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Axial Deformation - in The Linear Portion of The Stress-Strain Diagram, The Tress Is

This document discusses axial deformation and stiffness. It explains that axial stress is proportional to strain for linear deformation according to Hooke's law. It also describes how to calculate axial deformation when the cross-sectional area is variable by using integration. Finally, it provides a formula to calculate the total elongation of a vertically suspended rod due to its own weight based on the rod's length, mass, cross-sectional area, and gravitational acceleration.

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Angelica Santos
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478 views1 page

Axial Deformation - in The Linear Portion of The Stress-Strain Diagram, The Tress Is

This document discusses axial deformation and stiffness. It explains that axial stress is proportional to strain for linear deformation according to Hooke's law. It also describes how to calculate axial deformation when the cross-sectional area is variable by using integration. Finally, it provides a formula to calculate the total elongation of a vertically suspended rod due to its own weight based on the rod's length, mass, cross-sectional area, and gravitational acceleration.

Uploaded by

Angelica Santos
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Axial Deformation -In the linear portion of the stress-strain diagram, the tress is

proportional to strain and is given by σ=Eε


𝑃 𝛿 𝑃 𝛿
since 𝜎 = 𝐴 and 𝜀 = 𝐿 , then 𝐴 = 𝐸 𝐿

To use this formula, the load must be axial, the bar must have a uniform cross-
sectional area, and the stress must not exceed the proportional limit.

If however, the cross-sectional area is not uniform, the axial deformation can be
determined by considering a differential length and applying integration.

where A = ty, and y and t if variable, must be expressed in terms of x.


For a rod of unit mass ρ suspended vertically from one end, the total elongation
due to its own weight is

where ρ is in kg/m3, L is the length of the rod in mm, M is the total mass of the rod
in kg, A is the cross-sectional area of the rod in mm2, and g = 9.81 m/s2.
Stiffness, k
Stiffness is the ratio of the steady force acting on an elastic body to the resulting
displacement. It has the unit of N/mm.

Engr MIMD Villalobos

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