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Macaulay brackets are a notation used to describe theramp function

A popular alternative transcription uses angle brackets,viz.${\displaystyle ⟨x⟩}$.^[1] Another commonly used notation is${\displaystyle x}$₊ or${\displaystyle (x)}$₊ for thepositive part of${\displaystyle x}$, which avoids conflicts with${\displaystyle \{...\}}$ forset notation.

Macaulay's notation is commonly used in the static analysis of bending moments of a beam. This is useful because shear forces applied on a member render theshear and moment diagram discontinuous. Macaulay's notation also provides an easy way of integrating these discontinuous curves to give bending moments, angular deflection, and so on. For engineering purposes, angle brackets are often used to denote the use ofMacaulay's method.

${\displaystyle (n\ge 0)}$

The above example simply states that the function takes the value${\displaystyle (x-a{)}^n}$ for allx values larger thana. With this, all the forces acting on a beam can be added, with their respective points of action being the value ofa.

A particular case is theunit step function,

• Singularity function

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