ME311-HW9 - Homework#8 Solution ME 311-Winter 2016 Due Date...

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Homework #8 Solution ME 311-Winter 2016 Due Date 03/18/2016
1 6.28. Find the torsional stiffness K for the closed thin-walled beam section of Figure P6.28. The wall thickness is everywhere equal to t . t a a a a a Figure P6.28 The perimeter of the section is 3 a + 7 × a = 10 a and the enclosed area is A = 3 a 2 + a 2 = 4 a 2 . It follows that contintegraldisplay S dS t = 10 a t and K = 4 A 2 slashbigg contintegraldisplay S dS t = 4 × 16 a 4 10 a / t = 6 . 4 a 3 t .
1 6.32. The torsional stiffness of a hat section is to be increased by bolting a flat plate to it, creating the closed section of Figure P6.32. The bolts are of 3 mm diameter and have an axial spacing of 50 mm. Estimate the shear stress in the bolts when the beam is loaded by a torque of 10 Nm. 2 2 20 20 20 20 all dimensions in mm Figure P6.32 The shear flow, q , is given by equation (6.29) as q = T 2 A , where A is the area enclosed by the mean line. The mean line is shown in Figure P6.32.1 and encloses an area A = 22 × 22 + 2 × 2 × 10 = 524 mm 2 , where we have assumed that the bolts are equidistant from the ends of the 20 mm