The Macaulay method for beam deflection analysis uses angle brackets <x-a>^n which are defined as:
Choose the correct answer
Always equal to (x-a)^n
Equal to (x-a)^n when x > a, and zero when x <= a, allowing a single bending moment expression to cover the entire beam with concentrated loads at various positions
Equal to (x-a) for all x
The product of x and a
Correct Answer
B. Equal to (x-a)^n when x > a, and zero when x <= a, allowing a single bending moment expression to cover the entire beam with concentrated loads at various positions
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Macaulay brackets: <x-a>^n = (x-a)^n for x > a; = 0 for x <= a. This allows M(x) to be written as a single expression for the entire span. Integrate twice with same brackets to get EI theta and EI y. Apply boundary conditions (y=0 at supports) to find constants. Valid for simply supported, cantilever, and propped beams with multiple loads.
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