δ=PL/AE gives elongation of a bar under axial load.
For a bar with constant force, δ=PL/(AE). For varying force or area, integrate δ=∫P dx/(AE). Composite bars share deformation and thus stress splits in proportion to stiffness AE.
A 3 m steel rod, 20 mm diameter, with 50 kN extends 2.4 mm.
The axial deformation formula gives the change in length of a bar or column, which is needed for fit, clearance and load sharing.
δ=PL/AE gives elongation of a bar under axial load.
The axial deformation formula gives the change in length of a bar or column, which is needed for fit, clearance and load sharing.
Consistent units. Newtons, metres and pascals give metres, and mixing millimetres with pascals is a common error.
Divide the bar into segments with constant properties and add the deformations of each segment.
Typical applications include checking the elongation of a tie rod in a bridge, calculating how much a column shortens under building load and designing the length of a spacer so a joint remains tight.
Study "Poisson's ratio" first (topic 48 of 106 in Engineering Mechanics). It covers the groundwork this topic builds on.
Stiffness k=AE/L. Statically indeterminate bars use compatibility. Deformation is cumulative.
A 3 m steel rod, 20 mm diameter, with 50 kN extends 2.4 mm.
The next topic is "Thermal stress", which builds directly on this one.
It is classed as Intermediate in Engineering Mechanics (topic 49 of 106). It is an intermediate topic. Work through the beginner topics in Engineering Mechanics first.
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