Slenderness ratio:
[ 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:
Where ( v(x) ) = vertical deflection. Common solutions: structural analysis formulas pdf
[ \delta = \fracPLAE ]
[ \fracKLr, \quad r = \sqrt\fracIA ] For a pin-jointed truss in equilibrium at each joint: Slenderness ratio: [ V(x) = -\int w(x) ,
Distribution factor at joint: [ DF = \frack_i\sum k ] Rectangle (width (b), height (h)): [ I = \fracb h^312, \quad A = bh ]
Effective length factors (K):
Integral forms:
