EWPAA Structural Plywood and LVL Design Manual - Engineered ...

The axial force is directed along the tangents to the arch profile whilst the shear force isperpendicular to the centroidal axis of the arch. Hence, to find the components of H B andV B in these directions requires determining the slope of the arch at the base. From:ydydx⎡ 2x⎤h ⎢⎛ ⎞= 1−⎜ ⎟ ⎥⎢ ⎝ L ⎠ ⎥⎣ ⎦⎛ x ⎞= −2⎜ ⎟hL2⎝ ⎠(12.6)Arch reactions are determined by application of the equilibrium equations of Equations12.5. From symmetry:V = V = wLVAA= VBB= 300kNFrom: ∑M CR = 00= 10HB10 x 30300 x 30 +22Hence:HBHB9000 4500=10= 450kNkNH A= 450kNFrom Equation 12.6 :when:dydxxdydxdydx⎛ x2 h2L⎟ ⎞= − ⎜⎝ ⎠= L = 30 gives:⎛ 30 ⎞= −2⎜⎟102⎝ 30 ⎠2= −3FIGURE 12.11 shows the normal (n) and tangential (t) co-ordinates at the base of the arch.FIGURE 12.11: Components of shear and axial forceSumming the axial (F A ) and shear (F s ) components at B in FIGURE 12.11 gives:166