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

FIGURE 12.13: Free body diagram of part of archTaking moments about D:∑MD− M− 2Mw− 2Mw0= 02wL w( )2= x y + L−x − wL( L−x)+ M2h 2wL2 ⎡ 2x⎤wxh⎢⎛ ⎞1L22 xL x2wL2= − ⎜ ⎟ ⎥ + ⎜⎛ − + ⎟⎞− + wxL2h ⎢ L ⎥ 2 ⎝⎠⎣⎝ ⎠⎦2 2 2 2 2= L − x + L − 2 xL+x − 2L + 2 xL2 2 2 2= 2L − 2L + x − x + 2 xL−2 xL= MHence, the parabolic profile for the arch is the most efficient obtainable arch wise, but only for the uniformlydistributed load. Bending presents itself for other load cases.12.10 Hyperbolic Paraboloids (Hypar) ShellsIntroductionBesides offering a roofing solution with many interesting alternatives the hyperbolic paraboloid (hypar) alsomakes efficient use of the timber through its shape. The hypar, which is a popular member of the saddleshell family, can be formed into roof shapes to cover square, rectangular or circular plans.FIGURE 12.14 shows how hypars can be used in configurations having straight boundaries (a,b,c) or assaddles (d and e).FIGURE 12.14: Various hypar configurations168