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9 results for “structures”

Formulae (9)

C_n = \frac{1}{n+1}\binom{2n}{n}

Counts many recursive structures such as balanced parentheses.

\delta = \frac{F L^3}{3 E I}

Maximum deflection of a cantilever with an end load.

I = \frac{b h^3}{12}

Second moment of area for a rectangular cross-section.

\sigma = \frac{M c}{I}

Stress in a beam due to a bending moment.

w = \frac{W}{L}

Load per unit length of a beam.

M_{max} = \frac{w L^2}{8}

Maximum bending moment for a simply supported beam under uniform load.

\lambda = \frac{L_e}{r}

Ratio governing column buckling.

P_{cr} = \frac{\pi^2 E I}{(K L)^2}

Critical axial load at which a column buckles.

N = 2^{h+1} - 1

Total nodes in a perfect binary tree of height h.