ME311-HW8 - 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 6.3. The wide flange I-beam of Figure P6.3 has second moment of area I x = 7 a 3 t / 12 and is loaded by a vertical shear force V y . Find (i) the shear stress at A , (ii) the shear stress at O and (iii) the average shear stress in the web. t t a a O A . Figure P6.3 For point A , A * = at 2 ; ¯ y * = a 2 and hence τ A = V y ( at / 2 )( a / 2 ) ( 7 a 3 t / 12 ) t = 3 V y 7 at . For the neutral axis O , A * ¯ y * = ( at ) parenleftBig a 2 parenrightBig + parenleftBig at 2 parenrightBigparenleftBig a 4 parenrightBig = 5 a 2 t 8 and τ B = V y ( 5 a 2 t / 8 ) ( 7 a 3 t / 12 ) t = 15 V y 14 at . The average shear stress in the web is τ ave web = V y at , since the flanges carry no vertical shear force for a thin walled section (the shear stresses there are horizontal). The maximum shear stress (at O ) is only slightly larger than the average shear stress in the web.
1 6.9. The beam of Figure P6.1 is fabricated from a channel and two bars by welding, details of the weld being shown in Figure P6.9. If the minimum weld thickness t = 1