DB cos αδα CB sin βδβ or DBcos 5 CBsin 10 2 da a db da da b 2 Substitute the

Db cos αδα cb sin βδβ or dbcos 5 cbsin 10 2 da

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DB cos αδα = CB sin βδβ . or, DBcos 5 CBsin 10 2 da a db da da b = = = (2) Substitute the relation (2) in Eq. (a) R CH 10 δα R CH × 5 × 2 da – 500 × 12.5 δα – 1500 × 5 δα – 1500 × 5 × 2 da = 0 or, R CH (10 – 2.5) = 500 × 12.5 + 1500 × 5 + 1500 × 2.5 or, R CH = 2333.34 Hence the horizontal reaction at C is 2333.34 N. 6.8 A rod of length L is attached to a collar at A and rests on a cylinder of radius r as shown in Fig.P6.8. The collar can slide freely through a vertical guide. Determine the expression for force P , acting vertically downward, required to maintain equilibrium. Solution Let AC member is given a counter-clockwise virtual rotation δα . Thus point C will move by an amount ( L δα ), per- pendicular to AC. Hence the displacement of point C along horizontal direction = ( L δα )sin α . Assume length OA = x in right angled ΔAOP. So, r = x cos α or, x = r sec α
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Allowing differential on both sides, δ x = r sec α tan αδα . (1) Now the displacement of point A along vertical direction = δ x. Thus frame the equation for virtual work as, F × ( L δα )sin α P × δ x = 0 or, F × ( L δα )sin α P × r sec α tan αδα = 0 [Substituting from Eq. (1)] or, sin sec tan FL P r α α α = 2 cos FL r α = . 6.9 A hollow cylindrical drum of radius R and height h rests on the top of a spherical surface, of radius r , as shown in Fig.P6.9. Assuming no slip condition, determine the relation between y and r consistent with stability.
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