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Review of Important Concepts

Lessandro Estelito O. GARCIANO

Associate Professor

Department of Civil Engineering

De La Salle University


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Class Policies

o Download the problem sets from my webpage

www.garcianopage.com/gigi. Important announcements will also be

posted in the website

o Problem Sets

should be written on an clean A4 size bond paper

must be handed in at the beginning of the class on the due date.

LATE problem sets will not be accepted !!!

o Seatwork - write it on yellow paper and hand it in before class time

ends. Late seatwork will not be accepted.

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http://www.garcianopage.com/gigihttp://www.garcianopage.com/gigihttp://www.garcianopage.com/gigihttp://www.garcianopage.com/gigihttp://www.garcianopage.com/gigihttp://www.garcianopage.com/gigi


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Class Policies

o Attendance in lectures is required. Student who is absent

for more than 5 meetings (7.5 hours) will receive a FDA.

o Missed quiz / final exam will be given a grade of 0 for thatquiz or exam.

o

Cheating will be penalized with a grade of zero in the LQ orFE.

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Assessment

The general average of each students grade will be

computed as follows:

Problem sets and seatwork - 10%

Average of the three (3) long quizzes - 60%

Final exam - 30%

100%

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Resources

o Textbook

Strength of Materials, 4thEdition, Singer and Pytel

o References

Mechanics of Materials, 8thedition, 2012, R. C. Hibbeler

Mechanics of Materials, 4thedition, 2012, Beer, Johnston

and DeWolf

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Observed failure modes

during the 2013 Bohol Earthquake

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What is Mechanics?

o Mechanics is the science which describes and

predicts the conditions of rest or motion of bodies

under the action of forces

o It is divided into three parts: Mechanics of Rigid

Bodies, Mechanics of Deformable Bodies, and

Mechanics of Fluids.

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Introductory Concepts

Engineering

Mechanics

Mechanics

of Fluids

Mechanics

of Solids

Rigid Bodies

Deformable Bodies

Ideal fluids

viscous fluids

compressible fluids

Strength of materials

Theory of elasticity

Theory of plasticity

statics

dynamics

kinematics

kinetics

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Definition

Mechanics of Deformable Bodies

o is a branch of mechanics that studies the

relationships between the external loads applied to

a deformable body and the intensity of internalforces acting within the body

o Involves computing the deformations of the body

and provides a study of the bodys stability when

the body is subjected to external forces

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External Loads

o Surface forces caused by the direct

contact of one body with the surface of

another

Concentrated force a force applied to

a point on the body

Surface loads a surface load applied

along a narrow area

o Body force is developed when one body

exerts a force on another body without

direct physical contact between the

bodies.

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Support Connection

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Support Connection

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Support Connection

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Support Reactions

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Support Reactions

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Definition and Meaning of Equilibrium

o Equilibrium is the term used to designate the conditionwhere the resultant of a force system is zero.

o

The physical meaning of equilibrium, as applied to a body,is that the body is either at rest or is moving along a

straight line path with constant velocity.

o Both these statements are implied in Newtonsfirst law of

motion; namely, a particle acted upon by a balanced force

system has no acceleration.16 /40


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Free-Body Diagrams

o Problems in mechanics always involve the interaction of bodies upon oneanother.

o Successful solution of these problems generally requires that the bodies

be isolated from one another so that the forces involved may be analyzed

and unknown forces determined.

o An isolated view of a body which shows only the external forces exerted

on the body is called a free-body diagram (or FBD).

o The external forces are caused either by direct bodily contact or by

gravitational or magnetic attraction.17 /40


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Mechanical action of Forces

in two-dimensional analysis

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Steps involved in drawing a FBD

1. Draw a diagram of the body completely isolated fromall bodies. The free body may consist of an entire

assembled structure or any combination or part of it.

2. Represent the action of each body or support that

has been removed by a force (or its components) as

given in the previous table

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Steps involved in drawing a FBD

3. Label each force by its magnitude if known, or by asymbol is unknown. If the sense of an unknown force

along its line of action should be incorrectly assumed,

the solution will give a negative sign, but its

magnitude will nevertheless be correct.

4. The FBD should be legibly and neatly drawn, and of

sufficient size that all pertinent data can be clearlydepicted.

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Sample FBDs

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Sample FBDs

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Sample Problem

In each of the following examples, the body to be isolated is shown inthe left-hand diagram, and an incomplete FBD of the isolated body is

shown on the right. Add whatever forces are necessary in each case

to form a complete FBD. The weights of the bodies are negligible

unless otherwise indicated. Dimensions and numerical values are

omitted for simplicity.

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Sample Problem

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Equations of Equilibrium

o Equilibrium is defined as the condition when the resultant of aforce system is equal to zero.

o The FBD should be legibly and neatly drawn, and of sufficient

size that all pertinent data can be clearly depicted.

o Recall that the most general force system may be reduced to a

concurrent force system at any arbitrary point plus a couple

which equals the moment sum of the original system about that

point.

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Equations of Equilibrium

o When the force-couple system is equal to zero, thebasic vector equations of equilibrium therefore are

and

which are equivalent to the following six scalar

equations:

and

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Categories of Equilibrium

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Categories of Equilibrium

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Internal Effects of Forces

(three dimension loadings)

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(Coplanar Loadings)

Internal forces and moments are classifiedaccording to their physical effects caused on the

member. These physical effects are

Axial force Ptends to pull (stretch, elongate) or

push (compress, shorten) the member in the x -

direction

Shear force Vtends to cause sliding of one part

of a member with respect to an adjacent part.

Torsional moment (torque) Mx or T tends to

twist the member about thexaxis

Bending Moments My and Mz tend to bend or

flex the member about the y and z axes,

respectively.32 /40


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Consider the fixture subjected to loads as shown below.

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Ph i l Eff t f


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Physical Effects of

internal forces / moments

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Check Your Understanding

A connecting rod is subjected to the axial forcesshown. Determine the internal reactions at sections

aa, bband cc.

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For the cantilever beam shown below, determine theinternal reactions at section aaand section bb.

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For the jib crane shownbelow, determine the

internal reactions at section

aa(just to the left of the

2000-lb force).

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For the simply supported beam subjected to theuniformly distributed load shown in the figure,

determine the internal reactions at section aa.

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Seatwork #1

(ID # ending in an even no.)

For the member BC supported by

a bar AB and pin at C and

subjected to the linearly varying

line load shown below, determine

the internal reactions at section a

a.

(ID # ending in an odd no.)

For the simply supported member

shown below, determine the

internal reactions at section aa.


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Seatwork #1

(ID # ending in an even no.)

Determine the internal reactions at

section aaand section bb for

the beam shown.

(ID # ending in an odd no.)

Determine the axial force, shear

force, and moment at point C.

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