young’s modulus has the units of a stress; the value of E defines the constant in the linear relation between stress and strain in the elastic range of the material. We have

for the linear-elastic range. If P is the total tensile load in a bar, A its cross-sectional area, and Lo its length, then

where e is the extension of the length Lo. Thus the expansion is given by

If the material is stressed beyond the linear-elastic range the limit of proportionality is exceeded, and the strains increase non-linearly with the stresses. Moreover, removal of the stress leaves the material with some permanent extension; h range is then bothnon-linear and inelastic.

The maximum stress attained may be of the order of 1500 MNlm’, and the total extension, or elongation, at this stage may be of the order of 10%. The curve of Figure 1.5 is typical of the behaviour of brittle materials as, for example, area characterized by small permanent elongation at the breaking point; in the case of metals this is usually lo%, or less.

When a material is stressed beyond the limit of proportionality and is then unloaded, permanent deformations of the material take place. Suppose the tensile test-specimen of Figure 1.5 is stressed beyond the limit of proportionality, to a point b on the stress-strain diagram. If the stress is now removed, the stress-strain relation follows the curve bc; when the stress is completely removed there is a residual strain given by the intercept Oc on the &-axis.

If the stress is applied again, the stress-strain relation follows the curve cd initially, and finally the curve df to the breaking point. Both the unloading curve bc and the reloading curve cd are approximately parallel to the elastic line Oa; they are curved slightly in opposite directions.

The process of unloading and reloading, bcd, had little or no effect on the stress at the breaking point, the stress-strain curve being interrupted by only a small amount bd, Figure 1.6. The stress-strain curves of brittle materials for tension and compression are usually similar in form, although the stresses at the limit of proportionality and at fracture may be very different for the two loading conditions.

Typical tensile and compressive stress-strain curves for concrete are shown in Figure 1.7; the maximum stress attainable in tension is only about one-tenth of that in compression, although the slopes of the stress strain curves in the region of zero stress are nearly equal.

LAME'S ELLIPSOID BASICS AND TUTORIALS

LAME'S ELLIPSOID BASIC INFORMATION
What Is Lam´e’s Ellipsoid?

There are always three orthogonal principal directions in a stress state. It is therefore always possible to choose a rectangular Cartesian reference system which coincides with the three principal directions. In this case, the shearing components of the stress tensor vanish and it takes the form

In an inclined facet, with a semi-normal defined by the direction cosines l,m, n, the relation between the components of the stress vector and the principal stresses may be deduced from expression 9, yielding

Since the direction cosines must obey the condition l2+m2+n2 = 1, expression gives

If we consider a Cartesian reference system T1, T2, T3, this expression represents the equation of an ellipsoid, whose principal axes are the reference system and where the points on the ellipsoid are the tips P of the stress vectors
−→
OP (T1, T2, T3) acting in facets containing the point with the stress state defined by expression 24 (point O, Fig. 9)

This ellipsoid is a complete representation of the magnitudes of the stress vectors in facets around point O. It allows an important conclusion about the stress state: the magnitude of the stress in any facet takes a value between the maximum principal stress σ1 and the minimum principal stress σ3.

It must be mentioned here that this conclusion is only valid for the absolute value of the stress, since in expression 26 only the squares of the stresses are considered.

From Fig. 9 we conclude immediately that if the absolute values of two principal stresses are equal the ellipsoid takes a shape of revolution around the third principal direction and if the three principal stresses have the same absolute value the ellipsoid becomes a sphere.

In the first case, the stress→T acting in facets, which are parallel to the third principal direction have the same absolute value. Besides, if these two principal stresses have the same sign, we have an axisymmetric stress state.