工程力学英文版课件07 Stress for Axial Loads

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[Example 1] The forces which magnitude are 5P, 8P, 4P, P act respectively at point A, B, C, and D of the rod. Their directions are shown in the figure. Plot the diagram of the axial force of the rod.
O A B C D PD
PA
PB
PC
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Solution: Determine the internal force N1 in segment OA. Draw the free body diagram as shown in the figure.
O A PA N1 A PA B PB B PB C PC C PC D D PD
P
Internal force P Crosssectional area
P P External force
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For equilibrium of the bottom segment, the internal resultant force acting on the cross-sectional area must be equal in magnitude, opposite in direction, and collinear to the external force acting at the bottom of the bar.
N2 B PB N3 C PC C PC N4 D PD
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D PD D PD
The diagram of axial forces of the rod can now be plotted.
O A PA F B PB 5P C PC
D
PD
2P
P
x -3P
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2. Stress The internal force per unit area is called the stress. It describes the intensity of the internal force on a specific plane (area) passing through a point. Stresses include normal stress and shear stress. A normal stress is called tensile stress when it stretches the material on which it acts, and compressive stress when it shortens the material on which it acts.
12பைடு நூலகம்
Substitute. Take arbitrary part and substitute the action of another part to it by the corresponding internal force in the cut-off section. 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）
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Consider the sectioned area to be subdivided into small areas, such as A shown in figure. A typical finite yet very small force F, acting on its associated area A. As the area approaches zero, so do the force; however, the quotient of the force and area will, in general, approach a finite limit. This limit is called stress.
F1
F2
F3
Fn
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Axial force FN,
Bending moment MB,
Shear force FQ,
FQ
Torque or twisting moment MX
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: 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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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.
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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.
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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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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
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. 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.
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A section was used to cut the member into two parts.
F1
F2
F3
Fn
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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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4. Stress in an Axially Loaded Member Frequently structural or mechanical members are made long and slender. Also, they are subjected to axial loads that are usually applied to the ends of the member.