6d-ex. Shear Stress Examples • Ex. 6d.1 • Ex. 6d.2 |
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Example 6d.2
Given: The I-beam at right is subjected to shear force, V = 5 kN. The flange and the web both have a thickness of 20 mm, the height of the beam is 150 mm and the width is 100 mm. The beam has a moment of inertia of I = 19x10^{6} mm^{4}. Req'd: Determine the shear stress at a-a' and b-b'. Sol'n: The first moment of area (about the neutral axis of the entire cross-section) of the area to the left of a-a' is: Q = A^{*}y^{*} = [(40 mm)(20 mm)](65 mm) = 5.2x10^{4} mm^{3} y* =[ (150/2 mm) - (20/2 mm)] = (half the height of the cross section) minus (half the thickness of the flange). |
Then the shear stress is in the flange is:
t^{xy} = 670 kPa The first moment of area of the area to below b-b' is: Q = A^{*}y^{*} = [(100 mm)(20 mm)](65 mm) = 1.3x10^{5}mm^{3} The shear stress in the web just above (below) the lower (upper) flange, is:
t^{xy} = 1.68 MPa |
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