Structural Analysis Formulas Pdf [Recent ✯]

[ V(x) = -\int w(x) , dx + C_1 ] [ M(x) = \int V(x) , dx + C_2 ] For pure bending of a linear-elastic, homogeneous beam:

[ \fracd^2 vdx^2 = \fracM(x)EI ]

| Case | Max Deflection (( \delta_\textmax )) | Location | |------|-------------------------------------------|----------| | Cantilever, end load (P) | (\fracPL^33EI) | free end | | Cantilever, uniform load (w) | (\fracwL^48EI) | free end | | Simply supported, center load (P) | (\fracPL^348EI) | center | | Simply supported, uniform load (w) | (\frac5wL^4384EI) | center | | Fixed-fixed, center load (P) | (\fracPL^3192EI) | center | | Fixed-fixed, uniform load (w) | (\fracwL^4384EI) | center | For a prismatic beam (rectangular cross-section approximation): structural analysis formulas pdf

[ \sigma_x = -\fracM yI ]

Slenderness ratio:

Integral forms:

[ \delta = \fracPLAE ]

[ \fracKLr, \quad r = \sqrt\fracIA ] For a pin-jointed truss in equilibrium at each joint: