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.

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.

REPEATED MECHANICAL LOADINGS: FATIGUE BASIC AND TUTORIALS

REPEATED MECHANICAL LOADINGS: FATIGUE BASIC INFORMATION
Effects Of Repeated Loadings

In the preceding sections we have considered the behavior of a test specimen subjected to an axial loading. We recall that, if the maximum stress in the specimen does not exceed the elastic limit of the material, the specimen returns to its initial condition when the load is removed.

You might conclude that a given loading may be repeated many times, provided that the stresses remain in the elastic range. Such a conclusion is correct for loadings repeated a few dozen or even a few hundred times.

However, as you will see, it is not correct when loadings are repeated thousands or millions of times. In such cases, rupture will occur at a stress much lower than the static breaking strength; this phenomenon is known as fatigue. A fatigue failure is of a brittle nature, even for materials that are normally ductile.

Fatigue must be considered in the design of all structural and machine components that are subjected to repeated or to fluctuating loads. The number of loading cycles that may be expected during the useful life of a component varies greatly.

For example, a beam supporting an industrial crane may be loaded as many as two million times in 25 years (about 300 loadings per working day), an automobile crankshaft will be loaded about half a billion times if the automobile is driven 200,000 miles, and an individual turbine blade may be loaded several hundred billion times during its lifetime.

Some loadings are of a fluctuating nature. For example, the passage of traffic over a bridge will cause stress levels that will fluctuate about the stress level due to the weight of the bridge. A more severe condition occurs when a complete reversal of the load occurs during the loading cycle.

The stresses in the axle of a railroad car, for example, are completely reversed after each half-revolution of the wheel. The number of loading cycles required to cause the failure of a specimen through repeated successive loadings and reverse loadings may be determined experimentally for any given maximum stress level.

If a series of tests is conducted, using different maximum stress levels, the resulting data may be plotted as a s-n curve. For each test, the maximum stress s is plotted as an ordinate and the number of cycles n as an abscissa; because of the large number of cycles required for rupture, the cycles n are plotted on a logarithmic scale.

A typical s-n curve for steel is shown in Fig. 2.16. We note that, if the applied maximum stress is high, relatively few cycles are required to cause rupture. As the magnitude of the maximum stress is reduced, the number of cycles required to cause rupture increases, until a stress, known as the endurance limit, is reached.

The endurance limit is the stress for which failure does not occur, even for an indefinitely large number of loading cycles. For a low-carbon steel, such as structural steel, the endurance limdecrease as the number of loading cycles is increased. For such metals, one defines the fatigue limit as the stress corresponding to failure after a specified number of loading cycles, such as 500 million.

Examination of test specimens, of shafts, of springs, and of other components that have failed in fatigue shows that the failure was initiated at a microscopic crack or at some similar imperfection. At each loading, the crack was very slightly enlarged.

During successive loading cycles, the crack propagated through the material until the amount of undamaged material was insufficient to carry the maximum load, and an abrupt, brittle failure occurred.

Because fatigue failure may be initiated at any crack or imperfection, the surface condition of a specimen has an important effect on the value of the endurance limit obtained in testing. The endurance limit for machined and polished specimens is higher than for rolled or forged components, or for components that are corroded.

In applications in or near seawater, or in other applications where corrosion is expected, a reduction of up to 50% in the endurance limit can be expected.is about one-half of the ultimate strength of the steel. For nonferrous metals, such as aluminum and copper, a typical s-n curve (Fig. 2.16) shows that the stress at failure continues to decrease as the number of loading cycles is increased. For such metals, one defines the fatigue limit as the stress corresponding to failure after a specified number of loading cycles, such as 500 million.

SCHAUMS OUTLINE OF ENGINEERING MECHANICS DYNAMICS FREE EBOOK DOWNLOAD LINK

SCHAUMS OUTLINE OF ENGINEERING MECHANICS DYNAMICS FREE EBOOK
Free E-Book Download Link Of The Book Schaums Outline Of Engineering Mechanics Dynamics

Modified to conform to the current curriculum, Schaum's Outline of Engineering Mechanics: Dynamics complements these courses in scope and sequence to help you understand its basic concepts.

The book offers extra practice on topics such as rectilinear motion, curvilinear motion, rectangular components, tangential and normal components, and radial and transverse components. You’ll also get coverage on acceleration, D'Alembert's Principle, plane of a rigid body, and rotation.

Appropriate for the following courses: Engineering Mechanics; Introduction to Mechanics; Dynamics; Fundamentals of Engineering.

Features:

765 solved problems
Additional material on instantaneous axis of rotation and Coriolis' Acceleration
Support for all the major textbooks for dynamics courses
Topics include: Kinematics of a Particle, Kinetics of a Particle, Kinematics of a Rigid Body, Kinetics of a Rigid Body, Work and Energy, Impulse and Momentum, Mechanical Vibrations


About the Author
E. W. Nelson taught Mechanical Engineering at Lafayette College and later joined the engineering organization of the Western Electric Company (now Lucent Technologies).

Charles L. Best is Emeritus Professor of Engineering at Lafayette College. W. G. McLean (Easton, PA) is Emeritus Director of Engineering at Lafayette College.

Merle Potter is professor emeritus of Mechanical Engineering at Michigan State University.

DOWNLOAD LINK!!!

MOHR'S CIRCLE BASICS AND TUTORIALS LINKS

MOHR'S CIRCLE BASIC DEFINITION AND INFORMATION LINKS
What Is Mohr's Circle? The Purpose Of Mohr's Circle


The shear strength of soil is generally characterized by the Mohr–Coulomb failure criterion. This criterion states that there is a linear relationship between the shear strength on the failure plane at failure (τff) and the normal stress on the failure plane at failure (σff) as given in the following equation:
                            τff = σff tanφ + c
where φ is the friction angle and c is the intrinsic cohesion. The strength parameters (φ, c) are used directly in many stability calculations, including bearing capacity of shallow footings, slope stability, and stability of retaining walls. The line defined by Eq. (17.1) is called the failure envelope.


A Mohr’s circle tangent to a point on the failure envelope (σff, τff) intersects the x-axis at the major and minor principal stresses at failure (σ1f, σ3f). For many soils, the failure envelope is actually slightly concave down rather than a straight line.

For a comprehensive review of Mohr’s circles and the Mohr–Coulomb failure criterion, see Lambe and Whitman [1969] and Holtz and Kovacs [1981]. But more online resource, below are links to articles that best explain and gives example on the application of Mohr's Circle:

Mohr's Circle Calculator
Given the stress components sx, sy, and txy, this calculator computes the principal stresses s1, s2, the principal angle qp, the maximum shear stress tmax and its angle qs. It also draws an approximate Mohr's cirlce for the given stress state. Continue reading...

Mohr's Circle for 2-D and 3-D Stress Analysis
After the data for the Mohr's circle are input, press the button "Draw", then the Mohr's circle can be created; press the button "fill", the Mohr's circle are created and filled with red color. If the Mohr's circles are too small, press the button "size 1" or "size 2" to enlarge them. Whenever the data for the Mohr's circle are modified, press "Draw" or "fill" button to get modified Mohr's circle. Besides, the paramters for the Mohr's circle and calculated principal stresses and maximum shear stress are given too. Continue reading...

Mohr's Circle Information
Mohr's circle, named after Christian Otto Mohr, is a two-dimensional graphical representation of the state of stress at a point. The abscissa, , and ordinate, , of each point on the circle are the normal stress and shear stress components, respectively, acting on a particular cut plane with a unit vector  with components. Continue reading...