## Why can maximum shear stress in a web be replaced by the average shear stress?

I've been reading my strength of materials text about design of steel beams. I understand everything up to the point where the text tells me to use the average web shear stress (V/dt) instead of max shear stress (VQ/It) to determine if a given beam is within the allowable shear stress. I calculated both to determine how close they are and found the average greater than the max! I've checked several times and don't see an error. What am I missing?

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 Quote by mtnmama I've been reading my strength of materials text about design of steel beams. I understand everything up to the point where the text tells me to use the average web shear stress (V/dt) instead of max shear stress (VQ/It) to determine if a given beam is within the allowable shear stress. I calculated both to determine how close they are and found the average greater than the max! I've checked several times and don't see an error. What am I missing?
Are you using a wide flange (I) beam? Max shear stress at the neutral axis (VQ/It) is approximately equal to the average shear stress when using the web area only (V/Aw).

 Yes, it is a wide flange. When I calculate an average and a max stress on the flange of a 8 ft section of W18 x 50 with a uniform load of 1.85 klb/in I get an average of 16.22 klb/sq in. The max I get is 6.56 klb/sq in. Is that considered close, or have I made an error somewhere?