torsion_st_v_multi_ce

torsion_st_v_multi_ce - St. Venant Torsion Multi-cell...

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St. Venant Torsion Multi-cell applied torque this is a combination of nomenclature from Hughes section 6.1 Multiple Cell Sections and Mixed Sections page 227 ff and Kollbrunner sectin 2.3 Multicelluar Box Section Members T cross section (partial) i-1 i i+1 shear flow (concept) q i-1 qi-1 q i-1 q i-1 qi qi qi qi q i+1 qi+1 q i+1 q i+1 shear flow constant, integral of shear first recall . .. torque in a cell = M x i = 2A i q i stress*h*dA = torque etc. .. => total torque M x = T = M x i = i q i H: 6.1.26 i i angle of twist (same φ ' = T i.e. . .. the derivative of the twist angle wrt the axial H: 6.1.21 for all cells) GJ coordinate is = applied torque/torsional stiffness and from our development of pure twist (closed section) s τ δφ () &H: 6.1.23a u = ds h D ds + u 0 x G δ x 0 if this quantity is integrated entirely around a closed section . .. s τ δφ G ds h D ds = 0 the axial displacement returns to the starting point δ x 0 rearranging and substituting q =
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This note was uploaded on 02/24/2012 for the course MECHANICAL 2.082 taught by Professor Davidburke during the Spring '03 term at MIT.

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torsion_st_v_multi_ce - St. Venant Torsion Multi-cell...

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