Closed section-shear flow

Closed section-shear flow - 93 Twisting of Single Cell...

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Unformatted text preview: 93 Twisting of Single Cell Closed Tubes dV 1 zs V zs = ( ) Gt s q zs = ( ) ( ) dz ds AGt 2 s q dz tds Gt s q At 2 1 d S S = = ( ) ds Gt s q A 2 1 dz d S = The increase of twist, , over a length dz of the tube is then d The unit load method then gives the section twist, , as At zs 2 1 = dV For a load applied at shear centre we require = dz d 94 Bredt-Batho Rate of Twist ( ) ds Gt s q A 2 1 dz d S = If only a torsion, T, is applied then the shear flow is A 2 T q = Substituting this into ( ) = = S S Gt ds A T ds Gt s q A dz d 2 4 2 1 for the rate of twist gives For a load applied at shear centre we require = dz d 95 Shear Centre Open section Close section x e y S e S y S x ds pq + = ( ) + + = = Gt ds q Gt ds D I S D I S ds Gt s q S y yy x x xx y S ) ( q D I S D I S s q y yy x x xx y + + = ) ( q D I S D I S s q y yy x x xx y + + = We have two unknowns: q and location of shear centre We have three unknowns: q o , q, and the location of shear centre x e y S e S y S x ds pq + = i) Find shear flow ii) Find the location shear centre i) Find shear flow q (equivalent to open section) ii) Find q o by requiring the twist to be zero iii) Find the location of shear centre 96 Shear Centre Closed Section 1 2 3 4 S y Length= 9 units X e Length= 4 units Find the shear centre (i.e. Xe) of the close section shown below. Thickness for all the webs = 0.1 units Sy= 1000 units Centroid (XG,YG) = (5.21, 3.5) Section Ixx = 37.52 Iyy = 74.43 Ixy = -15.50 Length= 13 units Length= 12 units 97 y x o D D q q 073 . 6 16 . 29 = 2 12 458 . 1 082 . 6 s s q q o = 2 23 2802 . 580 . 5 . 1 s s q q o = 2 34 458 . 1 87 . 12 9 . 118 s s q q o + = 2 41 3036 . 37 . 13 6 . 116 s s q q o + = 1 2 3 4 S y 9 units X e 4 units cut = s x ds y t ) s ( D ( ) = s y ds x t s D Solving as an open section 98...
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This note was uploaded on 03/24/2010 for the course AE A.213 taught by Professor S.pinhoandm.aliabadi during the Winter '09 term at Imperial College.

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Closed section-shear flow - 93 Twisting of Single Cell...

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