HW10_EML3011C_Summer2009

HW10_EML3011C_Summer2009 - EML3011C, Quiz #10 7/18/06 Name...

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EML3011C, Quiz #10 7/18/06 Name SPH page 1 of 2 1 2 T o t a l 20 10 30 1. A beam has the cross section shown below. On a section where the shear force is – 75 kN, determine (a) The maximum transverse shear stress. (b) The transverse shear stress at a point that is 20 mm down from the top. (c) The transverse shear stress at a point that is 20 mm up from the bottom. (d) The average shear stress on the cross section. The centroid is 87.5 mm up from the bottom surface. The moment of inertia about the neutral axis is 82.29 x 10 6 mm 4 . dA y I A x = 2 2 ' y x x Ad I I + = ( ) + = 2 ' y x x Ad I I = = A A x dA dA x x A A ~ ~ dA x I A y = 2 2 ' x y y Ad I I + = ( ) + = 2 ' x y y Ad I I = = A A y dA dA y y A A ~ ~ I y M = σ A F = J T ρ τ = A V = It VQ = ' ' A y Q = 25 mm 75 mm 100 mm 25 25 100 mm y
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EML3011C, Quiz #10 7/18/06 Name SPH page 2 of 2 2. A beam is loaded as shown below, with the FBD, shear force and bending moment diagrams as indicated. If the cross section is as shown in the second figure below, determine, (a) The maximum transverse shear stress. (b) The position along the length of the beam where the maximum transverse shear stress occurs. (c) The location on the cross section where the maximum transverse shear stress occurs. The centroid is 36.4 mm up from the bottom
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HW10_EML3011C_Summer2009 - EML3011C, Quiz #10 7/18/06 Name...

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