AERSP_301_HW_5_Shear_and_Torsion

AERSP_301_HW_5_Shear_and_Torsion - s ξ s s a 2a 3 2 12 1...

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AERSP 301: HW #5 Shear and Torsion of Beams Assigned: Wednesday, September 23, 2009 Due: Wednesday, October 7, 2009 Problem 1: Show that the position of the shear centre S with respect to the intersection of the web and lower flange of the thin-walled section shown below is given by: ξ s = -45a/97, η s = 46a/97 Problem 2: A uniform thin-walled beam of constant wall thickness t has a cross-section in the shape of an isosceles triangle and is loaded with a vertical shear force Sy applied at the apex. Assuming that the distribution of shear stress is according to the basic theory of bending, calculate the distribution of shear flow over the cross-section. Illustrate your answer with a suitable sketch, marking in carefully with arrows the direction of the shear flows and noting the principal values. EXTRA CREDIT (15 points): Show that I xx is equal to: 2t 2a t
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Unformatted text preview: s ξ s η s a 2a 3 2 12 1 12 2 th dth I xx + = Problem 3: A uniform, thin-walled, cantilever beam of closed rectangular cross-section has the dimensions shown below. The shear modulus G at the top and bottom covers of the beam is 18 000 N/mm 2 while that of the vertical webs is 26 000 N/mm 2 . The beam is subjected to a uniformly distributed torque of 20 Nm/mm along its length. Calculate the maximum shear stress according to the Bredt-Batho theory of torsion (distribution of twist). Calculate also, and sketch, the distribution of twist along the length of the cantilever assuming that the axial constraint effects are negligible. Problem 4: Determine the maximum shear stress in the beam section shown stating clearly the point at which it occurs. Determine also the rate of twist of the beam section if the shear modulus is 25 000 N/mm 2 ....
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