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

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

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

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12.14 Methodology - Principal Membrane ForcesWhen the projected plan of the hypar is a diamond shape the tension (t) <strong>and</strong> compression(c) forces shown in FIGURE 12.17 can be resolved by proportion. The principal tensile force(t) / metre width is:t1/ 2t=sa'1 x s=2a'(12.12)The principal compressive force (c) / metre width is:Hence:cc/ 22=sa'= 2 x s(12.13)2a'When the projected plan of the hypar is square in shape (t) <strong>and</strong> (c)/metre width will be equalin magnitude to the boundary shears/metre length of perimeter member.12.15 Methodology - Twist in Perimeter MembersSince the hypar is a doubly curved shell the sheathing slope constantly <strong>and</strong> uniformlychanges along the length of the perimeter member hence its contacting surface needs to beappropriately shaped. This necessitates in the determination of the total angle of twistshown in FIGURE 12.18(b) which applies to hypars having plan projections which are eitherdiamond or square in shape. For the diamond shaped projection:where:hatan of angleof twist = 2(a') cosis that shown in FIGURE 12.18 (a)For the square shaped projection angle ABC becomes zero <strong>and</strong> Equation 12.14 becomes:The total angle of twist between the ends of a perimeter member is twice that determinedby Equations 12.14 or 12.15.173

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