Often practicing engineers must ask what they need to know in order to tackle the task they have been assigned. So too we will ask you to step back from a prob-lem and pose a new problem that will help you address the original problem. We will label these exercises need to know. A good bit of engineering work is variation on a theme, changing things around, recasting a story line, and putting it into your own language for produc-tive and profitable use.
Doing this requires experimentation, not just with hard-ware, but with concepts and existing designs. Engineering analysis as well as prototype testing and market studies is what justifies engineering designs. As an engineer you will be asked to show that your 3.
Introduction 3 design will actually work. More specifically, in the terms of this subject, you will be asked to show the requirements of static equilibrium ensure your proposed structure will bear the anticipated loading, that the maximum deflection of simply supported beam at midspan does not exceed the value specified in the contract, that the lowest resonant frequency of the payload is above Hz.
The show that. Most often this kind of problem will admit of a single solution — in contrast to the estimate, need to know, or even what if exercise. This is the form of the traditional textbook prob-lem set. Here, too, construct better reflects what engineers actually do at work.
Finally, what engineers do most of the time is design, design in the broadest sense of the term;the y play out scenarios of things working, construct stories and plans that inform others how to make things that will work according to their plans. These design exercises are the most open-ended and unconstrained exer-cises you will find in this text. We will have more to say about them later. In working all of these different kinds of exercises, we want you to use the lan-guage with others.
Your abil-ity to speak and think in the language of engineering mechanics is best developed through dialogue with your peers, your tutors, and your teacher. Exercise 1. It is meant as an overview;do not be disturbed by the variety of concepts or range of vocabulary. We will try to grasp the essen-tial workings of the device and begin to see the relevance of the concepts and principles of engineering mechanics to an understanding of how it functions and how it might be made to work better We will apply the requirements of static equilibrium.
We will analyze the dis-placements of different points of the structure, e. We will consider the deformation of the springs which connect points A and C to ground and posit a relationship between the force each one bears and the relative displacement of one end with respect to the other end. We will learn to read the figure; k is the constant of proportionality in the equation relating the force in the spring to its deformation;the little circles are frictionless pins, members AB and BC are two-force members — as straight mem-bers they carry only tension and compression.
The grey shading represents rigid ground. Our aim is to determine the behavior of the structure as the applied load increases from zero to some or any finite value. We will allow for relatively large displacements and rotations. We will investigate the possibility of snap-through, a type of instability, if P gets too large. We will discuss how this funny looking linkage of impossible parts friction-less pins, rollers, rigid grey matter, point loads, ever linear springs can be a use-ful model of real-world structures.
There is much to be said;all of this italicized language important. We assume our system is symmetric; the figure suggests this;if A moves out a dis-tance u, C displaces to the right the same distance. This engenders a compressive force in the springs and in the members AB and BC, albeit of a different magnitude, which in turn, ensures static equilibrium of the system and every point within it including the node B where the load P is applied.
But enough talk;enough story telling. We formulate some equations and try to solve them.
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Introduction 5 Static Equilibrium of Node B. The figure at the right shows an isola-tion of node B. It is a free body diagram; i. We defer a proof that the force must act along the member to a later date. F F Equilibrium requires that the resultant force on the node vanish;symmetry , with respect to a vertical plane containing P and perpendicular to the page, assures this requirement is satisfied in the horizontal direction;equilibrium in the vertical direction gives: Static Equilibrium of Node C.
The figure at the right shows an isolation of node C.
Engineering Mechanics for Structures
Note how I have drawn F in this isola-tion acting opposite to the direction of F shown in the isolation of node B. This is because member BC is in compression. The member is compressing node C as it is compressing node B. R is the reaction force on the node due to the ground. It is vertical since the rollers signify that there is no resistance to motion in the hori-zontal direction;there is no friction.
Equilibrium requires that the resultant of the three forces vanish. Requiring that the sum of the horizontal components and that the sum of the vertical compo-nents vanish independently will ensure that the vector sum, which is the resultant, will vanish. This yields two scalar equations: The first ensures equilibrium in the horizontal direction, the second, in the vertical direc-tion.
Theta serves as an intermediary - a parameter whose value we can choose - guided by our sketch of the geometry of our struc-ture. For each value of theta, the above two equations then fix the value of the vertical dis-placement and the applied load. This is left as an exercise for the reader. They neither lengthen nor contract when loaded.
Introduction 7 1. A textbook is only one resource available to you in learning a new language.
The exercises are another, pehaps the most important other resource you have avail-able. Still others are the interactive short simulations — computer representations of specific problems or phenomena — made available to you over the web. You will find there as well more sophisticated and generally applicable tools which will enable you to model truss and frame structures - structures which have many members. Another more standard and commonly available tool is the spreadsheet. You will find all these modeling tools to be essential and powerful aids when con-fronted with an open-ended design exercise where the emphasis is on what if and show that.
Another resource to you is your peers. We expect you to learn from your class-mates, to collaborate with them in figuring out how to set up a problem, how to use a spreadsheet, where on the web to find a useful reference. Often you will be asked to work in groups of two or three, in class - especially when a design exer-cise is on the table - to help formulate a specification and flesh out the context of the exercise.
Yet your work is to be your own.
Civil Engineering and Engineering Mechanics
The correct response is zero: For a particle at rest, or moving with constant velocity relative to an inertial frame, the resultant force acting on the isolated particle must be zero, must vanish. We usually attribute this to the unquestion-able authority of Newton. The essential phrases in the question are constant velocity, resultant force and particle. The latter concepts are abstractions which you must learn to identify in the world around you in order to work effectively as an engineer, e.
The problems that appear in engineering text books are a kind of middle ground between abstract theory and everyday reality. We want you to learn to read and see through the superficial appearances, these descriptions which mask certain scientific concepts and principles, in order to grasp and appropriate the underlying forms that provide the basis for engineering analysis and design. Here is how it would look. An Isolated Particle: You, in an elevator. You are to take the dot drawn as the representation of a thing, all things, that can be thought of as an isolated particle.
Now show all the forces acting on the particle. Who said the elevator was oriented vertically? Who said it was on the surface of the earth? This information is not given; indeed, you could press the point, arguing that the ques-tion is not well posed. But is this information essential?
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We return to this point at the end of this chapter. We have the reaction force of the elevator floor acting vertically upward on you, on you as an abstraction, as an isolated particle. This is how our particle looks with all forces acting upon it.
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The resultant force is the vector sum of all the forces acting on the isolated particle. For static equilibrium of the isolated particle, the resultant of the two forces — W acting downward and R acting upward — must be zero. You will find it takes courage, as well as facility with the language of engineering mechanics, to venture forth and construct reaction forces out of thin air.
They are there, hidden at the interface of your particle with the rest of the world.
Some, like gravity, act at a distance, across all boundaries you may draw. Exercise 2. We can use the same isolation, or free-body diagram, of the figures above where now the point represents the Boeing , rather than you in an elevator, and the reaction force represents the lift force acting on the airplane, rather than the force acting on you at your interface with the elevator floor. From the requirement of static equilibrium, we implicitly acknowledge that the is moving with con-stant velocity , we conclude that lift force is equal to the weight, so to estimate the lift force we estimate the weight.