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Metallurgical Engineering

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Axially Loaded Materials

Axially loaded members are members that only carry tensile or compressive loads.

Basic Equations

There are a few basic equations that every student of material mechanics must know. They are the following:

Other equations can be derived from these basic equations:

Cables, which are helically wound strands around a central strand, require the use of an effective area and an effective modulus of elasticity.

Non-uniform Bars

If a member has several prismatic parts with different axial forces or stiffnesses:

Statically Indeterminate Structures

Some structures cannot be simply determined by the equations of static equilibrium alone. Usually in these cases the number of unknowns is greater than the number of unique equations we can build from static equilibrium. This is called a statically indeterminate structure. In most cases, we can use the equations of axial loading to be able to obtain enough equations to solve for all the unknowns. Let's consider the following example:

Bars with continuously varying loads and/or dimensions

The bar has a cross-sectional area A(x) that varies gradually along its length.

The bar is subjected to concentrated loads at its ends and a variable external load P(x) distributed along its length (e.g. weight of a vertical bar or friction forces on the surface of the bar).

After unloading, there is a certain amount of elastic recovery and some residual strain, that is, a permanent elongation of the specimen. Upon reloading, the unloading curve is followed.