Statics of Rigid Bodies Study Set, Summaries of Civil Engineering

Download Statics of Rigid Bodies Study Set and more Summaries Civil Engineering in PDF only on Docsity!

ENS 231

STATICS OF

RIGID BODIES

Prepared by: Engr. John Ronald R. Fortuito Instructor/Reg. Civil Engineer

Grading System

Chapter Exams - 40%

Midterm Exam - 30%

Final Exam - 30%

Total 100%

Passing: 75%

Passing score

per exam : 50/

Total Equivalent Remarks 1% – 49% FAILED 5. 50% 75% 3. 51% - 52% 76% 2. 53% - 54% 77% 2. 55% - 56% 78% 2. 57% - 58% 79% 2. 59% - 60% 80% 2. 61% - 62% 81% 2. 63% - 64% 82% 2. 65% - 66% 83% 2. 67% - 69% 84% 2. Total Equivalent Remarks 70% – 72% 85% 2. 73% – 75% 86% 1. 76% - 77% 87% 1. 78% - 79% 88% 1. 80% - 82% 89% 1. 83% - 85% 90% 1. 86% - 88% 91% 1. 89% - 90% 92% 1. 91% - 92% 93% 1. 93% - 94% 94% 1. 95% - 100% 95% - 100% 1.

Course Outcomes

At the end of the course, the students must be able to:

1. Understand the concepts of forces and moments of forces
2. Apply the principles of static equilibrium from the knowledge of resultants of forces and moments
3. Relate the course to other engineering situations that involves the concepts of forces and moments of forces.

Course Outline

1. Fundamental Concepts

1.1 Force and their characteristics

1.2 External and internal effects of forces

1.3 Force systems; concurrent, non-concurrent, parallel, non-parallel,

coplanar and spatial force systems

1.4 Components of a force; resolution of forces into planar and spatial

components

1.5 Moment of a force

1.6 Vector analysis; addition, subtraction and multiplication of vectors

2. Resultants of force systems

2.1 Resultant of coplanar force systems

2.2 The couple and its characteristics

2.3 Resultant of spatial force systems

3. Equilibrium

3.1 Free-body diagrams

3.2 Equations of equilibrium for a coplanar concurrent force system

3.3 Equilibrium of bodies acted upon by two or three forces

Course Outline

5.3 Application of friction in machine elements – wedges, square-

threaded screws, belt-friction

5.4 Equilibrium of forces involving friction

6. Centroids and Center of Gravity

6.1 Center of gravity of a two-dimensional body; flat plate

6.2 Determination of centroids by integration

6.3 Centroids of composite bodies - approximation

7. Moment of Inertia; Product of Inertia

7.1 Moment of inertia

7.2 Area moment of inertia by integration

7.3 Transfer formula for moment of inertia

7.4 Polar moment of inertia

7.5 Radius of gyration

7.6 Moment of inertia for composite sections

7.7 Product of inertia

7.8 Transfer formula for product of inertia

Reference Book

Singer, Ferdinand L., Engineering Mechanics, Statics and Dynamics, Harper and Row, latest edition

1-1. Introduction Engineering Mechanics may be defined as the science which considers the effects of forces on rigid bodies. The subject divides naturally into two parts: statics and dynamics. In statics we consider the effects and distribution of forces on rigid bodies which are and remain at rest. Engineering Mechanics Statics Dynamics Force Systems Applications Kinematics Kinetics Concurrent Trusses Translation Translation Parallel Centroids Rotation Rotation Non-Concurrent Friction Plane Motion Plane Motion

1-2. Fundamental Concepts and Definitions Rigid Body. A rigid body is defined as a definite amount of matter the parts of which are fixed in position relative to each other. Force. Force may be defined as that which changes, or tends to change, the state of motion of a body. This definition applies to the external effect of a force. The internal effect of a force is to produce stress and deformation in the body on which the force acts. External effects of forces are considered in engineering mechanics; internal effects, in strength of materials. The characteristics of a force are (1) its magnitude, (2) the position of its line of action, and (3) the direction (or sense) in which the force acts along its line of action. The principle of transmissibility of a force states that the external effect of a force on a body is the same for all points of application along its line of action; i.e., it is independent of the point of application. The internal effect of a force, however, is definitely dependent on its point of application.

Classification of a Force Systems

1-4. Axioms of Mechanics The principles of mechanics are postulated upon several more or less self-evident facts which cannot be proved mathematically but can only be demonstrated to be true. We shall call these facts the fundamental axioms of mechanics.

1. The Parallelogram Law: The resultant of two forces is the diagonal of the parallelogram formed on the vectors of these forces.
2. Two forces are in equilibrium only when equal in magnitude, opposite in direction, and collinear in action.
3. A set of forces in equilibrium may be added to any system of forces without changing the effect of the original system.
4. Action and reaction forces are equal but oppositely directed.

1-6. Scalar and Vector Quantities Scalars. Quantities which possess magnitude only and can be added arithmetically are defined as scalar quantities. Vectors. At point C of the FBD suppose the weight W and the Tension T were each of 100 lb. What is the force P in the boom? By arithmetical addition the answer is 200 lb. This result, however, is incorrect, as can be determined by means of a measuring device placed in the boom. Actually the force in the boom would vary as the boom was lifted. The error is due to the fact that arithmetical addition was applied to quantities which possess direction as well as magnitude. Such quantities can be combined only by geometric addition, usually called vector addition. A vector of a quantity can be represented geometrically (i.e., graphically) by drawing a line acting in the direction of the quantity, the length of the line representing to some scale the magnitude of the quantity. An arrow is placed on the line, usually at the end, to denote the sense of the direction. C P T = 100 lb W = 100 lb

1-7. Parallelogram Law

The method of vector addition is based on

what is known as the parallelogram law. The

parallelogram law cannot be proved; it can

only be demonstrated by experiment. It is

one of the fundamental axioms of mechanics.

One method of demonstrating the law is by

means of the apparatus shown in the Figure.

Tie three cords together and fasten the weights P, Q, and W to the free ends. (The

sum of P and Q must be greater than W.) Place the cords to which P and Q are

attached over the smooth pegs as shown and allow the system to reach a position of

equilibrium. The tensions in these cords will then be equal to the weights P and Q.

Draw vectors P and Q to scale from point A where the cords are tied together and

construct a parallelogram with these vectors as the initial sides. It will be found that

the diagonal R of the parallelogram scales exactly to the value of W and is in line with

the vector representing W.

Q (^) P W R Q P A W

1-8. Triangle Law If we examine closely the parallelogram formed by forces P and Q, we observe that side BC is parallel and equal to side AD. If the triangle ABC were drawn alone in the 3rd^ figure, the resultant R joining A to C would have the same magnitude and direction as the diagonal of the parallelogram ABCD. In this instance, force Q has been represented by the free vector BC. A free vector is defined as one which does not show the point of application of the vector, as distinguished from a localized vector which does. It is also evident that, as DC is equal and parallel to P, the triangle ADC may also be used to determine R. In this case, P is taken as the free vector whereas Q is the localized vector. We may now state the triangle law as a convenient corollary of the parallelogram law: If two forces are represented by their free vectors placed tip to tail, their resultant vector is the third side of the triangle, the direction of the resultant being from the tail of the first vector to the tip of the last vector. Special Case. If the angle between two forces becomes zero or 180°, the forces act along the same line; i.e., the forces are collinear. By taking one direction as positive and the other direction as negative, it will be apparent that the resultant of two collinear forces is their algebraic sum. C P R D Q A C P R D Q A B C P R Q A B

Chapter 2 Resultants of Force Systems