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Chapter One:
Introduction—Concept of Stress
1.1 INTRODUCTION
The main objective of the study of the mechanics of materials is to provide the future
engineer with the means of analyzing and designing various machines and load-
bearing structures. Both the analysis and the design of a given structure involve the
determination of stresses and deformations. Mechanics of materials is a branch of
mechanics that studies the internal effects of stress and strain in a solid body that is
subjected to an external loading. Stress is associated with the strength of the material
from which the body is made, while strain is a measure of the deformation of the
body.
1.2 A SHORT REVIEW OF THE METHODS OF STATICS
In this section you will review the basic methods of statics while determining the
forces in the members of a simple structure.Consider the structure shown in Fig. 1.1,
which was designed to support a 30-kN load.
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Substituting for Ay from (1.4) into (1.3), we obtain Cy 5 130 kN. Expressing the
results obtained for the reactions at A and C in vector form, we have
These results could have been anticipated by recognizing that AB and BC are two-
force members, i.e., members that are subjected to forces at only two points, these
points being A and B for member AB, and B and C for member BC. Indeed, for a two-
force member the lines of action of the resultants of the forces acting at each of the
two points are equal and opposite and pass through both points. Using this property,
we could have obtained a simpler solution by considering the free-body diagram of
pin B. The forces on pin B are the forces FAB and FBC exerted, respectively, by
members AB and BC, and the 30-kN load (Fig. 1.4a). We can express that pin B is in
equilibrium by drawing the corresponding force triangle (Fig. 1.4b).
Since the force FBC is directed along member BC, its slope is the same as that of BC,
namely, 3/4. We can, therefore, write the proportion
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PDFelement
Page 1
, Remove Watermark Wondershare
PDFelement
Page 5
, Remove Watermark Wondershare
PDFelement
Chapter One:
Introduction—Concept of Stress
1.1 INTRODUCTION
The main objective of the study of the mechanics of materials is to provide the future
engineer with the means of analyzing and designing various machines and load-
bearing structures. Both the analysis and the design of a given structure involve the
determination of stresses and deformations. Mechanics of materials is a branch of
mechanics that studies the internal effects of stress and strain in a solid body that is
subjected to an external loading. Stress is associated with the strength of the material
from which the body is made, while strain is a measure of the deformation of the
body.
1.2 A SHORT REVIEW OF THE METHODS OF STATICS
In this section you will review the basic methods of statics while determining the
forces in the members of a simple structure.Consider the structure shown in Fig. 1.1,
which was designed to support a 30-kN load.
Page 6
, Remove Watermark Wondershare
PDFelement
Substituting for Ay from (1.4) into (1.3), we obtain Cy 5 130 kN. Expressing the
results obtained for the reactions at A and C in vector form, we have
These results could have been anticipated by recognizing that AB and BC are two-
force members, i.e., members that are subjected to forces at only two points, these
points being A and B for member AB, and B and C for member BC. Indeed, for a two-
force member the lines of action of the resultants of the forces acting at each of the
two points are equal and opposite and pass through both points. Using this property,
we could have obtained a simpler solution by considering the free-body diagram of
pin B. The forces on pin B are the forces FAB and FBC exerted, respectively, by
members AB and BC, and the 30-kN load (Fig. 1.4a). We can express that pin B is in
equilibrium by drawing the corresponding force triangle (Fig. 1.4b).
Since the force FBC is directed along member BC, its slope is the same as that of BC,
namely, 3/4. We can, therefore, write the proportion
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