F1
F2
F3
Fn
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Axial force FN, Shear force FQ,
Bending moment MB,
Torque or twisting moment MX
FQ
FR
Mx
FN
MB
M
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Procedure for the method of section
Calculation of the internal forces is foundation to analyze the problems of strength, rigidity, stability etc. General method to determine internal forces is the method of section. The following steps should be performed:
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A section was used to cut the member into two parts.
F1Biblioteka F2F3Fn
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The internal forces of the member cut became the external forces, and can be found by the equilibrium equations.
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Internal Reactions: Stress for Axial Loads
§10–1 Introduction §10–2 Problems Involving Normal,
Shear and Bearing Stress §10–3 Allowable Stress §10–4 Stresses on Oblique Sections
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Internal forces in an axially loaded member
P
P
P
P
Sign Convention. When the internal force acting outwards from the section (‘pulls’) is termed tensile force and given a positive sign. Force acting towards the section (‘pushes’) is termed compressive force and is negative in sign.
In order to find internal forces in members of a system, the member was cut with a section. Then a free-body diagram of either part of this member was constructed. The forces in the members cut became external forces and were found by the equilibrium equations.
Equilibrium. Set up equilibrium equations for the remained part and determine the unknown internal forces according to the external forces acted it.（Here the internal forces in the cutoff section are the external forces for the remained part）
Cut off. Assume to separate the member into two distinct parts in the section in which the internal forces want to be determined.
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Substitute. Take arbitrary part and substitute the action of another part to it by the corresponding internal force in the cut-off section.
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This subject also involves computing the deformations of the body when the body is subjected to external forces.
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And it provides a study of the body’s stability when the body is subjected to external forces.
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§10-1 Introduction
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Mechanics of materials is a branch of mechanics that studies the relationships between the external loads applied to a deformable body and the intensity of internal forces acting within the body.
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Strength：
Capacity of a component or a structural element to resist failure.
Rigidity (Stiffness)：
Capacity of a component or a structural element to resist deformation.
Stability:
Capacity of a component or a structural element to retain the original state of equilibrium.
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1. Internal Reactions
Forces created within objects that are acted upon by external loads, including axial force, shear force, bending moment, and torque or twisting moment.